From 5bf68dad940b2c2641796badd928faea9fb963a7 Mon Sep 17 00:00:00 2001 From: Lorenz Meier Date: Sat, 7 Jun 2014 12:52:06 +0200 Subject: [PATCH 1/3] Rename / move 23 state filter --- .../{estimator.cpp => estimator_23states.cpp} | 143 +----------------- .../{estimator.h => estimator_23states.h} | 76 +--------- 2 files changed, 4 insertions(+), 215 deletions(-) rename src/modules/ekf_att_pos_estimator/{estimator.cpp => estimator_23states.cpp} (98%) rename src/modules/ekf_att_pos_estimator/{estimator.h => estimator_23states.h} (87%) diff --git a/src/modules/ekf_att_pos_estimator/estimator.cpp b/src/modules/ekf_att_pos_estimator/estimator_23states.cpp similarity index 98% rename from src/modules/ekf_att_pos_estimator/estimator.cpp rename to src/modules/ekf_att_pos_estimator/estimator_23states.cpp index 89e137adcf..ca9db96855 100644 --- a/src/modules/ekf_att_pos_estimator/estimator.cpp +++ b/src/modules/ekf_att_pos_estimator/estimator_23states.cpp @@ -2,143 +2,6 @@ #include #include -// Define EKF_DEBUG here to enable the debug print calls -// if the macro is not set, these will be completely -// optimized out by the compiler. -//#define EKF_DEBUG - -#ifdef EKF_DEBUG -#include - -static void -ekf_debug_print(const char *fmt, va_list args) -{ - fprintf(stderr, "%s: ", "[ekf]"); - vfprintf(stderr, fmt, args); - - fprintf(stderr, "\n"); -} - -static void -ekf_debug(const char *fmt, ...) -{ - va_list args; - - va_start(args, fmt); - ekf_debug_print(fmt, args); -} - -#else - -static void ekf_debug(const char *fmt, ...) { while(0){} } -#endif - -float Vector3f::length(void) const -{ - return sqrt(x*x + y*y + z*z); -} - -void Vector3f::zero(void) -{ - x = 0.0f; - y = 0.0f; - z = 0.0f; -} - -Mat3f::Mat3f() { - identity(); -} - -void Mat3f::identity() { - x.x = 1.0f; - x.y = 0.0f; - x.z = 0.0f; - - y.x = 0.0f; - y.y = 1.0f; - y.z = 0.0f; - - z.x = 0.0f; - z.y = 0.0f; - z.z = 1.0f; -} - -Mat3f Mat3f::transpose(void) const -{ - Mat3f ret = *this; - swap_var(ret.x.y, ret.y.x); - swap_var(ret.x.z, ret.z.x); - swap_var(ret.y.z, ret.z.y); - return ret; -} - -// overload + operator to provide a vector addition -Vector3f operator+( Vector3f vecIn1, Vector3f vecIn2) -{ - Vector3f vecOut; - vecOut.x = vecIn1.x + vecIn2.x; - vecOut.y = vecIn1.y + vecIn2.y; - vecOut.z = vecIn1.z + vecIn2.z; - return vecOut; -} - -// overload - operator to provide a vector subtraction -Vector3f operator-( Vector3f vecIn1, Vector3f vecIn2) -{ - Vector3f vecOut; - vecOut.x = vecIn1.x - vecIn2.x; - vecOut.y = vecIn1.y - vecIn2.y; - vecOut.z = vecIn1.z - vecIn2.z; - return vecOut; -} - -// overload * operator to provide a matrix vector product -Vector3f operator*( Mat3f matIn, Vector3f vecIn) -{ - Vector3f vecOut; - vecOut.x = matIn.x.x*vecIn.x + matIn.x.y*vecIn.y + matIn.x.z*vecIn.z; - vecOut.y = matIn.y.x*vecIn.x + matIn.y.y*vecIn.y + matIn.y.z*vecIn.z; - vecOut.z = matIn.x.x*vecIn.x + matIn.z.y*vecIn.y + matIn.z.z*vecIn.z; - return vecOut; -} - -// overload % operator to provide a vector cross product -Vector3f operator%( Vector3f vecIn1, Vector3f vecIn2) -{ - Vector3f vecOut; - vecOut.x = vecIn1.y*vecIn2.z - vecIn1.z*vecIn2.y; - vecOut.y = vecIn1.z*vecIn2.x - vecIn1.x*vecIn2.z; - vecOut.z = vecIn1.x*vecIn2.y - vecIn1.y*vecIn2.x; - return vecOut; -} - -// overload * operator to provide a vector scaler product -Vector3f operator*(Vector3f vecIn1, float sclIn1) -{ - Vector3f vecOut; - vecOut.x = vecIn1.x * sclIn1; - vecOut.y = vecIn1.y * sclIn1; - vecOut.z = vecIn1.z * sclIn1; - return vecOut; -} - -// overload * operator to provide a vector scaler product -Vector3f operator*(float sclIn1, Vector3f vecIn1) -{ - Vector3f vecOut; - vecOut.x = vecIn1.x * sclIn1; - vecOut.y = vecIn1.y * sclIn1; - vecOut.z = vecIn1.z * sclIn1; - return vecOut; -} - -void swap_var(float &d1, float &d2) -{ - float tmp = d1; - d1 = d2; - d2 = tmp; -} - AttPosEKF::AttPosEKF() /* NOTE: DO NOT initialize class members here. Use ZeroVariables() @@ -170,7 +33,7 @@ void AttPosEKF::UpdateStrapdownEquationsNED() float rotationMag; float qUpdated[4]; float quatMag; - float deltaQuat[4]; + double deltaQuat[4]; const Vector3f gravityNED = {0.0,0.0,GRAVITY_MSS}; // Remove sensor bias errors @@ -199,8 +62,8 @@ void AttPosEKF::UpdateStrapdownEquationsNED() } else { - deltaQuat[0] = cosf(0.5f*rotationMag); - float rotScaler = (sinf(0.5f*rotationMag))/rotationMag; + deltaQuat[0] = cos(0.5f*rotationMag); + double rotScaler = (sin(0.5f*rotationMag))/rotationMag; deltaQuat[1] = correctedDelAng.x*rotScaler; deltaQuat[2] = correctedDelAng.y*rotScaler; deltaQuat[3] = correctedDelAng.z*rotScaler; diff --git a/src/modules/ekf_att_pos_estimator/estimator.h b/src/modules/ekf_att_pos_estimator/estimator_23states.h similarity index 87% rename from src/modules/ekf_att_pos_estimator/estimator.h rename to src/modules/ekf_att_pos_estimator/estimator_23states.h index 4014629237..6d3b891081 100644 --- a/src/modules/ekf_att_pos_estimator/estimator.h +++ b/src/modules/ekf_att_pos_estimator/estimator_23states.h @@ -1,80 +1,6 @@ -#include -#include - #pragma once -#define GRAVITY_MSS 9.80665f -#define deg2rad 0.017453292f -#define rad2deg 57.295780f -#define pi 3.141592657f -#define earthRate 0.000072921f -#define earthRadius 6378145.0f -#define earthRadiusInv 1.5678540e-7f - -class Vector3f -{ -private: -public: - float x; - float y; - float z; - - float length(void) const; - void zero(void); -}; - -class Mat3f -{ -private: -public: - Vector3f x; - Vector3f y; - Vector3f z; - - Mat3f(); - - void identity(); - Mat3f transpose(void) const; -}; - -Vector3f operator*(float sclIn1, Vector3f vecIn1); -Vector3f operator+( Vector3f vecIn1, Vector3f vecIn2); -Vector3f operator-( Vector3f vecIn1, Vector3f vecIn2); -Vector3f operator*( Mat3f matIn, Vector3f vecIn); -Vector3f operator%( Vector3f vecIn1, Vector3f vecIn2); -Vector3f operator*(Vector3f vecIn1, float sclIn1); - -void swap_var(float &d1, float &d2); - -const unsigned int n_states = 23; -const unsigned int data_buffer_size = 50; - -enum GPS_FIX { - GPS_FIX_NOFIX = 0, - GPS_FIX_2D = 2, - GPS_FIX_3D = 3 -}; - -struct ekf_status_report { - bool velHealth; - bool posHealth; - bool hgtHealth; - bool velTimeout; - bool posTimeout; - bool hgtTimeout; - uint32_t velFailTime; - uint32_t posFailTime; - uint32_t hgtFailTime; - float states[n_states]; - bool angNaN; - bool summedDelVelNaN; - bool KHNaN; - bool KHPNaN; - bool PNaN; - bool covarianceNaN; - bool kalmanGainsNaN; - bool statesNaN; -}; +#include "estimator_utilities.h" class AttPosEKF { From b9a3fa60bc06b31d4862919398c1161e6a35f360 Mon Sep 17 00:00:00 2001 From: Lorenz Meier Date: Sat, 7 Jun 2014 13:03:11 +0200 Subject: [PATCH 2/3] Add support for 21 and 23 state estimators. Promoto a number of small delta variables to double --- .../ekf_att_pos_estimator_main.cpp | 75 +- .../estimator_21states.cpp | 2143 +++++++++++++++++ .../estimator_21states.h | 247 ++ .../estimator_utilities.cpp | 139 ++ .../estimator_utilities.h | 79 + src/modules/ekf_att_pos_estimator/module.mk | 3 +- 6 files changed, 2660 insertions(+), 26 deletions(-) create mode 100644 src/modules/ekf_att_pos_estimator/estimator_21states.cpp create mode 100644 src/modules/ekf_att_pos_estimator/estimator_21states.h create mode 100644 src/modules/ekf_att_pos_estimator/estimator_utilities.cpp create mode 100644 src/modules/ekf_att_pos_estimator/estimator_utilities.h diff --git a/src/modules/ekf_att_pos_estimator/ekf_att_pos_estimator_main.cpp b/src/modules/ekf_att_pos_estimator/ekf_att_pos_estimator_main.cpp index ee3c60e633..86f7eb99f6 100644 --- a/src/modules/ekf_att_pos_estimator/ekf_att_pos_estimator_main.cpp +++ b/src/modules/ekf_att_pos_estimator/ekf_att_pos_estimator_main.cpp @@ -83,7 +83,7 @@ #include #include -#include "estimator.h" +#include "estimator_21states.h" @@ -1455,30 +1455,55 @@ FixedwingEstimator::print_status() // 16-18: Earth Magnetic Field Vector - gauss (North, East, Down) // 19-21: Body Magnetic Field Vector - gauss (X,Y,Z) - printf("dtIMU: %8.6f IMUmsec: %d\n", (double)_ekf->dtIMU, (int)IMUmsec); - printf("ref alt: %8.6f\n", (double)_local_pos.ref_alt); - printf("dvel: %8.6f %8.6f %8.6f accel: %8.6f %8.6f %8.6f\n", (double)_ekf->dVelIMU.x, (double)_ekf->dVelIMU.y, (double)_ekf->dVelIMU.z, (double)_ekf->accel.x, (double)_ekf->accel.y, (double)_ekf->accel.z); - printf("dang: %8.4f %8.4f %8.4f dang corr: %8.4f %8.4f %8.4f\n" , (double)_ekf->dAngIMU.x, (double)_ekf->dAngIMU.y, (double)_ekf->dAngIMU.z, (double)_ekf->correctedDelAng.x, (double)_ekf->correctedDelAng.y, (double)_ekf->correctedDelAng.z); - printf("states (quat) [0-3]: %8.4f, %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[0], (double)_ekf->states[1], (double)_ekf->states[2], (double)_ekf->states[3]); - printf("states (vel m/s) [4-6]: %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[4], (double)_ekf->states[5], (double)_ekf->states[6]); - printf("states (pos m) [7-9]: %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[7], (double)_ekf->states[8], (double)_ekf->states[9]); - printf("states (delta ang) [10-12]: %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[10], (double)_ekf->states[11], (double)_ekf->states[12]); - printf("states (accel offs) [13]: %8.4f\n", (double)_ekf->states[13]); - printf("states (wind) [14-15]: %8.4f, %8.4f\n", (double)_ekf->states[14], (double)_ekf->states[15]); - printf("states (earth mag) [16-18]: %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[16], (double)_ekf->states[17], (double)_ekf->states[18]); - printf("states (body mag) [19-21]: %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[19], (double)_ekf->states[20], (double)_ekf->states[21]); - printf("states (terrain) [22]: %8.4f\n", (double)_ekf->states[22]); - printf("states: %s %s %s %s %s %s %s %s %s %s\n", - (_ekf->statesInitialised) ? "INITIALIZED" : "NON_INIT", - (_ekf->onGround) ? "ON_GROUND" : "AIRBORNE", - (_ekf->fuseVelData) ? "FUSE_VEL" : "INH_VEL", - (_ekf->fusePosData) ? "FUSE_POS" : "INH_POS", - (_ekf->fuseHgtData) ? "FUSE_HGT" : "INH_HGT", - (_ekf->fuseMagData) ? "FUSE_MAG" : "INH_MAG", - (_ekf->fuseVtasData) ? "FUSE_VTAS" : "INH_VTAS", - (_ekf->useAirspeed) ? "USE_AIRSPD" : "IGN_AIRSPD", - (_ekf->useCompass) ? "USE_COMPASS" : "IGN_COMPASS", - (_ekf->staticMode) ? "STATIC_MODE" : "DYNAMIC_MODE"); + if (n_states == 23) { + printf("dtIMU: %8.6f IMUmsec: %d\n", (double)_ekf->dtIMU, (int)IMUmsec); + printf("ref alt: %8.6f\n", (double)_local_pos.ref_alt); + printf("dvel: %8.6f %8.6f %8.6f accel: %8.6f %8.6f %8.6f\n", (double)_ekf->dVelIMU.x, (double)_ekf->dVelIMU.y, (double)_ekf->dVelIMU.z, (double)_ekf->accel.x, (double)_ekf->accel.y, (double)_ekf->accel.z); + printf("dang: %8.4f %8.4f %8.4f dang corr: %8.4f %8.4f %8.4f\n" , (double)_ekf->dAngIMU.x, (double)_ekf->dAngIMU.y, (double)_ekf->dAngIMU.z, (double)_ekf->correctedDelAng.x, (double)_ekf->correctedDelAng.y, (double)_ekf->correctedDelAng.z); + printf("states (quat) [0-3]: %8.4f, %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[0], (double)_ekf->states[1], (double)_ekf->states[2], (double)_ekf->states[3]); + printf("states (vel m/s) [4-6]: %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[4], (double)_ekf->states[5], (double)_ekf->states[6]); + printf("states (pos m) [7-9]: %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[7], (double)_ekf->states[8], (double)_ekf->states[9]); + printf("states (delta ang) [10-12]: %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[10], (double)_ekf->states[11], (double)_ekf->states[12]); + printf("states (accel offs) [13]: %8.4f\n", (double)_ekf->states[13]); + printf("states (wind) [14-15]: %8.4f, %8.4f\n", (double)_ekf->states[14], (double)_ekf->states[15]); + printf("states (earth mag) [16-18]: %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[16], (double)_ekf->states[17], (double)_ekf->states[18]); + printf("states (body mag) [19-21]: %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[19], (double)_ekf->states[20], (double)_ekf->states[21]); + printf("states (terrain) [22]: %8.4f\n", (double)_ekf->states[22]); + printf("states: %s %s %s %s %s %s %s %s %s %s\n", + (_ekf->statesInitialised) ? "INITIALIZED" : "NON_INIT", + (_ekf->onGround) ? "ON_GROUND" : "AIRBORNE", + (_ekf->fuseVelData) ? "FUSE_VEL" : "INH_VEL", + (_ekf->fusePosData) ? "FUSE_POS" : "INH_POS", + (_ekf->fuseHgtData) ? "FUSE_HGT" : "INH_HGT", + (_ekf->fuseMagData) ? "FUSE_MAG" : "INH_MAG", + (_ekf->fuseVtasData) ? "FUSE_VTAS" : "INH_VTAS", + (_ekf->useAirspeed) ? "USE_AIRSPD" : "IGN_AIRSPD", + (_ekf->useCompass) ? "USE_COMPASS" : "IGN_COMPASS", + (_ekf->staticMode) ? "STATIC_MODE" : "DYNAMIC_MODE"); + } else { + printf("dtIMU: %8.6f IMUmsec: %d\n", (double)_ekf->dtIMU, (int)IMUmsec); + printf("ref alt: %8.6f\n", (double)_local_pos.ref_alt); + printf("dvel: %8.6f %8.6f %8.6f accel: %8.6f %8.6f %8.6f\n", (double)_ekf->dVelIMU.x, (double)_ekf->dVelIMU.y, (double)_ekf->dVelIMU.z, (double)_ekf->accel.x, (double)_ekf->accel.y, (double)_ekf->accel.z); + printf("dang: %8.4f %8.4f %8.4f dang corr: %8.4f %8.4f %8.4f\n" , (double)_ekf->dAngIMU.x, (double)_ekf->dAngIMU.y, (double)_ekf->dAngIMU.z, (double)_ekf->correctedDelAng.x, (double)_ekf->correctedDelAng.y, (double)_ekf->correctedDelAng.z); + printf("states (quat) [0-3]: %8.4f, %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[0], (double)_ekf->states[1], (double)_ekf->states[2], (double)_ekf->states[3]); + printf("states (vel m/s) [4-6]: %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[4], (double)_ekf->states[5], (double)_ekf->states[6]); + printf("states (pos m) [7-9]: %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[7], (double)_ekf->states[8], (double)_ekf->states[9]); + printf("states (delta ang) [10-12]: %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[10], (double)_ekf->states[11], (double)_ekf->states[12]); + printf("states (wind) [13-14]: %8.4f, %8.4f\n", (double)_ekf->states[13], (double)_ekf->states[14]); + printf("states (earth mag) [15-17]: %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[15], (double)_ekf->states[16], (double)_ekf->states[17]); + printf("states (body mag) [18-20]: %8.4f, %8.4f, %8.4f\n", (double)_ekf->states[18], (double)_ekf->states[19], (double)_ekf->states[20]); + printf("states: %s %s %s %s %s %s %s %s %s %s\n", + (_ekf->statesInitialised) ? "INITIALIZED" : "NON_INIT", + (_ekf->onGround) ? "ON_GROUND" : "AIRBORNE", + (_ekf->fuseVelData) ? "FUSE_VEL" : "INH_VEL", + (_ekf->fusePosData) ? "FUSE_POS" : "INH_POS", + (_ekf->fuseHgtData) ? "FUSE_HGT" : "INH_HGT", + (_ekf->fuseMagData) ? "FUSE_MAG" : "INH_MAG", + (_ekf->fuseVtasData) ? "FUSE_VTAS" : "INH_VTAS", + (_ekf->useAirspeed) ? "USE_AIRSPD" : "IGN_AIRSPD", + (_ekf->useCompass) ? "USE_COMPASS" : "IGN_COMPASS", + (_ekf->staticMode) ? "STATIC_MODE" : "DYNAMIC_MODE"); + } } int FixedwingEstimator::trip_nan() { diff --git a/src/modules/ekf_att_pos_estimator/estimator_21states.cpp b/src/modules/ekf_att_pos_estimator/estimator_21states.cpp new file mode 100644 index 0000000000..5a60ac1c01 --- /dev/null +++ b/src/modules/ekf_att_pos_estimator/estimator_21states.cpp @@ -0,0 +1,2143 @@ +#include "estimator_21states.h" + +#include + +AttPosEKF::AttPosEKF() : + fusionModeGPS(0), + covSkipCount(0), + EAS2TAS(1.0f), + statesInitialised(false), + fuseVelData(false), + fusePosData(false), + fuseHgtData(false), + fuseMagData(false), + fuseVtasData(false), + onGround(true), + staticMode(true), + useAirspeed(true), + useCompass(true), + numericalProtection(true), + storeIndex(0), + magDeclination(0.0f) +{ + InitialiseParameters(); +} + +AttPosEKF::~AttPosEKF() +{ +} + +void AttPosEKF::UpdateStrapdownEquationsNED() +{ + Vector3f delVelNav; + float q00; + float q11; + float q22; + float q33; + float q01; + float q02; + float q03; + float q12; + float q13; + float q23; + Mat3f Tbn; + Mat3f Tnb; + float rotationMag; + float qUpdated[4]; + float quatMag; + double deltaQuat[4]; + const Vector3f gravityNED = {0.0,0.0,GRAVITY_MSS}; + +// Remove sensor bias errors + correctedDelAng.x = dAngIMU.x - states[10]; + correctedDelAng.y = dAngIMU.y - states[11]; + correctedDelAng.z = dAngIMU.z - states[12]; + dVelIMU.x = dVelIMU.x; + dVelIMU.y = dVelIMU.y; + dVelIMU.z = dVelIMU.z; + +// Save current measurements + Vector3f prevDelAng = correctedDelAng; + +// Apply corrections for earths rotation rate and coning errors +// * and + operators have been overloaded + correctedDelAng = correctedDelAng - Tnb*earthRateNED*dtIMU + 8.333333333333333e-2f*(prevDelAng % correctedDelAng); + +// Convert the rotation vector to its equivalent quaternion + rotationMag = correctedDelAng.length(); + if (rotationMag < 1e-12f) + { + deltaQuat[0] = 1.0; + deltaQuat[1] = 0.0; + deltaQuat[2] = 0.0; + deltaQuat[3] = 0.0; + } + else + { + deltaQuat[0] = cos(0.5f*rotationMag); + double rotScaler = (sin(0.5f*rotationMag))/rotationMag; + deltaQuat[1] = correctedDelAng.x*rotScaler; + deltaQuat[2] = correctedDelAng.y*rotScaler; + deltaQuat[3] = correctedDelAng.z*rotScaler; + } + +// Update the quaternions by rotating from the previous attitude through +// the delta angle rotation quaternion + qUpdated[0] = states[0]*deltaQuat[0] - states[1]*deltaQuat[1] - states[2]*deltaQuat[2] - states[3]*deltaQuat[3]; + qUpdated[1] = states[0]*deltaQuat[1] + states[1]*deltaQuat[0] + states[2]*deltaQuat[3] - states[3]*deltaQuat[2]; + qUpdated[2] = states[0]*deltaQuat[2] + states[2]*deltaQuat[0] + states[3]*deltaQuat[1] - states[1]*deltaQuat[3]; + qUpdated[3] = states[0]*deltaQuat[3] + states[3]*deltaQuat[0] + states[1]*deltaQuat[2] - states[2]*deltaQuat[1]; + +// Normalise the quaternions and update the quaternion states + quatMag = sqrtf(sq(qUpdated[0]) + sq(qUpdated[1]) + sq(qUpdated[2]) + sq(qUpdated[3])); + if (quatMag > 1e-16f) + { + float quatMagInv = 1.0f/quatMag; + states[0] = quatMagInv*qUpdated[0]; + states[1] = quatMagInv*qUpdated[1]; + states[2] = quatMagInv*qUpdated[2]; + states[3] = quatMagInv*qUpdated[3]; + } + +// Calculate the body to nav cosine matrix + q00 = sq(states[0]); + q11 = sq(states[1]); + q22 = sq(states[2]); + q33 = sq(states[3]); + q01 = states[0]*states[1]; + q02 = states[0]*states[2]; + q03 = states[0]*states[3]; + q12 = states[1]*states[2]; + q13 = states[1]*states[3]; + q23 = states[2]*states[3]; + + Tbn.x.x = q00 + q11 - q22 - q33; + Tbn.y.y = q00 - q11 + q22 - q33; + Tbn.z.z = q00 - q11 - q22 + q33; + Tbn.x.y = 2*(q12 - q03); + Tbn.x.z = 2*(q13 + q02); + Tbn.y.x = 2*(q12 + q03); + Tbn.y.z = 2*(q23 - q01); + Tbn.z.x = 2*(q13 - q02); + Tbn.z.y = 2*(q23 + q01); + + Tnb = Tbn.transpose(); + +// transform body delta velocities to delta velocities in the nav frame +// * and + operators have been overloaded + //delVelNav = Tbn*dVelIMU + gravityNED*dtIMU; + delVelNav.x = Tbn.x.x*dVelIMU.x + Tbn.x.y*dVelIMU.y + Tbn.x.z*dVelIMU.z + gravityNED.x*dtIMU; + delVelNav.y = Tbn.y.x*dVelIMU.x + Tbn.y.y*dVelIMU.y + Tbn.y.z*dVelIMU.z + gravityNED.y*dtIMU; + delVelNav.z = Tbn.z.x*dVelIMU.x + Tbn.z.y*dVelIMU.y + Tbn.z.z*dVelIMU.z + gravityNED.z*dtIMU; + +// calculate the magnitude of the nav acceleration (required for GPS +// variance estimation) + accNavMag = delVelNav.length()/dtIMU; + +// If calculating position save previous velocity + float lastVelocity[3]; + lastVelocity[0] = states[4]; + lastVelocity[1] = states[5]; + lastVelocity[2] = states[6]; + +// Sum delta velocities to get velocity + states[4] = states[4] + delVelNav.x; + states[5] = states[5] + delVelNav.y; + states[6] = states[6] + delVelNav.z; + +// If calculating postions, do a trapezoidal integration for position + states[7] = states[7] + 0.5f*(states[4] + lastVelocity[0])*dtIMU; + states[8] = states[8] + 0.5f*(states[5] + lastVelocity[1])*dtIMU; + states[9] = states[9] + 0.5f*(states[6] + lastVelocity[2])*dtIMU; + + // Constrain states (to protect against filter divergence) + ConstrainStates(); +} + +void AttPosEKF::CovariancePrediction(float dt) +{ + // scalars + float daxCov; + float dayCov; + float dazCov; + float dvxCov; + float dvyCov; + float dvzCov; + float dvx; + float dvy; + float dvz; + float dax; + float day; + float daz; + float q0; + float q1; + float q2; + float q3; + float dax_b; + float day_b; + float daz_b; + + // arrays + float processNoise[21]; + float SF[14]; + float SG[8]; + float SQ[11]; + float SPP[13] = {0}; + float nextP[21][21]; + + // calculate covariance prediction process noise + windVelSigma = dt*0.1f; + dAngBiasSigma = dt*5.0e-7f; + magEarthSigma = dt*3.0e-4f; + magBodySigma = dt*3.0e-4f; + for (uint8_t i= 0; i<=9; i++) processNoise[i] = 1.0e-9f; + for (uint8_t i=10; i<=12; i++) processNoise[i] = dAngBiasSigma; + if (onGround) processNoise[12] = dAngBiasSigma * yawVarScale; + for (uint8_t i=13; i<=14; i++) processNoise[i] = windVelSigma; + for (uint8_t i=15; i<=17; i++) processNoise[i] = magEarthSigma; + for (uint8_t i=18; i<=20; i++) processNoise[i] = magBodySigma; + for (uint8_t i= 0; i<=20; i++) processNoise[i] = sq(processNoise[i]); + + // set variables used to calculate covariance growth + dvx = summedDelVel.x; + dvy = summedDelVel.y; + dvz = summedDelVel.z; + dax = summedDelAng.x; + day = summedDelAng.y; + daz = summedDelAng.z; + q0 = states[0]; + q1 = states[1]; + q2 = states[2]; + q3 = states[3]; + dax_b = states[10]; + day_b = states[11]; + daz_b = states[12]; + daxCov = sq(dt*1.4544411e-2f); + dayCov = sq(dt*1.4544411e-2f); + dazCov = sq(dt*1.4544411e-2f); + if (onGround) dazCov = dazCov * sq(yawVarScale); + dvxCov = sq(dt*0.5f); + dvyCov = sq(dt*0.5f); + dvzCov = sq(dt*0.5f); + + // Predicted covariance calculation + SF[0] = 2*dvx*q1 + 2*dvy*q2 + 2*dvz*q3; + SF[1] = 2*dvx*q3 + 2*dvy*q0 - 2*dvz*q1; + SF[2] = 2*dvx*q0 - 2*dvy*q3 + 2*dvz*q2; + SF[3] = day/2 - day_b/2; + SF[4] = daz/2 - daz_b/2; + SF[5] = dax/2 - dax_b/2; + SF[6] = dax_b/2 - dax/2; + SF[7] = daz_b/2 - daz/2; + SF[8] = day_b/2 - day/2; + SF[9] = q1/2; + SF[10] = q2/2; + SF[11] = q3/2; + SF[12] = 2*dvz*q0; + SF[13] = 2*dvy*q1; + + SG[0] = q0/2; + SG[1] = sq(q3); + SG[2] = sq(q2); + SG[3] = sq(q1); + SG[4] = sq(q0); + SG[5] = 2*q2*q3; + SG[6] = 2*q1*q3; + SG[7] = 2*q1*q2; + + SQ[0] = dvzCov*(SG[5] - 2*q0*q1)*(SG[1] - SG[2] - SG[3] + SG[4]) - dvyCov*(SG[5] + 2*q0*q1)*(SG[1] - SG[2] + SG[3] - SG[4]) + dvxCov*(SG[6] - 2*q0*q2)*(SG[7] + 2*q0*q3); + SQ[1] = dvzCov*(SG[6] + 2*q0*q2)*(SG[1] - SG[2] - SG[3] + SG[4]) - dvxCov*(SG[6] - 2*q0*q2)*(SG[1] + SG[2] - SG[3] - SG[4]) + dvyCov*(SG[5] + 2*q0*q1)*(SG[7] - 2*q0*q3); + SQ[2] = dvzCov*(SG[5] - 2*q0*q1)*(SG[6] + 2*q0*q2) - dvyCov*(SG[7] - 2*q0*q3)*(SG[1] - SG[2] + SG[3] - SG[4]) - dvxCov*(SG[7] + 2*q0*q3)*(SG[1] + SG[2] - SG[3] - SG[4]); + SQ[3] = (dayCov*q1*SG[0])/2 - (dazCov*q1*SG[0])/2 - (daxCov*q2*q3)/4; + SQ[4] = (dazCov*q2*SG[0])/2 - (daxCov*q2*SG[0])/2 - (dayCov*q1*q3)/4; + SQ[5] = (daxCov*q3*SG[0])/2 - (dayCov*q3*SG[0])/2 - (dazCov*q1*q2)/4; + SQ[6] = (daxCov*q1*q2)/4 - (dazCov*q3*SG[0])/2 - (dayCov*q1*q2)/4; + SQ[7] = (dazCov*q1*q3)/4 - (daxCov*q1*q3)/4 - (dayCov*q2*SG[0])/2; + SQ[8] = (dayCov*q2*q3)/4 - (daxCov*q1*SG[0])/2 - (dazCov*q2*q3)/4; + SQ[9] = sq(SG[0]); + SQ[10] = sq(q1); + + SPP[0] = SF[12] + SF[13] - 2*dvx*q2; + SPP[1] = 2*dvx*q0 - 2*dvy*q3 + 2*dvz*q2; + SPP[2] = 2*dvx*q3 + 2*dvy*q0 - 2*dvz*q1; + SPP[3] = SF[11]; + SPP[4] = SF[10]; + SPP[5] = SF[9]; + SPP[6] = SF[7]; + SPP[7] = SF[8]; + + nextP[0][0] = P[0][0] + P[1][0]*SF[6] + P[2][0]*SPP[7] + P[3][0]*SPP[6] + P[10][0]*SPP[5] + P[11][0]*SPP[4] + P[12][0]*SPP[3] + (daxCov*SQ[10])/4 + SF[6]*(P[0][1] + P[1][1]*SF[6] + P[2][1]*SPP[7] + P[3][1]*SPP[6] + P[10][1]*SPP[5] + P[11][1]*SPP[4] + P[12][1]*SPP[3]) + SPP[7]*(P[0][2] + P[1][2]*SF[6] + P[2][2]*SPP[7] + P[3][2]*SPP[6] + P[10][2]*SPP[5] + P[11][2]*SPP[4] + P[12][2]*SPP[3]) + SPP[6]*(P[0][3] + P[1][3]*SF[6] + P[2][3]*SPP[7] + P[3][3]*SPP[6] + P[10][3]*SPP[5] + P[11][3]*SPP[4] + P[12][3]*SPP[3]) + SPP[5]*(P[0][10] + P[1][10]*SF[6] + P[2][10]*SPP[7] + P[3][10]*SPP[6] + P[10][10]*SPP[5] + P[11][10]*SPP[4] + P[12][10]*SPP[3]) + SPP[4]*(P[0][11] + P[1][11]*SF[6] + P[2][11]*SPP[7] + P[3][11]*SPP[6] + P[10][11]*SPP[5] + P[11][11]*SPP[4] + P[12][11]*SPP[3]) + SPP[3]*(P[0][12] + P[1][12]*SF[6] + P[2][12]*SPP[7] + P[3][12]*SPP[6] + P[10][12]*SPP[5] + P[11][12]*SPP[4] + P[12][12]*SPP[3]) + (dayCov*sq(q2))/4 + (dazCov*sq(q3))/4; + nextP[0][1] = P[0][1] + SQ[8] + P[1][1]*SF[6] + P[2][1]*SPP[7] + P[3][1]*SPP[6] + P[10][1]*SPP[5] + P[11][1]*SPP[4] + P[12][1]*SPP[3] + SF[5]*(P[0][0] + P[1][0]*SF[6] + P[2][0]*SPP[7] + P[3][0]*SPP[6] + P[10][0]*SPP[5] + P[11][0]*SPP[4] + P[12][0]*SPP[3]) + SF[4]*(P[0][2] + P[1][2]*SF[6] + P[2][2]*SPP[7] + P[3][2]*SPP[6] + P[10][2]*SPP[5] + P[11][2]*SPP[4] + P[12][2]*SPP[3]) + SPP[7]*(P[0][3] + P[1][3]*SF[6] + P[2][3]*SPP[7] + P[3][3]*SPP[6] + P[10][3]*SPP[5] + P[11][3]*SPP[4] + P[12][3]*SPP[3]) + SPP[3]*(P[0][11] + P[1][11]*SF[6] + P[2][11]*SPP[7] + P[3][11]*SPP[6] + P[10][11]*SPP[5] + P[11][11]*SPP[4] + P[12][11]*SPP[3]) - SPP[4]*(P[0][12] + P[1][12]*SF[6] + P[2][12]*SPP[7] + P[3][12]*SPP[6] + P[10][12]*SPP[5] + P[11][12]*SPP[4] + P[12][12]*SPP[3]) - (q0*(P[0][10] + P[1][10]*SF[6] + P[2][10]*SPP[7] + P[3][10]*SPP[6] + P[10][10]*SPP[5] + P[11][10]*SPP[4] + P[12][10]*SPP[3]))/2; + nextP[0][2] = P[0][2] + SQ[7] + P[1][2]*SF[6] + P[2][2]*SPP[7] + P[3][2]*SPP[6] + P[10][2]*SPP[5] + P[11][2]*SPP[4] + P[12][2]*SPP[3] + SF[3]*(P[0][0] + P[1][0]*SF[6] + P[2][0]*SPP[7] + P[3][0]*SPP[6] + P[10][0]*SPP[5] + P[11][0]*SPP[4] + P[12][0]*SPP[3]) + SF[5]*(P[0][3] + P[1][3]*SF[6] + P[2][3]*SPP[7] + P[3][3]*SPP[6] + P[10][3]*SPP[5] + P[11][3]*SPP[4] + P[12][3]*SPP[3]) + SPP[6]*(P[0][1] + P[1][1]*SF[6] + P[2][1]*SPP[7] + P[3][1]*SPP[6] + P[10][1]*SPP[5] + P[11][1]*SPP[4] + P[12][1]*SPP[3]) - SPP[3]*(P[0][10] + P[1][10]*SF[6] + P[2][10]*SPP[7] + P[3][10]*SPP[6] + P[10][10]*SPP[5] + P[11][10]*SPP[4] + P[12][10]*SPP[3]) + SPP[5]*(P[0][12] + P[1][12]*SF[6] + P[2][12]*SPP[7] + P[3][12]*SPP[6] + P[10][12]*SPP[5] + P[11][12]*SPP[4] + P[12][12]*SPP[3]) - (q0*(P[0][11] + P[1][11]*SF[6] + P[2][11]*SPP[7] + P[3][11]*SPP[6] + P[10][11]*SPP[5] + P[11][11]*SPP[4] + P[12][11]*SPP[3]))/2; + nextP[0][3] = P[0][3] + SQ[6] + P[1][3]*SF[6] + P[2][3]*SPP[7] + P[3][3]*SPP[6] + P[10][3]*SPP[5] + P[11][3]*SPP[4] + P[12][3]*SPP[3] + SF[4]*(P[0][0] + P[1][0]*SF[6] + P[2][0]*SPP[7] + P[3][0]*SPP[6] + P[10][0]*SPP[5] + P[11][0]*SPP[4] + P[12][0]*SPP[3]) + SF[3]*(P[0][1] + P[1][1]*SF[6] + P[2][1]*SPP[7] + P[3][1]*SPP[6] + P[10][1]*SPP[5] + P[11][1]*SPP[4] + P[12][1]*SPP[3]) + SF[6]*(P[0][2] + P[1][2]*SF[6] + P[2][2]*SPP[7] + P[3][2]*SPP[6] + P[10][2]*SPP[5] + P[11][2]*SPP[4] + P[12][2]*SPP[3]) + SPP[4]*(P[0][10] + P[1][10]*SF[6] + P[2][10]*SPP[7] + P[3][10]*SPP[6] + P[10][10]*SPP[5] + P[11][10]*SPP[4] + P[12][10]*SPP[3]) - SPP[5]*(P[0][11] + P[1][11]*SF[6] + P[2][11]*SPP[7] + P[3][11]*SPP[6] + P[10][11]*SPP[5] + P[11][11]*SPP[4] + P[12][11]*SPP[3]) - (q0*(P[0][12] + P[1][12]*SF[6] + P[2][12]*SPP[7] + P[3][12]*SPP[6] + P[10][12]*SPP[5] + P[11][12]*SPP[4] + P[12][12]*SPP[3]))/2; + nextP[0][4] = P[0][4] + P[1][4]*SF[6] + P[2][4]*SPP[7] + P[3][4]*SPP[6] + P[10][4]*SPP[5] + P[11][4]*SPP[4] + P[12][4]*SPP[3] + SF[2]*(P[0][0] + P[1][0]*SF[6] + P[2][0]*SPP[7] + P[3][0]*SPP[6] + P[10][0]*SPP[5] + P[11][0]*SPP[4] + P[12][0]*SPP[3]) + SF[0]*(P[0][1] + P[1][1]*SF[6] + P[2][1]*SPP[7] + P[3][1]*SPP[6] + P[10][1]*SPP[5] + P[11][1]*SPP[4] + P[12][1]*SPP[3]) + SPP[0]*(P[0][2] + P[1][2]*SF[6] + P[2][2]*SPP[7] + P[3][2]*SPP[6] + P[10][2]*SPP[5] + P[11][2]*SPP[4] + P[12][2]*SPP[3]) - SPP[2]*(P[0][3] + P[1][3]*SF[6] + P[2][3]*SPP[7] + P[3][3]*SPP[6] + P[10][3]*SPP[5] + P[11][3]*SPP[4] + P[12][3]*SPP[3]); + nextP[0][5] = P[0][5] + P[1][5]*SF[6] + P[2][5]*SPP[7] + P[3][5]*SPP[6] + P[10][5]*SPP[5] + P[11][5]*SPP[4] + P[12][5]*SPP[3] + SF[1]*(P[0][0] + P[1][0]*SF[6] + P[2][0]*SPP[7] + P[3][0]*SPP[6] + P[10][0]*SPP[5] + P[11][0]*SPP[4] + P[12][0]*SPP[3]) + SF[0]*(P[0][2] + P[1][2]*SF[6] + P[2][2]*SPP[7] + P[3][2]*SPP[6] + P[10][2]*SPP[5] + P[11][2]*SPP[4] + P[12][2]*SPP[3]) + SF[2]*(P[0][3] + P[1][3]*SF[6] + P[2][3]*SPP[7] + P[3][3]*SPP[6] + P[10][3]*SPP[5] + P[11][3]*SPP[4] + P[12][3]*SPP[3]) - SPP[0]*(P[0][1] + P[1][1]*SF[6] + P[2][1]*SPP[7] + P[3][1]*SPP[6] + P[10][1]*SPP[5] + P[11][1]*SPP[4] + P[12][1]*SPP[3]); + nextP[0][6] = P[0][6] + P[1][6]*SF[6] + P[2][6]*SPP[7] + P[3][6]*SPP[6] + P[10][6]*SPP[5] + P[11][6]*SPP[4] + P[12][6]*SPP[3] + SF[1]*(P[0][1] + P[1][1]*SF[6] + P[2][1]*SPP[7] + P[3][1]*SPP[6] + P[10][1]*SPP[5] + P[11][1]*SPP[4] + P[12][1]*SPP[3]) + SF[0]*(P[0][3] + P[1][3]*SF[6] + P[2][3]*SPP[7] + P[3][3]*SPP[6] + P[10][3]*SPP[5] + P[11][3]*SPP[4] + P[12][3]*SPP[3]) + SPP[0]*(P[0][0] + P[1][0]*SF[6] + P[2][0]*SPP[7] + P[3][0]*SPP[6] + P[10][0]*SPP[5] + P[11][0]*SPP[4] + P[12][0]*SPP[3]) - SPP[1]*(P[0][2] + P[1][2]*SF[6] + P[2][2]*SPP[7] + P[3][2]*SPP[6] + P[10][2]*SPP[5] + P[11][2]*SPP[4] + P[12][2]*SPP[3]); + nextP[0][7] = P[0][7] + P[1][7]*SF[6] + P[2][7]*SPP[7] + P[3][7]*SPP[6] + P[10][7]*SPP[5] + P[11][7]*SPP[4] + P[12][7]*SPP[3] + dt*(P[0][4] + P[1][4]*SF[6] + P[2][4]*SPP[7] + P[3][4]*SPP[6] + P[10][4]*SPP[5] + P[11][4]*SPP[4] + P[12][4]*SPP[3]); + nextP[0][8] = P[0][8] + P[1][8]*SF[6] + P[2][8]*SPP[7] + P[3][8]*SPP[6] + P[10][8]*SPP[5] + P[11][8]*SPP[4] + P[12][8]*SPP[3] + dt*(P[0][5] + P[1][5]*SF[6] + P[2][5]*SPP[7] + P[3][5]*SPP[6] + P[10][5]*SPP[5] + P[11][5]*SPP[4] + P[12][5]*SPP[3]); + nextP[0][9] = P[0][9] + P[1][9]*SF[6] + P[2][9]*SPP[7] + P[3][9]*SPP[6] + P[10][9]*SPP[5] + P[11][9]*SPP[4] + P[12][9]*SPP[3] + dt*(P[0][6] + P[1][6]*SF[6] + P[2][6]*SPP[7] + P[3][6]*SPP[6] + P[10][6]*SPP[5] + P[11][6]*SPP[4] + P[12][6]*SPP[3]); + nextP[0][10] = P[0][10] + P[1][10]*SF[6] + P[2][10]*SPP[7] + P[3][10]*SPP[6] + P[10][10]*SPP[5] + P[11][10]*SPP[4] + P[12][10]*SPP[3]; + nextP[0][11] = P[0][11] + P[1][11]*SF[6] + P[2][11]*SPP[7] + P[3][11]*SPP[6] + P[10][11]*SPP[5] + P[11][11]*SPP[4] + P[12][11]*SPP[3]; + nextP[0][12] = P[0][12] + P[1][12]*SF[6] + P[2][12]*SPP[7] + P[3][12]*SPP[6] + P[10][12]*SPP[5] + P[11][12]*SPP[4] + P[12][12]*SPP[3]; + nextP[0][13] = P[0][13] + P[1][13]*SF[6] + P[2][13]*SPP[7] + P[3][13]*SPP[6] + P[10][13]*SPP[5] + P[11][13]*SPP[4] + P[12][13]*SPP[3]; + nextP[0][14] = P[0][14] + P[1][14]*SF[6] + P[2][14]*SPP[7] + P[3][14]*SPP[6] + P[10][14]*SPP[5] + P[11][14]*SPP[4] + P[12][14]*SPP[3]; + nextP[0][15] = P[0][15] + P[1][15]*SF[6] + P[2][15]*SPP[7] + P[3][15]*SPP[6] + P[10][15]*SPP[5] + P[11][15]*SPP[4] + P[12][15]*SPP[3]; + nextP[0][16] = P[0][16] + P[1][16]*SF[6] + P[2][16]*SPP[7] + P[3][16]*SPP[6] + P[10][16]*SPP[5] + P[11][16]*SPP[4] + P[12][16]*SPP[3]; + nextP[0][17] = P[0][17] + P[1][17]*SF[6] + P[2][17]*SPP[7] + P[3][17]*SPP[6] + P[10][17]*SPP[5] + P[11][17]*SPP[4] + P[12][17]*SPP[3]; + nextP[0][18] = P[0][18] + P[1][18]*SF[6] + P[2][18]*SPP[7] + P[3][18]*SPP[6] + P[10][18]*SPP[5] + P[11][18]*SPP[4] + P[12][18]*SPP[3]; + nextP[0][19] = P[0][19] + P[1][19]*SF[6] + P[2][19]*SPP[7] + P[3][19]*SPP[6] + P[10][19]*SPP[5] + P[11][19]*SPP[4] + P[12][19]*SPP[3]; + nextP[0][20] = P[0][20] + P[1][20]*SF[6] + P[2][20]*SPP[7] + P[3][20]*SPP[6] + P[10][20]*SPP[5] + P[11][20]*SPP[4] + P[12][20]*SPP[3]; + nextP[1][0] = P[1][0] + SQ[8] + P[0][0]*SF[5] + P[2][0]*SF[4] + P[3][0]*SPP[7] + P[11][0]*SPP[3] - P[12][0]*SPP[4] - (P[10][0]*q0)/2 + SF[6]*(P[1][1] + P[0][1]*SF[5] + P[2][1]*SF[4] + P[3][1]*SPP[7] + P[11][1]*SPP[3] - P[12][1]*SPP[4] - (P[10][1]*q0)/2) + SPP[7]*(P[1][2] + P[0][2]*SF[5] + P[2][2]*SF[4] + P[3][2]*SPP[7] + P[11][2]*SPP[3] - P[12][2]*SPP[4] - (P[10][2]*q0)/2) + SPP[6]*(P[1][3] + P[0][3]*SF[5] + P[2][3]*SF[4] + P[3][3]*SPP[7] + P[11][3]*SPP[3] - P[12][3]*SPP[4] - (P[10][3]*q0)/2) + SPP[5]*(P[1][10] + P[0][10]*SF[5] + P[2][10]*SF[4] + P[3][10]*SPP[7] + P[11][10]*SPP[3] - P[12][10]*SPP[4] - (P[10][10]*q0)/2) + SPP[4]*(P[1][11] + P[0][11]*SF[5] + P[2][11]*SF[4] + P[3][11]*SPP[7] + P[11][11]*SPP[3] - P[12][11]*SPP[4] - (P[10][11]*q0)/2) + SPP[3]*(P[1][12] + P[0][12]*SF[5] + P[2][12]*SF[4] + P[3][12]*SPP[7] + P[11][12]*SPP[3] - P[12][12]*SPP[4] - (P[10][12]*q0)/2); + nextP[1][1] = P[1][1] + P[0][1]*SF[5] + P[2][1]*SF[4] + P[3][1]*SPP[7] + P[11][1]*SPP[3] - P[12][1]*SPP[4] + daxCov*SQ[9] - (P[10][1]*q0)/2 + SF[5]*(P[1][0] + P[0][0]*SF[5] + P[2][0]*SF[4] + P[3][0]*SPP[7] + P[11][0]*SPP[3] - P[12][0]*SPP[4] - (P[10][0]*q0)/2) + SF[4]*(P[1][2] + P[0][2]*SF[5] + P[2][2]*SF[4] + P[3][2]*SPP[7] + P[11][2]*SPP[3] - P[12][2]*SPP[4] - (P[10][2]*q0)/2) + SPP[7]*(P[1][3] + P[0][3]*SF[5] + P[2][3]*SF[4] + P[3][3]*SPP[7] + P[11][3]*SPP[3] - P[12][3]*SPP[4] - (P[10][3]*q0)/2) + SPP[3]*(P[1][11] + P[0][11]*SF[5] + P[2][11]*SF[4] + P[3][11]*SPP[7] + P[11][11]*SPP[3] - P[12][11]*SPP[4] - (P[10][11]*q0)/2) - SPP[4]*(P[1][12] + P[0][12]*SF[5] + P[2][12]*SF[4] + P[3][12]*SPP[7] + P[11][12]*SPP[3] - P[12][12]*SPP[4] - (P[10][12]*q0)/2) + (dayCov*sq(q3))/4 + (dazCov*sq(q2))/4 - (q0*(P[1][10] + P[0][10]*SF[5] + P[2][10]*SF[4] + P[3][10]*SPP[7] + P[11][10]*SPP[3] - P[12][10]*SPP[4] - (P[10][10]*q0)/2))/2; + nextP[1][2] = P[1][2] + SQ[5] + P[0][2]*SF[5] + P[2][2]*SF[4] + P[3][2]*SPP[7] + P[11][2]*SPP[3] - P[12][2]*SPP[4] - (P[10][2]*q0)/2 + SF[3]*(P[1][0] + P[0][0]*SF[5] + P[2][0]*SF[4] + P[3][0]*SPP[7] + P[11][0]*SPP[3] - P[12][0]*SPP[4] - (P[10][0]*q0)/2) + SF[5]*(P[1][3] + P[0][3]*SF[5] + P[2][3]*SF[4] + P[3][3]*SPP[7] + P[11][3]*SPP[3] - P[12][3]*SPP[4] - (P[10][3]*q0)/2) + SPP[6]*(P[1][1] + P[0][1]*SF[5] + P[2][1]*SF[4] + P[3][1]*SPP[7] + P[11][1]*SPP[3] - P[12][1]*SPP[4] - (P[10][1]*q0)/2) - SPP[3]*(P[1][10] + P[0][10]*SF[5] + P[2][10]*SF[4] + P[3][10]*SPP[7] + P[11][10]*SPP[3] - P[12][10]*SPP[4] - (P[10][10]*q0)/2) + SPP[5]*(P[1][12] + P[0][12]*SF[5] + P[2][12]*SF[4] + P[3][12]*SPP[7] + P[11][12]*SPP[3] - P[12][12]*SPP[4] - (P[10][12]*q0)/2) - (q0*(P[1][11] + P[0][11]*SF[5] + P[2][11]*SF[4] + P[3][11]*SPP[7] + P[11][11]*SPP[3] - P[12][11]*SPP[4] - (P[10][11]*q0)/2))/2; + nextP[1][3] = P[1][3] + SQ[4] + P[0][3]*SF[5] + P[2][3]*SF[4] + P[3][3]*SPP[7] + P[11][3]*SPP[3] - P[12][3]*SPP[4] - (P[10][3]*q0)/2 + SF[4]*(P[1][0] + P[0][0]*SF[5] + P[2][0]*SF[4] + P[3][0]*SPP[7] + P[11][0]*SPP[3] - P[12][0]*SPP[4] - (P[10][0]*q0)/2) + SF[3]*(P[1][1] + P[0][1]*SF[5] + P[2][1]*SF[4] + P[3][1]*SPP[7] + P[11][1]*SPP[3] - P[12][1]*SPP[4] - (P[10][1]*q0)/2) + SF[6]*(P[1][2] + P[0][2]*SF[5] + P[2][2]*SF[4] + P[3][2]*SPP[7] + P[11][2]*SPP[3] - P[12][2]*SPP[4] - (P[10][2]*q0)/2) + SPP[4]*(P[1][10] + P[0][10]*SF[5] + P[2][10]*SF[4] + P[3][10]*SPP[7] + P[11][10]*SPP[3] - P[12][10]*SPP[4] - (P[10][10]*q0)/2) - SPP[5]*(P[1][11] + P[0][11]*SF[5] + P[2][11]*SF[4] + P[3][11]*SPP[7] + P[11][11]*SPP[3] - P[12][11]*SPP[4] - (P[10][11]*q0)/2) - (q0*(P[1][12] + P[0][12]*SF[5] + P[2][12]*SF[4] + P[3][12]*SPP[7] + P[11][12]*SPP[3] - P[12][12]*SPP[4] - (P[10][12]*q0)/2))/2; + nextP[1][4] = P[1][4] + P[0][4]*SF[5] + P[2][4]*SF[4] + P[3][4]*SPP[7] + P[11][4]*SPP[3] - P[12][4]*SPP[4] - (P[10][4]*q0)/2 + SF[2]*(P[1][0] + P[0][0]*SF[5] + P[2][0]*SF[4] + P[3][0]*SPP[7] + P[11][0]*SPP[3] - P[12][0]*SPP[4] - (P[10][0]*q0)/2) + SF[0]*(P[1][1] + P[0][1]*SF[5] + P[2][1]*SF[4] + P[3][1]*SPP[7] + P[11][1]*SPP[3] - P[12][1]*SPP[4] - (P[10][1]*q0)/2) + SPP[0]*(P[1][2] + P[0][2]*SF[5] + P[2][2]*SF[4] + P[3][2]*SPP[7] + P[11][2]*SPP[3] - P[12][2]*SPP[4] - (P[10][2]*q0)/2) - SPP[2]*(P[1][3] + P[0][3]*SF[5] + P[2][3]*SF[4] + P[3][3]*SPP[7] + P[11][3]*SPP[3] - P[12][3]*SPP[4] - (P[10][3]*q0)/2); + nextP[1][5] = P[1][5] + P[0][5]*SF[5] + P[2][5]*SF[4] + P[3][5]*SPP[7] + P[11][5]*SPP[3] - P[12][5]*SPP[4] - (P[10][5]*q0)/2 + SF[1]*(P[1][0] + P[0][0]*SF[5] + P[2][0]*SF[4] + P[3][0]*SPP[7] + P[11][0]*SPP[3] - P[12][0]*SPP[4] - (P[10][0]*q0)/2) + SF[0]*(P[1][2] + P[0][2]*SF[5] + P[2][2]*SF[4] + P[3][2]*SPP[7] + P[11][2]*SPP[3] - P[12][2]*SPP[4] - (P[10][2]*q0)/2) + SF[2]*(P[1][3] + P[0][3]*SF[5] + P[2][3]*SF[4] + P[3][3]*SPP[7] + P[11][3]*SPP[3] - P[12][3]*SPP[4] - (P[10][3]*q0)/2) - SPP[0]*(P[1][1] + P[0][1]*SF[5] + P[2][1]*SF[4] + P[3][1]*SPP[7] + P[11][1]*SPP[3] - P[12][1]*SPP[4] - (P[10][1]*q0)/2); + nextP[1][6] = P[1][6] + P[0][6]*SF[5] + P[2][6]*SF[4] + P[3][6]*SPP[7] + P[11][6]*SPP[3] - P[12][6]*SPP[4] - (P[10][6]*q0)/2 + SF[1]*(P[1][1] + P[0][1]*SF[5] + P[2][1]*SF[4] + P[3][1]*SPP[7] + P[11][1]*SPP[3] - P[12][1]*SPP[4] - (P[10][1]*q0)/2) + SF[0]*(P[1][3] + P[0][3]*SF[5] + P[2][3]*SF[4] + P[3][3]*SPP[7] + P[11][3]*SPP[3] - P[12][3]*SPP[4] - (P[10][3]*q0)/2) + SPP[0]*(P[1][0] + P[0][0]*SF[5] + P[2][0]*SF[4] + P[3][0]*SPP[7] + P[11][0]*SPP[3] - P[12][0]*SPP[4] - (P[10][0]*q0)/2) - SPP[1]*(P[1][2] + P[0][2]*SF[5] + P[2][2]*SF[4] + P[3][2]*SPP[7] + P[11][2]*SPP[3] - P[12][2]*SPP[4] - (P[10][2]*q0)/2); + nextP[1][7] = P[1][7] + P[0][7]*SF[5] + P[2][7]*SF[4] + P[3][7]*SPP[7] + P[11][7]*SPP[3] - P[12][7]*SPP[4] - (P[10][7]*q0)/2 + dt*(P[1][4] + P[0][4]*SF[5] + P[2][4]*SF[4] + P[3][4]*SPP[7] + P[11][4]*SPP[3] - P[12][4]*SPP[4] - (P[10][4]*q0)/2); + nextP[1][8] = P[1][8] + P[0][8]*SF[5] + P[2][8]*SF[4] + P[3][8]*SPP[7] + P[11][8]*SPP[3] - P[12][8]*SPP[4] - (P[10][8]*q0)/2 + dt*(P[1][5] + P[0][5]*SF[5] + P[2][5]*SF[4] + P[3][5]*SPP[7] + P[11][5]*SPP[3] - P[12][5]*SPP[4] - (P[10][5]*q0)/2); + nextP[1][9] = P[1][9] + P[0][9]*SF[5] + P[2][9]*SF[4] + P[3][9]*SPP[7] + P[11][9]*SPP[3] - P[12][9]*SPP[4] - (P[10][9]*q0)/2 + dt*(P[1][6] + P[0][6]*SF[5] + P[2][6]*SF[4] + P[3][6]*SPP[7] + P[11][6]*SPP[3] - P[12][6]*SPP[4] - (P[10][6]*q0)/2); + nextP[1][10] = P[1][10] + P[0][10]*SF[5] + P[2][10]*SF[4] + P[3][10]*SPP[7] + P[11][10]*SPP[3] - P[12][10]*SPP[4] - (P[10][10]*q0)/2; + nextP[1][11] = P[1][11] + P[0][11]*SF[5] + P[2][11]*SF[4] + P[3][11]*SPP[7] + P[11][11]*SPP[3] - P[12][11]*SPP[4] - (P[10][11]*q0)/2; + nextP[1][12] = P[1][12] + P[0][12]*SF[5] + P[2][12]*SF[4] + P[3][12]*SPP[7] + P[11][12]*SPP[3] - P[12][12]*SPP[4] - (P[10][12]*q0)/2; + nextP[1][13] = P[1][13] + P[0][13]*SF[5] + P[2][13]*SF[4] + P[3][13]*SPP[7] + P[11][13]*SPP[3] - P[12][13]*SPP[4] - (P[10][13]*q0)/2; + nextP[1][14] = P[1][14] + P[0][14]*SF[5] + P[2][14]*SF[4] + P[3][14]*SPP[7] + P[11][14]*SPP[3] - P[12][14]*SPP[4] - (P[10][14]*q0)/2; + nextP[1][15] = P[1][15] + P[0][15]*SF[5] + P[2][15]*SF[4] + P[3][15]*SPP[7] + P[11][15]*SPP[3] - P[12][15]*SPP[4] - (P[10][15]*q0)/2; + nextP[1][16] = P[1][16] + P[0][16]*SF[5] + P[2][16]*SF[4] + P[3][16]*SPP[7] + P[11][16]*SPP[3] - P[12][16]*SPP[4] - (P[10][16]*q0)/2; + nextP[1][17] = P[1][17] + P[0][17]*SF[5] + P[2][17]*SF[4] + P[3][17]*SPP[7] + P[11][17]*SPP[3] - P[12][17]*SPP[4] - (P[10][17]*q0)/2; + nextP[1][18] = P[1][18] + P[0][18]*SF[5] + P[2][18]*SF[4] + P[3][18]*SPP[7] + P[11][18]*SPP[3] - P[12][18]*SPP[4] - (P[10][18]*q0)/2; + nextP[1][19] = P[1][19] + P[0][19]*SF[5] + P[2][19]*SF[4] + P[3][19]*SPP[7] + P[11][19]*SPP[3] - P[12][19]*SPP[4] - (P[10][19]*q0)/2; + nextP[1][20] = P[1][20] + P[0][20]*SF[5] + P[2][20]*SF[4] + P[3][20]*SPP[7] + P[11][20]*SPP[3] - P[12][20]*SPP[4] - (P[10][20]*q0)/2; + nextP[2][0] = P[2][0] + SQ[7] + P[0][0]*SF[3] + P[3][0]*SF[5] + P[1][0]*SPP[6] - P[10][0]*SPP[3] + P[12][0]*SPP[5] - (P[11][0]*q0)/2 + SF[6]*(P[2][1] + P[0][1]*SF[3] + P[3][1]*SF[5] + P[1][1]*SPP[6] - P[10][1]*SPP[3] + P[12][1]*SPP[5] - (P[11][1]*q0)/2) + SPP[7]*(P[2][2] + P[0][2]*SF[3] + P[3][2]*SF[5] + P[1][2]*SPP[6] - P[10][2]*SPP[3] + P[12][2]*SPP[5] - (P[11][2]*q0)/2) + SPP[6]*(P[2][3] + P[0][3]*SF[3] + P[3][3]*SF[5] + P[1][3]*SPP[6] - P[10][3]*SPP[3] + P[12][3]*SPP[5] - (P[11][3]*q0)/2) + SPP[5]*(P[2][10] + P[0][10]*SF[3] + P[3][10]*SF[5] + P[1][10]*SPP[6] - P[10][10]*SPP[3] + P[12][10]*SPP[5] - (P[11][10]*q0)/2) + SPP[4]*(P[2][11] + P[0][11]*SF[3] + P[3][11]*SF[5] + P[1][11]*SPP[6] - P[10][11]*SPP[3] + P[12][11]*SPP[5] - (P[11][11]*q0)/2) + SPP[3]*(P[2][12] + P[0][12]*SF[3] + P[3][12]*SF[5] + P[1][12]*SPP[6] - P[10][12]*SPP[3] + P[12][12]*SPP[5] - (P[11][12]*q0)/2); + nextP[2][1] = P[2][1] + SQ[5] + P[0][1]*SF[3] + P[3][1]*SF[5] + P[1][1]*SPP[6] - P[10][1]*SPP[3] + P[12][1]*SPP[5] - (P[11][1]*q0)/2 + SF[5]*(P[2][0] + P[0][0]*SF[3] + P[3][0]*SF[5] + P[1][0]*SPP[6] - P[10][0]*SPP[3] + P[12][0]*SPP[5] - (P[11][0]*q0)/2) + SF[4]*(P[2][2] + P[0][2]*SF[3] + P[3][2]*SF[5] + P[1][2]*SPP[6] - P[10][2]*SPP[3] + P[12][2]*SPP[5] - (P[11][2]*q0)/2) + SPP[7]*(P[2][3] + P[0][3]*SF[3] + P[3][3]*SF[5] + P[1][3]*SPP[6] - P[10][3]*SPP[3] + P[12][3]*SPP[5] - (P[11][3]*q0)/2) + SPP[3]*(P[2][11] + P[0][11]*SF[3] + P[3][11]*SF[5] + P[1][11]*SPP[6] - P[10][11]*SPP[3] + P[12][11]*SPP[5] - (P[11][11]*q0)/2) - SPP[4]*(P[2][12] + P[0][12]*SF[3] + P[3][12]*SF[5] + P[1][12]*SPP[6] - P[10][12]*SPP[3] + P[12][12]*SPP[5] - (P[11][12]*q0)/2) - (q0*(P[2][10] + P[0][10]*SF[3] + P[3][10]*SF[5] + P[1][10]*SPP[6] - P[10][10]*SPP[3] + P[12][10]*SPP[5] - (P[11][10]*q0)/2))/2; + nextP[2][2] = P[2][2] + P[0][2]*SF[3] + P[3][2]*SF[5] + P[1][2]*SPP[6] - P[10][2]*SPP[3] + P[12][2]*SPP[5] + dayCov*SQ[9] + (dazCov*SQ[10])/4 - (P[11][2]*q0)/2 + SF[3]*(P[2][0] + P[0][0]*SF[3] + P[3][0]*SF[5] + P[1][0]*SPP[6] - P[10][0]*SPP[3] + P[12][0]*SPP[5] - (P[11][0]*q0)/2) + SF[5]*(P[2][3] + P[0][3]*SF[3] + P[3][3]*SF[5] + P[1][3]*SPP[6] - P[10][3]*SPP[3] + P[12][3]*SPP[5] - (P[11][3]*q0)/2) + SPP[6]*(P[2][1] + P[0][1]*SF[3] + P[3][1]*SF[5] + P[1][1]*SPP[6] - P[10][1]*SPP[3] + P[12][1]*SPP[5] - (P[11][1]*q0)/2) - SPP[3]*(P[2][10] + P[0][10]*SF[3] + P[3][10]*SF[5] + P[1][10]*SPP[6] - P[10][10]*SPP[3] + P[12][10]*SPP[5] - (P[11][10]*q0)/2) + SPP[5]*(P[2][12] + P[0][12]*SF[3] + P[3][12]*SF[5] + P[1][12]*SPP[6] - P[10][12]*SPP[3] + P[12][12]*SPP[5] - (P[11][12]*q0)/2) + (daxCov*sq(q3))/4 - (q0*(P[2][11] + P[0][11]*SF[3] + P[3][11]*SF[5] + P[1][11]*SPP[6] - P[10][11]*SPP[3] + P[12][11]*SPP[5] - (P[11][11]*q0)/2))/2; + nextP[2][3] = P[2][3] + SQ[3] + P[0][3]*SF[3] + P[3][3]*SF[5] + P[1][3]*SPP[6] - P[10][3]*SPP[3] + P[12][3]*SPP[5] - (P[11][3]*q0)/2 + SF[4]*(P[2][0] + P[0][0]*SF[3] + P[3][0]*SF[5] + P[1][0]*SPP[6] - P[10][0]*SPP[3] + P[12][0]*SPP[5] - (P[11][0]*q0)/2) + SF[3]*(P[2][1] + P[0][1]*SF[3] + P[3][1]*SF[5] + P[1][1]*SPP[6] - P[10][1]*SPP[3] + P[12][1]*SPP[5] - (P[11][1]*q0)/2) + SF[6]*(P[2][2] + P[0][2]*SF[3] + P[3][2]*SF[5] + P[1][2]*SPP[6] - P[10][2]*SPP[3] + P[12][2]*SPP[5] - (P[11][2]*q0)/2) + SPP[4]*(P[2][10] + P[0][10]*SF[3] + P[3][10]*SF[5] + P[1][10]*SPP[6] - P[10][10]*SPP[3] + P[12][10]*SPP[5] - (P[11][10]*q0)/2) - SPP[5]*(P[2][11] + P[0][11]*SF[3] + P[3][11]*SF[5] + P[1][11]*SPP[6] - P[10][11]*SPP[3] + P[12][11]*SPP[5] - (P[11][11]*q0)/2) - (q0*(P[2][12] + P[0][12]*SF[3] + P[3][12]*SF[5] + P[1][12]*SPP[6] - P[10][12]*SPP[3] + P[12][12]*SPP[5] - (P[11][12]*q0)/2))/2; + nextP[2][4] = P[2][4] + P[0][4]*SF[3] + P[3][4]*SF[5] + P[1][4]*SPP[6] - P[10][4]*SPP[3] + P[12][4]*SPP[5] - (P[11][4]*q0)/2 + SF[2]*(P[2][0] + P[0][0]*SF[3] + P[3][0]*SF[5] + P[1][0]*SPP[6] - P[10][0]*SPP[3] + P[12][0]*SPP[5] - (P[11][0]*q0)/2) + SF[0]*(P[2][1] + P[0][1]*SF[3] + P[3][1]*SF[5] + P[1][1]*SPP[6] - P[10][1]*SPP[3] + P[12][1]*SPP[5] - (P[11][1]*q0)/2) + SPP[0]*(P[2][2] + P[0][2]*SF[3] + P[3][2]*SF[5] + P[1][2]*SPP[6] - P[10][2]*SPP[3] + P[12][2]*SPP[5] - (P[11][2]*q0)/2) - SPP[2]*(P[2][3] + P[0][3]*SF[3] + P[3][3]*SF[5] + P[1][3]*SPP[6] - P[10][3]*SPP[3] + P[12][3]*SPP[5] - (P[11][3]*q0)/2); + nextP[2][5] = P[2][5] + P[0][5]*SF[3] + P[3][5]*SF[5] + P[1][5]*SPP[6] - P[10][5]*SPP[3] + P[12][5]*SPP[5] - (P[11][5]*q0)/2 + SF[1]*(P[2][0] + P[0][0]*SF[3] + P[3][0]*SF[5] + P[1][0]*SPP[6] - P[10][0]*SPP[3] + P[12][0]*SPP[5] - (P[11][0]*q0)/2) + SF[0]*(P[2][2] + P[0][2]*SF[3] + P[3][2]*SF[5] + P[1][2]*SPP[6] - P[10][2]*SPP[3] + P[12][2]*SPP[5] - (P[11][2]*q0)/2) + SF[2]*(P[2][3] + P[0][3]*SF[3] + P[3][3]*SF[5] + P[1][3]*SPP[6] - P[10][3]*SPP[3] + P[12][3]*SPP[5] - (P[11][3]*q0)/2) - SPP[0]*(P[2][1] + P[0][1]*SF[3] + P[3][1]*SF[5] + P[1][1]*SPP[6] - P[10][1]*SPP[3] + P[12][1]*SPP[5] - (P[11][1]*q0)/2); + nextP[2][6] = P[2][6] + P[0][6]*SF[3] + P[3][6]*SF[5] + P[1][6]*SPP[6] - P[10][6]*SPP[3] + P[12][6]*SPP[5] - (P[11][6]*q0)/2 + SF[1]*(P[2][1] + P[0][1]*SF[3] + P[3][1]*SF[5] + P[1][1]*SPP[6] - P[10][1]*SPP[3] + P[12][1]*SPP[5] - (P[11][1]*q0)/2) + SF[0]*(P[2][3] + P[0][3]*SF[3] + P[3][3]*SF[5] + P[1][3]*SPP[6] - P[10][3]*SPP[3] + P[12][3]*SPP[5] - (P[11][3]*q0)/2) + SPP[0]*(P[2][0] + P[0][0]*SF[3] + P[3][0]*SF[5] + P[1][0]*SPP[6] - P[10][0]*SPP[3] + P[12][0]*SPP[5] - (P[11][0]*q0)/2) - SPP[1]*(P[2][2] + P[0][2]*SF[3] + P[3][2]*SF[5] + P[1][2]*SPP[6] - P[10][2]*SPP[3] + P[12][2]*SPP[5] - (P[11][2]*q0)/2); + nextP[2][7] = P[2][7] + P[0][7]*SF[3] + P[3][7]*SF[5] + P[1][7]*SPP[6] - P[10][7]*SPP[3] + P[12][7]*SPP[5] - (P[11][7]*q0)/2 + dt*(P[2][4] + P[0][4]*SF[3] + P[3][4]*SF[5] + P[1][4]*SPP[6] - P[10][4]*SPP[3] + P[12][4]*SPP[5] - (P[11][4]*q0)/2); + nextP[2][8] = P[2][8] + P[0][8]*SF[3] + P[3][8]*SF[5] + P[1][8]*SPP[6] - P[10][8]*SPP[3] + P[12][8]*SPP[5] - (P[11][8]*q0)/2 + dt*(P[2][5] + P[0][5]*SF[3] + P[3][5]*SF[5] + P[1][5]*SPP[6] - P[10][5]*SPP[3] + P[12][5]*SPP[5] - (P[11][5]*q0)/2); + nextP[2][9] = P[2][9] + P[0][9]*SF[3] + P[3][9]*SF[5] + P[1][9]*SPP[6] - P[10][9]*SPP[3] + P[12][9]*SPP[5] - (P[11][9]*q0)/2 + dt*(P[2][6] + P[0][6]*SF[3] + P[3][6]*SF[5] + P[1][6]*SPP[6] - P[10][6]*SPP[3] + P[12][6]*SPP[5] - (P[11][6]*q0)/2); + nextP[2][10] = P[2][10] + P[0][10]*SF[3] + P[3][10]*SF[5] + P[1][10]*SPP[6] - P[10][10]*SPP[3] + P[12][10]*SPP[5] - (P[11][10]*q0)/2; + nextP[2][11] = P[2][11] + P[0][11]*SF[3] + P[3][11]*SF[5] + P[1][11]*SPP[6] - P[10][11]*SPP[3] + P[12][11]*SPP[5] - (P[11][11]*q0)/2; + nextP[2][12] = P[2][12] + P[0][12]*SF[3] + P[3][12]*SF[5] + P[1][12]*SPP[6] - P[10][12]*SPP[3] + P[12][12]*SPP[5] - (P[11][12]*q0)/2; + nextP[2][13] = P[2][13] + P[0][13]*SF[3] + P[3][13]*SF[5] + P[1][13]*SPP[6] - P[10][13]*SPP[3] + P[12][13]*SPP[5] - (P[11][13]*q0)/2; + nextP[2][14] = P[2][14] + P[0][14]*SF[3] + P[3][14]*SF[5] + P[1][14]*SPP[6] - P[10][14]*SPP[3] + P[12][14]*SPP[5] - (P[11][14]*q0)/2; + nextP[2][15] = P[2][15] + P[0][15]*SF[3] + P[3][15]*SF[5] + P[1][15]*SPP[6] - P[10][15]*SPP[3] + P[12][15]*SPP[5] - (P[11][15]*q0)/2; + nextP[2][16] = P[2][16] + P[0][16]*SF[3] + P[3][16]*SF[5] + P[1][16]*SPP[6] - P[10][16]*SPP[3] + P[12][16]*SPP[5] - (P[11][16]*q0)/2; + nextP[2][17] = P[2][17] + P[0][17]*SF[3] + P[3][17]*SF[5] + P[1][17]*SPP[6] - P[10][17]*SPP[3] + P[12][17]*SPP[5] - (P[11][17]*q0)/2; + nextP[2][18] = P[2][18] + P[0][18]*SF[3] + P[3][18]*SF[5] + P[1][18]*SPP[6] - P[10][18]*SPP[3] + P[12][18]*SPP[5] - (P[11][18]*q0)/2; + nextP[2][19] = P[2][19] + P[0][19]*SF[3] + P[3][19]*SF[5] + P[1][19]*SPP[6] - P[10][19]*SPP[3] + P[12][19]*SPP[5] - (P[11][19]*q0)/2; + nextP[2][20] = P[2][20] + P[0][20]*SF[3] + P[3][20]*SF[5] + P[1][20]*SPP[6] - P[10][20]*SPP[3] + P[12][20]*SPP[5] - (P[11][20]*q0)/2; + nextP[3][0] = P[3][0] + SQ[6] + P[0][0]*SF[4] + P[1][0]*SF[3] + P[2][0]*SF[6] + P[10][0]*SPP[4] - P[11][0]*SPP[5] - (P[12][0]*q0)/2 + SF[6]*(P[3][1] + P[0][1]*SF[4] + P[1][1]*SF[3] + P[2][1]*SF[6] + P[10][1]*SPP[4] - P[11][1]*SPP[5] - (P[12][1]*q0)/2) + SPP[7]*(P[3][2] + P[0][2]*SF[4] + P[1][2]*SF[3] + P[2][2]*SF[6] + P[10][2]*SPP[4] - P[11][2]*SPP[5] - (P[12][2]*q0)/2) + SPP[6]*(P[3][3] + P[0][3]*SF[4] + P[1][3]*SF[3] + P[2][3]*SF[6] + P[10][3]*SPP[4] - P[11][3]*SPP[5] - (P[12][3]*q0)/2) + SPP[5]*(P[3][10] + P[0][10]*SF[4] + P[1][10]*SF[3] + P[2][10]*SF[6] + P[10][10]*SPP[4] - P[11][10]*SPP[5] - (P[12][10]*q0)/2) + SPP[4]*(P[3][11] + P[0][11]*SF[4] + P[1][11]*SF[3] + P[2][11]*SF[6] + P[10][11]*SPP[4] - P[11][11]*SPP[5] - (P[12][11]*q0)/2) + SPP[3]*(P[3][12] + P[0][12]*SF[4] + P[1][12]*SF[3] + P[2][12]*SF[6] + P[10][12]*SPP[4] - P[11][12]*SPP[5] - (P[12][12]*q0)/2); + nextP[3][1] = P[3][1] + SQ[4] + P[0][1]*SF[4] + P[1][1]*SF[3] + P[2][1]*SF[6] + P[10][1]*SPP[4] - P[11][1]*SPP[5] - (P[12][1]*q0)/2 + SF[5]*(P[3][0] + P[0][0]*SF[4] + P[1][0]*SF[3] + P[2][0]*SF[6] + P[10][0]*SPP[4] - P[11][0]*SPP[5] - (P[12][0]*q0)/2) + SF[4]*(P[3][2] + P[0][2]*SF[4] + P[1][2]*SF[3] + P[2][2]*SF[6] + P[10][2]*SPP[4] - P[11][2]*SPP[5] - (P[12][2]*q0)/2) + SPP[7]*(P[3][3] + P[0][3]*SF[4] + P[1][3]*SF[3] + P[2][3]*SF[6] + P[10][3]*SPP[4] - P[11][3]*SPP[5] - (P[12][3]*q0)/2) + SPP[3]*(P[3][11] + P[0][11]*SF[4] + P[1][11]*SF[3] + P[2][11]*SF[6] + P[10][11]*SPP[4] - P[11][11]*SPP[5] - (P[12][11]*q0)/2) - SPP[4]*(P[3][12] + P[0][12]*SF[4] + P[1][12]*SF[3] + P[2][12]*SF[6] + P[10][12]*SPP[4] - P[11][12]*SPP[5] - (P[12][12]*q0)/2) - (q0*(P[3][10] + P[0][10]*SF[4] + P[1][10]*SF[3] + P[2][10]*SF[6] + P[10][10]*SPP[4] - P[11][10]*SPP[5] - (P[12][10]*q0)/2))/2; + nextP[3][2] = P[3][2] + SQ[3] + P[0][2]*SF[4] + P[1][2]*SF[3] + P[2][2]*SF[6] + P[10][2]*SPP[4] - P[11][2]*SPP[5] - (P[12][2]*q0)/2 + SF[3]*(P[3][0] + P[0][0]*SF[4] + P[1][0]*SF[3] + P[2][0]*SF[6] + P[10][0]*SPP[4] - P[11][0]*SPP[5] - (P[12][0]*q0)/2) + SF[5]*(P[3][3] + P[0][3]*SF[4] + P[1][3]*SF[3] + P[2][3]*SF[6] + P[10][3]*SPP[4] - P[11][3]*SPP[5] - (P[12][3]*q0)/2) + SPP[6]*(P[3][1] + P[0][1]*SF[4] + P[1][1]*SF[3] + P[2][1]*SF[6] + P[10][1]*SPP[4] - P[11][1]*SPP[5] - (P[12][1]*q0)/2) - SPP[3]*(P[3][10] + P[0][10]*SF[4] + P[1][10]*SF[3] + P[2][10]*SF[6] + P[10][10]*SPP[4] - P[11][10]*SPP[5] - (P[12][10]*q0)/2) + SPP[5]*(P[3][12] + P[0][12]*SF[4] + P[1][12]*SF[3] + P[2][12]*SF[6] + P[10][12]*SPP[4] - P[11][12]*SPP[5] - (P[12][12]*q0)/2) - (q0*(P[3][11] + P[0][11]*SF[4] + P[1][11]*SF[3] + P[2][11]*SF[6] + P[10][11]*SPP[4] - P[11][11]*SPP[5] - (P[12][11]*q0)/2))/2; + nextP[3][3] = P[3][3] + P[0][3]*SF[4] + P[1][3]*SF[3] + P[2][3]*SF[6] + P[10][3]*SPP[4] - P[11][3]*SPP[5] + (dayCov*SQ[10])/4 + dazCov*SQ[9] - (P[12][3]*q0)/2 + SF[4]*(P[3][0] + P[0][0]*SF[4] + P[1][0]*SF[3] + P[2][0]*SF[6] + P[10][0]*SPP[4] - P[11][0]*SPP[5] - (P[12][0]*q0)/2) + SF[3]*(P[3][1] + P[0][1]*SF[4] + P[1][1]*SF[3] + P[2][1]*SF[6] + P[10][1]*SPP[4] - P[11][1]*SPP[5] - (P[12][1]*q0)/2) + SF[6]*(P[3][2] + P[0][2]*SF[4] + P[1][2]*SF[3] + P[2][2]*SF[6] + P[10][2]*SPP[4] - P[11][2]*SPP[5] - (P[12][2]*q0)/2) + SPP[4]*(P[3][10] + P[0][10]*SF[4] + P[1][10]*SF[3] + P[2][10]*SF[6] + P[10][10]*SPP[4] - P[11][10]*SPP[5] - (P[12][10]*q0)/2) - SPP[5]*(P[3][11] + P[0][11]*SF[4] + P[1][11]*SF[3] + P[2][11]*SF[6] + P[10][11]*SPP[4] - P[11][11]*SPP[5] - (P[12][11]*q0)/2) + (daxCov*sq(q2))/4 - (q0*(P[3][12] + P[0][12]*SF[4] + P[1][12]*SF[3] + P[2][12]*SF[6] + P[10][12]*SPP[4] - P[11][12]*SPP[5] - (P[12][12]*q0)/2))/2; + nextP[3][4] = P[3][4] + P[0][4]*SF[4] + P[1][4]*SF[3] + P[2][4]*SF[6] + P[10][4]*SPP[4] - P[11][4]*SPP[5] - (P[12][4]*q0)/2 + SF[2]*(P[3][0] + P[0][0]*SF[4] + P[1][0]*SF[3] + P[2][0]*SF[6] + P[10][0]*SPP[4] - P[11][0]*SPP[5] - (P[12][0]*q0)/2) + SF[0]*(P[3][1] + P[0][1]*SF[4] + P[1][1]*SF[3] + P[2][1]*SF[6] + P[10][1]*SPP[4] - P[11][1]*SPP[5] - (P[12][1]*q0)/2) + SPP[0]*(P[3][2] + P[0][2]*SF[4] + P[1][2]*SF[3] + P[2][2]*SF[6] + P[10][2]*SPP[4] - P[11][2]*SPP[5] - (P[12][2]*q0)/2) - SPP[2]*(P[3][3] + P[0][3]*SF[4] + P[1][3]*SF[3] + P[2][3]*SF[6] + P[10][3]*SPP[4] - P[11][3]*SPP[5] - (P[12][3]*q0)/2); + nextP[3][5] = P[3][5] + P[0][5]*SF[4] + P[1][5]*SF[3] + P[2][5]*SF[6] + P[10][5]*SPP[4] - P[11][5]*SPP[5] - (P[12][5]*q0)/2 + SF[1]*(P[3][0] + P[0][0]*SF[4] + P[1][0]*SF[3] + P[2][0]*SF[6] + P[10][0]*SPP[4] - P[11][0]*SPP[5] - (P[12][0]*q0)/2) + SF[0]*(P[3][2] + P[0][2]*SF[4] + P[1][2]*SF[3] + P[2][2]*SF[6] + P[10][2]*SPP[4] - P[11][2]*SPP[5] - (P[12][2]*q0)/2) + SF[2]*(P[3][3] + P[0][3]*SF[4] + P[1][3]*SF[3] + P[2][3]*SF[6] + P[10][3]*SPP[4] - P[11][3]*SPP[5] - (P[12][3]*q0)/2) - SPP[0]*(P[3][1] + P[0][1]*SF[4] + P[1][1]*SF[3] + P[2][1]*SF[6] + P[10][1]*SPP[4] - P[11][1]*SPP[5] - (P[12][1]*q0)/2); + nextP[3][6] = P[3][6] + P[0][6]*SF[4] + P[1][6]*SF[3] + P[2][6]*SF[6] + P[10][6]*SPP[4] - P[11][6]*SPP[5] - (P[12][6]*q0)/2 + SF[1]*(P[3][1] + P[0][1]*SF[4] + P[1][1]*SF[3] + P[2][1]*SF[6] + P[10][1]*SPP[4] - P[11][1]*SPP[5] - (P[12][1]*q0)/2) + SF[0]*(P[3][3] + P[0][3]*SF[4] + P[1][3]*SF[3] + P[2][3]*SF[6] + P[10][3]*SPP[4] - P[11][3]*SPP[5] - (P[12][3]*q0)/2) + SPP[0]*(P[3][0] + P[0][0]*SF[4] + P[1][0]*SF[3] + P[2][0]*SF[6] + P[10][0]*SPP[4] - P[11][0]*SPP[5] - (P[12][0]*q0)/2) - SPP[1]*(P[3][2] + P[0][2]*SF[4] + P[1][2]*SF[3] + P[2][2]*SF[6] + P[10][2]*SPP[4] - P[11][2]*SPP[5] - (P[12][2]*q0)/2); + nextP[3][7] = P[3][7] + P[0][7]*SF[4] + P[1][7]*SF[3] + P[2][7]*SF[6] + P[10][7]*SPP[4] - P[11][7]*SPP[5] - (P[12][7]*q0)/2 + dt*(P[3][4] + P[0][4]*SF[4] + P[1][4]*SF[3] + P[2][4]*SF[6] + P[10][4]*SPP[4] - P[11][4]*SPP[5] - (P[12][4]*q0)/2); + nextP[3][8] = P[3][8] + P[0][8]*SF[4] + P[1][8]*SF[3] + P[2][8]*SF[6] + P[10][8]*SPP[4] - P[11][8]*SPP[5] - (P[12][8]*q0)/2 + dt*(P[3][5] + P[0][5]*SF[4] + P[1][5]*SF[3] + P[2][5]*SF[6] + P[10][5]*SPP[4] - P[11][5]*SPP[5] - (P[12][5]*q0)/2); + nextP[3][9] = P[3][9] + P[0][9]*SF[4] + P[1][9]*SF[3] + P[2][9]*SF[6] + P[10][9]*SPP[4] - P[11][9]*SPP[5] - (P[12][9]*q0)/2 + dt*(P[3][6] + P[0][6]*SF[4] + P[1][6]*SF[3] + P[2][6]*SF[6] + P[10][6]*SPP[4] - P[11][6]*SPP[5] - (P[12][6]*q0)/2); + nextP[3][10] = P[3][10] + P[0][10]*SF[4] + P[1][10]*SF[3] + P[2][10]*SF[6] + P[10][10]*SPP[4] - P[11][10]*SPP[5] - (P[12][10]*q0)/2; + nextP[3][11] = P[3][11] + P[0][11]*SF[4] + P[1][11]*SF[3] + P[2][11]*SF[6] + P[10][11]*SPP[4] - P[11][11]*SPP[5] - (P[12][11]*q0)/2; + nextP[3][12] = P[3][12] + P[0][12]*SF[4] + P[1][12]*SF[3] + P[2][12]*SF[6] + P[10][12]*SPP[4] - P[11][12]*SPP[5] - (P[12][12]*q0)/2; + nextP[3][13] = P[3][13] + P[0][13]*SF[4] + P[1][13]*SF[3] + P[2][13]*SF[6] + P[10][13]*SPP[4] - P[11][13]*SPP[5] - (P[12][13]*q0)/2; + nextP[3][14] = P[3][14] + P[0][14]*SF[4] + P[1][14]*SF[3] + P[2][14]*SF[6] + P[10][14]*SPP[4] - P[11][14]*SPP[5] - (P[12][14]*q0)/2; + nextP[3][15] = P[3][15] + P[0][15]*SF[4] + P[1][15]*SF[3] + P[2][15]*SF[6] + P[10][15]*SPP[4] - P[11][15]*SPP[5] - (P[12][15]*q0)/2; + nextP[3][16] = P[3][16] + P[0][16]*SF[4] + P[1][16]*SF[3] + P[2][16]*SF[6] + P[10][16]*SPP[4] - P[11][16]*SPP[5] - (P[12][16]*q0)/2; + nextP[3][17] = P[3][17] + P[0][17]*SF[4] + P[1][17]*SF[3] + P[2][17]*SF[6] + P[10][17]*SPP[4] - P[11][17]*SPP[5] - (P[12][17]*q0)/2; + nextP[3][18] = P[3][18] + P[0][18]*SF[4] + P[1][18]*SF[3] + P[2][18]*SF[6] + P[10][18]*SPP[4] - P[11][18]*SPP[5] - (P[12][18]*q0)/2; + nextP[3][19] = P[3][19] + P[0][19]*SF[4] + P[1][19]*SF[3] + P[2][19]*SF[6] + P[10][19]*SPP[4] - P[11][19]*SPP[5] - (P[12][19]*q0)/2; + nextP[3][20] = P[3][20] + P[0][20]*SF[4] + P[1][20]*SF[3] + P[2][20]*SF[6] + P[10][20]*SPP[4] - P[11][20]*SPP[5] - (P[12][20]*q0)/2; + nextP[4][0] = P[4][0] + P[0][0]*SF[2] + P[1][0]*SF[0] + P[2][0]*SPP[0] - P[3][0]*SPP[2] + SF[6]*(P[4][1] + P[0][1]*SF[2] + P[1][1]*SF[0] + P[2][1]*SPP[0] - P[3][1]*SPP[2]) + SPP[7]*(P[4][2] + P[0][2]*SF[2] + P[1][2]*SF[0] + P[2][2]*SPP[0] - P[3][2]*SPP[2]) + SPP[6]*(P[4][3] + P[0][3]*SF[2] + P[1][3]*SF[0] + P[2][3]*SPP[0] - P[3][3]*SPP[2]) + SPP[5]*(P[4][10] + P[0][10]*SF[2] + P[1][10]*SF[0] + P[2][10]*SPP[0] - P[3][10]*SPP[2]) + SPP[4]*(P[4][11] + P[0][11]*SF[2] + P[1][11]*SF[0] + P[2][11]*SPP[0] - P[3][11]*SPP[2]) + SPP[3]*(P[4][12] + P[0][12]*SF[2] + P[1][12]*SF[0] + P[2][12]*SPP[0] - P[3][12]*SPP[2]); + nextP[4][1] = P[4][1] + P[0][1]*SF[2] + P[1][1]*SF[0] + P[2][1]*SPP[0] - P[3][1]*SPP[2] + SF[5]*(P[4][0] + P[0][0]*SF[2] + P[1][0]*SF[0] + P[2][0]*SPP[0] - P[3][0]*SPP[2]) + SF[4]*(P[4][2] + P[0][2]*SF[2] + P[1][2]*SF[0] + P[2][2]*SPP[0] - P[3][2]*SPP[2]) + SPP[7]*(P[4][3] + P[0][3]*SF[2] + P[1][3]*SF[0] + P[2][3]*SPP[0] - P[3][3]*SPP[2]) + SPP[3]*(P[4][11] + P[0][11]*SF[2] + P[1][11]*SF[0] + P[2][11]*SPP[0] - P[3][11]*SPP[2]) - SPP[4]*(P[4][12] + P[0][12]*SF[2] + P[1][12]*SF[0] + P[2][12]*SPP[0] - P[3][12]*SPP[2]) - (q0*(P[4][10] + P[0][10]*SF[2] + P[1][10]*SF[0] + P[2][10]*SPP[0] - P[3][10]*SPP[2]))/2; + nextP[4][2] = P[4][2] + P[0][2]*SF[2] + P[1][2]*SF[0] + P[2][2]*SPP[0] - P[3][2]*SPP[2] + SF[3]*(P[4][0] + P[0][0]*SF[2] + P[1][0]*SF[0] + P[2][0]*SPP[0] - P[3][0]*SPP[2]) + SF[5]*(P[4][3] + P[0][3]*SF[2] + P[1][3]*SF[0] + P[2][3]*SPP[0] - P[3][3]*SPP[2]) + SPP[6]*(P[4][1] + P[0][1]*SF[2] + P[1][1]*SF[0] + P[2][1]*SPP[0] - P[3][1]*SPP[2]) - SPP[3]*(P[4][10] + P[0][10]*SF[2] + P[1][10]*SF[0] + P[2][10]*SPP[0] - P[3][10]*SPP[2]) + SPP[5]*(P[4][12] + P[0][12]*SF[2] + P[1][12]*SF[0] + P[2][12]*SPP[0] - P[3][12]*SPP[2]) - (q0*(P[4][11] + P[0][11]*SF[2] + P[1][11]*SF[0] + P[2][11]*SPP[0] - P[3][11]*SPP[2]))/2; + nextP[4][3] = P[4][3] + P[0][3]*SF[2] + P[1][3]*SF[0] + P[2][3]*SPP[0] - P[3][3]*SPP[2] + SF[4]*(P[4][0] + P[0][0]*SF[2] + P[1][0]*SF[0] + P[2][0]*SPP[0] - P[3][0]*SPP[2]) + SF[3]*(P[4][1] + P[0][1]*SF[2] + P[1][1]*SF[0] + P[2][1]*SPP[0] - P[3][1]*SPP[2]) + SF[6]*(P[4][2] + P[0][2]*SF[2] + P[1][2]*SF[0] + P[2][2]*SPP[0] - P[3][2]*SPP[2]) + SPP[4]*(P[4][10] + P[0][10]*SF[2] + P[1][10]*SF[0] + P[2][10]*SPP[0] - P[3][10]*SPP[2]) - SPP[5]*(P[4][11] + P[0][11]*SF[2] + P[1][11]*SF[0] + P[2][11]*SPP[0] - P[3][11]*SPP[2]) - (q0*(P[4][12] + P[0][12]*SF[2] + P[1][12]*SF[0] + P[2][12]*SPP[0] - P[3][12]*SPP[2]))/2; + nextP[4][4] = P[4][4] + P[0][4]*SF[2] + P[1][4]*SF[0] + P[2][4]*SPP[0] - P[3][4]*SPP[2] + dvyCov*sq(SG[7] - 2*q0*q3) + dvzCov*sq(SG[6] + 2*q0*q2) + SF[2]*(P[4][0] + P[0][0]*SF[2] + P[1][0]*SF[0] + P[2][0]*SPP[0] - P[3][0]*SPP[2]) + SF[0]*(P[4][1] + P[0][1]*SF[2] + P[1][1]*SF[0] + P[2][1]*SPP[0] - P[3][1]*SPP[2]) + SPP[0]*(P[4][2] + P[0][2]*SF[2] + P[1][2]*SF[0] + P[2][2]*SPP[0] - P[3][2]*SPP[2]) - SPP[2]*(P[4][3] + P[0][3]*SF[2] + P[1][3]*SF[0] + P[2][3]*SPP[0] - P[3][3]*SPP[2]) + dvxCov*sq(SG[1] + SG[2] - SG[3] - SG[4]); + nextP[4][5] = P[4][5] + SQ[2] + P[0][5]*SF[2] + P[1][5]*SF[0] + P[2][5]*SPP[0] - P[3][5]*SPP[2] + SF[1]*(P[4][0] + P[0][0]*SF[2] + P[1][0]*SF[0] + P[2][0]*SPP[0] - P[3][0]*SPP[2]) + SF[0]*(P[4][2] + P[0][2]*SF[2] + P[1][2]*SF[0] + P[2][2]*SPP[0] - P[3][2]*SPP[2]) + SF[2]*(P[4][3] + P[0][3]*SF[2] + P[1][3]*SF[0] + P[2][3]*SPP[0] - P[3][3]*SPP[2]) - SPP[0]*(P[4][1] + P[0][1]*SF[2] + P[1][1]*SF[0] + P[2][1]*SPP[0] - P[3][1]*SPP[2]); + nextP[4][6] = P[4][6] + SQ[1] + P[0][6]*SF[2] + P[1][6]*SF[0] + P[2][6]*SPP[0] - P[3][6]*SPP[2] + SF[1]*(P[4][1] + P[0][1]*SF[2] + P[1][1]*SF[0] + P[2][1]*SPP[0] - P[3][1]*SPP[2]) + SF[0]*(P[4][3] + P[0][3]*SF[2] + P[1][3]*SF[0] + P[2][3]*SPP[0] - P[3][3]*SPP[2]) + SPP[0]*(P[4][0] + P[0][0]*SF[2] + P[1][0]*SF[0] + P[2][0]*SPP[0] - P[3][0]*SPP[2]) - SPP[1]*(P[4][2] + P[0][2]*SF[2] + P[1][2]*SF[0] + P[2][2]*SPP[0] - P[3][2]*SPP[2]); + nextP[4][7] = P[4][7] + P[0][7]*SF[2] + P[1][7]*SF[0] + P[2][7]*SPP[0] - P[3][7]*SPP[2] + dt*(P[4][4] + P[0][4]*SF[2] + P[1][4]*SF[0] + P[2][4]*SPP[0] - P[3][4]*SPP[2]); + nextP[4][8] = P[4][8] + P[0][8]*SF[2] + P[1][8]*SF[0] + P[2][8]*SPP[0] - P[3][8]*SPP[2] + dt*(P[4][5] + P[0][5]*SF[2] + P[1][5]*SF[0] + P[2][5]*SPP[0] - P[3][5]*SPP[2]); + nextP[4][9] = P[4][9] + P[0][9]*SF[2] + P[1][9]*SF[0] + P[2][9]*SPP[0] - P[3][9]*SPP[2] + dt*(P[4][6] + P[0][6]*SF[2] + P[1][6]*SF[0] + P[2][6]*SPP[0] - P[3][6]*SPP[2]); + nextP[4][10] = P[4][10] + P[0][10]*SF[2] + P[1][10]*SF[0] + P[2][10]*SPP[0] - P[3][10]*SPP[2]; + nextP[4][11] = P[4][11] + P[0][11]*SF[2] + P[1][11]*SF[0] + P[2][11]*SPP[0] - P[3][11]*SPP[2]; + nextP[4][12] = P[4][12] + P[0][12]*SF[2] + P[1][12]*SF[0] + P[2][12]*SPP[0] - P[3][12]*SPP[2]; + nextP[4][13] = P[4][13] + P[0][13]*SF[2] + P[1][13]*SF[0] + P[2][13]*SPP[0] - P[3][13]*SPP[2]; + nextP[4][14] = P[4][14] + P[0][14]*SF[2] + P[1][14]*SF[0] + P[2][14]*SPP[0] - P[3][14]*SPP[2]; + nextP[4][15] = P[4][15] + P[0][15]*SF[2] + P[1][15]*SF[0] + P[2][15]*SPP[0] - P[3][15]*SPP[2]; + nextP[4][16] = P[4][16] + P[0][16]*SF[2] + P[1][16]*SF[0] + P[2][16]*SPP[0] - P[3][16]*SPP[2]; + nextP[4][17] = P[4][17] + P[0][17]*SF[2] + P[1][17]*SF[0] + P[2][17]*SPP[0] - P[3][17]*SPP[2]; + nextP[4][18] = P[4][18] + P[0][18]*SF[2] + P[1][18]*SF[0] + P[2][18]*SPP[0] - P[3][18]*SPP[2]; + nextP[4][19] = P[4][19] + P[0][19]*SF[2] + P[1][19]*SF[0] + P[2][19]*SPP[0] - P[3][19]*SPP[2]; + nextP[4][20] = P[4][20] + P[0][20]*SF[2] + P[1][20]*SF[0] + P[2][20]*SPP[0] - P[3][20]*SPP[2]; + nextP[5][0] = P[5][0] + P[0][0]*SF[1] + P[2][0]*SF[0] + P[3][0]*SF[2] - P[1][0]*SPP[0] + SF[6]*(P[5][1] + P[0][1]*SF[1] + P[2][1]*SF[0] + P[3][1]*SF[2] - P[1][1]*SPP[0]) + SPP[7]*(P[5][2] + P[0][2]*SF[1] + P[2][2]*SF[0] + P[3][2]*SF[2] - P[1][2]*SPP[0]) + SPP[6]*(P[5][3] + P[0][3]*SF[1] + P[2][3]*SF[0] + P[3][3]*SF[2] - P[1][3]*SPP[0]) + SPP[5]*(P[5][10] + P[0][10]*SF[1] + P[2][10]*SF[0] + P[3][10]*SF[2] - P[1][10]*SPP[0]) + SPP[4]*(P[5][11] + P[0][11]*SF[1] + P[2][11]*SF[0] + P[3][11]*SF[2] - P[1][11]*SPP[0]) + SPP[3]*(P[5][12] + P[0][12]*SF[1] + P[2][12]*SF[0] + P[3][12]*SF[2] - P[1][12]*SPP[0]); + nextP[5][1] = P[5][1] + P[0][1]*SF[1] + P[2][1]*SF[0] + P[3][1]*SF[2] - P[1][1]*SPP[0] + SF[5]*(P[5][0] + P[0][0]*SF[1] + P[2][0]*SF[0] + P[3][0]*SF[2] - P[1][0]*SPP[0]) + SF[4]*(P[5][2] + P[0][2]*SF[1] + P[2][2]*SF[0] + P[3][2]*SF[2] - P[1][2]*SPP[0]) + SPP[7]*(P[5][3] + P[0][3]*SF[1] + P[2][3]*SF[0] + P[3][3]*SF[2] - P[1][3]*SPP[0]) + SPP[3]*(P[5][11] + P[0][11]*SF[1] + P[2][11]*SF[0] + P[3][11]*SF[2] - P[1][11]*SPP[0]) - SPP[4]*(P[5][12] + P[0][12]*SF[1] + P[2][12]*SF[0] + P[3][12]*SF[2] - P[1][12]*SPP[0]) - (q0*(P[5][10] + P[0][10]*SF[1] + P[2][10]*SF[0] + P[3][10]*SF[2] - P[1][10]*SPP[0]))/2; + nextP[5][2] = P[5][2] + P[0][2]*SF[1] + P[2][2]*SF[0] + P[3][2]*SF[2] - P[1][2]*SPP[0] + SF[3]*(P[5][0] + P[0][0]*SF[1] + P[2][0]*SF[0] + P[3][0]*SF[2] - P[1][0]*SPP[0]) + SF[5]*(P[5][3] + P[0][3]*SF[1] + P[2][3]*SF[0] + P[3][3]*SF[2] - P[1][3]*SPP[0]) + SPP[6]*(P[5][1] + P[0][1]*SF[1] + P[2][1]*SF[0] + P[3][1]*SF[2] - P[1][1]*SPP[0]) - SPP[3]*(P[5][10] + P[0][10]*SF[1] + P[2][10]*SF[0] + P[3][10]*SF[2] - P[1][10]*SPP[0]) + SPP[5]*(P[5][12] + P[0][12]*SF[1] + P[2][12]*SF[0] + P[3][12]*SF[2] - P[1][12]*SPP[0]) - (q0*(P[5][11] + P[0][11]*SF[1] + P[2][11]*SF[0] + P[3][11]*SF[2] - P[1][11]*SPP[0]))/2; + nextP[5][3] = P[5][3] + P[0][3]*SF[1] + P[2][3]*SF[0] + P[3][3]*SF[2] - P[1][3]*SPP[0] + SF[4]*(P[5][0] + P[0][0]*SF[1] + P[2][0]*SF[0] + P[3][0]*SF[2] - P[1][0]*SPP[0]) + SF[3]*(P[5][1] + P[0][1]*SF[1] + P[2][1]*SF[0] + P[3][1]*SF[2] - P[1][1]*SPP[0]) + SF[6]*(P[5][2] + P[0][2]*SF[1] + P[2][2]*SF[0] + P[3][2]*SF[2] - P[1][2]*SPP[0]) + SPP[4]*(P[5][10] + P[0][10]*SF[1] + P[2][10]*SF[0] + P[3][10]*SF[2] - P[1][10]*SPP[0]) - SPP[5]*(P[5][11] + P[0][11]*SF[1] + P[2][11]*SF[0] + P[3][11]*SF[2] - P[1][11]*SPP[0]) - (q0*(P[5][12] + P[0][12]*SF[1] + P[2][12]*SF[0] + P[3][12]*SF[2] - P[1][12]*SPP[0]))/2; + nextP[5][4] = P[5][4] + SQ[2] + P[0][4]*SF[1] + P[2][4]*SF[0] + P[3][4]*SF[2] - P[1][4]*SPP[0] + SF[2]*(P[5][0] + P[0][0]*SF[1] + P[2][0]*SF[0] + P[3][0]*SF[2] - P[1][0]*SPP[0]) + SF[0]*(P[5][1] + P[0][1]*SF[1] + P[2][1]*SF[0] + P[3][1]*SF[2] - P[1][1]*SPP[0]) + SPP[0]*(P[5][2] + P[0][2]*SF[1] + P[2][2]*SF[0] + P[3][2]*SF[2] - P[1][2]*SPP[0]) - SPP[2]*(P[5][3] + P[0][3]*SF[1] + P[2][3]*SF[0] + P[3][3]*SF[2] - P[1][3]*SPP[0]); + nextP[5][5] = P[5][5] + P[0][5]*SF[1] + P[2][5]*SF[0] + P[3][5]*SF[2] - P[1][5]*SPP[0] + dvxCov*sq(SG[7] + 2*q0*q3) + dvzCov*sq(SG[5] - 2*q0*q1) + SF[1]*(P[5][0] + P[0][0]*SF[1] + P[2][0]*SF[0] + P[3][0]*SF[2] - P[1][0]*SPP[0]) + SF[0]*(P[5][2] + P[0][2]*SF[1] + P[2][2]*SF[0] + P[3][2]*SF[2] - P[1][2]*SPP[0]) + SF[2]*(P[5][3] + P[0][3]*SF[1] + P[2][3]*SF[0] + P[3][3]*SF[2] - P[1][3]*SPP[0]) - SPP[0]*(P[5][1] + P[0][1]*SF[1] + P[2][1]*SF[0] + P[3][1]*SF[2] - P[1][1]*SPP[0]) + dvyCov*sq(SG[1] - SG[2] + SG[3] - SG[4]); + nextP[5][6] = P[5][6] + SQ[0] + P[0][6]*SF[1] + P[2][6]*SF[0] + P[3][6]*SF[2] - P[1][6]*SPP[0] + SF[1]*(P[5][1] + P[0][1]*SF[1] + P[2][1]*SF[0] + P[3][1]*SF[2] - P[1][1]*SPP[0]) + SF[0]*(P[5][3] + P[0][3]*SF[1] + P[2][3]*SF[0] + P[3][3]*SF[2] - P[1][3]*SPP[0]) + SPP[0]*(P[5][0] + P[0][0]*SF[1] + P[2][0]*SF[0] + P[3][0]*SF[2] - P[1][0]*SPP[0]) - SPP[1]*(P[5][2] + P[0][2]*SF[1] + P[2][2]*SF[0] + P[3][2]*SF[2] - P[1][2]*SPP[0]); + nextP[5][7] = P[5][7] + P[0][7]*SF[1] + P[2][7]*SF[0] + P[3][7]*SF[2] - P[1][7]*SPP[0] + dt*(P[5][4] + P[0][4]*SF[1] + P[2][4]*SF[0] + P[3][4]*SF[2] - P[1][4]*SPP[0]); + nextP[5][8] = P[5][8] + P[0][8]*SF[1] + P[2][8]*SF[0] + P[3][8]*SF[2] - P[1][8]*SPP[0] + dt*(P[5][5] + P[0][5]*SF[1] + P[2][5]*SF[0] + P[3][5]*SF[2] - P[1][5]*SPP[0]); + nextP[5][9] = P[5][9] + P[0][9]*SF[1] + P[2][9]*SF[0] + P[3][9]*SF[2] - P[1][9]*SPP[0] + dt*(P[5][6] + P[0][6]*SF[1] + P[2][6]*SF[0] + P[3][6]*SF[2] - P[1][6]*SPP[0]); + nextP[5][10] = P[5][10] + P[0][10]*SF[1] + P[2][10]*SF[0] + P[3][10]*SF[2] - P[1][10]*SPP[0]; + nextP[5][11] = P[5][11] + P[0][11]*SF[1] + P[2][11]*SF[0] + P[3][11]*SF[2] - P[1][11]*SPP[0]; + nextP[5][12] = P[5][12] + P[0][12]*SF[1] + P[2][12]*SF[0] + P[3][12]*SF[2] - P[1][12]*SPP[0]; + nextP[5][13] = P[5][13] + P[0][13]*SF[1] + P[2][13]*SF[0] + P[3][13]*SF[2] - P[1][13]*SPP[0]; + nextP[5][14] = P[5][14] + P[0][14]*SF[1] + P[2][14]*SF[0] + P[3][14]*SF[2] - P[1][14]*SPP[0]; + nextP[5][15] = P[5][15] + P[0][15]*SF[1] + P[2][15]*SF[0] + P[3][15]*SF[2] - P[1][15]*SPP[0]; + nextP[5][16] = P[5][16] + P[0][16]*SF[1] + P[2][16]*SF[0] + P[3][16]*SF[2] - P[1][16]*SPP[0]; + nextP[5][17] = P[5][17] + P[0][17]*SF[1] + P[2][17]*SF[0] + P[3][17]*SF[2] - P[1][17]*SPP[0]; + nextP[5][18] = P[5][18] + P[0][18]*SF[1] + P[2][18]*SF[0] + P[3][18]*SF[2] - P[1][18]*SPP[0]; + nextP[5][19] = P[5][19] + P[0][19]*SF[1] + P[2][19]*SF[0] + P[3][19]*SF[2] - P[1][19]*SPP[0]; + nextP[5][20] = P[5][20] + P[0][20]*SF[1] + P[2][20]*SF[0] + P[3][20]*SF[2] - P[1][20]*SPP[0]; + nextP[6][0] = P[6][0] + P[1][0]*SF[1] + P[3][0]*SF[0] + P[0][0]*SPP[0] - P[2][0]*SPP[1] + SF[6]*(P[6][1] + P[1][1]*SF[1] + P[3][1]*SF[0] + P[0][1]*SPP[0] - P[2][1]*SPP[1]) + SPP[7]*(P[6][2] + P[1][2]*SF[1] + P[3][2]*SF[0] + P[0][2]*SPP[0] - P[2][2]*SPP[1]) + SPP[6]*(P[6][3] + P[1][3]*SF[1] + P[3][3]*SF[0] + P[0][3]*SPP[0] - P[2][3]*SPP[1]) + SPP[5]*(P[6][10] + P[1][10]*SF[1] + P[3][10]*SF[0] + P[0][10]*SPP[0] - P[2][10]*SPP[1]) + SPP[4]*(P[6][11] + P[1][11]*SF[1] + P[3][11]*SF[0] + P[0][11]*SPP[0] - P[2][11]*SPP[1]) + SPP[3]*(P[6][12] + P[1][12]*SF[1] + P[3][12]*SF[0] + P[0][12]*SPP[0] - P[2][12]*SPP[1]); + nextP[6][1] = P[6][1] + P[1][1]*SF[1] + P[3][1]*SF[0] + P[0][1]*SPP[0] - P[2][1]*SPP[1] + SF[5]*(P[6][0] + P[1][0]*SF[1] + P[3][0]*SF[0] + P[0][0]*SPP[0] - P[2][0]*SPP[1]) + SF[4]*(P[6][2] + P[1][2]*SF[1] + P[3][2]*SF[0] + P[0][2]*SPP[0] - P[2][2]*SPP[1]) + SPP[7]*(P[6][3] + P[1][3]*SF[1] + P[3][3]*SF[0] + P[0][3]*SPP[0] - P[2][3]*SPP[1]) + SPP[3]*(P[6][11] + P[1][11]*SF[1] + P[3][11]*SF[0] + P[0][11]*SPP[0] - P[2][11]*SPP[1]) - SPP[4]*(P[6][12] + P[1][12]*SF[1] + P[3][12]*SF[0] + P[0][12]*SPP[0] - P[2][12]*SPP[1]) - (q0*(P[6][10] + P[1][10]*SF[1] + P[3][10]*SF[0] + P[0][10]*SPP[0] - P[2][10]*SPP[1]))/2; + nextP[6][2] = P[6][2] + P[1][2]*SF[1] + P[3][2]*SF[0] + P[0][2]*SPP[0] - P[2][2]*SPP[1] + SF[3]*(P[6][0] + P[1][0]*SF[1] + P[3][0]*SF[0] + P[0][0]*SPP[0] - P[2][0]*SPP[1]) + SF[5]*(P[6][3] + P[1][3]*SF[1] + P[3][3]*SF[0] + P[0][3]*SPP[0] - P[2][3]*SPP[1]) + SPP[6]*(P[6][1] + P[1][1]*SF[1] + P[3][1]*SF[0] + P[0][1]*SPP[0] - P[2][1]*SPP[1]) - SPP[3]*(P[6][10] + P[1][10]*SF[1] + P[3][10]*SF[0] + P[0][10]*SPP[0] - P[2][10]*SPP[1]) + SPP[5]*(P[6][12] + P[1][12]*SF[1] + P[3][12]*SF[0] + P[0][12]*SPP[0] - P[2][12]*SPP[1]) - (q0*(P[6][11] + P[1][11]*SF[1] + P[3][11]*SF[0] + P[0][11]*SPP[0] - P[2][11]*SPP[1]))/2; + nextP[6][3] = P[6][3] + P[1][3]*SF[1] + P[3][3]*SF[0] + P[0][3]*SPP[0] - P[2][3]*SPP[1] + SF[4]*(P[6][0] + P[1][0]*SF[1] + P[3][0]*SF[0] + P[0][0]*SPP[0] - P[2][0]*SPP[1]) + SF[3]*(P[6][1] + P[1][1]*SF[1] + P[3][1]*SF[0] + P[0][1]*SPP[0] - P[2][1]*SPP[1]) + SF[6]*(P[6][2] + P[1][2]*SF[1] + P[3][2]*SF[0] + P[0][2]*SPP[0] - P[2][2]*SPP[1]) + SPP[4]*(P[6][10] + P[1][10]*SF[1] + P[3][10]*SF[0] + P[0][10]*SPP[0] - P[2][10]*SPP[1]) - SPP[5]*(P[6][11] + P[1][11]*SF[1] + P[3][11]*SF[0] + P[0][11]*SPP[0] - P[2][11]*SPP[1]) - (q0*(P[6][12] + P[1][12]*SF[1] + P[3][12]*SF[0] + P[0][12]*SPP[0] - P[2][12]*SPP[1]))/2; + nextP[6][4] = P[6][4] + SQ[1] + P[1][4]*SF[1] + P[3][4]*SF[0] + P[0][4]*SPP[0] - P[2][4]*SPP[1] + SF[2]*(P[6][0] + P[1][0]*SF[1] + P[3][0]*SF[0] + P[0][0]*SPP[0] - P[2][0]*SPP[1]) + SF[0]*(P[6][1] + P[1][1]*SF[1] + P[3][1]*SF[0] + P[0][1]*SPP[0] - P[2][1]*SPP[1]) + SPP[0]*(P[6][2] + P[1][2]*SF[1] + P[3][2]*SF[0] + P[0][2]*SPP[0] - P[2][2]*SPP[1]) - SPP[2]*(P[6][3] + P[1][3]*SF[1] + P[3][3]*SF[0] + P[0][3]*SPP[0] - P[2][3]*SPP[1]); + nextP[6][5] = P[6][5] + SQ[0] + P[1][5]*SF[1] + P[3][5]*SF[0] + P[0][5]*SPP[0] - P[2][5]*SPP[1] + SF[1]*(P[6][0] + P[1][0]*SF[1] + P[3][0]*SF[0] + P[0][0]*SPP[0] - P[2][0]*SPP[1]) + SF[0]*(P[6][2] + P[1][2]*SF[1] + P[3][2]*SF[0] + P[0][2]*SPP[0] - P[2][2]*SPP[1]) + SF[2]*(P[6][3] + P[1][3]*SF[1] + P[3][3]*SF[0] + P[0][3]*SPP[0] - P[2][3]*SPP[1]) - SPP[0]*(P[6][1] + P[1][1]*SF[1] + P[3][1]*SF[0] + P[0][1]*SPP[0] - P[2][1]*SPP[1]); + nextP[6][6] = P[6][6] + P[1][6]*SF[1] + P[3][6]*SF[0] + P[0][6]*SPP[0] - P[2][6]*SPP[1] + dvxCov*sq(SG[6] - 2*q0*q2) + dvyCov*sq(SG[5] + 2*q0*q1) + SF[1]*(P[6][1] + P[1][1]*SF[1] + P[3][1]*SF[0] + P[0][1]*SPP[0] - P[2][1]*SPP[1]) + SF[0]*(P[6][3] + P[1][3]*SF[1] + P[3][3]*SF[0] + P[0][3]*SPP[0] - P[2][3]*SPP[1]) + SPP[0]*(P[6][0] + P[1][0]*SF[1] + P[3][0]*SF[0] + P[0][0]*SPP[0] - P[2][0]*SPP[1]) - SPP[1]*(P[6][2] + P[1][2]*SF[1] + P[3][2]*SF[0] + P[0][2]*SPP[0] - P[2][2]*SPP[1]) + dvzCov*sq(SG[1] - SG[2] - SG[3] + SG[4]); + nextP[6][7] = P[6][7] + P[1][7]*SF[1] + P[3][7]*SF[0] + P[0][7]*SPP[0] - P[2][7]*SPP[1] + dt*(P[6][4] + P[1][4]*SF[1] + P[3][4]*SF[0] + P[0][4]*SPP[0] - P[2][4]*SPP[1]); + nextP[6][8] = P[6][8] + P[1][8]*SF[1] + P[3][8]*SF[0] + P[0][8]*SPP[0] - P[2][8]*SPP[1] + dt*(P[6][5] + P[1][5]*SF[1] + P[3][5]*SF[0] + P[0][5]*SPP[0] - P[2][5]*SPP[1]); + nextP[6][9] = P[6][9] + P[1][9]*SF[1] + P[3][9]*SF[0] + P[0][9]*SPP[0] - P[2][9]*SPP[1] + dt*(P[6][6] + P[1][6]*SF[1] + P[3][6]*SF[0] + P[0][6]*SPP[0] - P[2][6]*SPP[1]); + nextP[6][10] = P[6][10] + P[1][10]*SF[1] + P[3][10]*SF[0] + P[0][10]*SPP[0] - P[2][10]*SPP[1]; + nextP[6][11] = P[6][11] + P[1][11]*SF[1] + P[3][11]*SF[0] + P[0][11]*SPP[0] - P[2][11]*SPP[1]; + nextP[6][12] = P[6][12] + P[1][12]*SF[1] + P[3][12]*SF[0] + P[0][12]*SPP[0] - P[2][12]*SPP[1]; + nextP[6][13] = P[6][13] + P[1][13]*SF[1] + P[3][13]*SF[0] + P[0][13]*SPP[0] - P[2][13]*SPP[1]; + nextP[6][14] = P[6][14] + P[1][14]*SF[1] + P[3][14]*SF[0] + P[0][14]*SPP[0] - P[2][14]*SPP[1]; + nextP[6][15] = P[6][15] + P[1][15]*SF[1] + P[3][15]*SF[0] + P[0][15]*SPP[0] - P[2][15]*SPP[1]; + nextP[6][16] = P[6][16] + P[1][16]*SF[1] + P[3][16]*SF[0] + P[0][16]*SPP[0] - P[2][16]*SPP[1]; + nextP[6][17] = P[6][17] + P[1][17]*SF[1] + P[3][17]*SF[0] + P[0][17]*SPP[0] - P[2][17]*SPP[1]; + nextP[6][18] = P[6][18] + P[1][18]*SF[1] + P[3][18]*SF[0] + P[0][18]*SPP[0] - P[2][18]*SPP[1]; + nextP[6][19] = P[6][19] + P[1][19]*SF[1] + P[3][19]*SF[0] + P[0][19]*SPP[0] - P[2][19]*SPP[1]; + nextP[6][20] = P[6][20] + P[1][20]*SF[1] + P[3][20]*SF[0] + P[0][20]*SPP[0] - P[2][20]*SPP[1]; + nextP[7][0] = P[7][0] + P[4][0]*dt + SF[6]*(P[7][1] + P[4][1]*dt) + SPP[7]*(P[7][2] + P[4][2]*dt) + SPP[6]*(P[7][3] + P[4][3]*dt) + SPP[5]*(P[7][10] + P[4][10]*dt) + SPP[4]*(P[7][11] + P[4][11]*dt) + SPP[3]*(P[7][12] + P[4][12]*dt); + nextP[7][1] = P[7][1] + P[4][1]*dt + SF[5]*(P[7][0] + P[4][0]*dt) + SF[4]*(P[7][2] + P[4][2]*dt) + SPP[7]*(P[7][3] + P[4][3]*dt) + SPP[3]*(P[7][11] + P[4][11]*dt) - SPP[4]*(P[7][12] + P[4][12]*dt) - (q0*(P[7][10] + P[4][10]*dt))/2; + nextP[7][2] = P[7][2] + P[4][2]*dt + SF[3]*(P[7][0] + P[4][0]*dt) + SF[5]*(P[7][3] + P[4][3]*dt) + SPP[6]*(P[7][1] + P[4][1]*dt) - SPP[3]*(P[7][10] + P[4][10]*dt) + SPP[5]*(P[7][12] + P[4][12]*dt) - (q0*(P[7][11] + P[4][11]*dt))/2; + nextP[7][3] = P[7][3] + P[4][3]*dt + SF[4]*(P[7][0] + P[4][0]*dt) + SF[3]*(P[7][1] + P[4][1]*dt) + SF[6]*(P[7][2] + P[4][2]*dt) + SPP[4]*(P[7][10] + P[4][10]*dt) - SPP[5]*(P[7][11] + P[4][11]*dt) - (q0*(P[7][12] + P[4][12]*dt))/2; + nextP[7][4] = P[7][4] + P[4][4]*dt + SF[0]*(P[7][1] + P[4][1]*dt) + SF[2]*(P[7][0] + P[4][0]*dt) + SPP[0]*(P[7][2] + P[4][2]*dt) - SPP[2]*(P[7][3] + P[4][3]*dt); + nextP[7][5] = P[7][5] + P[4][5]*dt + SF[1]*(P[7][0] + P[4][0]*dt) + SF[0]*(P[7][2] + P[4][2]*dt) + SF[2]*(P[7][3] + P[4][3]*dt) - SPP[0]*(P[7][1] + P[4][1]*dt); + nextP[7][6] = P[7][6] + P[4][6]*dt + SF[1]*(P[7][1] + P[4][1]*dt) + SF[0]*(P[7][3] + P[4][3]*dt) + SPP[0]*(P[7][0] + P[4][0]*dt) - SPP[1]*(P[7][2] + P[4][2]*dt); + nextP[7][7] = P[7][7] + P[4][7]*dt + dt*(P[7][4] + P[4][4]*dt); + nextP[7][8] = P[7][8] + P[4][8]*dt + dt*(P[7][5] + P[4][5]*dt); + nextP[7][9] = P[7][9] + P[4][9]*dt + dt*(P[7][6] + P[4][6]*dt); + nextP[7][10] = P[7][10] + P[4][10]*dt; + nextP[7][11] = P[7][11] + P[4][11]*dt; + nextP[7][12] = P[7][12] + P[4][12]*dt; + nextP[7][13] = P[7][13] + P[4][13]*dt; + nextP[7][14] = P[7][14] + P[4][14]*dt; + nextP[7][15] = P[7][15] + P[4][15]*dt; + nextP[7][16] = P[7][16] + P[4][16]*dt; + nextP[7][17] = P[7][17] + P[4][17]*dt; + nextP[7][18] = P[7][18] + P[4][18]*dt; + nextP[7][19] = P[7][19] + P[4][19]*dt; + nextP[7][20] = P[7][20] + P[4][20]*dt; + nextP[8][0] = P[8][0] + P[5][0]*dt + SF[6]*(P[8][1] + P[5][1]*dt) + SPP[7]*(P[8][2] + P[5][2]*dt) + SPP[6]*(P[8][3] + P[5][3]*dt) + SPP[5]*(P[8][10] + P[5][10]*dt) + SPP[4]*(P[8][11] + P[5][11]*dt) + SPP[3]*(P[8][12] + P[5][12]*dt); + nextP[8][1] = P[8][1] + P[5][1]*dt + SF[5]*(P[8][0] + P[5][0]*dt) + SF[4]*(P[8][2] + P[5][2]*dt) + SPP[7]*(P[8][3] + P[5][3]*dt) + SPP[3]*(P[8][11] + P[5][11]*dt) - SPP[4]*(P[8][12] + P[5][12]*dt) - (q0*(P[8][10] + P[5][10]*dt))/2; + nextP[8][2] = P[8][2] + P[5][2]*dt + SF[3]*(P[8][0] + P[5][0]*dt) + SF[5]*(P[8][3] + P[5][3]*dt) + SPP[6]*(P[8][1] + P[5][1]*dt) - SPP[3]*(P[8][10] + P[5][10]*dt) + SPP[5]*(P[8][12] + P[5][12]*dt) - (q0*(P[8][11] + P[5][11]*dt))/2; + nextP[8][3] = P[8][3] + P[5][3]*dt + SF[4]*(P[8][0] + P[5][0]*dt) + SF[3]*(P[8][1] + P[5][1]*dt) + SF[6]*(P[8][2] + P[5][2]*dt) + SPP[4]*(P[8][10] + P[5][10]*dt) - SPP[5]*(P[8][11] + P[5][11]*dt) - (q0*(P[8][12] + P[5][12]*dt))/2; + nextP[8][4] = P[8][4] + P[5][4]*dt + SF[0]*(P[8][1] + P[5][1]*dt) + SF[2]*(P[8][0] + P[5][0]*dt) + SPP[0]*(P[8][2] + P[5][2]*dt) - SPP[2]*(P[8][3] + P[5][3]*dt); + nextP[8][5] = P[8][5] + P[5][5]*dt + SF[1]*(P[8][0] + P[5][0]*dt) + SF[0]*(P[8][2] + P[5][2]*dt) + SF[2]*(P[8][3] + P[5][3]*dt) - SPP[0]*(P[8][1] + P[5][1]*dt); + nextP[8][6] = P[8][6] + P[5][6]*dt + SF[1]*(P[8][1] + P[5][1]*dt) + SF[0]*(P[8][3] + P[5][3]*dt) + SPP[0]*(P[8][0] + P[5][0]*dt) - SPP[1]*(P[8][2] + P[5][2]*dt); + nextP[8][7] = P[8][7] + P[5][7]*dt + dt*(P[8][4] + P[5][4]*dt); + nextP[8][8] = P[8][8] + P[5][8]*dt + dt*(P[8][5] + P[5][5]*dt); + nextP[8][9] = P[8][9] + P[5][9]*dt + dt*(P[8][6] + P[5][6]*dt); + nextP[8][10] = P[8][10] + P[5][10]*dt; + nextP[8][11] = P[8][11] + P[5][11]*dt; + nextP[8][12] = P[8][12] + P[5][12]*dt; + nextP[8][13] = P[8][13] + P[5][13]*dt; + nextP[8][14] = P[8][14] + P[5][14]*dt; + nextP[8][15] = P[8][15] + P[5][15]*dt; + nextP[8][16] = P[8][16] + P[5][16]*dt; + nextP[8][17] = P[8][17] + P[5][17]*dt; + nextP[8][18] = P[8][18] + P[5][18]*dt; + nextP[8][19] = P[8][19] + P[5][19]*dt; + nextP[8][20] = P[8][20] + P[5][20]*dt; + nextP[9][0] = P[9][0] + P[6][0]*dt + SF[6]*(P[9][1] + P[6][1]*dt) + SPP[7]*(P[9][2] + P[6][2]*dt) + SPP[6]*(P[9][3] + P[6][3]*dt) + SPP[5]*(P[9][10] + P[6][10]*dt) + SPP[4]*(P[9][11] + P[6][11]*dt) + SPP[3]*(P[9][12] + P[6][12]*dt); + nextP[9][1] = P[9][1] + P[6][1]*dt + SF[5]*(P[9][0] + P[6][0]*dt) + SF[4]*(P[9][2] + P[6][2]*dt) + SPP[7]*(P[9][3] + P[6][3]*dt) + SPP[3]*(P[9][11] + P[6][11]*dt) - SPP[4]*(P[9][12] + P[6][12]*dt) - (q0*(P[9][10] + P[6][10]*dt))/2; + nextP[9][2] = P[9][2] + P[6][2]*dt + SF[3]*(P[9][0] + P[6][0]*dt) + SF[5]*(P[9][3] + P[6][3]*dt) + SPP[6]*(P[9][1] + P[6][1]*dt) - SPP[3]*(P[9][10] + P[6][10]*dt) + SPP[5]*(P[9][12] + P[6][12]*dt) - (q0*(P[9][11] + P[6][11]*dt))/2; + nextP[9][3] = P[9][3] + P[6][3]*dt + SF[4]*(P[9][0] + P[6][0]*dt) + SF[3]*(P[9][1] + P[6][1]*dt) + SF[6]*(P[9][2] + P[6][2]*dt) + SPP[4]*(P[9][10] + P[6][10]*dt) - SPP[5]*(P[9][11] + P[6][11]*dt) - (q0*(P[9][12] + P[6][12]*dt))/2; + nextP[9][4] = P[9][4] + P[6][4]*dt + SF[0]*(P[9][1] + P[6][1]*dt) + SF[2]*(P[9][0] + P[6][0]*dt) + SPP[0]*(P[9][2] + P[6][2]*dt) - SPP[2]*(P[9][3] + P[6][3]*dt); + nextP[9][5] = P[9][5] + P[6][5]*dt + SF[1]*(P[9][0] + P[6][0]*dt) + SF[0]*(P[9][2] + P[6][2]*dt) + SF[2]*(P[9][3] + P[6][3]*dt) - SPP[0]*(P[9][1] + P[6][1]*dt); + nextP[9][6] = P[9][6] + P[6][6]*dt + SF[1]*(P[9][1] + P[6][1]*dt) + SF[0]*(P[9][3] + P[6][3]*dt) + SPP[0]*(P[9][0] + P[6][0]*dt) - SPP[1]*(P[9][2] + P[6][2]*dt); + nextP[9][7] = P[9][7] + P[6][7]*dt + dt*(P[9][4] + P[6][4]*dt); + nextP[9][8] = P[9][8] + P[6][8]*dt + dt*(P[9][5] + P[6][5]*dt); + nextP[9][9] = P[9][9] + P[6][9]*dt + dt*(P[9][6] + P[6][6]*dt); + nextP[9][10] = P[9][10] + P[6][10]*dt; + nextP[9][11] = P[9][11] + P[6][11]*dt; + nextP[9][12] = P[9][12] + P[6][12]*dt; + nextP[9][13] = P[9][13] + P[6][13]*dt; + nextP[9][14] = P[9][14] + P[6][14]*dt; + nextP[9][15] = P[9][15] + P[6][15]*dt; + nextP[9][16] = P[9][16] + P[6][16]*dt; + nextP[9][17] = P[9][17] + P[6][17]*dt; + nextP[9][18] = P[9][18] + P[6][18]*dt; + nextP[9][19] = P[9][19] + P[6][19]*dt; + nextP[9][20] = P[9][20] + P[6][20]*dt; + nextP[10][0] = P[10][0] + P[10][1]*SF[6] + P[10][2]*SPP[7] + P[10][3]*SPP[6] + P[10][10]*SPP[5] + P[10][11]*SPP[4] + P[10][12]*SPP[3]; + nextP[10][1] = P[10][1] + P[10][0]*SF[5] + P[10][2]*SF[4] + P[10][3]*SPP[7] + P[10][11]*SPP[3] - P[10][12]*SPP[4] - (P[10][10]*q0)/2; + nextP[10][2] = P[10][2] + P[10][0]*SF[3] + P[10][3]*SF[5] + P[10][1]*SPP[6] - P[10][10]*SPP[3] + P[10][12]*SPP[5] - (P[10][11]*q0)/2; + nextP[10][3] = P[10][3] + P[10][0]*SF[4] + P[10][1]*SF[3] + P[10][2]*SF[6] + P[10][10]*SPP[4] - P[10][11]*SPP[5] - (P[10][12]*q0)/2; + nextP[10][4] = P[10][4] + P[10][1]*SF[0] + P[10][0]*SF[2] + P[10][2]*SPP[0] - P[10][3]*SPP[2]; + nextP[10][5] = P[10][5] + P[10][0]*SF[1] + P[10][2]*SF[0] + P[10][3]*SF[2] - P[10][1]*SPP[0]; + nextP[10][6] = P[10][6] + P[10][1]*SF[1] + P[10][3]*SF[0] + P[10][0]*SPP[0] - P[10][2]*SPP[1]; + nextP[10][7] = P[10][7] + P[10][4]*dt; + nextP[10][8] = P[10][8] + P[10][5]*dt; + nextP[10][9] = P[10][9] + P[10][6]*dt; + nextP[10][10] = P[10][10]; + nextP[10][11] = P[10][11]; + nextP[10][12] = P[10][12]; + nextP[10][13] = P[10][13]; + nextP[10][14] = P[10][14]; + nextP[10][15] = P[10][15]; + nextP[10][16] = P[10][16]; + nextP[10][17] = P[10][17]; + nextP[10][18] = P[10][18]; + nextP[10][19] = P[10][19]; + nextP[10][20] = P[10][20]; + nextP[11][0] = P[11][0] + P[11][1]*SF[6] + P[11][2]*SPP[7] + P[11][3]*SPP[6] + P[11][10]*SPP[5] + P[11][11]*SPP[4] + P[11][12]*SPP[3]; + nextP[11][1] = P[11][1] + P[11][0]*SF[5] + P[11][2]*SF[4] + P[11][3]*SPP[7] + P[11][11]*SPP[3] - P[11][12]*SPP[4] - (P[11][10]*q0)/2; + nextP[11][2] = P[11][2] + P[11][0]*SF[3] + P[11][3]*SF[5] + P[11][1]*SPP[6] - P[11][10]*SPP[3] + P[11][12]*SPP[5] - (P[11][11]*q0)/2; + nextP[11][3] = P[11][3] + P[11][0]*SF[4] + P[11][1]*SF[3] + P[11][2]*SF[6] + P[11][10]*SPP[4] - P[11][11]*SPP[5] - (P[11][12]*q0)/2; + nextP[11][4] = P[11][4] + P[11][1]*SF[0] + P[11][0]*SF[2] + P[11][2]*SPP[0] - P[11][3]*SPP[2]; + nextP[11][5] = P[11][5] + P[11][0]*SF[1] + P[11][2]*SF[0] + P[11][3]*SF[2] - P[11][1]*SPP[0]; + nextP[11][6] = P[11][6] + P[11][1]*SF[1] + P[11][3]*SF[0] + P[11][0]*SPP[0] - P[11][2]*SPP[1]; + nextP[11][7] = P[11][7] + P[11][4]*dt; + nextP[11][8] = P[11][8] + P[11][5]*dt; + nextP[11][9] = P[11][9] + P[11][6]*dt; + nextP[11][10] = P[11][10]; + nextP[11][11] = P[11][11]; + nextP[11][12] = P[11][12]; + nextP[11][13] = P[11][13]; + nextP[11][14] = P[11][14]; + nextP[11][15] = P[11][15]; + nextP[11][16] = P[11][16]; + nextP[11][17] = P[11][17]; + nextP[11][18] = P[11][18]; + nextP[11][19] = P[11][19]; + nextP[11][20] = P[11][20]; + nextP[12][0] = P[12][0] + P[12][1]*SF[6] + P[12][2]*SPP[7] + P[12][3]*SPP[6] + P[12][10]*SPP[5] + P[12][11]*SPP[4] + P[12][12]*SPP[3]; + nextP[12][1] = P[12][1] + P[12][0]*SF[5] + P[12][2]*SF[4] + P[12][3]*SPP[7] + P[12][11]*SPP[3] - P[12][12]*SPP[4] - (P[12][10]*q0)/2; + nextP[12][2] = P[12][2] + P[12][0]*SF[3] + P[12][3]*SF[5] + P[12][1]*SPP[6] - P[12][10]*SPP[3] + P[12][12]*SPP[5] - (P[12][11]*q0)/2; + nextP[12][3] = P[12][3] + P[12][0]*SF[4] + P[12][1]*SF[3] + P[12][2]*SF[6] + P[12][10]*SPP[4] - P[12][11]*SPP[5] - (P[12][12]*q0)/2; + nextP[12][4] = P[12][4] + P[12][1]*SF[0] + P[12][0]*SF[2] + P[12][2]*SPP[0] - P[12][3]*SPP[2]; + nextP[12][5] = P[12][5] + P[12][0]*SF[1] + P[12][2]*SF[0] + P[12][3]*SF[2] - P[12][1]*SPP[0]; + nextP[12][6] = P[12][6] + P[12][1]*SF[1] + P[12][3]*SF[0] + P[12][0]*SPP[0] - P[12][2]*SPP[1]; + nextP[12][7] = P[12][7] + P[12][4]*dt; + nextP[12][8] = P[12][8] + P[12][5]*dt; + nextP[12][9] = P[12][9] + P[12][6]*dt; + nextP[12][10] = P[12][10]; + nextP[12][11] = P[12][11]; + nextP[12][12] = P[12][12]; + nextP[12][13] = P[12][13]; + nextP[12][14] = P[12][14]; + nextP[12][15] = P[12][15]; + nextP[12][16] = P[12][16]; + nextP[12][17] = P[12][17]; + nextP[12][18] = P[12][18]; + nextP[12][19] = P[12][19]; + nextP[12][20] = P[12][20]; + nextP[13][0] = P[13][0] + P[13][1]*SF[6] + P[13][2]*SPP[7] + P[13][3]*SPP[6] + P[13][10]*SPP[5] + P[13][11]*SPP[4] + P[13][12]*SPP[3]; + nextP[13][1] = P[13][1] + P[13][0]*SF[5] + P[13][2]*SF[4] + P[13][3]*SPP[7] + P[13][11]*SPP[3] - P[13][12]*SPP[4] - (P[13][10]*q0)/2; + nextP[13][2] = P[13][2] + P[13][0]*SF[3] + P[13][3]*SF[5] + P[13][1]*SPP[6] - P[13][10]*SPP[3] + P[13][12]*SPP[5] - (P[13][11]*q0)/2; + nextP[13][3] = P[13][3] + P[13][0]*SF[4] + P[13][1]*SF[3] + P[13][2]*SF[6] + P[13][10]*SPP[4] - P[13][11]*SPP[5] - (P[13][12]*q0)/2; + nextP[13][4] = P[13][4] + P[13][1]*SF[0] + P[13][0]*SF[2] + P[13][2]*SPP[0] - P[13][3]*SPP[2]; + nextP[13][5] = P[13][5] + P[13][0]*SF[1] + P[13][2]*SF[0] + P[13][3]*SF[2] - P[13][1]*SPP[0]; + nextP[13][6] = P[13][6] + P[13][1]*SF[1] + P[13][3]*SF[0] + P[13][0]*SPP[0] - P[13][2]*SPP[1]; + nextP[13][7] = P[13][7] + P[13][4]*dt; + nextP[13][8] = P[13][8] + P[13][5]*dt; + nextP[13][9] = P[13][9] + P[13][6]*dt; + nextP[13][10] = P[13][10]; + nextP[13][11] = P[13][11]; + nextP[13][12] = P[13][12]; + nextP[13][13] = P[13][13]; + nextP[13][14] = P[13][14]; + nextP[13][15] = P[13][15]; + nextP[13][16] = P[13][16]; + nextP[13][17] = P[13][17]; + nextP[13][18] = P[13][18]; + nextP[13][19] = P[13][19]; + nextP[13][20] = P[13][20]; + nextP[14][0] = P[14][0] + P[14][1]*SF[6] + P[14][2]*SPP[7] + P[14][3]*SPP[6] + P[14][10]*SPP[5] + P[14][11]*SPP[4] + P[14][12]*SPP[3]; + nextP[14][1] = P[14][1] + P[14][0]*SF[5] + P[14][2]*SF[4] + P[14][3]*SPP[7] + P[14][11]*SPP[3] - P[14][12]*SPP[4] - (P[14][10]*q0)/2; + nextP[14][2] = P[14][2] + P[14][0]*SF[3] + P[14][3]*SF[5] + P[14][1]*SPP[6] - P[14][10]*SPP[3] + P[14][12]*SPP[5] - (P[14][11]*q0)/2; + nextP[14][3] = P[14][3] + P[14][0]*SF[4] + P[14][1]*SF[3] + P[14][2]*SF[6] + P[14][10]*SPP[4] - P[14][11]*SPP[5] - (P[14][12]*q0)/2; + nextP[14][4] = P[14][4] + P[14][1]*SF[0] + P[14][0]*SF[2] + P[14][2]*SPP[0] - P[14][3]*SPP[2]; + nextP[14][5] = P[14][5] + P[14][0]*SF[1] + P[14][2]*SF[0] + P[14][3]*SF[2] - P[14][1]*SPP[0]; + nextP[14][6] = P[14][6] + P[14][1]*SF[1] + P[14][3]*SF[0] + P[14][0]*SPP[0] - P[14][2]*SPP[1]; + nextP[14][7] = P[14][7] + P[14][4]*dt; + nextP[14][8] = P[14][8] + P[14][5]*dt; + nextP[14][9] = P[14][9] + P[14][6]*dt; + nextP[14][10] = P[14][10]; + nextP[14][11] = P[14][11]; + nextP[14][12] = P[14][12]; + nextP[14][13] = P[14][13]; + nextP[14][14] = P[14][14]; + nextP[14][15] = P[14][15]; + nextP[14][16] = P[14][16]; + nextP[14][17] = P[14][17]; + nextP[14][18] = P[14][18]; + nextP[14][19] = P[14][19]; + nextP[14][20] = P[14][20]; + nextP[15][0] = P[15][0] + P[15][1]*SF[6] + P[15][2]*SPP[7] + P[15][3]*SPP[6] + P[15][10]*SPP[5] + P[15][11]*SPP[4] + P[15][12]*SPP[3]; + nextP[15][1] = P[15][1] + P[15][0]*SF[5] + P[15][2]*SF[4] + P[15][3]*SPP[7] + P[15][11]*SPP[3] - P[15][12]*SPP[4] - (P[15][10]*q0)/2; + nextP[15][2] = P[15][2] + P[15][0]*SF[3] + P[15][3]*SF[5] + P[15][1]*SPP[6] - P[15][10]*SPP[3] + P[15][12]*SPP[5] - (P[15][11]*q0)/2; + nextP[15][3] = P[15][3] + P[15][0]*SF[4] + P[15][1]*SF[3] + P[15][2]*SF[6] + P[15][10]*SPP[4] - P[15][11]*SPP[5] - (P[15][12]*q0)/2; + nextP[15][4] = P[15][4] + P[15][1]*SF[0] + P[15][0]*SF[2] + P[15][2]*SPP[0] - P[15][3]*SPP[2]; + nextP[15][5] = P[15][5] + P[15][0]*SF[1] + P[15][2]*SF[0] + P[15][3]*SF[2] - P[15][1]*SPP[0]; + nextP[15][6] = P[15][6] + P[15][1]*SF[1] + P[15][3]*SF[0] + P[15][0]*SPP[0] - P[15][2]*SPP[1]; + nextP[15][7] = P[15][7] + P[15][4]*dt; + nextP[15][8] = P[15][8] + P[15][5]*dt; + nextP[15][9] = P[15][9] + P[15][6]*dt; + nextP[15][10] = P[15][10]; + nextP[15][11] = P[15][11]; + nextP[15][12] = P[15][12]; + nextP[15][13] = P[15][13]; + nextP[15][14] = P[15][14]; + nextP[15][15] = P[15][15]; + nextP[15][16] = P[15][16]; + nextP[15][17] = P[15][17]; + nextP[15][18] = P[15][18]; + nextP[15][19] = P[15][19]; + nextP[15][20] = P[15][20]; + nextP[16][0] = P[16][0] + P[16][1]*SF[6] + P[16][2]*SPP[7] + P[16][3]*SPP[6] + P[16][10]*SPP[5] + P[16][11]*SPP[4] + P[16][12]*SPP[3]; + nextP[16][1] = P[16][1] + P[16][0]*SF[5] + P[16][2]*SF[4] + P[16][3]*SPP[7] + P[16][11]*SPP[3] - P[16][12]*SPP[4] - (P[16][10]*q0)/2; + nextP[16][2] = P[16][2] + P[16][0]*SF[3] + P[16][3]*SF[5] + P[16][1]*SPP[6] - P[16][10]*SPP[3] + P[16][12]*SPP[5] - (P[16][11]*q0)/2; + nextP[16][3] = P[16][3] + P[16][0]*SF[4] + P[16][1]*SF[3] + P[16][2]*SF[6] + P[16][10]*SPP[4] - P[16][11]*SPP[5] - (P[16][12]*q0)/2; + nextP[16][4] = P[16][4] + P[16][1]*SF[0] + P[16][0]*SF[2] + P[16][2]*SPP[0] - P[16][3]*SPP[2]; + nextP[16][5] = P[16][5] + P[16][0]*SF[1] + P[16][2]*SF[0] + P[16][3]*SF[2] - P[16][1]*SPP[0]; + nextP[16][6] = P[16][6] + P[16][1]*SF[1] + P[16][3]*SF[0] + P[16][0]*SPP[0] - P[16][2]*SPP[1]; + nextP[16][7] = P[16][7] + P[16][4]*dt; + nextP[16][8] = P[16][8] + P[16][5]*dt; + nextP[16][9] = P[16][9] + P[16][6]*dt; + nextP[16][10] = P[16][10]; + nextP[16][11] = P[16][11]; + nextP[16][12] = P[16][12]; + nextP[16][13] = P[16][13]; + nextP[16][14] = P[16][14]; + nextP[16][15] = P[16][15]; + nextP[16][16] = P[16][16]; + nextP[16][17] = P[16][17]; + nextP[16][18] = P[16][18]; + nextP[16][19] = P[16][19]; + nextP[16][20] = P[16][20]; + nextP[17][0] = P[17][0] + P[17][1]*SF[6] + P[17][2]*SPP[7] + P[17][3]*SPP[6] + P[17][10]*SPP[5] + P[17][11]*SPP[4] + P[17][12]*SPP[3]; + nextP[17][1] = P[17][1] + P[17][0]*SF[5] + P[17][2]*SF[4] + P[17][3]*SPP[7] + P[17][11]*SPP[3] - P[17][12]*SPP[4] - (P[17][10]*q0)/2; + nextP[17][2] = P[17][2] + P[17][0]*SF[3] + P[17][3]*SF[5] + P[17][1]*SPP[6] - P[17][10]*SPP[3] + P[17][12]*SPP[5] - (P[17][11]*q0)/2; + nextP[17][3] = P[17][3] + P[17][0]*SF[4] + P[17][1]*SF[3] + P[17][2]*SF[6] + P[17][10]*SPP[4] - P[17][11]*SPP[5] - (P[17][12]*q0)/2; + nextP[17][4] = P[17][4] + P[17][1]*SF[0] + P[17][0]*SF[2] + P[17][2]*SPP[0] - P[17][3]*SPP[2]; + nextP[17][5] = P[17][5] + P[17][0]*SF[1] + P[17][2]*SF[0] + P[17][3]*SF[2] - P[17][1]*SPP[0]; + nextP[17][6] = P[17][6] + P[17][1]*SF[1] + P[17][3]*SF[0] + P[17][0]*SPP[0] - P[17][2]*SPP[1]; + nextP[17][7] = P[17][7] + P[17][4]*dt; + nextP[17][8] = P[17][8] + P[17][5]*dt; + nextP[17][9] = P[17][9] + P[17][6]*dt; + nextP[17][10] = P[17][10]; + nextP[17][11] = P[17][11]; + nextP[17][12] = P[17][12]; + nextP[17][13] = P[17][13]; + nextP[17][14] = P[17][14]; + nextP[17][15] = P[17][15]; + nextP[17][16] = P[17][16]; + nextP[17][17] = P[17][17]; + nextP[17][18] = P[17][18]; + nextP[17][19] = P[17][19]; + nextP[17][20] = P[17][20]; + nextP[18][0] = P[18][0] + P[18][1]*SF[6] + P[18][2]*SPP[7] + P[18][3]*SPP[6] + P[18][10]*SPP[5] + P[18][11]*SPP[4] + P[18][12]*SPP[3]; + nextP[18][1] = P[18][1] + P[18][0]*SF[5] + P[18][2]*SF[4] + P[18][3]*SPP[7] + P[18][11]*SPP[3] - P[18][12]*SPP[4] - (P[18][10]*q0)/2; + nextP[18][2] = P[18][2] + P[18][0]*SF[3] + P[18][3]*SF[5] + P[18][1]*SPP[6] - P[18][10]*SPP[3] + P[18][12]*SPP[5] - (P[18][11]*q0)/2; + nextP[18][3] = P[18][3] + P[18][0]*SF[4] + P[18][1]*SF[3] + P[18][2]*SF[6] + P[18][10]*SPP[4] - P[18][11]*SPP[5] - (P[18][12]*q0)/2; + nextP[18][4] = P[18][4] + P[18][1]*SF[0] + P[18][0]*SF[2] + P[18][2]*SPP[0] - P[18][3]*SPP[2]; + nextP[18][5] = P[18][5] + P[18][0]*SF[1] + P[18][2]*SF[0] + P[18][3]*SF[2] - P[18][1]*SPP[0]; + nextP[18][6] = P[18][6] + P[18][1]*SF[1] + P[18][3]*SF[0] + P[18][0]*SPP[0] - P[18][2]*SPP[1]; + nextP[18][7] = P[18][7] + P[18][4]*dt; + nextP[18][8] = P[18][8] + P[18][5]*dt; + nextP[18][9] = P[18][9] + P[18][6]*dt; + nextP[18][10] = P[18][10]; + nextP[18][11] = P[18][11]; + nextP[18][12] = P[18][12]; + nextP[18][13] = P[18][13]; + nextP[18][14] = P[18][14]; + nextP[18][15] = P[18][15]; + nextP[18][16] = P[18][16]; + nextP[18][17] = P[18][17]; + nextP[18][18] = P[18][18]; + nextP[18][19] = P[18][19]; + nextP[18][20] = P[18][20]; + nextP[19][0] = P[19][0] + P[19][1]*SF[6] + P[19][2]*SPP[7] + P[19][3]*SPP[6] + P[19][10]*SPP[5] + P[19][11]*SPP[4] + P[19][12]*SPP[3]; + nextP[19][1] = P[19][1] + P[19][0]*SF[5] + P[19][2]*SF[4] + P[19][3]*SPP[7] + P[19][11]*SPP[3] - P[19][12]*SPP[4] - (P[19][10]*q0)/2; + nextP[19][2] = P[19][2] + P[19][0]*SF[3] + P[19][3]*SF[5] + P[19][1]*SPP[6] - P[19][10]*SPP[3] + P[19][12]*SPP[5] - (P[19][11]*q0)/2; + nextP[19][3] = P[19][3] + P[19][0]*SF[4] + P[19][1]*SF[3] + P[19][2]*SF[6] + P[19][10]*SPP[4] - P[19][11]*SPP[5] - (P[19][12]*q0)/2; + nextP[19][4] = P[19][4] + P[19][1]*SF[0] + P[19][0]*SF[2] + P[19][2]*SPP[0] - P[19][3]*SPP[2]; + nextP[19][5] = P[19][5] + P[19][0]*SF[1] + P[19][2]*SF[0] + P[19][3]*SF[2] - P[19][1]*SPP[0]; + nextP[19][6] = P[19][6] + P[19][1]*SF[1] + P[19][3]*SF[0] + P[19][0]*SPP[0] - P[19][2]*SPP[1]; + nextP[19][7] = P[19][7] + P[19][4]*dt; + nextP[19][8] = P[19][8] + P[19][5]*dt; + nextP[19][9] = P[19][9] + P[19][6]*dt; + nextP[19][10] = P[19][10]; + nextP[19][11] = P[19][11]; + nextP[19][12] = P[19][12]; + nextP[19][13] = P[19][13]; + nextP[19][14] = P[19][14]; + nextP[19][15] = P[19][15]; + nextP[19][16] = P[19][16]; + nextP[19][17] = P[19][17]; + nextP[19][18] = P[19][18]; + nextP[19][19] = P[19][19]; + nextP[19][20] = P[19][20]; + nextP[20][0] = P[20][0] + P[20][1]*SF[6] + P[20][2]*SPP[7] + P[20][3]*SPP[6] + P[20][10]*SPP[5] + P[20][11]*SPP[4] + P[20][12]*SPP[3]; + nextP[20][1] = P[20][1] + P[20][0]*SF[5] + P[20][2]*SF[4] + P[20][3]*SPP[7] + P[20][11]*SPP[3] - P[20][12]*SPP[4] - (P[20][10]*q0)/2; + nextP[20][2] = P[20][2] + P[20][0]*SF[3] + P[20][3]*SF[5] + P[20][1]*SPP[6] - P[20][10]*SPP[3] + P[20][12]*SPP[5] - (P[20][11]*q0)/2; + nextP[20][3] = P[20][3] + P[20][0]*SF[4] + P[20][1]*SF[3] + P[20][2]*SF[6] + P[20][10]*SPP[4] - P[20][11]*SPP[5] - (P[20][12]*q0)/2; + nextP[20][4] = P[20][4] + P[20][1]*SF[0] + P[20][0]*SF[2] + P[20][2]*SPP[0] - P[20][3]*SPP[2]; + nextP[20][5] = P[20][5] + P[20][0]*SF[1] + P[20][2]*SF[0] + P[20][3]*SF[2] - P[20][1]*SPP[0]; + nextP[20][6] = P[20][6] + P[20][1]*SF[1] + P[20][3]*SF[0] + P[20][0]*SPP[0] - P[20][2]*SPP[1]; + nextP[20][7] = P[20][7] + P[20][4]*dt; + nextP[20][8] = P[20][8] + P[20][5]*dt; + nextP[20][9] = P[20][9] + P[20][6]*dt; + nextP[20][10] = P[20][10]; + nextP[20][11] = P[20][11]; + nextP[20][12] = P[20][12]; + nextP[20][13] = P[20][13]; + nextP[20][14] = P[20][14]; + nextP[20][15] = P[20][15]; + nextP[20][16] = P[20][16]; + nextP[20][17] = P[20][17]; + nextP[20][18] = P[20][18]; + nextP[20][19] = P[20][19]; + nextP[20][20] = P[20][20]; + + for (unsigned i = 0; i < n_states; i++) + { + nextP[i][i] = nextP[i][i] + processNoise[i]; + } + + // If on ground or no magnetometer fitted, inhibit magnetometer bias updates by + // setting the coresponding covariance terms to zero. + if (onGround || !useCompass) + { + zeroRows(nextP,15,20); + zeroCols(nextP,15,20); + } + + // If on ground or not using airspeed sensing, inhibit wind velocity + // covariance growth. + if (onGround || !useAirspeed) + { + zeroRows(nextP,13,14); + zeroCols(nextP,13,14); + } + + // If the total position variance exceds 1E6 (1000m), then stop covariance + // growth by setting the predicted to the previous values + // This prevent an ill conditioned matrix from occurring for long periods + // without GPS + if ((P[7][7] + P[8][8]) > 1E6f) + { + for (uint8_t i=7; i<=8; i++) + { + for (unsigned j = 0; j < n_states; j++) + { + nextP[i][j] = P[i][j]; + nextP[j][i] = P[j][i]; + } + } + } + + if (onGround || staticMode) { + // copy the portion of the variances we want to + // propagate + for (unsigned i = 0; i < 14; i++) { + P[i][i] = nextP[i][i]; + + // force symmetry for observable states + // force zero for non-observable states + for (unsigned i = 1; i < n_states; i++) + { + for (uint8_t j = 0; j < i; j++) + { + if ((i > 12) || (j > 12)) { + P[i][j] = 0.0f; + } else { + P[i][j] = 0.5f * (nextP[i][j] + nextP[j][i]); + } + P[j][i] = P[i][j]; + } + } + } + + } else { + + // Copy covariance + for (unsigned i = 0; i < n_states; i++) { + P[i][i] = nextP[i][i]; + } + + // force symmetry for observable states + for (unsigned i = 1; i < n_states; i++) + { + for (uint8_t j = 0; j < i; j++) + { + P[i][j] = 0.5f * (nextP[i][j] + nextP[j][i]); + P[j][i] = P[i][j]; + } + } + + } + + ConstrainVariances(); +} + +void AttPosEKF::FuseVelposNED() +{ + +// declare variables used by fault isolation logic + uint32_t gpsRetryTime = 30000; // time in msec before GPS fusion will be retried following innovation consistency failure + uint32_t gpsRetryTimeNoTAS = 5000; // retry time if no TAS measurement available + uint32_t hgtRetryTime = 5000; // height measurement retry time + uint32_t horizRetryTime; + +// declare variables used to check measurement errors + float velInnov[3] = {0.0f,0.0f,0.0f}; + float posInnov[2] = {0.0f,0.0f}; + float hgtInnov = 0.0f; + +// declare variables used to control access to arrays + bool fuseData[6] = {false,false,false,false,false,false}; + uint8_t stateIndex; + uint8_t obsIndex; + uint8_t indexLimit; + +// declare variables used by state and covariance update calculations + float velErr; + float posErr; + float R_OBS[6]; + float observation[6]; + float SK; + float quatMag; + +// Perform sequential fusion of GPS measurements. This assumes that the +// errors in the different velocity and position components are +// uncorrelated which is not true, however in the absence of covariance +// data from the GPS receiver it is the only assumption we can make +// so we might as well take advantage of the computational efficiencies +// associated with sequential fusion + if (fuseVelData || fusePosData || fuseHgtData) + { + // set the GPS data timeout depending on whether airspeed data is present + if (useAirspeed) horizRetryTime = gpsRetryTime; + else horizRetryTime = gpsRetryTimeNoTAS; + + // Form the observation vector + for (uint8_t i=0; i<=2; i++) observation[i] = velNED[i]; + for (uint8_t i=3; i<=4; i++) observation[i] = posNE[i-3]; + observation[5] = -(hgtMea); + + // Estimate the GPS Velocity, GPS horiz position and height measurement variances. + velErr = 0.2f*accNavMag; // additional error in GPS velocities caused by manoeuvring + posErr = 0.2f*accNavMag; // additional error in GPS position caused by manoeuvring + R_OBS[0] = 0.04f + sq(velErr); + R_OBS[1] = R_OBS[0]; + R_OBS[2] = 0.08f + sq(velErr); + R_OBS[3] = R_OBS[2]; + R_OBS[4] = 4.0f + sq(posErr); + R_OBS[5] = 4.0f; + + // Set innovation variances to zero default + for (uint8_t i = 0; i<=5; i++) + { + varInnovVelPos[i] = 0.0f; + } + // calculate innovations and check GPS data validity using an innovation consistency check + if (fuseVelData) + { + // test velocity measurements + uint8_t imax = 2; + if (fusionModeGPS == 1) imax = 1; + for (uint8_t i = 0; i<=imax; i++) + { + velInnov[i] = statesAtVelTime[i+4] - velNED[i]; + stateIndex = 4 + i; + varInnovVelPos[i] = P[stateIndex][stateIndex] + R_OBS[i]; + } + // apply a 5-sigma threshold + current_ekf_state.velHealth = (sq(velInnov[0]) + sq(velInnov[1]) + sq(velInnov[2])) < 25.0f * (varInnovVelPos[0] + varInnovVelPos[1] + varInnovVelPos[2]); + current_ekf_state.velTimeout = (millis() - current_ekf_state.velFailTime) > horizRetryTime; + if (current_ekf_state.velHealth || current_ekf_state.velTimeout) + { + current_ekf_state.velHealth = true; + current_ekf_state.velFailTime = millis(); + } + else + { + current_ekf_state.velHealth = false; + } + } + if (fusePosData) + { + // test horizontal position measurements + posInnov[0] = statesAtPosTime[7] - posNE[0]; + posInnov[1] = statesAtPosTime[8] - posNE[1]; + varInnovVelPos[3] = P[7][7] + R_OBS[3]; + varInnovVelPos[4] = P[8][8] + R_OBS[4]; + // apply a 10-sigma threshold + current_ekf_state.posHealth = (sq(posInnov[0]) + sq(posInnov[1])) < 100.0f*(varInnovVelPos[3] + varInnovVelPos[4]); + current_ekf_state.posTimeout = (millis() - current_ekf_state.posFailTime) > horizRetryTime; + if (current_ekf_state.posHealth || current_ekf_state.posTimeout) + { + current_ekf_state.posHealth = true; + current_ekf_state.posFailTime = millis(); + } + else + { + current_ekf_state.posHealth = false; + } + } + // test height measurements + if (fuseHgtData) + { + hgtInnov = statesAtHgtTime[9] + hgtMea; + varInnovVelPos[5] = P[9][9] + R_OBS[5]; + // apply a 10-sigma threshold + current_ekf_state.hgtHealth = sq(hgtInnov) < 100.0f*varInnovVelPos[5]; + current_ekf_state.hgtTimeout = (millis() - current_ekf_state.hgtFailTime) > hgtRetryTime; + if (current_ekf_state.hgtHealth || current_ekf_state.hgtTimeout) + { + current_ekf_state.hgtHealth = true; + current_ekf_state.hgtFailTime = millis(); + } + else + { + current_ekf_state.hgtHealth = false; + } + } + // Set range for sequential fusion of velocity and position measurements depending + // on which data is available and its health + if (fuseVelData && fusionModeGPS == 0 && current_ekf_state.velHealth) + { + fuseData[0] = true; + fuseData[1] = true; + fuseData[2] = true; + } + if (fuseVelData && fusionModeGPS == 1 && current_ekf_state.velHealth) + { + fuseData[0] = true; + fuseData[1] = true; + } + if (fusePosData && fusionModeGPS <= 2 && current_ekf_state.posHealth) + { + fuseData[3] = true; + fuseData[4] = true; + } + if (fuseHgtData && current_ekf_state.hgtHealth) + { + fuseData[5] = true; + } + // Limit range of states modified when on ground + if(!onGround) + { + indexLimit = 20; + } + else + { + indexLimit = 12; + } + // Fuse measurements sequentially + for (obsIndex=0; obsIndex<=5; obsIndex++) + { + if (fuseData[obsIndex]) + { + stateIndex = 4 + obsIndex; + // Calculate the measurement innovation, using states from a + // different time coordinate if fusing height data + if (obsIndex >= 0 && obsIndex <= 2) + { + innovVelPos[obsIndex] = statesAtVelTime[stateIndex] - observation[obsIndex]; + } + else if (obsIndex == 3 || obsIndex == 4) + { + innovVelPos[obsIndex] = statesAtPosTime[stateIndex] - observation[obsIndex]; + } + else if (obsIndex == 5) + { + innovVelPos[obsIndex] = statesAtHgtTime[stateIndex] - observation[obsIndex]; + } + // Calculate the Kalman Gain + // Calculate innovation variances - also used for data logging + varInnovVelPos[obsIndex] = P[stateIndex][stateIndex] + R_OBS[obsIndex]; + SK = 1.0/varInnovVelPos[obsIndex]; + for (uint8_t i= 0; i<=indexLimit; i++) + { + Kfusion[i] = P[i][stateIndex]*SK; + } + // Calculate state corrections and re-normalise the quaternions + for (uint8_t i = 0; i<=indexLimit; i++) + { + states[i] = states[i] - Kfusion[i] * innovVelPos[obsIndex]; + } + quatMag = sqrt(states[0]*states[0] + states[1]*states[1] + states[2]*states[2] + states[3]*states[3]); + if (quatMag > 1e-12f) // divide by 0 protection + { + for (uint8_t i = 0; i<=3; i++) + { + states[i] = states[i] / quatMag; + } + } + // Update the covariance - take advantage of direct observation of a + // single state at index = stateIndex to reduce computations + // Optimised implementation of standard equation P = (I - K*H)*P; + for (uint8_t i= 0; i<=indexLimit; i++) + { + for (uint8_t j= 0; j<=indexLimit; j++) + { + KHP[i][j] = Kfusion[i] * P[stateIndex][j]; + } + } + for (uint8_t i= 0; i<=indexLimit; i++) + { + for (uint8_t j= 0; j<=indexLimit; j++) + { + P[i][j] = P[i][j] - KHP[i][j]; + } + } + } + } + } + + ForceSymmetry(); + ConstrainVariances(); + + //printf("velh: %s, posh: %s, hgth: %s\n", ((velHealth) ? "OK" : "FAIL"), ((posHealth) ? "OK" : "FAIL"), ((hgtHealth) ? "OK" : "FAIL")); +} + +void AttPosEKF::FuseMagnetometer() +{ + uint8_t obsIndex; + uint8_t indexLimit; + float DCM[3][3] = + { + {1.0f,0.0f,0.0f} , + {0.0f,1.0f,0.0f} , + {0.0f,0.0f,1.0f} + }; + float MagPred[3] = {0.0f,0.0f,0.0f}; + float SK_MX[6]; + float SK_MY[5]; + float SK_MZ[6]; + float SH_MAG[9] = {0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f}; + +// Perform sequential fusion of Magnetometer measurements. +// This assumes that the errors in the different components are +// uncorrelated which is not true, however in the absence of covariance +// data fit is the only assumption we can make +// so we might as well take advantage of the computational efficiencies +// associated with sequential fusion + if (useCompass && (fuseMagData || obsIndex == 1 || obsIndex == 2)) + { + // Limit range of states modified when on ground + if(!onGround) + { + indexLimit = 20; + } + else + { + indexLimit = 12; + } + + static float q0 = 0.0f; + static float q1 = 0.0f; + static float q2 = 0.0f; + static float q3 = 1.0f; + static float magN = 0.4f; + static float magE = 0.0f; + static float magD = 0.3f; + + static float R_MAG = 0.0025f; + + float H_MAG[21] = {0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f}; + + // Sequential fusion of XYZ components to spread processing load across + // three prediction time steps. + + // Calculate observation jacobians and Kalman gains + if (fuseMagData) + { + static float magXbias = 0.0f; + static float magYbias = 0.0f; + static float magZbias = 0.0f; + + // Copy required states to local variable names + q0 = statesAtMagMeasTime[0]; + q1 = statesAtMagMeasTime[1]; + q2 = statesAtMagMeasTime[2]; + q3 = statesAtMagMeasTime[3]; + magN = statesAtMagMeasTime[15]; + magE = statesAtMagMeasTime[16]; + magD = statesAtMagMeasTime[17]; + magXbias = statesAtMagMeasTime[18]; + magYbias = statesAtMagMeasTime[19]; + magZbias = statesAtMagMeasTime[20]; + + // rotate predicted earth components into body axes and calculate + // predicted measurments + DCM[0][0] = q0*q0 + q1*q1 - q2*q2 - q3*q3; + DCM[0][1] = 2*(q1*q2 + q0*q3); + DCM[0][2] = 2*(q1*q3-q0*q2); + DCM[1][0] = 2*(q1*q2 - q0*q3); + DCM[1][1] = q0*q0 - q1*q1 + q2*q2 - q3*q3; + DCM[1][2] = 2*(q2*q3 + q0*q1); + DCM[2][0] = 2*(q1*q3 + q0*q2); + DCM[2][1] = 2*(q2*q3 - q0*q1); + DCM[2][2] = q0*q0 - q1*q1 - q2*q2 + q3*q3; + MagPred[0] = DCM[0][0]*magN + DCM[0][1]*magE + DCM[0][2]*magD + magXbias; + MagPred[1] = DCM[1][0]*magN + DCM[1][1]*magE + DCM[1][2]*magD + magYbias; + MagPred[2] = DCM[2][0]*magN + DCM[2][1]*magE + DCM[2][2]*magD + magZbias; + + // scale magnetometer observation error with total angular rate + R_MAG = 0.0025f + sq(0.05f*dAngIMU.length()/dtIMU); + + // Calculate observation jacobians + SH_MAG[0] = 2*magD*q3 + 2*magE*q2 + 2*magN*q1; + SH_MAG[1] = 2*magD*q0 - 2*magE*q1 + 2*magN*q2; + SH_MAG[2] = 2*magD*q1 + 2*magE*q0 - 2*magN*q3; + SH_MAG[3] = sq(q3); + SH_MAG[4] = sq(q2); + SH_MAG[5] = sq(q1); + SH_MAG[6] = sq(q0); + SH_MAG[7] = 2*magN*q0; + SH_MAG[8] = 2*magE*q3; + + for (uint8_t i=0; i<=20; i++) H_MAG[i] = 0; + H_MAG[0] = SH_MAG[7] + SH_MAG[8] - 2*magD*q2; + H_MAG[1] = SH_MAG[0]; + H_MAG[2] = 2*magE*q1 - 2*magD*q0 - 2*magN*q2; + H_MAG[3] = SH_MAG[2]; + H_MAG[15] = SH_MAG[5] - SH_MAG[4] - SH_MAG[3] + SH_MAG[6]; + H_MAG[16] = 2*q0*q3 + 2*q1*q2; + H_MAG[17] = 2*q1*q3 - 2*q0*q2; + H_MAG[18] = 1.0f; + + // Calculate Kalman gain + SK_MX[0] = 1/(P[18][18] + R_MAG + P[1][18]*SH_MAG[0] + P[3][18]*SH_MAG[2] - P[15][18]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) - (2*magD*q0 - 2*magE*q1 + 2*magN*q2)*(P[18][2] + P[1][2]*SH_MAG[0] + P[3][2]*SH_MAG[2] - P[15][2]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[16][2]*(2*q0*q3 + 2*q1*q2) - P[17][2]*(2*q0*q2 - 2*q1*q3) - P[2][2]*(2*magD*q0 - 2*magE*q1 + 2*magN*q2) + P[0][2]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + (SH_MAG[7] + SH_MAG[8] - 2*magD*q2)*(P[18][0] + P[1][0]*SH_MAG[0] + P[3][0]*SH_MAG[2] - P[15][0]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[16][0]*(2*q0*q3 + 2*q1*q2) - P[17][0]*(2*q0*q2 - 2*q1*q3) - P[2][0]*(2*magD*q0 - 2*magE*q1 + 2*magN*q2) + P[0][0]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + SH_MAG[0]*(P[18][1] + P[1][1]*SH_MAG[0] + P[3][1]*SH_MAG[2] - P[15][1]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[16][1]*(2*q0*q3 + 2*q1*q2) - P[17][1]*(2*q0*q2 - 2*q1*q3) - P[2][1]*(2*magD*q0 - 2*magE*q1 + 2*magN*q2) + P[0][1]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + SH_MAG[2]*(P[18][3] + P[1][3]*SH_MAG[0] + P[3][3]*SH_MAG[2] - P[15][3]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[16][3]*(2*q0*q3 + 2*q1*q2) - P[17][3]*(2*q0*q2 - 2*q1*q3) - P[2][3]*(2*magD*q0 - 2*magE*q1 + 2*magN*q2) + P[0][3]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) - (SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6])*(P[18][15] + P[1][15]*SH_MAG[0] + P[3][15]*SH_MAG[2] - P[15][15]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[16][15]*(2*q0*q3 + 2*q1*q2) - P[17][15]*(2*q0*q2 - 2*q1*q3) - P[2][15]*(2*magD*q0 - 2*magE*q1 + 2*magN*q2) + P[0][15]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + P[16][18]*(2*q0*q3 + 2*q1*q2) - P[17][18]*(2*q0*q2 - 2*q1*q3) - P[2][18]*(2*magD*q0 - 2*magE*q1 + 2*magN*q2) + (2*q0*q3 + 2*q1*q2)*(P[18][16] + P[1][16]*SH_MAG[0] + P[3][16]*SH_MAG[2] - P[15][16]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[16][16]*(2*q0*q3 + 2*q1*q2) - P[17][16]*(2*q0*q2 - 2*q1*q3) - P[2][16]*(2*magD*q0 - 2*magE*q1 + 2*magN*q2) + P[0][16]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) - (2*q0*q2 - 2*q1*q3)*(P[18][17] + P[1][17]*SH_MAG[0] + P[3][17]*SH_MAG[2] - P[15][17]*(SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]) + P[16][17]*(2*q0*q3 + 2*q1*q2) - P[17][17]*(2*q0*q2 - 2*q1*q3) - P[2][17]*(2*magD*q0 - 2*magE*q1 + 2*magN*q2) + P[0][17]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)) + P[0][18]*(SH_MAG[7] + SH_MAG[8] - 2*magD*q2)); + SK_MX[1] = SH_MAG[3] + SH_MAG[4] - SH_MAG[5] - SH_MAG[6]; + SK_MX[2] = 2*magD*q0 - 2*magE*q1 + 2*magN*q2; + SK_MX[3] = SH_MAG[7] + SH_MAG[8] - 2*magD*q2; + SK_MX[4] = 2*q0*q2 - 2*q1*q3; + SK_MX[5] = 2*q0*q3 + 2*q1*q2; + Kfusion[0] = SK_MX[0]*(P[0][18] + P[0][1]*SH_MAG[0] + P[0][3]*SH_MAG[2] + P[0][0]*SK_MX[3] - P[0][2]*SK_MX[2] - P[0][15]*SK_MX[1] + P[0][16]*SK_MX[5] - P[0][17]*SK_MX[4]); + Kfusion[1] = SK_MX[0]*(P[1][18] + P[1][1]*SH_MAG[0] + P[1][3]*SH_MAG[2] + P[1][0]*SK_MX[3] - P[1][2]*SK_MX[2] - P[1][15]*SK_MX[1] + P[1][16]*SK_MX[5] - P[1][17]*SK_MX[4]); + Kfusion[2] = SK_MX[0]*(P[2][18] + P[2][1]*SH_MAG[0] + P[2][3]*SH_MAG[2] + P[2][0]*SK_MX[3] - P[2][2]*SK_MX[2] - P[2][15]*SK_MX[1] + P[2][16]*SK_MX[5] - P[2][17]*SK_MX[4]); + Kfusion[3] = SK_MX[0]*(P[3][18] + P[3][1]*SH_MAG[0] + P[3][3]*SH_MAG[2] + P[3][0]*SK_MX[3] - P[3][2]*SK_MX[2] - P[3][15]*SK_MX[1] + P[3][16]*SK_MX[5] - P[3][17]*SK_MX[4]); + Kfusion[4] = SK_MX[0]*(P[4][18] + P[4][1]*SH_MAG[0] + P[4][3]*SH_MAG[2] + P[4][0]*SK_MX[3] - P[4][2]*SK_MX[2] - P[4][15]*SK_MX[1] + P[4][16]*SK_MX[5] - P[4][17]*SK_MX[4]); + Kfusion[5] = SK_MX[0]*(P[5][18] + P[5][1]*SH_MAG[0] + P[5][3]*SH_MAG[2] + P[5][0]*SK_MX[3] - P[5][2]*SK_MX[2] - P[5][15]*SK_MX[1] + P[5][16]*SK_MX[5] - P[5][17]*SK_MX[4]); + Kfusion[6] = SK_MX[0]*(P[6][18] + P[6][1]*SH_MAG[0] + P[6][3]*SH_MAG[2] + P[6][0]*SK_MX[3] - P[6][2]*SK_MX[2] - P[6][15]*SK_MX[1] + P[6][16]*SK_MX[5] - P[6][17]*SK_MX[4]); + Kfusion[7] = SK_MX[0]*(P[7][18] + P[7][1]*SH_MAG[0] + P[7][3]*SH_MAG[2] + P[7][0]*SK_MX[3] - P[7][2]*SK_MX[2] - P[7][15]*SK_MX[1] + P[7][16]*SK_MX[5] - P[7][17]*SK_MX[4]); + Kfusion[8] = SK_MX[0]*(P[8][18] + P[8][1]*SH_MAG[0] + P[8][3]*SH_MAG[2] + P[8][0]*SK_MX[3] - P[8][2]*SK_MX[2] - P[8][15]*SK_MX[1] + P[8][16]*SK_MX[5] - P[8][17]*SK_MX[4]); + Kfusion[9] = SK_MX[0]*(P[9][18] + P[9][1]*SH_MAG[0] + P[9][3]*SH_MAG[2] + P[9][0]*SK_MX[3] - P[9][2]*SK_MX[2] - P[9][15]*SK_MX[1] + P[9][16]*SK_MX[5] - P[9][17]*SK_MX[4]); + Kfusion[10] = SK_MX[0]*(P[10][18] + P[10][1]*SH_MAG[0] + P[10][3]*SH_MAG[2] + P[10][0]*SK_MX[3] - P[10][2]*SK_MX[2] - P[10][15]*SK_MX[1] + P[10][16]*SK_MX[5] - P[10][17]*SK_MX[4]); + Kfusion[11] = SK_MX[0]*(P[11][18] + P[11][1]*SH_MAG[0] + P[11][3]*SH_MAG[2] + P[11][0]*SK_MX[3] - P[11][2]*SK_MX[2] - P[11][15]*SK_MX[1] + P[11][16]*SK_MX[5] - P[11][17]*SK_MX[4]); + Kfusion[12] = SK_MX[0]*(P[12][18] + P[12][1]*SH_MAG[0] + P[12][3]*SH_MAG[2] + P[12][0]*SK_MX[3] - P[12][2]*SK_MX[2] - P[12][15]*SK_MX[1] + P[12][16]*SK_MX[5] - P[12][17]*SK_MX[4]); + Kfusion[13] = SK_MX[0]*(P[13][18] + P[13][1]*SH_MAG[0] + P[13][3]*SH_MAG[2] + P[13][0]*SK_MX[3] - P[13][2]*SK_MX[2] - P[13][15]*SK_MX[1] + P[13][16]*SK_MX[5] - P[13][17]*SK_MX[4]); + Kfusion[14] = SK_MX[0]*(P[14][18] + P[14][1]*SH_MAG[0] + P[14][3]*SH_MAG[2] + P[14][0]*SK_MX[3] - P[14][2]*SK_MX[2] - P[14][15]*SK_MX[1] + P[14][16]*SK_MX[5] - P[14][17]*SK_MX[4]); + Kfusion[15] = SK_MX[0]*(P[15][18] + P[15][1]*SH_MAG[0] + P[15][3]*SH_MAG[2] + P[15][0]*SK_MX[3] - P[15][2]*SK_MX[2] - P[15][15]*SK_MX[1] + P[15][16]*SK_MX[5] - P[15][17]*SK_MX[4]); + Kfusion[16] = SK_MX[0]*(P[16][18] + P[16][1]*SH_MAG[0] + P[16][3]*SH_MAG[2] + P[16][0]*SK_MX[3] - P[16][2]*SK_MX[2] - P[16][15]*SK_MX[1] + P[16][16]*SK_MX[5] - P[16][17]*SK_MX[4]); + Kfusion[17] = SK_MX[0]*(P[17][18] + P[17][1]*SH_MAG[0] + P[17][3]*SH_MAG[2] + P[17][0]*SK_MX[3] - P[17][2]*SK_MX[2] - P[17][15]*SK_MX[1] + P[17][16]*SK_MX[5] - P[17][17]*SK_MX[4]); + Kfusion[18] = SK_MX[0]*(P[18][18] + P[18][1]*SH_MAG[0] + P[18][3]*SH_MAG[2] + P[18][0]*SK_MX[3] - P[18][2]*SK_MX[2] - P[18][15]*SK_MX[1] + P[18][16]*SK_MX[5] - P[18][17]*SK_MX[4]); + Kfusion[19] = SK_MX[0]*(P[19][18] + P[19][1]*SH_MAG[0] + P[19][3]*SH_MAG[2] + P[19][0]*SK_MX[3] - P[19][2]*SK_MX[2] - P[19][15]*SK_MX[1] + P[19][16]*SK_MX[5] - P[19][17]*SK_MX[4]); + Kfusion[20] = SK_MX[0]*(P[20][18] + P[20][1]*SH_MAG[0] + P[20][3]*SH_MAG[2] + P[20][0]*SK_MX[3] - P[20][2]*SK_MX[2] - P[20][15]*SK_MX[1] + P[20][16]*SK_MX[5] - P[20][17]*SK_MX[4]); + varInnovMag[0] = 1.0f/SK_MX[0]; + innovMag[0] = MagPred[0] - magData.x; + + // reset the observation index to 0 (we start by fusing the X + // measurement) + obsIndex = 0; + } + else if (obsIndex == 1) // we are now fusing the Y measurement + { + // Calculate observation jacobians + for (unsigned int i=0; i 5Sigma + if ((innovMag[obsIndex]*innovMag[obsIndex]/varInnovMag[obsIndex]) < 25.0) + { + // correct the state vector + for (uint8_t j= 0; j<=indexLimit; j++) + { + states[j] = states[j] - Kfusion[j] * innovMag[obsIndex]; + } + // normalise the quaternion states + float quatMag = sqrt(states[0]*states[0] + states[1]*states[1] + states[2]*states[2] + states[3]*states[3]); + if (quatMag > 1e-12) + { + for (uint8_t j= 0; j<=3; j++) + { + float quatMagInv = 1.0f/quatMag; + states[j] = states[j] * quatMagInv; + } + } + // correct the covariance P = (I - K*H)*P + // take advantage of the empty columns in KH to reduce the + // number of operations + for (uint8_t i = 0; i<=indexLimit; i++) + { + for (uint8_t j = 0; j<=3; j++) + { + KH[i][j] = Kfusion[i] * H_MAG[j]; + } + for (uint8_t j = 4; j<=17; j++) KH[i][j] = 0.0f; + if (!onGround) + { + for (uint8_t j = 15; j<=20; j++) + { + KH[i][j] = Kfusion[i] * H_MAG[j]; + } + } + else + { + for (uint8_t j = 15; j<=20; j++) + { + KH[i][j] = 0.0f; + } + } + } + for (uint8_t i = 0; i<=indexLimit; i++) + { + for (uint8_t j = 0; j<=indexLimit; j++) + { + KHP[i][j] = 0.0f; + for (uint8_t k = 0; k<=3; k++) + { + KHP[i][j] = KHP[i][j] + KH[i][k] * P[k][j]; + } + if (!onGround) + { + for (uint8_t k = 15; k<=20; k++) + { + KHP[i][j] = KHP[i][j] + KH[i][k] * P[k][j]; + } + } + } + } + } + for (uint8_t i = 0; i<=indexLimit; i++) + { + for (uint8_t j = 0; j<=indexLimit; j++) + { + P[i][j] = P[i][j] - KHP[i][j]; + } + } + } + obsIndex = obsIndex + 1; + + ForceSymmetry(); + ConstrainVariances(); +} + +void AttPosEKF::FuseAirspeed() +{ + float vn; + float ve; + float vd; + float vwn; + float vwe; + const float R_TAS = 2.0f; + float SH_TAS[3]; + float Kfusion[21]; + float VtasPred; + + // Copy required states to local variable names + vn = statesAtVtasMeasTime[4]; + ve = statesAtVtasMeasTime[5]; + vd = statesAtVtasMeasTime[6]; + vwn = statesAtVtasMeasTime[13]; + vwe = statesAtVtasMeasTime[14]; + + // Need to check that it is flying before fusing airspeed data + // Calculate the predicted airspeed + VtasPred = sqrtf((ve - vwe)*(ve - vwe) + (vn - vwn)*(vn - vwn) + vd*vd); + // Perform fusion of True Airspeed measurement + if (useAirspeed && fuseVtasData && (VtasPred > 1.0f) && (VtasMeas > 8.0f)) + { + // Calculate observation jacobians + SH_TAS[0] = 1/(sqrt(sq(ve - vwe) + sq(vn - vwn) + sq(vd))); + SH_TAS[1] = (SH_TAS[0]*(2.0f*ve - 2*vwe))/2.0f; + SH_TAS[2] = (SH_TAS[0]*(2.0f*vn - 2*vwn))/2.0f; + + float H_TAS[21]; + for (uint8_t i=0; i<=20; i++) H_TAS[i] = 0.0f; + H_TAS[4] = SH_TAS[2]; + H_TAS[5] = SH_TAS[1]; + H_TAS[6] = vd*SH_TAS[0]; + H_TAS[13] = -SH_TAS[2]; + H_TAS[14] = -SH_TAS[1]; + + // Calculate Kalman gains + float SK_TAS = 1.0f/(R_TAS + SH_TAS[2]*(P[4][4]*SH_TAS[2] + P[5][4]*SH_TAS[1] - P[13][4]*SH_TAS[2] - P[14][4]*SH_TAS[1] + P[6][4]*vd*SH_TAS[0]) + SH_TAS[1]*(P[4][5]*SH_TAS[2] + P[5][5]*SH_TAS[1] - P[13][5]*SH_TAS[2] - P[14][5]*SH_TAS[1] + P[6][5]*vd*SH_TAS[0]) - SH_TAS[2]*(P[4][13]*SH_TAS[2] + P[5][13]*SH_TAS[1] - P[13][13]*SH_TAS[2] - P[14][13]*SH_TAS[1] + P[6][13]*vd*SH_TAS[0]) - SH_TAS[1]*(P[4][14]*SH_TAS[2] + P[5][14]*SH_TAS[1] - P[13][14]*SH_TAS[2] - P[14][14]*SH_TAS[1] + P[6][14]*vd*SH_TAS[0]) + vd*SH_TAS[0]*(P[4][6]*SH_TAS[2] + P[5][6]*SH_TAS[1] - P[13][6]*SH_TAS[2] - P[14][6]*SH_TAS[1] + P[6][6]*vd*SH_TAS[0])); + Kfusion[0] = SK_TAS*(P[0][4]*SH_TAS[2] - P[0][13]*SH_TAS[2] + P[0][5]*SH_TAS[1] - P[0][14]*SH_TAS[1] + P[0][6]*vd*SH_TAS[0]); + Kfusion[1] = SK_TAS*(P[1][4]*SH_TAS[2] - P[1][13]*SH_TAS[2] + P[1][5]*SH_TAS[1] - P[1][14]*SH_TAS[1] + P[1][6]*vd*SH_TAS[0]); + Kfusion[2] = SK_TAS*(P[2][4]*SH_TAS[2] - P[2][13]*SH_TAS[2] + P[2][5]*SH_TAS[1] - P[2][14]*SH_TAS[1] + P[2][6]*vd*SH_TAS[0]); + Kfusion[3] = SK_TAS*(P[3][4]*SH_TAS[2] - P[3][13]*SH_TAS[2] + P[3][5]*SH_TAS[1] - P[3][14]*SH_TAS[1] + P[3][6]*vd*SH_TAS[0]); + Kfusion[4] = SK_TAS*(P[4][4]*SH_TAS[2] - P[4][13]*SH_TAS[2] + P[4][5]*SH_TAS[1] - P[4][14]*SH_TAS[1] + P[4][6]*vd*SH_TAS[0]); + Kfusion[5] = SK_TAS*(P[5][4]*SH_TAS[2] - P[5][13]*SH_TAS[2] + P[5][5]*SH_TAS[1] - P[5][14]*SH_TAS[1] + P[5][6]*vd*SH_TAS[0]); + Kfusion[6] = SK_TAS*(P[6][4]*SH_TAS[2] - P[6][13]*SH_TAS[2] + P[6][5]*SH_TAS[1] - P[6][14]*SH_TAS[1] + P[6][6]*vd*SH_TAS[0]); + Kfusion[7] = SK_TAS*(P[7][4]*SH_TAS[2] - P[7][13]*SH_TAS[2] + P[7][5]*SH_TAS[1] - P[7][14]*SH_TAS[1] + P[7][6]*vd*SH_TAS[0]); + Kfusion[8] = SK_TAS*(P[8][4]*SH_TAS[2] - P[8][13]*SH_TAS[2] + P[8][5]*SH_TAS[1] - P[8][14]*SH_TAS[1] + P[8][6]*vd*SH_TAS[0]); + Kfusion[9] = SK_TAS*(P[9][4]*SH_TAS[2] - P[9][13]*SH_TAS[2] + P[9][5]*SH_TAS[1] - P[9][14]*SH_TAS[1] + P[9][6]*vd*SH_TAS[0]); + Kfusion[10] = SK_TAS*(P[10][4]*SH_TAS[2] - P[10][13]*SH_TAS[2] + P[10][5]*SH_TAS[1] - P[10][14]*SH_TAS[1] + P[10][6]*vd*SH_TAS[0]); + Kfusion[11] = SK_TAS*(P[11][4]*SH_TAS[2] - P[11][13]*SH_TAS[2] + P[11][5]*SH_TAS[1] - P[11][14]*SH_TAS[1] + P[11][6]*vd*SH_TAS[0]); + Kfusion[12] = SK_TAS*(P[12][4]*SH_TAS[2] - P[12][13]*SH_TAS[2] + P[12][5]*SH_TAS[1] - P[12][14]*SH_TAS[1] + P[12][6]*vd*SH_TAS[0]); + Kfusion[13] = SK_TAS*(P[13][4]*SH_TAS[2] - P[13][13]*SH_TAS[2] + P[13][5]*SH_TAS[1] - P[13][14]*SH_TAS[1] + P[13][6]*vd*SH_TAS[0]); + Kfusion[14] = SK_TAS*(P[14][4]*SH_TAS[2] - P[14][13]*SH_TAS[2] + P[14][5]*SH_TAS[1] - P[14][14]*SH_TAS[1] + P[14][6]*vd*SH_TAS[0]); + Kfusion[15] = SK_TAS*(P[15][4]*SH_TAS[2] - P[15][13]*SH_TAS[2] + P[15][5]*SH_TAS[1] - P[15][14]*SH_TAS[1] + P[15][6]*vd*SH_TAS[0]); + Kfusion[16] = SK_TAS*(P[16][4]*SH_TAS[2] - P[16][13]*SH_TAS[2] + P[16][5]*SH_TAS[1] - P[16][14]*SH_TAS[1] + P[16][6]*vd*SH_TAS[0]); + Kfusion[17] = SK_TAS*(P[17][4]*SH_TAS[2] - P[17][13]*SH_TAS[2] + P[17][5]*SH_TAS[1] - P[17][14]*SH_TAS[1] + P[17][6]*vd*SH_TAS[0]); + Kfusion[18] = SK_TAS*(P[18][4]*SH_TAS[2] - P[18][13]*SH_TAS[2] + P[18][5]*SH_TAS[1] - P[18][14]*SH_TAS[1] + P[18][6]*vd*SH_TAS[0]); + Kfusion[19] = SK_TAS*(P[19][4]*SH_TAS[2] - P[19][13]*SH_TAS[2] + P[19][5]*SH_TAS[1] - P[19][14]*SH_TAS[1] + P[19][6]*vd*SH_TAS[0]); + Kfusion[20] = SK_TAS*(P[20][4]*SH_TAS[2] - P[20][13]*SH_TAS[2] + P[20][5]*SH_TAS[1] - P[20][14]*SH_TAS[1] + P[20][6]*vd*SH_TAS[0]); + varInnovVtas = 1.0f/SK_TAS; + + // Calculate the measurement innovation + innovVtas = VtasPred - VtasMeas; + // Check the innovation for consistency and don't fuse if > 5Sigma + if ((innovVtas*innovVtas*SK_TAS) < 25.0) + { + // correct the state vector + for (uint8_t j=0; j<=20; j++) + { + states[j] = states[j] - Kfusion[j] * innovVtas; + } + // normalise the quaternion states + float quatMag = sqrt(states[0]*states[0] + states[1]*states[1] + states[2]*states[2] + states[3]*states[3]); + if (quatMag > 1e-12f) + { + for (uint8_t j= 0; j<=3; j++) + { + float quatMagInv = 1.0f/quatMag; + states[j] = states[j] * quatMagInv; + } + } + // correct the covariance P = (I - K*H)*P + // take advantage of the empty columns in H to reduce the + // number of operations + for (uint8_t i = 0; i<=20; i++) + { + for (uint8_t j = 0; j<=3; j++) KH[i][j] = 0.0; + for (uint8_t j = 4; j<=6; j++) + { + KH[i][j] = Kfusion[i] * H_TAS[j]; + } + for (uint8_t j = 7; j<=12; j++) KH[i][j] = 0.0; + for (uint8_t j = 13; j<=14; j++) + { + KH[i][j] = Kfusion[i] * H_TAS[j]; + } + for (uint8_t j = 15; j<=20; j++) KH[i][j] = 0.0; + } + for (uint8_t i = 0; i<=20; i++) + { + for (uint8_t j = 0; j<=20; j++) + { + KHP[i][j] = 0.0; + for (uint8_t k = 4; k<=6; k++) + { + KHP[i][j] = KHP[i][j] + KH[i][k] * P[k][j]; + } + for (uint8_t k = 13; k<=14; k++) + { + KHP[i][j] = KHP[i][j] + KH[i][k] * P[k][j]; + } + } + } + for (uint8_t i = 0; i<=20; i++) + { + for (uint8_t j = 0; j<=20; j++) + { + P[i][j] = P[i][j] - KHP[i][j]; + } + } + } + } + + ForceSymmetry(); + ConstrainVariances(); +} + +void AttPosEKF::zeroRows(float (&covMat)[n_states][n_states], uint8_t first, uint8_t last) +{ + uint8_t row; + uint8_t col; + for (row=first; row<=last; row++) + { + for (col=0; col GPS_FIX_2D); + } +} + +void AttPosEKF::calcEarthRateNED(Vector3f &omega, float latitude) +{ + //Define Earth rotation vector in the NED navigation frame + omega.x = earthRate*cosf(latitude); + omega.y = 0.0f; + omega.z = -earthRate*sinf(latitude); +} + +void AttPosEKF::CovarianceInit() +{ + // Calculate the initial covariance matrix P + P[0][0] = 0.25f * sq(1.0f*deg2rad); + P[1][1] = 0.25f * sq(1.0f*deg2rad); + P[2][2] = 0.25f * sq(1.0f*deg2rad); + P[3][3] = 0.25f * sq(10.0f*deg2rad); + P[4][4] = sq(0.7); + P[5][5] = P[4][4]; + P[6][6] = sq(0.7); + P[7][7] = sq(15.0); + P[8][8] = P[7][7]; + P[9][9] = sq(5.0); + P[10][10] = sq(0.1*deg2rad*dtIMU); + P[11][11] = P[10][10]; + P[12][12] = P[10][10]; + P[13][13] = sq(8.0f); + P[14][4] = P[13][13]; + P[15][15] = sq(0.02f); + P[16][16] = P[15][15]; + P[17][17] = P[15][15]; + P[18][18] = sq(0.02f); + P[19][19] = P[18][18]; + P[20][20] = P[18][18]; +} + +float AttPosEKF::ConstrainFloat(float val, float min, float max) +{ + return (val > max) ? max : ((val < min) ? min : val); +} + +void AttPosEKF::ConstrainVariances() +{ + if (!numericalProtection) { + return; + } + + // State vector: + // 0-3: quaternions (q0, q1, q2, q3) + // 4-6: Velocity - m/sec (North, East, Down) + // 7-9: Position - m (North, East, Down) + // 10-12: Delta Angle bias - rad (X,Y,Z) + // 13-14: Wind Vector - m/sec (North,East) + // 15-17: Earth Magnetic Field Vector - gauss (North, East, Down) + // 18-20: Body Magnetic Field Vector - gauss (X,Y,Z) + + // Constrain quaternion variances + for (unsigned i = 0; i < 4; i++) { + P[i][i] = ConstrainFloat(P[i][i], 0.0f, 1.0f); + } + + // Constrain velocitie variances + for (unsigned i = 4; i < 7; i++) { + P[i][i] = ConstrainFloat(P[i][i], 0.0f, 1.0e3f); + } + + // Constrain position variances + for (unsigned i = 7; i < 10; i++) { + P[i][i] = ConstrainFloat(P[i][i], 0.0f, 1.0e6f); + } + + // Angle bias variances + for (unsigned i = 10; i < 13; i++) { + P[i][i] = ConstrainFloat(P[i][i], 0.0f, sq(0.175f * dtIMU)); + } + + // Wind velocity variances + for (unsigned i = 13; i < 15; i++) { + P[i][i] = ConstrainFloat(P[i][i], 0.0f, 1.0e3f); + } + + // Earth magnetic field variances + for (unsigned i = 15; i < 18; i++) { + P[i][i] = ConstrainFloat(P[i][i], 0.0f, 1.0f); + } + + // Body magnetic field variances + for (unsigned i = 18; i < 21; i++) { + P[i][i] = ConstrainFloat(P[i][i], 0.0f, 1.0f); + } + +} + +void AttPosEKF::ConstrainStates() +{ + if (!numericalProtection) { + return; + } + + // State vector: + // 0-3: quaternions (q0, q1, q2, q3) + // 4-6: Velocity - m/sec (North, East, Down) + // 7-9: Position - m (North, East, Down) + // 10-12: Delta Angle bias - rad (X,Y,Z) + // 13-14: Wind Vector - m/sec (North,East) + // 15-17: Earth Magnetic Field Vector - gauss (North, East, Down) + // 18-20: Body Magnetic Field Vector - gauss (X,Y,Z) + + + // Constrain quaternion + for (unsigned i = 0; i < 4; i++) { + states[i] = ConstrainFloat(states[i], -1.0f, 1.0f); + } + + // Constrain velocities to what GPS can do for us + for (unsigned i = 4; i < 7; i++) { + states[i] = ConstrainFloat(states[i], -5.0e2f, 5.0e2f); + } + + // Constrain position to a reasonable vehicle range (in meters) + for (unsigned i = 7; i < 9; i++) { + states[i] = ConstrainFloat(states[i], -1.0e6f, 1.0e6f); + } + + // Constrain altitude + states[9] = ConstrainFloat(states[9], -4.0e4f, 1.0e4f); + + // Angle bias limit - set to 8 degrees / sec + for (unsigned i = 10; i < 13; i++) { + states[i] = ConstrainFloat(states[i], -0.12f * dtIMU, 0.12f * dtIMU); + } + + // Wind velocity limits - assume 120 m/s max velocity + for (unsigned i = 13; i < 15; i++) { + states[i] = ConstrainFloat(states[i], -120.0f, 120.0f); + } + + // Earth magnetic field limits (in Gauss) + for (unsigned i = 15; i < 18; i++) { + states[i] = ConstrainFloat(states[i], -1.0f, 1.0f); + } + + // Body magnetic field variances (in Gauss). + // the max offset should be in this range. + for (unsigned i = 18; i < 21; i++) { + states[i] = ConstrainFloat(states[i], -0.5f, 0.5f); + } + +} + +void AttPosEKF::ForceSymmetry() +{ + if (!numericalProtection) { + return; + } + + // Force symmetry on the covariance matrix to prevent ill-conditioning + // of the matrix which would cause the filter to blow-up + for (unsigned i = 1; i < n_states; i++) + { + for (uint8_t j = 0; j < i; j++) + { + P[i][j] = 0.5f * (P[i][j] + P[j][i]); + P[j][i] = P[i][j]; + } + } +} + +bool AttPosEKF::FilterHealthy() +{ + if (!statesInitialised) { + return false; + } + + // XXX Check state vector for NaNs and ill-conditioning + + // Check if any of the major inputs timed out + if (current_ekf_state.posTimeout || current_ekf_state.velTimeout || current_ekf_state.hgtTimeout) { + return false; + } + + // Nothing fired, return ok. + return true; +} + +/** + * Reset the filter position states + * + * This resets the position to the last GPS measurement + * or to zero in case of static position. + */ +void AttPosEKF::ResetPosition(void) +{ + if (staticMode) { + states[7] = 0; + states[8] = 0; + } else if (GPSstatus >= GPS_FIX_3D) { + + // reset the states from the GPS measurements + states[7] = posNE[0]; + states[8] = posNE[1]; + } +} + +/** + * Reset the height state. + * + * This resets the height state with the last altitude measurements + */ +void AttPosEKF::ResetHeight(void) +{ + // write to the state vector + states[9] = -hgtMea; +} + +/** + * Reset the velocity state. + */ +void AttPosEKF::ResetVelocity(void) +{ + if (staticMode) { + states[4] = 0.0f; + states[5] = 0.0f; + states[6] = 0.0f; + } else if (GPSstatus >= GPS_FIX_3D) { + + states[4] = velNED[0]; // north velocity from last reading + states[5] = velNED[1]; // east velocity from last reading + states[6] = velNED[2]; // down velocity from last reading + } +} + + +void AttPosEKF::FillErrorReport(struct ekf_status_report *err) +{ + for (int i = 0; i < n_states; i++) + { + err->states[i] = states[i]; + } + + err->velHealth = current_ekf_state.velHealth; + err->posHealth = current_ekf_state.posHealth; + err->hgtHealth = current_ekf_state.hgtHealth; + err->velTimeout = current_ekf_state.velTimeout; + err->posTimeout = current_ekf_state.posTimeout; + err->hgtTimeout = current_ekf_state.hgtTimeout; +} + +bool AttPosEKF::StatesNaN(struct ekf_status_report *err_report) { + bool err = false; + + // check all states and covariance matrices + for (unsigned i = 0; i < n_states; i++) { + for (unsigned j = 0; j < n_states; j++) { + if (!isfinite(KH[i][j])) { + + err_report->covarianceNaN = true; + err = true; + } // intermediate result used for covariance updates + if (!isfinite(KHP[i][j])) { + + err_report->covarianceNaN = true; + err = true; + } // intermediate result used for covariance updates + if (!isfinite(P[i][j])) { + + err_report->covarianceNaN = true; + err = true; + } // covariance matrix + } + + if (!isfinite(Kfusion[i])) { + + err_report->kalmanGainsNaN = true; + err = true; + } // Kalman gains + + if (!isfinite(states[i])) { + + err_report->statesNaN = true; + err = true; + } // state matrix + } + + if (err) { + FillErrorReport(err_report); + } + + return err; + +} + +/** + * Check the filter inputs and bound its operational state + * + * This check will reset the filter states if required + * due to a failure of consistency or timeout checks. + * it should be run after the measurement data has been + * updated, but before any of the fusion steps are + * executed. + */ +int AttPosEKF::CheckAndBound() +{ + + // Store the old filter state + bool currStaticMode = staticMode; + + // Reset the filter if the states went NaN + if (StatesNaN(&last_ekf_error)) { + + InitializeDynamic(velNED, magDeclination); + + return 1; + } + + // Reset the filter if the IMU data is too old + if (dtIMU > 0.2f) { + + ResetVelocity(); + ResetPosition(); + ResetHeight(); + ResetStoredStates(); + + // that's all we can do here, return + return 2; + } + + // Check if we're on ground - this also sets static mode. + OnGroundCheck(); + + // Check if we switched between states + if (currStaticMode != staticMode) { + ResetVelocity(); + ResetPosition(); + ResetHeight(); + ResetStoredStates(); + + return 3; + } + + return 0; +} + +void AttPosEKF::AttitudeInit(float ax, float ay, float az, float mx, float my, float mz, float declination, float *initQuat) +{ + float initialRoll, initialPitch; + float cosRoll, sinRoll, cosPitch, sinPitch; + float magX, magY; + float initialHdg, cosHeading, sinHeading; + + initialRoll = atan2(-ay, -az); + initialPitch = atan2(ax, -az); + + cosRoll = cosf(initialRoll); + sinRoll = sinf(initialRoll); + cosPitch = cosf(initialPitch); + sinPitch = sinf(initialPitch); + + magX = mx * cosPitch + my * sinRoll * sinPitch + mz * cosRoll * sinPitch; + + magY = my * cosRoll - mz * sinRoll; + + initialHdg = atan2f(-magY, magX); + /* true heading is the mag heading minus declination */ + initialHdg += declination; + + cosRoll = cosf(initialRoll * 0.5f); + sinRoll = sinf(initialRoll * 0.5f); + + cosPitch = cosf(initialPitch * 0.5f); + sinPitch = sinf(initialPitch * 0.5f); + + cosHeading = cosf(initialHdg * 0.5f); + sinHeading = sinf(initialHdg * 0.5f); + + initQuat[0] = cosRoll * cosPitch * cosHeading + sinRoll * sinPitch * sinHeading; + initQuat[1] = sinRoll * cosPitch * cosHeading - cosRoll * sinPitch * sinHeading; + initQuat[2] = cosRoll * sinPitch * cosHeading + sinRoll * cosPitch * sinHeading; + initQuat[3] = cosRoll * cosPitch * sinHeading - sinRoll * sinPitch * cosHeading; +} + +void AttPosEKF::InitializeDynamic(float (&initvelNED)[3], float declination) +{ + + // Clear the init flag + statesInitialised = false; + + magDeclination = declination; + + ZeroVariables(); + + // Calculate initial filter quaternion states from raw measurements + float initQuat[4]; + Vector3f initMagXYZ; + initMagXYZ = magData - magBias; + AttitudeInit(accel.x, accel.y, accel.z, initMagXYZ.x, initMagXYZ.y, initMagXYZ.z, magDeclination, initQuat); + + // Calculate initial Tbn matrix and rotate Mag measurements into NED + // to set initial NED magnetic field states + Mat3f DCM; + quat2Tbn(DCM, initQuat); + Vector3f initMagNED; + initMagXYZ = magData - magBias; + initMagNED.x = DCM.x.x*initMagXYZ.x + DCM.x.y*initMagXYZ.y + DCM.x.z*initMagXYZ.z; + initMagNED.y = DCM.y.x*initMagXYZ.x + DCM.y.y*initMagXYZ.y + DCM.y.z*initMagXYZ.z; + initMagNED.z = DCM.z.x*initMagXYZ.x + DCM.z.y*initMagXYZ.y + DCM.z.z*initMagXYZ.z; + + + + // write to state vector + for (uint8_t j=0; j<=3; j++) states[j] = initQuat[j]; // quaternions + for (uint8_t j=0; j<=2; j++) states[j+4] = initvelNED[j]; // velocities + for (uint8_t j=0; j<=7; j++) states[j+7] = 0.0f; // positiions, dAngBias, windVel + states[15] = initMagNED.x; // Magnetic Field North + states[16] = initMagNED.y; // Magnetic Field East + states[17] = initMagNED.z; // Magnetic Field Down + states[18] = magBias.x; // Magnetic Field Bias X + states[19] = magBias.y; // Magnetic Field Bias Y + states[20] = magBias.z; // Magnetic Field Bias Z + + statesInitialised = true; + + // initialise the covariance matrix + CovarianceInit(); + + //Define Earth rotation vector in the NED navigation frame + calcEarthRateNED(earthRateNED, latRef); + + //Initialise summed variables used by covariance prediction + summedDelAng.x = 0.0f; + summedDelAng.y = 0.0f; + summedDelAng.z = 0.0f; + summedDelVel.x = 0.0f; + summedDelVel.y = 0.0f; + summedDelVel.z = 0.0f; +} + +void AttPosEKF::InitialiseFilter(float (&initvelNED)[3], double referenceLat, double referenceLon, float referenceHgt, float declination) +{ + //store initial lat,long and height + latRef = referenceLat; + lonRef = referenceLon; + hgtRef = referenceHgt; + + memset(&last_ekf_error, 0, sizeof(last_ekf_error)); + + InitializeDynamic(initvelNED, declination); +} + +void AttPosEKF::ZeroVariables() +{ + // Do the data structure init + for (unsigned i = 0; i < n_states; i++) { + for (unsigned j = 0; j < n_states; j++) { + KH[i][j] = 0.0f; // intermediate result used for covariance updates + KHP[i][j] = 0.0f; // intermediate result used for covariance updates + P[i][j] = 0.0f; // covariance matrix + } + + Kfusion[i] = 0.0f; // Kalman gains + states[i] = 0.0f; // state matrix + } + + for (unsigned i = 0; i < data_buffer_size; i++) { + + for (unsigned j = 0; j < n_states; j++) { + storedStates[j][i] = 0.0f; + } + + statetimeStamp[i] = 0; + } + + memset(¤t_ekf_state, 0, sizeof(current_ekf_state)); +} + +void AttPosEKF::GetFilterState(struct ekf_status_report *state) +{ + memcpy(state, ¤t_ekf_state, sizeof(state)); +} + +void AttPosEKF::GetLastErrorState(struct ekf_status_report *last_error) +{ + memcpy(last_error, &last_ekf_error, sizeof(last_error)); +} diff --git a/src/modules/ekf_att_pos_estimator/estimator_21states.h b/src/modules/ekf_att_pos_estimator/estimator_21states.h new file mode 100644 index 0000000000..a19ff19952 --- /dev/null +++ b/src/modules/ekf_att_pos_estimator/estimator_21states.h @@ -0,0 +1,247 @@ +#pragma once + +#include "estimator_utilities.h" + +class AttPosEKF { + +public: + + AttPosEKF(); + ~AttPosEKF(); + + /* ############################################## + * + * M A I N F I L T E R P A R A M E T E R S + * + * ########################################### */ + + /* + * parameters are defined here and initialised in + * the InitialiseParameters() (which is just 20 lines down) + */ + + float covTimeStepMax; // maximum time allowed between covariance predictions + float covDelAngMax; // maximum delta angle between covariance predictions + float rngFinderPitch; // pitch angle of laser range finder in radians. Zero is aligned with the Z body axis. Positive is RH rotation about Y body axis. + + float yawVarScale; + float windVelSigma; + float dAngBiasSigma; + float dVelBiasSigma; + float magEarthSigma; + float magBodySigma; + float gndHgtSigma; + + float vneSigma; + float vdSigma; + float posNeSigma; + float posDSigma; + float magMeasurementSigma; + float airspeedMeasurementSigma; + + float gyroProcessNoise; + float accelProcessNoise; + + float EAS2TAS; // ratio f true to equivalent airspeed + + void InitialiseParameters() + { + covTimeStepMax = 0.07f; // maximum time allowed between covariance predictions + covDelAngMax = 0.02f; // maximum delta angle between covariance predictions + rngFinderPitch = 0.0f; // pitch angle of laser range finder in radians. Zero is aligned with the Z body axis. Positive is RH rotation about Y body axis. + EAS2TAS = 1.0f; + + yawVarScale = 1.0f; + windVelSigma = 0.1f; + dAngBiasSigma = 5.0e-7f; + dVelBiasSigma = 1e-4f; + magEarthSigma = 3.0e-4f; + magBodySigma = 3.0e-4f; + gndHgtSigma = 0.02f; // assume 2% terrain gradient 1-sigma + + vneSigma = 0.2f; + vdSigma = 0.3f; + posNeSigma = 2.0f; + posDSigma = 2.0f; + + magMeasurementSigma = 0.05; + airspeedMeasurementSigma = 1.4f; + gyroProcessNoise = 1.4544411e-2f; + accelProcessNoise = 0.5f; + } + + // Global variables + float KH[n_states][n_states]; // intermediate result used for covariance updates + float KHP[n_states][n_states]; // intermediate result used for covariance updates + float P[n_states][n_states]; // covariance matrix + float Kfusion[n_states]; // Kalman gains + float states[n_states]; // state matrix + float storedStates[n_states][data_buffer_size]; // state vectors stored for the last 50 time steps + uint32_t statetimeStamp[data_buffer_size]; // time stamp for each state vector stored + + float statesAtVelTime[n_states]; // States at the effective measurement time for posNE and velNED measurements + float statesAtPosTime[n_states]; // States at the effective measurement time for posNE and velNED measurements + float statesAtHgtTime[n_states]; // States at the effective measurement time for the hgtMea measurement + float statesAtMagMeasTime[n_states]; // filter satates at the effective measurement time + float statesAtVtasMeasTime[n_states]; // filter states at the effective measurement time + + Vector3f correctedDelAng; // delta angles about the xyz body axes corrected for errors (rad) + Vector3f correctedDelVel; // delta velocities along the XYZ body axes corrected for errors (m/s) + Vector3f summedDelAng; // summed delta angles about the xyz body axes corrected for errors (rad) + Vector3f summedDelVel; // summed delta velocities along the XYZ body axes corrected for errors (m/s) + float accNavMag; // magnitude of navigation accel (- used to adjust GPS obs variance (m/s^2) + Vector3f earthRateNED; // earths angular rate vector in NED (rad/s) + Vector3f angRate; // angular rate vector in XYZ body axes measured by the IMU (rad/s) + Vector3f accel; // acceleration vector in XYZ body axes measured by the IMU (m/s^2) + Vector3f dVelIMU; + Vector3f dAngIMU; + float dtIMU; // time lapsed since the last IMU measurement or covariance update (sec) + uint8_t fusionModeGPS; // 0 = GPS outputs 3D velocity, 1 = GPS outputs 2D velocity, 2 = GPS outputs no velocity + float innovVelPos[6]; // innovation output + float varInnovVelPos[6]; // innovation variance output + + float velNED[3]; // North, East, Down velocity obs (m/s) + float posNE[2]; // North, East position obs (m) + float hgtMea; // measured height (m) + float posNED[3]; // North, East Down position (m) + + float innovMag[3]; // innovation output + float varInnovMag[3]; // innovation variance output + Vector3f magData; // magnetometer flux radings in X,Y,Z body axes + float innovVtas; // innovation output + float varInnovVtas; // innovation variance output + float VtasMeas; // true airspeed measurement (m/s) + float magDeclination; + float latRef; // WGS-84 latitude of reference point (rad) + float lonRef; // WGS-84 longitude of reference point (rad) + float hgtRef; // WGS-84 height of reference point (m) + Vector3f magBias; // states representing magnetometer bias vector in XYZ body axes + uint8_t covSkipCount; // Number of state prediction frames (IMU daya updates to skip before doing the covariance prediction + + // GPS input data variables + float gpsCourse; + float gpsVelD; + float gpsLat; + float gpsLon; + float gpsHgt; + uint8_t GPSstatus; + + // Baro input + float baroHgt; + + bool statesInitialised; + + bool fuseVelData; // this boolean causes the posNE and velNED obs to be fused + bool fusePosData; // this boolean causes the posNE and velNED obs to be fused + bool fuseHgtData; // this boolean causes the hgtMea obs to be fused + bool fuseMagData; // boolean true when magnetometer data is to be fused + bool fuseVtasData; // boolean true when airspeed data is to be fused + + bool onGround; ///< boolean true when the flight vehicle is on the ground (not flying) + bool staticMode; ///< boolean true if no position feedback is fused + bool useAirspeed; ///< boolean true if airspeed data is being used + bool useCompass; ///< boolean true if magnetometer data is being used + + struct ekf_status_report current_ekf_state; + struct ekf_status_report last_ekf_error; + + bool numericalProtection; + + unsigned storeIndex; + + +void UpdateStrapdownEquationsNED(); + +void CovariancePrediction(float dt); + +void FuseVelposNED(); + +void FuseMagnetometer(); + +void FuseAirspeed(); + +void zeroRows(float (&covMat)[n_states][n_states], uint8_t first, uint8_t last); + +void zeroCols(float (&covMat)[n_states][n_states], uint8_t first, uint8_t last); + +void quatNorm(float (&quatOut)[4], const float quatIn[4]); + +// store staes along with system time stamp in msces +void StoreStates(uint64_t timestamp_ms); + +/** + * Recall the state vector. + * + * Recalls the vector stored at closest time to the one specified by msec + * + * @return zero on success, integer indicating the number of invalid states on failure. + * Does only copy valid states, if the statesForFusion vector was initialized + * correctly by the caller, the result can be safely used, but is a mixture + * time-wise where valid states were updated and invalid remained at the old + * value. + */ +int RecallStates(float statesForFusion[n_states], uint64_t msec); + +void ResetStoredStates(); + +void quat2Tbn(Mat3f &Tbn, const float (&quat)[4]); + +void calcEarthRateNED(Vector3f &omega, float latitude); + +static void eul2quat(float (&quat)[4], const float (&eul)[3]); + +static void quat2eul(float (&eul)[3], const float (&quat)[4]); + +static void calcvelNED(float (&velNED)[3], float gpsCourse, float gpsGndSpd, float gpsVelD); + +static void calcposNED(float (&posNED)[3], float lat, float lon, float hgt, float latRef, float lonRef, float hgtRef); + +static void calcLLH(float (&posNED)[3], float lat, float lon, float hgt, float latRef, float lonRef, float hgtRef); + +static void quat2Tnb(Mat3f &Tnb, const float (&quat)[4]); + +static float sq(float valIn); + +void OnGroundCheck(); + +void CovarianceInit(); + +void InitialiseFilter(float (&initvelNED)[3], double referenceLat, double referenceLon, float referenceHgt, float declination); + +float ConstrainFloat(float val, float min, float max); + +void ConstrainVariances(); + +void ConstrainStates(); + +void ForceSymmetry(); + +int CheckAndBound(); + +void ResetPosition(); + +void ResetVelocity(); + +void ZeroVariables(); + +void GetFilterState(struct ekf_status_report *state); + +void GetLastErrorState(struct ekf_status_report *last_error); + +bool StatesNaN(struct ekf_status_report *err_report); +void FillErrorReport(struct ekf_status_report *err); + +void InitializeDynamic(float (&initvelNED)[3], float declination); + +protected: + +bool FilterHealthy(); + +void ResetHeight(void); + +void AttitudeInit(float ax, float ay, float az, float mx, float my, float mz, float declination, float *initQuat); + +}; + +uint32_t millis(); + diff --git a/src/modules/ekf_att_pos_estimator/estimator_utilities.cpp b/src/modules/ekf_att_pos_estimator/estimator_utilities.cpp new file mode 100644 index 0000000000..b4767a0d34 --- /dev/null +++ b/src/modules/ekf_att_pos_estimator/estimator_utilities.cpp @@ -0,0 +1,139 @@ + +#include "estimator_utilities.h" + +// Define EKF_DEBUG here to enable the debug print calls +// if the macro is not set, these will be completely +// optimized out by the compiler. +//#define EKF_DEBUG + +#ifdef EKF_DEBUG +#include + +static void +ekf_debug_print(const char *fmt, va_list args) +{ + fprintf(stderr, "%s: ", "[ekf]"); + vfprintf(stderr, fmt, args); + + fprintf(stderr, "\n"); +} + +void +ekf_debug(const char *fmt, ...) +{ + va_list args; + + va_start(args, fmt); + ekf_debug_print(fmt, args); +} + +#else + +void ekf_debug(const char *fmt, ...) { while(0){} } +#endif + +float Vector3f::length(void) const +{ + return sqrt(x*x + y*y + z*z); +} + +void Vector3f::zero(void) +{ + x = 0.0f; + y = 0.0f; + z = 0.0f; +} + +Mat3f::Mat3f() { + identity(); +} + +void Mat3f::identity() { + x.x = 1.0f; + x.y = 0.0f; + x.z = 0.0f; + + y.x = 0.0f; + y.y = 1.0f; + y.z = 0.0f; + + z.x = 0.0f; + z.y = 0.0f; + z.z = 1.0f; +} + +Mat3f Mat3f::transpose(void) const +{ + Mat3f ret = *this; + swap_var(ret.x.y, ret.y.x); + swap_var(ret.x.z, ret.z.x); + swap_var(ret.y.z, ret.z.y); + return ret; +} + +// overload + operator to provide a vector addition +Vector3f operator+( Vector3f vecIn1, Vector3f vecIn2) +{ + Vector3f vecOut; + vecOut.x = vecIn1.x + vecIn2.x; + vecOut.y = vecIn1.y + vecIn2.y; + vecOut.z = vecIn1.z + vecIn2.z; + return vecOut; +} + +// overload - operator to provide a vector subtraction +Vector3f operator-( Vector3f vecIn1, Vector3f vecIn2) +{ + Vector3f vecOut; + vecOut.x = vecIn1.x - vecIn2.x; + vecOut.y = vecIn1.y - vecIn2.y; + vecOut.z = vecIn1.z - vecIn2.z; + return vecOut; +} + +// overload * operator to provide a matrix vector product +Vector3f operator*( Mat3f matIn, Vector3f vecIn) +{ + Vector3f vecOut; + vecOut.x = matIn.x.x*vecIn.x + matIn.x.y*vecIn.y + matIn.x.z*vecIn.z; + vecOut.y = matIn.y.x*vecIn.x + matIn.y.y*vecIn.y + matIn.y.z*vecIn.z; + vecOut.z = matIn.x.x*vecIn.x + matIn.z.y*vecIn.y + matIn.z.z*vecIn.z; + return vecOut; +} + +// overload % operator to provide a vector cross product +Vector3f operator%( Vector3f vecIn1, Vector3f vecIn2) +{ + Vector3f vecOut; + vecOut.x = vecIn1.y*vecIn2.z - vecIn1.z*vecIn2.y; + vecOut.y = vecIn1.z*vecIn2.x - vecIn1.x*vecIn2.z; + vecOut.z = vecIn1.x*vecIn2.y - vecIn1.y*vecIn2.x; + return vecOut; +} + +// overload * operator to provide a vector scaler product +Vector3f operator*(Vector3f vecIn1, float sclIn1) +{ + Vector3f vecOut; + vecOut.x = vecIn1.x * sclIn1; + vecOut.y = vecIn1.y * sclIn1; + vecOut.z = vecIn1.z * sclIn1; + return vecOut; +} + +// overload * operator to provide a vector scaler product +Vector3f operator*(float sclIn1, Vector3f vecIn1) +{ + Vector3f vecOut; + vecOut.x = vecIn1.x * sclIn1; + vecOut.y = vecIn1.y * sclIn1; + vecOut.z = vecIn1.z * sclIn1; + return vecOut; +} + +void swap_var(float &d1, float &d2) +{ + float tmp = d1; + d1 = d2; + d2 = tmp; +} diff --git a/src/modules/ekf_att_pos_estimator/estimator_utilities.h b/src/modules/ekf_att_pos_estimator/estimator_utilities.h new file mode 100644 index 0000000000..7dddee4685 --- /dev/null +++ b/src/modules/ekf_att_pos_estimator/estimator_utilities.h @@ -0,0 +1,79 @@ +#include +#include + +#pragma once + +#define GRAVITY_MSS 9.80665f +#define deg2rad 0.017453292f +#define rad2deg 57.295780f +#define pi 3.141592657f +#define earthRate 0.000072921f +#define earthRadius 6378145.0f +#define earthRadiusInv 1.5678540e-7f + +class Vector3f +{ +private: +public: + float x; + float y; + float z; + + float length(void) const; + void zero(void); +}; + +class Mat3f +{ +private: +public: + Vector3f x; + Vector3f y; + Vector3f z; + + Mat3f(); + + void identity(); + Mat3f transpose(void) const; +}; + +Vector3f operator*(float sclIn1, Vector3f vecIn1); +Vector3f operator+( Vector3f vecIn1, Vector3f vecIn2); +Vector3f operator-( Vector3f vecIn1, Vector3f vecIn2); +Vector3f operator*( Mat3f matIn, Vector3f vecIn); +Vector3f operator%( Vector3f vecIn1, Vector3f vecIn2); +Vector3f operator*(Vector3f vecIn1, float sclIn1); + +void swap_var(float &d1, float &d2); + +const unsigned int n_states = 21; +const unsigned int data_buffer_size = 50; + +enum GPS_FIX { + GPS_FIX_NOFIX = 0, + GPS_FIX_2D = 2, + GPS_FIX_3D = 3 +}; + +struct ekf_status_report { + bool velHealth; + bool posHealth; + bool hgtHealth; + bool velTimeout; + bool posTimeout; + bool hgtTimeout; + uint32_t velFailTime; + uint32_t posFailTime; + uint32_t hgtFailTime; + float states[n_states]; + bool angNaN; + bool summedDelVelNaN; + bool KHNaN; + bool KHPNaN; + bool PNaN; + bool covarianceNaN; + bool kalmanGainsNaN; + bool statesNaN; +}; + +void ekf_debug(const char *fmt, ...); \ No newline at end of file diff --git a/src/modules/ekf_att_pos_estimator/module.mk b/src/modules/ekf_att_pos_estimator/module.mk index 6fefec2c2a..0058b3fd18 100644 --- a/src/modules/ekf_att_pos_estimator/module.mk +++ b/src/modules/ekf_att_pos_estimator/module.mk @@ -39,4 +39,5 @@ MODULE_COMMAND = ekf_att_pos_estimator SRCS = ekf_att_pos_estimator_main.cpp \ ekf_att_pos_estimator_params.c \ - estimator.cpp + estimator_21states.cpp \ + estimator_utilities.cpp From f4075b5623bb9c92dd46e92b97bc363a91498ff6 Mon Sep 17 00:00:00 2001 From: Lorenz Meier Date: Sat, 7 Jun 2014 16:06:18 +0200 Subject: [PATCH 3/3] Switching back to 23 states, fixed mag update logic --- .../ekf_att_pos_estimator_main.cpp | 15 +++++++++++---- .../ekf_att_pos_estimator/estimator_21states.cpp | 6 +++--- .../ekf_att_pos_estimator/estimator_23states.cpp | 11 +++-------- .../ekf_att_pos_estimator/estimator_23states.h | 2 +- .../ekf_att_pos_estimator/estimator_utilities.h | 2 +- src/modules/ekf_att_pos_estimator/module.mk | 2 +- 6 files changed, 20 insertions(+), 18 deletions(-) diff --git a/src/modules/ekf_att_pos_estimator/ekf_att_pos_estimator_main.cpp b/src/modules/ekf_att_pos_estimator/ekf_att_pos_estimator_main.cpp index 86f7eb99f6..9cff9fab0b 100644 --- a/src/modules/ekf_att_pos_estimator/ekf_att_pos_estimator_main.cpp +++ b/src/modules/ekf_att_pos_estimator/ekf_att_pos_estimator_main.cpp @@ -83,7 +83,7 @@ #include #include -#include "estimator_21states.h" +#include "estimator_23states.h" @@ -451,6 +451,8 @@ FixedwingEstimator::~FixedwingEstimator() } while (_estimator_task != -1); } + delete _ekf; + estimator::g_estimator = nullptr; } @@ -564,7 +566,7 @@ FixedwingEstimator::task_main() #else _sensor_combined_sub = orb_subscribe(ORB_ID(sensor_combined)); /* XXX remove this!, BUT increase the data buffer size! */ - orb_set_interval(_sensor_combined_sub, 4); + orb_set_interval(_sensor_combined_sub, 9); #endif /* sets also parameters in the EKF object */ @@ -809,6 +811,8 @@ FixedwingEstimator::task_main() #endif + //warnx("dang: %8.4f %8.4f dvel: %8.4f %8.4f", _ekf->dAngIMU.x, _ekf->dAngIMU.z, _ekf->dVelIMU.x, _ekf->dVelIMU.z); + bool airspeed_updated; orb_check(_airspeed_sub, &airspeed_updated); @@ -1247,12 +1251,15 @@ FixedwingEstimator::task_main() _ekf->fuseMagData = true; _ekf->RecallStates(_ekf->statesAtMagMeasTime, (IMUmsec - _parameters.mag_delay_ms)); // Assume 50 msec avg delay for magnetometer data + _ekf->magstate.obsIndex = 0; + _ekf->FuseMagnetometer(); + _ekf->FuseMagnetometer(); + _ekf->FuseMagnetometer(); + } else { _ekf->fuseMagData = false; } - if (_ekf->statesInitialised) _ekf->FuseMagnetometer(); - // Fuse Airspeed Measurements if (newAdsData && _ekf->statesInitialised && _ekf->VtasMeas > 8.0f) { _ekf->fuseVtasData = true; diff --git a/src/modules/ekf_att_pos_estimator/estimator_21states.cpp b/src/modules/ekf_att_pos_estimator/estimator_21states.cpp index 5a60ac1c01..0f5a17a335 100644 --- a/src/modules/ekf_att_pos_estimator/estimator_21states.cpp +++ b/src/modules/ekf_att_pos_estimator/estimator_21states.cpp @@ -61,8 +61,8 @@ void AttPosEKF::UpdateStrapdownEquationsNED() // Apply corrections for earths rotation rate and coning errors // * and + operators have been overloaded - correctedDelAng = correctedDelAng - Tnb*earthRateNED*dtIMU + 8.333333333333333e-2f*(prevDelAng % correctedDelAng); - + correctedDelAng = dAngIMU;//correctedDelAng - Tnb*earthRateNED*dtIMU + 8.333333333333333e-2f*(prevDelAng % correctedDelAng); + correctedDelAng.z = 0; // Convert the rotation vector to its equivalent quaternion rotationMag = correctedDelAng.length(); if (rotationMag < 1e-12f) @@ -151,7 +151,7 @@ void AttPosEKF::UpdateStrapdownEquationsNED() states[9] = states[9] + 0.5f*(states[6] + lastVelocity[2])*dtIMU; // Constrain states (to protect against filter divergence) - ConstrainStates(); + //ConstrainStates(); } void AttPosEKF::CovariancePrediction(float dt) diff --git a/src/modules/ekf_att_pos_estimator/estimator_23states.cpp b/src/modules/ekf_att_pos_estimator/estimator_23states.cpp index ca9db96855..89e6d3948c 100644 --- a/src/modules/ekf_att_pos_estimator/estimator_23states.cpp +++ b/src/modules/ekf_att_pos_estimator/estimator_23states.cpp @@ -1,4 +1,4 @@ -#include "estimator.h" +#include "estimator_23states.h" #include #include @@ -1140,7 +1140,7 @@ void AttPosEKF::FuseMagnetometer() // data fit is the only assumption we can make // so we might as well take advantage of the computational efficiencies // associated with sequential fusion - if (useCompass && (fuseMagData || obsIndex == 1 || obsIndex == 2)) + if (useCompass && fuseMagData && (obsIndex < 3)) { // Limit range of states modified when on ground if(!onGround) @@ -1156,7 +1156,7 @@ void AttPosEKF::FuseMagnetometer() // three prediction time steps. // Calculate observation jacobians and Kalman gains - if (fuseMagData) + if (obsIndex == 0) { // Copy required states to local variable names q0 = statesAtMagMeasTime[0]; @@ -1251,11 +1251,6 @@ void AttPosEKF::FuseMagnetometer() Kfusion[22] = SK_MX[0]*(P[22][19] + P[22][1]*SH_MAG[0] + P[22][3]*SH_MAG[2] + P[22][0]*SK_MX[3] - P[22][2]*SK_MX[2] - P[22][16]*SK_MX[1] + P[22][17]*SK_MX[5] - P[22][18]*SK_MX[4]); varInnovMag[0] = 1.0f/SK_MX[0]; innovMag[0] = MagPred[0] - magData.x; - - // reset the observation index to 0 (we start by fusing the X - // measurement) - obsIndex = 0; - fuseMagData = false; } else if (obsIndex == 1) // we are now fusing the Y measurement { diff --git a/src/modules/ekf_att_pos_estimator/estimator_23states.h b/src/modules/ekf_att_pos_estimator/estimator_23states.h index 6d3b891081..851e46371a 100644 --- a/src/modules/ekf_att_pos_estimator/estimator_23states.h +++ b/src/modules/ekf_att_pos_estimator/estimator_23states.h @@ -229,7 +229,7 @@ static void quat2eul(float (&eul)[3], const float (&quat)[4]); static void calcvelNED(float (&velNED)[3], float gpsCourse, float gpsGndSpd, float gpsVelD); -static void calcposNED(float (&posNED)[3], double lat, double lon, float hgt, double latRef, double lonRef, float hgtRef); +void calcposNED(float (&posNED)[3], double lat, double lon, float hgt, double latRef, double lonRef, float hgtRef); static void calcLLH(float (&posNED)[3], float lat, float lon, float hgt, float latRef, float lonRef, float hgtRef); diff --git a/src/modules/ekf_att_pos_estimator/estimator_utilities.h b/src/modules/ekf_att_pos_estimator/estimator_utilities.h index 7dddee4685..714dfe623a 100644 --- a/src/modules/ekf_att_pos_estimator/estimator_utilities.h +++ b/src/modules/ekf_att_pos_estimator/estimator_utilities.h @@ -46,7 +46,7 @@ Vector3f operator*(Vector3f vecIn1, float sclIn1); void swap_var(float &d1, float &d2); -const unsigned int n_states = 21; +const unsigned int n_states = 23; const unsigned int data_buffer_size = 50; enum GPS_FIX { diff --git a/src/modules/ekf_att_pos_estimator/module.mk b/src/modules/ekf_att_pos_estimator/module.mk index 0058b3fd18..dc5220bf0c 100644 --- a/src/modules/ekf_att_pos_estimator/module.mk +++ b/src/modules/ekf_att_pos_estimator/module.mk @@ -39,5 +39,5 @@ MODULE_COMMAND = ekf_att_pos_estimator SRCS = ekf_att_pos_estimator_main.cpp \ ekf_att_pos_estimator_params.c \ - estimator_21states.cpp \ + estimator_23states.cpp \ estimator_utilities.cpp