forked from Archive/PX4-Autopilot
ekf2: change delta angle and delta velocity bias states to accel and gyro bias (#21901)
* ekf2-test: remove outdated codegen comparison The definition of states changed so the comparison with the old derivation cannot work anymore. --------- Co-authored-by: bresch <brescianimathieu@gmail.com>
This commit is contained in:
Daniel Agar
GitHub
parent
444e5d2d4a
commit
84b6b472b4
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@ -39,7 +39,6 @@
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#include <mathlib/mathlib.h>
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#include "common.h"
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#include "utils.hpp"
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using matrix::AxisAnglef;
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using matrix::Dcmf;
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@ -276,8 +276,8 @@ struct stateSample {
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Quatf quat_nominal{}; ///< quaternion defining the rotation from body to earth frame
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Vector3f vel{}; ///< NED velocity in earth frame in m/s
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Vector3f pos{}; ///< NED position in earth frame in m
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Vector3f delta_ang_bias{}; ///< delta angle bias estimate in rad
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Vector3f delta_vel_bias{}; ///< delta velocity bias estimate in m/s
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Vector3f gyro_bias{}; ///< gyro bias estimate in rad/s
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Vector3f accel_bias{}; ///< accel bias estimate in m/s^2
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Vector3f mag_I{}; ///< NED earth magnetic field in gauss
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Vector3f mag_B{}; ///< magnetometer bias estimate in body frame in gauss
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Vector2f wind_vel{}; ///< horizontal wind velocity in earth frame in m/s
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@ -43,7 +43,6 @@
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#include "ekf.h"
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#include "python/ekf_derivation/generated/predict_covariance.h"
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#include "utils.hpp"
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#include <math.h>
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#include <mathlib/mathlib.h>
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@ -54,11 +53,6 @@ void Ekf::initialiseCovariance()
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{
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P.zero();
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_delta_angle_bias_var_accum.setZero();
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_delta_vel_bias_var_accum.setZero();
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const float dt = _dt_ekf_avg;
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resetQuatCov();
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// velocity
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@ -82,14 +76,14 @@ void Ekf::initialiseCovariance()
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#endif // CONFIG_EKF2_RANGE_FINDER
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// gyro bias
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_prev_delta_ang_bias_var(0) = P(10,10) = sq(_params.switch_on_gyro_bias * dt);
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_prev_delta_ang_bias_var(1) = P(11,11) = P(10,10);
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_prev_delta_ang_bias_var(2) = P(12,12) = P(10,10);
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_prev_gyro_bias_var(0) = P(10,10) = sq(_params.switch_on_gyro_bias);
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_prev_gyro_bias_var(1) = P(11,11) = P(10,10);
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_prev_gyro_bias_var(2) = P(12,12) = P(10,10);
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// accel bias
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_prev_dvel_bias_var(0) = P(13,13) = sq(_params.switch_on_accel_bias * dt);
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_prev_dvel_bias_var(1) = P(14,14) = P(13,13);
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_prev_dvel_bias_var(2) = P(15,15) = P(13,13);
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_prev_accel_bias_var(0) = P(13,13) = sq(_params.switch_on_accel_bias);
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_prev_accel_bias_var(1) = P(14,14) = P(13,13);
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_prev_accel_bias_var(2) = P(15,15) = P(13,13);
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resetMagCov();
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@ -105,12 +99,6 @@ void Ekf::predictCovariance(const imuSample &imu_delayed)
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const float dt = _dt_ekf_avg;
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const float dt_inv = 1.f / dt;
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// convert rate of change of rate gyro bias (rad/s**2) as specified by the parameter to an expected change in delta angle (rad) since the last update
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const float d_ang_bias_sig = dt * dt * math::constrain(_params.gyro_bias_p_noise, 0.0f, 1.0f);
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// convert rate of change of accelerometer bias (m/s**3) as specified by the parameter to an expected change in delta velocity (m/s) since the last update
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const float d_vel_bias_sig = dt * dt * math::constrain(_params.accel_bias_p_noise, 0.0f, 1.0f);
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// inhibit learning of imu accel bias if the manoeuvre levels are too high to protect against the effect of sensor nonlinearities or bad accel data is detected
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// xy accel bias learning is also disabled on ground as those states are poorly observable when perpendicular to the gravity vector
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const float alpha = math::constrain((dt / _params.acc_bias_learn_tc), 0.0f, 1.0f);
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@ -137,14 +125,14 @@ void Ekf::predictCovariance(const imuSample &imu_delayed)
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if (do_inhibit_axis) {
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// store the bias state variances to be reinstated later
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if (!_gyro_bias_inhibit[index]) {
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_prev_delta_ang_bias_var(index) = P(stateIndex, stateIndex);
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_prev_gyro_bias_var(index) = P(stateIndex, stateIndex);
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_gyro_bias_inhibit[index] = true;
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}
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} else {
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if (_gyro_bias_inhibit[index]) {
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// reinstate the bias state variances
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P(stateIndex, stateIndex) = _prev_delta_ang_bias_var(index);
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P(stateIndex, stateIndex) = _prev_gyro_bias_var(index);
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_gyro_bias_inhibit[index] = false;
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}
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}
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@ -176,14 +164,14 @@ void Ekf::predictCovariance(const imuSample &imu_delayed)
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if (do_inhibit_axis) {
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// store the bias state variances to be reinstated later
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if (!_accel_bias_inhibit[index]) {
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_prev_dvel_bias_var(index) = P(stateIndex, stateIndex);
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_prev_accel_bias_var(index) = P(stateIndex, stateIndex);
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_accel_bias_inhibit[index] = true;
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}
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} else {
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if (_accel_bias_inhibit[index]) {
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// reinstate the bias state variances
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P(stateIndex, stateIndex) = _prev_dvel_bias_var(index);
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P(stateIndex, stateIndex) = _prev_accel_bias_var(index);
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_accel_bias_inhibit[index] = false;
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}
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}
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@ -223,22 +211,6 @@ void Ekf::predictCovariance(const imuSample &imu_delayed)
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wind_vel_nsd_scaled = 0.0f;
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}
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// compute noise variance for stationary processes
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Vector24f process_noise;
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// Construct the process noise variance diagonal for those states with a stationary process model
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// These are kinematic states and their error growth is controlled separately by the IMU noise variances
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// delta angle bias states
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process_noise.slice<3, 1>(10, 0) = sq(d_ang_bias_sig);
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// delta_velocity bias states
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process_noise.slice<3, 1>(13, 0) = sq(d_vel_bias_sig);
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// earth frame magnetic field states
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process_noise.slice<3, 1>(16, 0) = sq(mag_I_sig);
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// body frame magnetic field states
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process_noise.slice<3, 1>(19, 0) = sq(mag_B_sig);
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// wind velocity states
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process_noise.slice<2, 1>(22, 0) = sq(wind_vel_nsd_scaled) * dt;
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// assign IMU noise variances
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// inputs to the system are 3 delta angles and 3 delta velocities
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@ -265,43 +237,52 @@ void Ekf::predictCovariance(const imuSample &imu_delayed)
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// calculate variances and upper diagonal covariances for quaternion, velocity, position and gyro bias states
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sym::PredictCovariance(getStateAtFusionHorizonAsVector(), P, imu_delayed.delta_vel, d_vel_var, imu_delayed.delta_ang, d_ang_var, dt, &nextP);
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// process noise contribution for delta angle states can be very small compared to
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// the variances, therefore use algorithm to minimise numerical error
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for (unsigned i = 10; i <= 12; i++) {
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const int index = i - 10;
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// compute noise variance for stationary processes
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Vector24f process_noise;
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if (!_gyro_bias_inhibit[index]) {
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// add process noise that is not from the IMU
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// process noise contribution for delta velocity states can be very small compared to
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// the variances, therefore use algorithm to minimise numerical error
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nextP(i, i) = kahanSummation(nextP(i, i), process_noise(i), _delta_angle_bias_var_accum(index));
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// Construct the process noise variance diagonal for those states with a stationary process model
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// These are kinematic states and their error growth is controlled separately by the IMU noise variances
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} else {
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nextP.uncorrelateCovarianceSetVariance<1>(i, _prev_delta_ang_bias_var(index));
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_delta_angle_bias_var_accum(index) = 0.f;
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}
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}
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for (int i = 13; i <= 15; i++) {
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const int index = i - 13;
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if (!_accel_bias_inhibit[index]) {
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// add process noise that is not from the IMU
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// process noise contribution for delta velocity states can be very small compared to
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// the variances, therefore use algorithm to minimise numerical error
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nextP(i, i) = kahanSummation(nextP(i, i), process_noise(i), _delta_vel_bias_var_accum(index));
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} else {
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nextP.uncorrelateCovarianceSetVariance<1>(i, _prev_dvel_bias_var(index));
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_delta_vel_bias_var_accum(index) = 0.f;
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}
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}
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// earth frame magnetic field states
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process_noise.slice<3, 1>(16, 0) = sq(mag_I_sig);
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// body frame magnetic field states
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process_noise.slice<3, 1>(19, 0) = sq(mag_B_sig);
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// wind velocity states
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process_noise.slice<2, 1>(22, 0) = sq(wind_vel_nsd_scaled) * dt;
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// add process noise that is not from the IMU
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for (unsigned i = 16; i <= 23; i++) {
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nextP(i, i) += process_noise(i);
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}
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// gyro bias: add process noise, or restore previous gyro bias var if state inhibited
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const float gyro_bias_sig = dt * math::constrain(_params.gyro_bias_p_noise, 0.f, 1.f);
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const float gyro_bias_process_noise = sq(gyro_bias_sig);
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for (unsigned i = 10; i <= 12; i++) {
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const int axis_index = i - 10;
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if (!_gyro_bias_inhibit[axis_index]) {
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nextP(i, i) += gyro_bias_process_noise;
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} else {
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nextP.uncorrelateCovarianceSetVariance<1>(i, _prev_gyro_bias_var(axis_index));
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}
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}
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// accel bias: add process noise, or restore previous accel bias var if state inhibited
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const float accel_bias_sig = dt * math::constrain(_params.accel_bias_p_noise, 0.f, 1.f);
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const float accel_bias_process_noise = sq(accel_bias_sig);
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for (int i = 13; i <= 15; i++) {
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const int axis_index = i - 13;
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if (!_accel_bias_inhibit[axis_index]) {
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nextP(i, i) += accel_bias_process_noise;
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} else {
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nextP.uncorrelateCovarianceSetVariance<1>(i, _prev_accel_bias_var(axis_index));
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}
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}
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// covariance matrix is symmetrical, so copy upper half to lower half
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for (unsigned row = 0; row <= 15; row++) {
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for (unsigned column = 0 ; column < row; column++) {
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@ -385,7 +366,7 @@ void Ekf::fixCovarianceErrors(bool force_symmetry)
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// accelerometer bias states
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if (!_accel_bias_inhibit[0] || !_accel_bias_inhibit[1] || !_accel_bias_inhibit[2]) {
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// Find the maximum delta velocity bias state variance and request a covariance reset if any variance is below the safe minimum
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const float minSafeStateVar = 1e-9f;
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const float minSafeStateVar = 1e-9f / sq(_dt_ekf_avg);
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float maxStateVar = minSafeStateVar;
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bool resetRequired = false;
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@ -406,7 +387,7 @@ void Ekf::fixCovarianceErrors(bool force_symmetry)
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// To ensure stability of the covariance matrix operations, the ratio of a max and min variance must
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// not exceed 100 and the minimum variance must not fall below the target minimum
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// Also limit variance to a maximum equivalent to a 0.1g uncertainty
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const float minStateVarTarget = 5E-8f;
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const float minStateVarTarget = 5E-8f / sq(_dt_ekf_avg);
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float minAllowedStateVar = fmaxf(0.01f * maxStateVar, minStateVarTarget);
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for (uint8_t stateIndex = 13; stateIndex <= 15; stateIndex++) {
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@ -415,8 +396,7 @@ void Ekf::fixCovarianceErrors(bool force_symmetry)
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continue;
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}
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P(stateIndex, stateIndex) = math::constrain(P(stateIndex, stateIndex), minAllowedStateVar,
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sq(0.1f * CONSTANTS_ONE_G * _dt_ekf_avg));
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P(stateIndex, stateIndex) = math::constrain(P(stateIndex, stateIndex), minAllowedStateVar, sq(0.1f * CONSTANTS_ONE_G));
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}
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// If any one axis has fallen below the safe minimum, all delta velocity covariance terms must be reset to zero
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@ -427,7 +407,8 @@ void Ekf::fixCovarianceErrors(bool force_symmetry)
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// Run additional checks to see if the delta velocity bias has hit limits in a direction that is clearly wrong
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// calculate accel bias term aligned with the gravity vector
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const float dVel_bias_lim = 0.9f * _params.acc_bias_lim * _dt_ekf_avg;
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const float down_dvel_bias = _state.delta_vel_bias.dot(Vector3f(_R_to_earth.row(2)));
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const Vector3f delta_vel_bias = _state.accel_bias * _dt_ekf_avg;
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const float down_dvel_bias = delta_vel_bias.dot(Vector3f(_R_to_earth.row(2)));
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// check that the vertical component of accel bias is consistent with both the vertical position and velocity innovation
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bool bad_acc_bias = false;
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@ -602,9 +583,9 @@ void Ekf::zeroMagCov()
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P.uncorrelateCovarianceSetVariance<3>(19, 0.0f);
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}
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void Ekf::resetZDeltaAngBiasCov()
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void Ekf::resetGyroBiasZCov()
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{
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const float init_delta_ang_bias_var = sq(_params.switch_on_gyro_bias * _dt_ekf_avg);
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const float init_gyro_bias_var = sq(_params.switch_on_gyro_bias);
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P.uncorrelateCovarianceSetVariance<1>(12, init_delta_ang_bias_var);
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P.uncorrelateCovarianceSetVariance<1>(12, init_gyro_bias_var);
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}
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@ -110,7 +110,7 @@ void Ekf::fuseDrag(const dragSample &drag_sample)
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// perform sequential fusion of XY specific forces
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for (uint8_t axis_index = 0; axis_index < 2; axis_index++) {
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// measured drag acceleration corrected for sensor bias
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const float mea_acc = drag_sample.accelXY(axis_index) - _state.delta_vel_bias(axis_index) / _dt_ekf_avg;
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const float mea_acc = drag_sample.accelXY(axis_index) - _state.accel_bias(axis_index);
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// Drag is modelled as an arbitrary combination of bluff body drag that proportional to
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// equivalent airspeed squared, and rotor momentum drag that is proportional to true airspeed
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@ -56,8 +56,8 @@ void Ekf::reset()
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_state.vel.setZero();
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_state.pos.setZero();
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_state.delta_ang_bias.setZero();
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_state.delta_vel_bias.setZero();
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_state.gyro_bias.setZero();
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_state.accel_bias.setZero();
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_state.mag_I.setZero();
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_state.mag_B.setZero();
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_state.wind_vel.setZero();
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@ -80,7 +80,8 @@ void Ekf::reset()
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_fault_status.value = 0;
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_innov_check_fail_status.value = 0;
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_prev_dvel_bias_var.zero();
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_prev_gyro_bias_var.zero();
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_prev_accel_bias_var.zero();
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resetGpsDriftCheckFilters();
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@ -185,8 +186,7 @@ bool Ekf::update()
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runTerrainEstimator(imu_sample_delayed);
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#endif // CONFIG_EKF2_RANGE_FINDER
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_output_predictor.correctOutputStates(imu_sample_delayed.time_us, getGyroBias(), getAccelBias(),
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_state.quat_nominal, _state.vel, _state.pos);
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_output_predictor.correctOutputStates(imu_sample_delayed.time_us, _state.quat_nominal, _state.vel, _state.pos, _state.gyro_bias, _state.accel_bias);
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return true;
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}
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@ -363,13 +363,13 @@ public:
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}
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// gyro bias (states 10, 11, 12)
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Vector3f getGyroBias() const { return _state.delta_ang_bias / _dt_ekf_avg; } // get the gyroscope bias in rad/s
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Vector3f getGyroBiasVariance() const { return Vector3f{P(10, 10), P(11, 11), P(12, 12)} / sq(_dt_ekf_avg); } // get the gyroscope bias variance in rad/s
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const Vector3f &getGyroBias() const { return _state.gyro_bias; } // get the gyroscope bias in rad/s
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Vector3f getGyroBiasVariance() const { return Vector3f{P(10, 10), P(11, 11), P(12, 12)}; } // get the gyroscope bias variance in rad/s
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float getGyroBiasLimit() const { return _params.gyro_bias_lim; }
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// accel bias (states 13, 14, 15)
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Vector3f getAccelBias() const { return _state.delta_vel_bias / _dt_ekf_avg; } // get the accelerometer bias in m/s**2
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Vector3f getAccelBiasVariance() const { return Vector3f{P(13, 13), P(14, 14), P(15, 15)} / sq(_dt_ekf_avg); } // get the accelerometer bias variance in m/s**2
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const Vector3f &getAccelBias() const { return _state.accel_bias; } // get the accelerometer bias in m/s**2
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Vector3f getAccelBiasVariance() const { return Vector3f{P(13, 13), P(14, 14), P(15, 15)}; } // get the accelerometer bias variance in m/s**2
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float getAccelBiasLimit() const { return _params.acc_bias_lim; }
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const Vector3f &getMagEarthField() const { return _state.mag_I; }
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@ -589,9 +589,6 @@ private:
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SquareMatrix24f P{}; ///< state covariance matrix
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Vector3f _delta_angle_bias_var_accum{}; ///< kahan summation algorithm accumulator for delta angle bias variance
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Vector3f _delta_vel_bias_var_accum{}; ///< kahan summation algorithm accumulator for delta velocity bias variance
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#if defined(CONFIG_EKF2_DRAG_FUSION)
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Vector2f _drag_innov{}; ///< multirotor drag measurement innovation (m/sec**2)
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Vector2f _drag_innov_var{}; ///< multirotor drag measurement innovation variance ((m/sec**2)**2)
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@ -721,8 +718,9 @@ private:
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Vector3f _accel_vec_filt{}; ///< acceleration vector after application of a low pass filter (m/sec**2)
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float _accel_magnitude_filt{0.0f}; ///< acceleration magnitude after application of a decaying envelope filter (rad/sec)
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float _ang_rate_magnitude_filt{0.0f}; ///< angular rate magnitude after application of a decaying envelope filter (rad/sec)
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Vector3f _prev_delta_ang_bias_var{}; ///< saved delta angle XYZ bias variances (rad/sec)
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Vector3f _prev_dvel_bias_var{}; ///< saved delta velocity XYZ bias variances (m/sec)**2
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Vector3f _prev_gyro_bias_var{}; ///< saved gyro XYZ bias variances
|
||||
Vector3f _prev_accel_bias_var{}; ///< saved accel XYZ bias variances
|
||||
|
||||
// height sensor status
|
||||
bool _baro_hgt_faulty{false}; ///< true if baro data have been declared faulty TODO: move to fault flags
|
||||
|
|
@ -1110,7 +1108,7 @@ private:
|
|||
void clearMagCov();
|
||||
void zeroMagCov();
|
||||
|
||||
void resetZDeltaAngBiasCov();
|
||||
void resetGyroBiasZCov();
|
||||
|
||||
// uncorrelate quaternion states from other states
|
||||
void uncorrelateQuatFromOtherStates();
|
||||
|
|
|
|||
|
|
@ -224,11 +224,11 @@ void Ekf::constrainStates()
|
|||
_state.vel = matrix::constrain(_state.vel, -1000.0f, 1000.0f);
|
||||
_state.pos = matrix::constrain(_state.pos, -1.e6f, 1.e6f);
|
||||
|
||||
const float delta_ang_bias_limit = getGyroBiasLimit() * _dt_ekf_avg;
|
||||
_state.delta_ang_bias = matrix::constrain(_state.delta_ang_bias, -delta_ang_bias_limit, delta_ang_bias_limit);
|
||||
const float gyro_bias_limit = getGyroBiasLimit();
|
||||
_state.gyro_bias = matrix::constrain(_state.gyro_bias, -gyro_bias_limit, gyro_bias_limit);
|
||||
|
||||
const float delta_vel_bias_limit = getAccelBiasLimit() * _dt_ekf_avg;
|
||||
_state.delta_vel_bias = matrix::constrain(_state.delta_vel_bias, -delta_vel_bias_limit, delta_vel_bias_limit);
|
||||
const float accel_bias_limit = getAccelBiasLimit();
|
||||
_state.accel_bias = matrix::constrain(_state.accel_bias, -accel_bias_limit, accel_bias_limit);
|
||||
|
||||
_state.mag_I = matrix::constrain(_state.mag_I, -1.0f, 1.0f);
|
||||
_state.mag_B = matrix::constrain(_state.mag_B, -getMagBiasLimit(), getMagBiasLimit());
|
||||
|
|
@ -390,8 +390,8 @@ matrix::Vector<float, 24> Ekf::getStateAtFusionHorizonAsVector() const
|
|||
state.slice<4, 1>(0, 0) = _state.quat_nominal;
|
||||
state.slice<3, 1>(4, 0) = _state.vel;
|
||||
state.slice<3, 1>(7, 0) = _state.pos;
|
||||
state.slice<3, 1>(10, 0) = _state.delta_ang_bias;
|
||||
state.slice<3, 1>(13, 0) = _state.delta_vel_bias;
|
||||
state.slice<3, 1>(10, 0) = _state.gyro_bias;
|
||||
state.slice<3, 1>(13, 0) = _state.accel_bias;
|
||||
state.slice<3, 1>(16, 0) = _state.mag_I;
|
||||
state.slice<3, 1>(19, 0) = _state.mag_B;
|
||||
state.slice<2, 1>(22, 0) = _state.wind_vel;
|
||||
|
|
@ -612,25 +612,28 @@ void Ekf::resetImuBias()
|
|||
|
||||
void Ekf::resetGyroBias()
|
||||
{
|
||||
// Zero the delta angle and delta velocity bias states
|
||||
_state.delta_ang_bias.zero();
|
||||
// Zero the gyro bias states
|
||||
_state.gyro_bias.zero();
|
||||
|
||||
// Zero the corresponding covariances and set
|
||||
// variances to the values use for initial alignment
|
||||
P.uncorrelateCovarianceSetVariance<3>(10, sq(_params.switch_on_gyro_bias * _dt_ekf_avg));
|
||||
P.uncorrelateCovarianceSetVariance<3>(10, sq(_params.switch_on_gyro_bias));
|
||||
|
||||
// Set previous frame values
|
||||
_prev_gyro_bias_var = P.slice<3, 3>(10, 10).diag();
|
||||
}
|
||||
|
||||
void Ekf::resetAccelBias()
|
||||
{
|
||||
// Zero the delta angle and delta velocity bias states
|
||||
_state.delta_vel_bias.zero();
|
||||
// Zero the accel bias states
|
||||
_state.accel_bias.zero();
|
||||
|
||||
// Zero the corresponding covariances and set
|
||||
// variances to the values use for initial alignment
|
||||
P.uncorrelateCovarianceSetVariance<3>(13, sq(_params.switch_on_accel_bias * _dt_ekf_avg));
|
||||
P.uncorrelateCovarianceSetVariance<3>(13, sq(_params.switch_on_accel_bias));
|
||||
|
||||
// Set previous frame values
|
||||
_prev_dvel_bias_var = P.slice<3, 3>(13, 13).diag();
|
||||
_prev_accel_bias_var = P.slice<3, 3>(13, 13).diag();
|
||||
}
|
||||
|
||||
// get EKF innovation consistency check status information comprising of:
|
||||
|
|
@ -792,13 +795,13 @@ void Ekf::fuse(const Vector24f &K, float innovation)
|
|||
_state.quat_nominal.normalize();
|
||||
_R_to_earth = Dcmf(_state.quat_nominal);
|
||||
|
||||
_state.vel -= K.slice<3, 1>(4, 0) * innovation;
|
||||
_state.pos -= K.slice<3, 1>(7, 0) * innovation;
|
||||
_state.delta_ang_bias -= K.slice<3, 1>(10, 0) * innovation;
|
||||
_state.delta_vel_bias -= K.slice<3, 1>(13, 0) * innovation;
|
||||
_state.mag_I -= K.slice<3, 1>(16, 0) * innovation;
|
||||
_state.mag_B -= K.slice<3, 1>(19, 0) * innovation;
|
||||
_state.wind_vel -= K.slice<2, 1>(22, 0) * innovation;
|
||||
_state.vel -= K.slice<3, 1>(4, 0) * innovation;
|
||||
_state.pos -= K.slice<3, 1>(7, 0) * innovation;
|
||||
_state.gyro_bias -= K.slice<3, 1>(10, 0) * innovation;
|
||||
_state.accel_bias -= K.slice<3, 1>(13, 0) * innovation;
|
||||
_state.mag_I -= K.slice<3, 1>(16, 0) * innovation;
|
||||
_state.mag_B -= K.slice<3, 1>(19, 0) * innovation;
|
||||
_state.wind_vel -= K.slice<2, 1>(22, 0) * innovation;
|
||||
}
|
||||
|
||||
void Ekf::uncorrelateQuatFromOtherStates()
|
||||
|
|
|
|||
|
|
@ -64,7 +64,6 @@
|
|||
#include "common.h"
|
||||
#include "RingBuffer.h"
|
||||
#include "imu_down_sampler.hpp"
|
||||
#include "utils.hpp"
|
||||
#include "output_predictor.h"
|
||||
|
||||
#if defined(CONFIG_EKF2_RANGE_FINDER)
|
||||
|
|
|
|||
|
|
@ -126,7 +126,7 @@ void Ekf::fuseGpsYaw()
|
|||
// A constant large signed test ratio is a sign of wrong gyro bias
|
||||
// Reset the yaw gyro variance to converge faster and avoid
|
||||
// being stuck on a previous bad estimate
|
||||
resetZDeltaAngBiasCov();
|
||||
resetGyroBiasZCov();
|
||||
}
|
||||
|
||||
// calculate the Kalman gains
|
||||
|
|
|
|||
|
|
@ -296,7 +296,7 @@ bool Ekf::fuseYaw(estimator_aid_source1d_s& aid_src_status, const Vector24f &H_Y
|
|||
|
||||
// also reset the yaw gyro variance to converge faster and avoid
|
||||
// being stuck on a previous bad estimate
|
||||
resetZDeltaAngBiasCov();
|
||||
resetGyroBiasZCov();
|
||||
|
||||
} else {
|
||||
return false;
|
||||
|
|
|
|||
|
|
@ -47,7 +47,6 @@
|
|||
#include <float.h>
|
||||
#include "python/ekf_derivation/generated/compute_flow_xy_innov_var_and_hx.h"
|
||||
#include "python/ekf_derivation/generated/compute_flow_y_innov_var_and_h.h"
|
||||
#include "utils.hpp"
|
||||
|
||||
void Ekf::updateOptFlow(estimator_aid_source2d_s &aid_src)
|
||||
{
|
||||
|
|
|
|||
|
|
@ -240,8 +240,7 @@ void OutputPredictor::calculateOutputStates(const uint64_t time_us, const Vector
|
|||
}
|
||||
|
||||
void OutputPredictor::correctOutputStates(const uint64_t time_delayed_us,
|
||||
const matrix::Vector3f &gyro_bias, const matrix::Vector3f &accel_bias,
|
||||
const Quatf &quat_state, const Vector3f &vel_state, const Vector3f &pos_state)
|
||||
const Quatf &quat_state, const Vector3f &vel_state, const Vector3f &pos_state, const matrix::Vector3f &gyro_bias, const matrix::Vector3f &accel_bias)
|
||||
{
|
||||
// calculate an average filter update time
|
||||
if (_time_last_correct_states_us != 0) {
|
||||
|
|
|
|||
|
|
@ -68,8 +68,7 @@ public:
|
|||
const matrix::Vector3f &delta_velocity, const float delta_velocity_dt);
|
||||
|
||||
void correctOutputStates(const uint64_t time_delayed_us,
|
||||
const matrix::Vector3f &gyro_bias, const matrix::Vector3f &accel_bias,
|
||||
const matrix::Quatf &quat_state, const matrix::Vector3f &vel_state, const matrix::Vector3f &pos_state);
|
||||
const matrix::Quatf &quat_state, const matrix::Vector3f &vel_state, const matrix::Vector3f &pos_state, const matrix::Vector3f &gyro_bias, const matrix::Vector3f &accel_bias);
|
||||
|
||||
void resetQuaternion(const matrix::Quatf &quat_change);
|
||||
|
||||
|
|
|
|||
|
|
@ -50,12 +50,12 @@ class State:
|
|||
px = 7
|
||||
py = 8
|
||||
pz = 9
|
||||
d_ang_bx = 10
|
||||
d_ang_by = 11
|
||||
d_ang_bz = 12
|
||||
d_vel_bx = 13
|
||||
d_vel_by = 14
|
||||
d_vel_bz = 15
|
||||
gyro_bx = 10
|
||||
gyro_by = 11
|
||||
gyro_bz = 12
|
||||
accel_bx = 13
|
||||
accel_by = 14
|
||||
accel_bz = 15
|
||||
ix = 16
|
||||
iy = 17
|
||||
iz = 18
|
||||
|
|
@ -89,10 +89,12 @@ def predict_covariance(
|
|||
):
|
||||
g = sf.Symbol("g") # does not appear in the jacobians
|
||||
|
||||
d_vel_b = sf.V3(state[State.d_vel_bx], state[State.d_vel_by], state[State.d_vel_bz])
|
||||
accel_b = sf.V3(state[State.accel_bx], state[State.accel_by], state[State.accel_bz])
|
||||
d_vel_b = accel_b * dt
|
||||
d_vel_true = d_vel - d_vel_b
|
||||
|
||||
d_ang_b = sf.V3(state[State.d_ang_bx], state[State.d_ang_by], state[State.d_ang_bz])
|
||||
gyro_b = sf.V3(state[State.gyro_bx], state[State.gyro_by], state[State.gyro_bz])
|
||||
d_ang_b = gyro_b * dt
|
||||
d_ang_true = d_ang - d_ang_b
|
||||
|
||||
q = state_to_quat(state)
|
||||
|
|
@ -100,12 +102,12 @@ def predict_covariance(
|
|||
v = sf.V3(state[State.vx], state[State.vy], state[State.vz])
|
||||
p = sf.V3(state[State.px], state[State.py], state[State.pz])
|
||||
|
||||
q_new = q * sf.Quaternion(sf.V3(0.5 * d_ang_true[0], 0.5 * d_ang_true[1], 0.5 * d_ang_true[2]), 1)
|
||||
v_new = v + R_to_earth * d_vel_true + sf.V3(0 ,0 ,g) * dt
|
||||
q_new = q * sf.Quaternion(sf.V3(0.5 * d_ang_true[0], 0.5 * d_ang_true[1], 0.5 * d_ang_true[2]), 1)
|
||||
v_new = v + R_to_earth * d_vel_true + sf.V3(0, 0, g) * dt
|
||||
p_new = p + v * dt
|
||||
|
||||
# Predicted state vector at time t + dt
|
||||
state_new = VState.block_matrix([[sf.V4(q_new.w, q_new.x, q_new.y, q_new.z)], [v_new], [p_new], [sf.Matrix(state[State.d_ang_bx:State.n_states])]])
|
||||
state_new = VState.block_matrix([[sf.V4(q_new.w, q_new.x, q_new.y, q_new.z)], [v_new], [p_new], [sf.Matrix(state[State.gyro_bx:State.n_states])]])
|
||||
|
||||
# State propagation jacobian
|
||||
A = state_new.jacobian(state)
|
||||
|
|
|
|||
File diff suppressed because it is too large
Load Diff
|
|
@ -1,75 +0,0 @@
|
|||
/****************************************************************************
|
||||
*
|
||||
* Copyright (c) 2020-2022 PX4 Development Team. All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
*
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in
|
||||
* the documentation and/or other materials provided with the
|
||||
* distribution.
|
||||
* 3. Neither the name PX4 nor the names of its contributors may be
|
||||
* used to endorse or promote products derived from this software
|
||||
* without specific prior written permission.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
||||
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
||||
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
|
||||
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
|
||||
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
|
||||
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
|
||||
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
|
||||
* OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
|
||||
* AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
|
||||
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
||||
* POSSIBILITY OF SUCH DAMAGE.
|
||||
*
|
||||
****************************************************************************/
|
||||
|
||||
#include <matrix/math.hpp>
|
||||
|
||||
#ifndef EKF_UTILS_HPP
|
||||
#define EKF_UTILS_HPP
|
||||
|
||||
// Use Kahan summation algorithm to get the sum of "sum_previous" and "input".
|
||||
// This function relies on the caller to be responsible for keeping a copy of
|
||||
// "accumulator" and passing this value at the next iteration.
|
||||
// Ref: https://en.wikipedia.org/wiki/Kahan_summation_algorithm
|
||||
inline float kahanSummation(float sum_previous, float input, float &accumulator)
|
||||
{
|
||||
const float y = input - accumulator;
|
||||
const float t = sum_previous + y;
|
||||
accumulator = (t - sum_previous) - y;
|
||||
return t;
|
||||
}
|
||||
|
||||
namespace ecl
|
||||
{
|
||||
inline float powf(float x, int exp)
|
||||
{
|
||||
float ret;
|
||||
|
||||
if (exp > 0) {
|
||||
ret = x;
|
||||
|
||||
for (int count = 1; count < exp; count++) {
|
||||
ret *= x;
|
||||
}
|
||||
|
||||
return ret;
|
||||
|
||||
} else if (exp < 0) {
|
||||
return 1.0f / ecl::powf(x, -exp);
|
||||
}
|
||||
|
||||
return 1.0f;
|
||||
}
|
||||
|
||||
} // namespace ecl
|
||||
|
||||
#endif // EKF_UTILS_HPP
|
||||
|
|
@ -54,12 +54,10 @@ void Ekf::controlZeroGyroUpdate(const imuSample &imu_delayed)
|
|||
const bool zero_gyro_update_data_ready = _zgup_delta_ang_dt >= zgup_dt;
|
||||
|
||||
if (zero_gyro_update_data_ready) {
|
||||
Vector3f delta_ang_scaled = _zgup_delta_ang / _zgup_delta_ang_dt * _dt_ekf_avg;
|
||||
Vector3f innovation = _state.delta_ang_bias - delta_ang_scaled;
|
||||
Vector3f gyro_bias = _zgup_delta_ang / _zgup_delta_ang_dt;
|
||||
Vector3f innovation = _state.gyro_bias - gyro_bias;
|
||||
|
||||
const float d_ang_sig = _dt_ekf_avg * math::constrain(_params.gyro_noise, 0.0f, 1.0f);
|
||||
//const float obs_var = sq(d_ang_sig) * (_dt_ekf_avg / _zgup_delta_ang_dt); // This is correct but too small for single precision
|
||||
const float obs_var = sq(d_ang_sig);
|
||||
const float obs_var = sq(math::constrain(_params.gyro_noise, 0.f, 1.f));
|
||||
|
||||
Vector3f innov_var{
|
||||
P(10, 10) + obs_var,
|
||||
|
|
|
|||
|
|
@ -40,7 +40,6 @@ px4_add_unit_gtest(SRC test_EKF_accelerometer.cpp LINKLIBS ecl_EKF ecl_sensor_si
|
|||
px4_add_unit_gtest(SRC test_EKF_airspeed_fusion_generated.cpp LINKLIBS ecl_EKF ecl_test_helper)
|
||||
px4_add_unit_gtest(SRC test_EKF_airspeed.cpp LINKLIBS ecl_EKF ecl_sensor_sim)
|
||||
px4_add_unit_gtest(SRC test_EKF_basics.cpp LINKLIBS ecl_EKF ecl_sensor_sim)
|
||||
px4_add_unit_gtest(SRC test_EKF_covariance_prediction_generated.cpp LINKLIBS ecl_EKF ecl_test_helper)
|
||||
px4_add_unit_gtest(SRC test_EKF_externalVision.cpp LINKLIBS ecl_EKF ecl_sensor_sim ecl_test_helper)
|
||||
px4_add_unit_gtest(SRC test_EKF_flow.cpp LINKLIBS ecl_EKF ecl_sensor_sim ecl_test_helper)
|
||||
px4_add_unit_gtest(SRC test_EKF_gyroscope.cpp LINKLIBS ecl_EKF ecl_sensor_sim)
|
||||
|
|
|
|||
|
|
@ -1,391 +1,391 @@
|
|||
Timestamp,state[0],state[1],state[2],state[3],state[4],state[5],state[6],state[7],state[8],state[9],state[10],state[11],state[12],state[13],state[14],state[15],state[16],state[17],state[18],state[19],state[20],state[21],state[22],state[23],variance[0],variance[1],variance[2],variance[3],variance[4],variance[5],variance[6],variance[7],variance[8],variance[9],variance[10],variance[11],variance[12],variance[13],variance[14],variance[15],variance[16],variance[17],variance[18],variance[19],variance[20],variance[21],variance[22],variance[23]
|
||||
10000,1,-0.0094,-0.01,-3.2e-06,0.00023,7.3e-05,-0.011,7.1e-06,2.2e-06,-0.00045,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4.9e-07,0.0025,0.0025,0.005,25,25,10,1e+02,1e+02,1e+02,1e-06,1e-06,1e-06,4e-06,4e-06,4e-06,0,0,0,0,0,0,0,0
|
||||
90000,1,-0.0096,-0.01,-0.02,-0.0004,0.0026,-0.026,-1.4e-05,0.00011,-0.0023,0,0,0,0,0,0,0.19,-9.3e-10,0.4,0,0,0,0,0,5.2e-07,0.0026,0.0026,0.0051,25,25,10,1e+02,1e+02,1e+02,1e-06,1e-06,1e-06,4e-06,4e-06,4e-06,0,0,0,0,0,0,0,0
|
||||
190000,1,-0.0096,-0.011,-0.02,0.0002,0.0039,-0.041,6e-06,0.00043,-0.0044,-3e-13,-2.3e-14,4.9e-15,0,0,-2e-11,0.19,-9.3e-10,0.4,0,0,0,0,0,5.8e-07,0.0027,0.0027,0.0052,25,25,10,1e+02,1e+02,1,1e-06,1e-06,1e-06,4e-06,4e-06,4e-06,0,0,0,0,0,0,0,0
|
||||
290000,1,-0.0097,-0.011,-0.02,0.0012,0.0063,-0.053,5e-05,0.00036,-0.007,9.1e-12,9.1e-13,-2.1e-13,0,0,-4.8e-09,0.19,-9.3e-10,0.4,0,0,0,0,0,6.8e-07,0.0029,0.0029,0.0054,25,25,9.6,0.37,0.37,0.41,1e-06,1e-06,1e-06,4e-06,4e-06,4e-06,0,0,0,0,0,0,0,0
|
||||
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18090000,0.71,0.00014,-0.013,0.71,0.012,-0.0018,0.0043,0.00083,-0.0019,-3.7e+02,-1.3e-05,-6.1e-05,4.5e-06,-1.7e-05,5.2e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00013,0.00013,5.1e-05,0.036,0.036,0.016,0.051,0.051,0.047,6.4e-10,6.4e-10,9.3e-10,3e-06,3e-06,9.7e-08,0,0,0,0,0,0,0,0
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18290000,0.71,4.6e-05,-0.013,0.71,0.013,-0.0013,0.0068,0.0029,-0.0016,-3.7e+02,-1.3e-05,-6e-05,4.6e-06,-1.7e-05,5.2e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00013,0.00013,5e-05,0.035,0.035,0.015,0.051,0.051,0.046,5.8e-10,5.8e-10,8.9e-10,3e-06,3e-06,8.9e-08,0,0,0,0,0,0,0,0
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18390000,0.71,6.1e-05,-0.013,0.71,0.014,0.00032,0.008,0.0034,-0.0012,-3.7e+02,-1.3e-05,-6e-05,4.9e-06,-1.6e-05,5.3e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00012,0.00012,4.9e-05,0.031,0.031,0.014,0.045,0.045,0.046,5.2e-10,5.2e-10,8.6e-10,3e-06,3e-06,8.4e-08,0,0,0,0,0,0,0,0
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18490000,0.71,7.6e-05,-0.013,0.71,0.015,0.00077,0.0076,0.0049,-0.0011,-3.7e+02,-1.3e-05,-6e-05,5e-06,-1.6e-05,5.3e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00013,0.00013,4.9e-05,0.034,0.034,0.014,0.051,0.051,0.046,5.2e-10,5.2e-10,8.5e-10,3e-06,3e-06,8.2e-08,0,0,0,0,0,0,0,0
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18590000,0.71,8.1e-05,-0.012,0.71,0.014,0.00095,0.0058,0.0037,-0.00098,-3.7e+02,-1.3e-05,-6e-05,5.4e-06,-1.6e-05,5.7e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00012,0.00012,4.9e-05,0.03,0.03,0.014,0.045,0.045,0.045,4.8e-10,4.8e-10,8.2e-10,3e-06,3e-06,7.8e-08,0,0,0,0,0,0,0,0
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18690000,0.71,5e-05,-0.012,0.71,0.014,0.00029,0.0039,0.0051,-0.00089,-3.7e+02,-1.3e-05,-6e-05,5.3e-06,-1.6e-05,5.7e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00012,0.00012,4.8e-05,0.033,0.033,0.013,0.051,0.051,0.045,4.8e-10,4.8e-10,8e-10,3e-06,3e-06,7.5e-08,0,0,0,0,0,0,0,0
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18790000,0.71,8.1e-05,-0.012,0.71,0.013,0.00054,0.0035,0.0039,-0.00071,-3.7e+02,-1.4e-05,-6e-05,5.1e-06,-1.6e-05,6e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00012,0.00012,4.8e-05,0.03,0.03,0.013,0.045,0.045,0.045,4.3e-10,4.3e-10,7.9e-10,3e-06,3e-06,7.2e-08,0,0,0,0,0,0,0,0
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18890000,0.71,0.0001,-0.012,0.71,0.013,0.0011,0.0042,0.0052,-0.0006,-3.7e+02,-1.4e-05,-6e-05,5.6e-06,-1.6e-05,6e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00012,0.00012,4.7e-05,0.033,0.033,0.013,0.051,0.051,0.045,4.3e-10,4.3e-10,7.7e-10,3e-06,3e-06,7e-08,0,0,0,0,0,0,0,0
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18990000,0.71,9.1e-05,-0.012,0.71,0.014,0.0019,0.0028,0.0065,-0.00051,-3.7e+02,-1.4e-05,-6e-05,5.7e-06,-1.6e-05,6e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00012,0.00012,4.7e-05,0.029,0.029,0.012,0.045,0.045,0.044,3.9e-10,3.9e-10,7.5e-10,2.9e-06,2.9e-06,6.6e-08,0,0,0,0,0,0,0,0
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19090000,0.71,7.5e-05,-0.012,0.71,0.015,0.0025,0.0058,0.008,-0.00026,-3.7e+02,-1.4e-05,-6e-05,5.7e-06,-1.6e-05,6e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00012,0.00012,4.7e-05,0.032,0.032,0.012,0.051,0.051,0.044,3.9e-10,3.9e-10,7.3e-10,2.9e-06,2.9e-06,6.5e-08,0,0,0,0,0,0,0,0
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19190000,0.71,7.7e-05,-0.012,0.71,0.015,0.0025,0.0059,0.0087,-0.00026,-3.7e+02,-1.4e-05,-6.1e-05,5.9e-06,-1.7e-05,5.9e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00011,0.00011,4.6e-05,0.028,0.028,0.012,0.045,0.045,0.044,3.6e-10,3.6e-10,7.2e-10,2.9e-06,2.9e-06,6.2e-08,0,0,0,0,0,0,0,0
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19290000,0.71,0.0001,-0.012,0.71,0.015,0.0018,0.0086,0.01,-2.8e-05,-3.7e+02,-1.4e-05,-6.1e-05,5.6e-06,-1.7e-05,5.9e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00011,0.00011,4.6e-05,0.031,0.031,0.012,0.05,0.05,0.044,3.6e-10,3.6e-10,7e-10,2.9e-06,2.9e-06,6e-08,0,0,0,0,0,0,0,0
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19390000,0.71,0.00011,-0.012,0.71,0.013,0.0008,0.012,0.0082,-9.1e-05,-3.7e+02,-1.4e-05,-6.1e-05,5.8e-06,-1.7e-05,6.3e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00011,0.00011,4.6e-05,0.027,0.027,0.012,0.044,0.044,0.043,3.3e-10,3.3e-10,6.8e-10,2.9e-06,2.9e-06,5.8e-08,0,0,0,0,0,0,0,0
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19490000,0.71,0.00014,-0.012,0.71,0.012,0.00011,0.0088,0.0094,-4.9e-05,-3.7e+02,-1.4e-05,-6.1e-05,6.1e-06,-1.7e-05,6.3e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00011,0.00011,4.5e-05,0.03,0.03,0.011,0.05,0.05,0.043,3.3e-10,3.3e-10,6.7e-10,2.9e-06,2.9e-06,5.6e-08,0,0,0,0,0,0,0,0
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19590000,0.71,0.00018,-0.012,0.71,0.01,-0.00096,0.0081,0.0076,-0.00011,-3.7e+02,-1.4e-05,-6.1e-05,6.5e-06,-1.7e-05,6.7e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00011,0.00011,4.5e-05,0.027,0.027,0.011,0.044,0.044,0.042,3e-10,3e-10,6.5e-10,2.9e-06,2.9e-06,5.4e-08,0,0,0,0,0,0,0,0
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19690000,0.71,0.00019,-0.012,0.71,0.01,-0.0031,0.0096,0.0086,-0.00032,-3.7e+02,-1.4e-05,-6.1e-05,6.3e-06,-1.7e-05,6.7e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00011,0.00011,4.5e-05,0.029,0.029,0.011,0.05,0.05,0.042,3e-10,3e-10,6.4e-10,2.9e-06,2.9e-06,5.2e-08,0,0,0,0,0,0,0,0
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19790000,0.71,0.00025,-0.012,0.71,0.008,-0.004,0.01,0.007,-0.00026,-3.7e+02,-1.4e-05,-6.1e-05,6.3e-06,-1.7e-05,6.9e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00011,0.00011,4.4e-05,0.026,0.026,0.011,0.044,0.044,0.042,2.7e-10,2.7e-10,6.3e-10,2.9e-06,2.9e-06,5e-08,0,0,0,0,0,0,0,0
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16490000,0.71,0.00015,-0.013,0.71,0.0061,-0.0031,-0.018,0.00074,-0.0032,-3.7e+02,-0.0012,-0.0061,0.00043,-0.0014,0.0035,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00017,0.00016,5.9e-05,0.041,0.041,0.023,0.052,0.052,0.052,1.4e-05,1.4e-05,1.4e-05,0.032,0.032,0.0021,0,0,0,0,0,0,0,0
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16590000,0.71,0.0004,-0.013,0.71,0.0025,-0.00048,-0.018,-0.0023,0.00012,-3.7e+02,-0.0013,-0.006,0.00044,-0.00074,0.0042,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00016,0.00016,5.8e-05,0.036,0.036,0.022,0.046,0.046,0.051,1.2e-05,1.2e-05,1.4e-05,0.032,0.032,0.002,0,0,0,0,0,0,0,0
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16690000,0.71,0.00039,-0.013,0.71,0.0027,4.3e-05,-0.015,-0.002,0.0001,-3.7e+02,-0.0013,-0.006,0.0004,-0.0008,0.0043,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00016,0.00016,5.7e-05,0.041,0.041,0.022,0.052,0.052,0.051,1.2e-05,1.2e-05,1.4e-05,0.032,0.032,0.0019,0,0,0,0,0,0,0,0
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16790000,0.71,0.00054,-0.013,0.71,-0.00072,0.0022,-0.014,-0.0044,0.0027,-3.7e+02,-0.0013,-0.006,0.00041,-0.00021,0.0049,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00015,0.00015,5.7e-05,0.036,0.036,0.021,0.046,0.046,0.05,1.1e-05,1.1e-05,1.3e-05,0.032,0.032,0.0018,0,0,0,0,0,0,0,0
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16890000,0.71,0.00056,-0.013,0.71,-0.00095,0.0031,-0.011,-0.0045,0.003,-3.7e+02,-0.0013,-0.006,0.00039,-0.00025,0.005,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00016,0.00016,5.6e-05,0.04,0.04,0.021,0.052,0.052,0.051,1.1e-05,1.1e-05,1.3e-05,0.032,0.032,0.0017,0,0,0,0,0,0,0,0
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16990000,0.71,0.0005,-0.013,0.71,-0.00098,0.001,-0.01,-0.005,0.0011,-3.7e+02,-0.0013,-0.006,0.00035,-0.00065,0.0052,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00015,0.00015,5.6e-05,0.035,0.035,0.02,0.046,0.046,0.05,1e-05,1e-05,1.2e-05,0.032,0.032,0.0016,0,0,0,0,0,0,0,0
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17090000,0.71,0.00046,-0.013,0.71,-0.00014,0.002,-0.01,-0.0051,0.0012,-3.7e+02,-0.0013,-0.006,0.00035,-0.00064,0.0052,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00015,0.00015,5.5e-05,0.039,0.039,0.02,0.052,0.052,0.05,1e-05,1e-05,1.2e-05,0.032,0.032,0.0016,0,0,0,0,0,0,0,0
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17190000,0.71,0.00045,-0.013,0.71,0.00024,0.0019,-0.011,-0.0054,-0.00032,-3.7e+02,-0.0013,-0.006,0.00038,-0.00099,0.0054,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00015,0.00015,5.5e-05,0.035,0.035,0.019,0.046,0.046,0.049,9.4e-06,9.4e-06,1.2e-05,0.031,0.031,0.0015,0,0,0,0,0,0,0,0
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17290000,0.71,0.00043,-0.013,0.71,0.0024,0.003,-0.0066,-0.0053,-9.1e-05,-3.7e+02,-0.0013,-0.006,0.00034,-0.001,0.0055,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00015,0.00015,5.4e-05,0.039,0.039,0.019,0.052,0.052,0.049,9.4e-06,9.4e-06,1.2e-05,0.031,0.031,0.0014,0,0,0,0,0,0,0,0
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17390000,0.71,0.00039,-0.013,0.71,0.003,0.0021,-0.0047,-0.0045,-0.0014,-3.7e+02,-0.0013,-0.006,0.00038,-0.0014,0.0055,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00014,0.00014,5.4e-05,0.034,0.034,0.018,0.046,0.046,0.048,8.5e-06,8.5e-06,1.1e-05,0.031,0.031,0.0013,0,0,0,0,0,0,0,0
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17490000,0.71,0.00039,-0.013,0.71,0.0035,0.0017,-0.003,-0.0042,-0.0012,-3.7e+02,-0.0013,-0.006,0.00038,-0.0014,0.0055,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00014,0.00014,5.3e-05,0.038,0.038,0.018,0.052,0.052,0.049,8.5e-06,8.5e-06,1.1e-05,0.031,0.031,0.0013,0,0,0,0,0,0,0,0
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17590000,0.71,0.0003,-0.013,0.71,0.0047,0.0005,0.0025,-0.0035,-0.0024,-3.7e+02,-0.0013,-0.0061,0.00039,-0.0018,0.0056,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00014,0.00014,5.3e-05,0.034,0.034,0.017,0.045,0.045,0.048,7.7e-06,7.7e-06,1.1e-05,0.031,0.031,0.0012,0,0,0,0,0,0,0,0
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17690000,0.71,0.00027,-0.013,0.71,0.0057,0.0013,0.0019,-0.003,-0.0023,-3.7e+02,-0.0013,-0.0061,0.00041,-0.0017,0.0056,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00014,0.00014,5.2e-05,0.037,0.037,0.017,0.052,0.052,0.048,7.7e-06,7.7e-06,1e-05,0.031,0.031,0.0012,0,0,0,0,0,0,0,0
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17790000,0.71,0.00018,-0.013,0.71,0.0082,0.0009,0.00059,-0.0019,-0.002,-3.7e+02,-0.0013,-0.0061,0.00048,-0.0017,0.0053,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00013,0.00013,5.2e-05,0.033,0.033,0.016,0.045,0.045,0.048,7e-06,7e-06,1e-05,0.031,0.031,0.0011,0,0,0,0,0,0,0,0
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17890000,0.71,0.00019,-0.013,0.71,0.0097,0.00018,0.00069,-0.00099,-0.0019,-3.7e+02,-0.0013,-0.0061,0.00051,-0.0017,0.0053,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00014,0.00014,5.2e-05,0.037,0.037,0.016,0.051,0.051,0.048,7e-06,7e-06,9.8e-06,0.031,0.031,0.0011,0,0,0,0,0,0,0,0
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17990000,0.71,0.00013,-0.013,0.71,0.011,-0.0016,0.0019,-0.00034,-0.0017,-3.7e+02,-0.0013,-0.0061,0.0005,-0.0017,0.0051,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00013,0.00013,5.1e-05,0.032,0.032,0.016,0.045,0.045,0.047,6.4e-06,6.4e-06,9.6e-06,0.03,0.03,0.001,0,0,0,0,0,0,0,0
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||||
18090000,0.71,0.00014,-0.013,0.71,0.012,-0.0018,0.0043,0.00083,-0.0019,-3.7e+02,-0.0013,-0.0061,0.00045,-0.0017,0.0052,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00013,0.00013,5.1e-05,0.036,0.036,0.016,0.051,0.051,0.047,6.4e-06,6.4e-06,9.3e-06,0.03,0.03,0.00097,0,0,0,0,0,0,0,0
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||||
18190000,0.71,0.0001,-0.013,0.71,0.013,-0.00074,0.0056,0.0016,-0.0015,-3.7e+02,-0.0013,-0.006,0.00048,-0.0017,0.0052,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00013,0.00013,5e-05,0.032,0.032,0.015,0.045,0.045,0.047,5.8e-06,5.8e-06,9.1e-06,0.03,0.03,0.00092,0,0,0,0,0,0,0,0
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||||
18290000,0.71,4.6e-05,-0.013,0.71,0.013,-0.0013,0.0068,0.0029,-0.0016,-3.7e+02,-0.0013,-0.006,0.00046,-0.0017,0.0052,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00013,0.00013,5e-05,0.035,0.035,0.015,0.051,0.051,0.046,5.8e-06,5.8e-06,8.9e-06,0.03,0.03,0.00089,0,0,0,0,0,0,0,0
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||||
18390000,0.71,6.1e-05,-0.013,0.71,0.014,0.00032,0.008,0.0034,-0.0012,-3.7e+02,-0.0013,-0.006,0.00049,-0.0016,0.0053,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00012,0.00012,4.9e-05,0.031,0.031,0.014,0.045,0.045,0.046,5.2e-06,5.2e-06,8.6e-06,0.03,0.03,0.00084,0,0,0,0,0,0,0,0
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||||
18490000,0.71,7.6e-05,-0.013,0.71,0.015,0.00077,0.0076,0.0049,-0.0011,-3.7e+02,-0.0013,-0.006,0.0005,-0.0016,0.0053,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00013,0.00013,4.9e-05,0.034,0.034,0.014,0.051,0.051,0.046,5.2e-06,5.2e-06,8.5e-06,0.03,0.03,0.00082,0,0,0,0,0,0,0,0
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||||
18590000,0.71,8.1e-05,-0.012,0.71,0.014,0.00095,0.0058,0.0037,-0.00098,-3.7e+02,-0.0013,-0.006,0.00054,-0.0016,0.0057,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00012,0.00012,4.9e-05,0.03,0.03,0.014,0.045,0.045,0.045,4.8e-06,4.8e-06,8.2e-06,0.03,0.03,0.00078,0,0,0,0,0,0,0,0
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||||
18690000,0.71,5e-05,-0.012,0.71,0.014,0.00029,0.0039,0.0051,-0.00089,-3.7e+02,-0.0013,-0.006,0.00053,-0.0016,0.0057,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00012,0.00012,4.8e-05,0.033,0.033,0.013,0.051,0.051,0.045,4.8e-06,4.8e-06,8e-06,0.03,0.03,0.00075,0,0,0,0,0,0,0,0
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||||
18790000,0.71,8.1e-05,-0.012,0.71,0.013,0.00054,0.0035,0.0039,-0.00071,-3.7e+02,-0.0014,-0.006,0.00051,-0.0016,0.006,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00012,0.00012,4.8e-05,0.03,0.03,0.013,0.045,0.045,0.045,4.3e-06,4.3e-06,7.9e-06,0.03,0.03,0.00072,0,0,0,0,0,0,0,0
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||||
18890000,0.71,0.0001,-0.012,0.71,0.013,0.0011,0.0042,0.0052,-0.0006,-3.7e+02,-0.0014,-0.006,0.00056,-0.0016,0.006,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00012,0.00012,4.7e-05,0.033,0.033,0.013,0.051,0.051,0.045,4.3e-06,4.3e-06,7.7e-06,0.03,0.03,0.0007,0,0,0,0,0,0,0,0
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||||
18990000,0.71,9.1e-05,-0.012,0.71,0.014,0.0019,0.0028,0.0065,-0.00051,-3.7e+02,-0.0014,-0.006,0.00057,-0.0016,0.006,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00012,0.00012,4.7e-05,0.029,0.029,0.012,0.045,0.045,0.044,3.9e-06,3.9e-06,7.5e-06,0.029,0.029,0.00066,0,0,0,0,0,0,0,0
|
||||
19090000,0.71,7.5e-05,-0.012,0.71,0.015,0.0025,0.0058,0.008,-0.00026,-3.7e+02,-0.0014,-0.006,0.00057,-0.0016,0.006,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00012,0.00012,4.7e-05,0.032,0.032,0.012,0.051,0.051,0.044,3.9e-06,3.9e-06,7.3e-06,0.029,0.03,0.00065,0,0,0,0,0,0,0,0
|
||||
19190000,0.71,7.7e-05,-0.012,0.71,0.015,0.0025,0.0059,0.0087,-0.00026,-3.7e+02,-0.0014,-0.0061,0.00059,-0.0017,0.0059,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00011,0.00011,4.6e-05,0.028,0.028,0.012,0.045,0.045,0.044,3.6e-06,3.6e-06,7.2e-06,0.029,0.029,0.00062,0,0,0,0,0,0,0,0
|
||||
19290000,0.71,0.0001,-0.012,0.71,0.015,0.0018,0.0086,0.01,-2.8e-05,-3.7e+02,-0.0014,-0.0061,0.00056,-0.0017,0.0059,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00011,0.00011,4.6e-05,0.031,0.031,0.012,0.05,0.05,0.044,3.6e-06,3.6e-06,7e-06,0.029,0.029,0.0006,0,0,0,0,0,0,0,0
|
||||
19390000,0.71,0.00011,-0.012,0.71,0.013,0.0008,0.012,0.0082,-9.1e-05,-3.7e+02,-0.0014,-0.0061,0.00058,-0.0017,0.0063,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00011,0.00011,4.6e-05,0.027,0.027,0.012,0.044,0.044,0.043,3.3e-06,3.3e-06,6.8e-06,0.029,0.029,0.00058,0,0,0,0,0,0,0,0
|
||||
19490000,0.71,0.00014,-0.012,0.71,0.012,0.00011,0.0088,0.0094,-4.9e-05,-3.7e+02,-0.0014,-0.0061,0.00061,-0.0017,0.0063,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00011,0.00011,4.5e-05,0.03,0.03,0.011,0.05,0.05,0.043,3.3e-06,3.3e-06,6.7e-06,0.029,0.029,0.00056,0,0,0,0,0,0,0,0
|
||||
19590000,0.71,0.00018,-0.012,0.71,0.01,-0.00096,0.0081,0.0076,-0.00011,-3.7e+02,-0.0014,-0.0061,0.00065,-0.0017,0.0067,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00011,0.00011,4.5e-05,0.027,0.027,0.011,0.044,0.044,0.042,3e-06,3e-06,6.5e-06,0.029,0.029,0.00054,0,0,0,0,0,0,0,0
|
||||
19690000,0.71,0.00019,-0.012,0.71,0.01,-0.0031,0.0096,0.0086,-0.00032,-3.7e+02,-0.0014,-0.0061,0.00063,-0.0017,0.0067,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00011,0.00011,4.5e-05,0.029,0.029,0.011,0.05,0.05,0.042,3e-06,3e-06,6.4e-06,0.029,0.029,0.00052,0,0,0,0,0,0,0,0
|
||||
19790000,0.71,0.00025,-0.012,0.71,0.008,-0.004,0.01,0.007,-0.00026,-3.7e+02,-0.0014,-0.0061,0.00063,-0.0017,0.0069,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00011,0.00011,4.4e-05,0.026,0.026,0.011,0.044,0.044,0.042,2.7e-06,2.7e-06,6.3e-06,0.029,0.029,0.0005,0,0,0,0,0,0,0,0
|
||||
19890000,0.71,0.0002,-0.012,0.71,0.0068,-0.0043,0.011,0.0077,-0.00069,-3.7e+02,-0.0014,-0.0061,0.00067,-0.0017,0.0069,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00011,0.00011,4.4e-05,0.029,0.029,0.011,0.05,0.05,0.042,2.7e-06,2.7e-06,6.1e-06,0.029,0.029,0.0005,0,0,0,0,0,0,0,0
|
||||
19990000,0.71,0.00019,-0.012,0.71,0.0043,-0.005,0.014,0.0063,-0.00058,-3.7e+02,-0.0014,-0.006,0.00073,-0.0016,0.0071,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.0001,0.0001,4.4e-05,0.026,0.026,0.01,0.044,0.044,0.041,2.5e-06,2.5e-06,6e-06,0.029,0.029,0.0005,0,0,0,0,0,0,0,0
|
||||
20090000,0.71,0.00018,-0.012,0.71,0.0041,-0.0069,0.014,0.0067,-0.0012,-3.7e+02,-0.0014,-0.006,0.00078,-0.0016,0.0071,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.00011,0.0001,4.4e-05,0.028,0.028,0.01,0.049,0.049,0.042,2.5e-06,2.5e-06,5.9e-06,0.029,0.029,0.0005,0,0,0,0,0,0,0,0
|
||||
20190000,0.71,0.00028,-0.012,0.71,0.0018,-0.0076,0.017,0.0044,-0.00092,-3.7e+02,-0.0014,-0.006,0.0008,-0.0015,0.0074,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.0001,0.0001,4.3e-05,0.025,0.025,0.01,0.044,0.044,0.041,2.3e-06,2.3e-06,5.7e-06,0.029,0.029,0.0005,0,0,0,0,0,0,0,0
|
||||
20290000,0.71,0.00024,-0.012,0.71,0.00064,-0.0092,0.015,0.0045,-0.0018,-3.7e+02,-0.0014,-0.006,0.00081,-0.0015,0.0074,-0.13,0.37,0.0037,0.025,0,0,0,0,0,0.0038,0.0001,0.0001,4.3e-05,0.027,0.027,0.0099,0.049,0.049,0.041,2.3e-06,2.3e-06,5.6e-06,0.029,0.029,0.0005,0,0,0,0,0,0,0,0
|
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|
|
|
|||
|
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@ -1,351 +1,351 @@
|
|||
Timestamp,state[0],state[1],state[2],state[3],state[4],state[5],state[6],state[7],state[8],state[9],state[10],state[11],state[12],state[13],state[14],state[15],state[16],state[17],state[18],state[19],state[20],state[21],state[22],state[23],variance[0],variance[1],variance[2],variance[3],variance[4],variance[5],variance[6],variance[7],variance[8],variance[9],variance[10],variance[11],variance[12],variance[13],variance[14],variance[15],variance[16],variance[17],variance[18],variance[19],variance[20],variance[21],variance[22],variance[23]
|
||||
10000,1,-0.011,-0.01,0.00023,0.00033,-0.00013,-0.01,1e-05,-3.8e-06,-0.00042,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5.8e-07,0.0025,0.0025,0.005,25,25,10,1e+02,1e+02,1e+02,1e-06,1e-06,1e-06,4e-06,4e-06,4e-06,0,0,0,0,0,0,0,0
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19090000,0.98,-0.007,-0.011,0.19,0.00087,-0.0062,0.023,0.0059,-0.0031,0.022,-1.5e-05,-6e-05,4.6e-06,0.00011,4.1e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.00018,0.00012,0.00012,9.4e-05,0.032,0.032,0.0087,0.051,0.051,0.036,4e-10,4e-10,7e-10,3e-06,3e-06,5e-08,0,0,0,0,0,0,0,0
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19190000,0.98,-0.0069,-0.011,0.19,-0.00064,-0.0059,0.022,0.0049,-0.0025,0.022,-1.5e-05,-6e-05,4.2e-06,0.00011,4.1e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.00018,0.00011,0.00011,9.4e-05,0.028,0.028,0.0086,0.045,0.045,0.036,3.6e-10,3.6e-10,6.8e-10,2.9e-06,3e-06,5e-08,0,0,0,0,0,0,0,0
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19390000,0.98,-0.0069,-0.011,0.19,-0.002,-0.0022,0.024,0.0041,-0.0012,0.019,-1.5e-05,-6e-05,3.9e-06,0.00011,4.1e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.00018,0.00011,0.00011,9.2e-05,0.028,0.028,0.0086,0.045,0.045,0.036,3.3e-10,3.3e-10,6.5e-10,2.9e-06,2.9e-06,5e-08,0,0,0,0,0,0,0,0
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19490000,0.98,-0.0069,-0.011,0.19,-0.0028,-0.0022,0.023,0.0039,-0.0014,0.019,-1.5e-05,-6e-05,3.6e-06,0.00011,4e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.00018,0.00011,0.00011,9.2e-05,0.03,0.03,0.0087,0.05,0.05,0.036,3.3e-10,3.3e-10,6.4e-10,2.9e-06,2.9e-06,5e-08,0,0,0,0,0,0,0,0
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19590000,0.98,-0.0069,-0.011,0.19,-0.0039,-0.0051,0.025,0.0044,-0.0024,0.019,-1.5e-05,-6e-05,3.4e-06,0.00012,3.7e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.00018,0.00011,0.00011,9.1e-05,0.027,0.027,0.0086,0.044,0.044,0.036,3e-10,3e-10,6.2e-10,2.9e-06,2.9e-06,5e-08,0,0,0,0,0,0,0,0
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19690000,0.98,-0.0069,-0.011,0.19,-0.0055,-0.0037,0.023,0.004,-0.0028,0.019,-1.5e-05,-6e-05,3.6e-06,0.00012,3.6e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.00018,0.00011,0.00011,9e-05,0.03,0.03,0.0086,0.05,0.05,0.036,3e-10,3e-10,6.1e-10,2.9e-06,2.9e-06,5e-08,0,0,0,0,0,0,0,0
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19790000,0.98,-0.007,-0.011,0.19,-0.0056,-0.0022,0.022,0.0064,-0.0023,0.014,-1.5e-05,-6e-05,3.3e-06,0.00012,3.3e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.00018,0.00011,0.0001,9e-05,0.026,0.026,0.0086,0.044,0.044,0.036,2.8e-10,2.8e-10,6e-10,2.9e-06,2.9e-06,5e-08,0,0,0,0,0,0,0,0
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19890000,0.98,-0.007,-0.011,0.19,-0.0056,-0.002,0.022,0.0058,-0.0025,0.013,-1.5e-05,-6e-05,3.2e-06,0.00013,3.2e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.00018,0.00011,0.00011,8.9e-05,0.029,0.029,0.0086,0.05,0.05,0.036,2.8e-10,2.8e-10,5.8e-10,2.9e-06,2.9e-06,5e-08,0,0,0,0,0,0,0,0
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19990000,0.98,-0.0071,-0.011,0.19,-0.0053,-0.0019,0.019,0.0062,-0.00091,0.0097,-1.5e-05,-5.9e-05,3.2e-06,0.00013,3.1e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.00018,0.0001,0.0001,8.8e-05,0.026,0.026,0.0085,0.044,0.044,0.036,2.5e-10,2.5e-10,5.7e-10,2.9e-06,2.9e-06,5e-08,0,0,0,0,0,0,0,0
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20090000,0.98,-0.0071,-0.011,0.19,-0.0048,-0.0042,0.019,0.0056,-0.0012,0.013,-1.5e-05,-5.9e-05,3.1e-06,0.00013,3.1e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.00018,0.00011,0.0001,8.8e-05,0.028,0.028,0.0086,0.05,0.05,0.036,2.5e-10,2.5e-10,5.6e-10,2.9e-06,2.9e-06,5e-08,0,0,0,0,0,0,0,0
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20190000,0.98,-0.0071,-0.011,0.19,-0.0038,-0.0016,0.02,0.0066,-0.00091,0.013,-1.5e-05,-5.9e-05,2.9e-06,0.00013,3.1e-05,-0.0013,0.37,0.0037,0.025,0,0,0,0,0,0.00018,0.0001,0.0001,8.7e-05,0.025,0.025,0.0085,0.044,0.044,0.036,2.3e-10,2.3e-10,5.5e-10,2.9e-06,2.9e-06,5e-08,0,0,0,0,0,0,0,0
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|
||||
34590000,0.98,-0.0068,-0.013,0.18,-0.014,-0.0053,0.71,0.073,-0.0089,-0.081,-0.0014,-0.0056,0.00024,0.016,-0.027,-0.11,0.37,0.0037,0.025,0,0,0,0,0,0.00017,3.1e-05,3.1e-05,4.7e-05,0.044,0.044,0.0059,0.045,0.045,0.032,2.6e-07,2.6e-07,8.2e-07,0.022,0.022,0.0005,0,0,0,0,0,0,0,0
|
||||
34690000,0.98,-0.0068,-0.012,0.18,-0.017,-0.0032,1.7,0.071,-0.0093,0.038,-0.0014,-0.0056,0.00023,0.016,-0.027,-0.11,0.37,0.0037,0.025,0,0,0,0,0,0.00017,3.1e-05,3.1e-05,4.7e-05,0.047,0.047,0.006,0.052,0.052,0.032,2.6e-07,2.6e-07,8.1e-07,0.022,0.022,0.0005,0,0,0,0,0,0,0,0
|
||||
34790000,0.98,-0.0068,-0.012,0.18,-0.019,0.0014,2.7,0.072,-0.0069,0.21,-0.0014,-0.0056,0.00023,0.018,-0.029,-0.1,0.37,0.0037,0.025,0,0,0,0,0,0.00017,2.9e-05,2.9e-05,4.7e-05,0.04,0.04,0.0061,0.045,0.045,0.032,2.6e-07,2.6e-07,8.1e-07,0.02,0.02,0.0005,0,0,0,0,0,0,0,0
|
||||
34890000,0.98,-0.0068,-0.012,0.18,-0.022,0.0038,3.6,0.07,-0.0065,0.5,-0.0014,-0.0056,0.00023,0.018,-0.029,-0.1,0.37,0.0037,0.025,0,0,0,0,0,0.00017,2.9e-05,2.9e-05,4.7e-05,0.043,0.043,0.0061,0.052,0.052,0.032,2.6e-07,2.6e-07,8e-07,0.02,0.02,0.0005,0,0,0,0,0,0,0,0
|
||||
|
|
|
|||
|
|
|
@ -288,11 +288,6 @@ int EkfWrapper::getQuaternionResetCounter() const
|
|||
return static_cast<int>(counter);
|
||||
}
|
||||
|
||||
matrix::Vector3f EkfWrapper::getDeltaVelBiasVariance() const
|
||||
{
|
||||
return _ekf->covariances_diagonal().slice<3, 1>(13, 0);
|
||||
}
|
||||
|
||||
void EkfWrapper::enableDragFusion()
|
||||
{
|
||||
_ekf_params->drag_ctrl = 1;
|
||||
|
|
|
|||
|
|
@ -120,8 +120,6 @@ public:
|
|||
matrix::Vector4f getQuaternionVariance() const;
|
||||
int getQuaternionResetCounter() const;
|
||||
|
||||
matrix::Vector3f getDeltaVelBiasVariance() const;
|
||||
|
||||
void enableDragFusion();
|
||||
void disableDragFusion();
|
||||
void setDragFusionParameters(const float &bcoef_x, const float &bcoef_y, const float &mcoef);
|
||||
|
|
|
|||
|
|
@ -62,7 +62,7 @@ TEST(AirspeedFusionGenerated, SympyVsSymforce)
|
|||
// Intermediate variables
|
||||
const float HK0 = vn - vwn;
|
||||
const float HK1 = ve - vwe;
|
||||
const float HK2 = ecl::powf(HK0, 2) + ecl::powf(HK1, 2) + ecl::powf(vd, 2);
|
||||
const float HK2 = powf(HK0, 2.f) + powf(HK1, 2.f) + powf(vd, 2.f);
|
||||
const float v_tas_pred = sqrtf(HK2); // predicted airspeed
|
||||
//const float HK3 = powf(HK2, -1.0F/2.0F);
|
||||
// calculation can be badly conditioned for very low airspeed values so don't fuse this time
|
||||
|
|
|
|||
|
|
@ -1,816 +0,0 @@
|
|||
/****************************************************************************
|
||||
*
|
||||
* Copyright (C) 2022 PX4 Development Team. All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
*
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in
|
||||
* the documentation and/or other materials provided with the
|
||||
* distribution.
|
||||
* 3. Neither the name PX4 nor the names of its contributors may be
|
||||
* used to endorse or promote products derived from this software
|
||||
* without specific prior written permission.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
||||
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
||||
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
|
||||
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
|
||||
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
|
||||
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
|
||||
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
|
||||
* OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
|
||||
* AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
|
||||
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
||||
* POSSIBILITY OF SUCH DAMAGE.
|
||||
*
|
||||
****************************************************************************/
|
||||
|
||||
#include <gtest/gtest.h>
|
||||
#include "EKF/ekf.h"
|
||||
#include "test_helper/comparison_helper.h"
|
||||
|
||||
#include "../EKF/python/ekf_derivation/generated/predict_covariance.h"
|
||||
|
||||
using namespace matrix;
|
||||
|
||||
TEST(CovariancePredictionGenerated, SympyVsSymforce)
|
||||
{
|
||||
// Compare calculation of observation Jacobians and Kalman gains for sympy and symforce generated equations
|
||||
const Quatf q(Eulerf(-M_PI_F / 2.f, M_PI_F / 3.f, M_PI_F * 4.f / 5.f));
|
||||
const float q0 = q(0);
|
||||
const float q1 = q(1);
|
||||
const float q2 = q(2);
|
||||
const float q3 = q(3);
|
||||
|
||||
const float dt = 0.01f;
|
||||
|
||||
// up to 1 rad/sec of rate
|
||||
const float dax = 2.0f * dt * ((float)randf() - 0.5f);
|
||||
const float day = 2.0f * dt * ((float)randf() - 0.5f);
|
||||
const float daz = 2.0f * dt * ((float)randf() - 0.5f);
|
||||
|
||||
// up to 2g of accel
|
||||
const float dvx = 2.0f * 20.0f * dt * ((float)randf() - 0.5f);
|
||||
const float dvy = 2.0f * 20.0f * dt * ((float)randf() - 0.5f);
|
||||
const float dvz = 2.0f * 20.0f * dt * ((float)randf() - 0.5f);
|
||||
|
||||
// up to 0.1 rad/sec of gyro bias
|
||||
const float dax_b = 2.0f * 0.1f * dt * ((float)randf() - 0.5f);
|
||||
const float day_b = 2.0f * 0.1f * dt * ((float)randf() - 0.5f);
|
||||
const float daz_b = 2.0f * 0.1f * dt * ((float)randf() - 0.5f);
|
||||
|
||||
// up to 0.5 m/s/s of accel bias
|
||||
const float dvx_b = 2.0f * 0.5f * dt * ((float)randf() - 0.5f);
|
||||
const float dvy_b = 2.0f * 0.5f * dt * ((float)randf() - 0.5f);
|
||||
const float dvz_b = 2.0f * 0.5f * dt * ((float)randf() - 0.5f);
|
||||
|
||||
const float daxVar = sq(dt * 0.015f);
|
||||
const float dayVar = daxVar;
|
||||
const float dazVar = daxVar;
|
||||
|
||||
const float dvxVar = sq(dt * 0.3f);
|
||||
const float dvyVar = dvxVar;
|
||||
const float dvzVar = dvxVar;
|
||||
|
||||
SquareMatrix24f P = createRandomCovarianceMatrix24f();
|
||||
SquareMatrix24f nextP_sympy;
|
||||
SquareMatrix24f nextP_symforce;
|
||||
|
||||
{
|
||||
SquareMatrix24f nextP;
|
||||
// Equations for covariance matrix prediction, without process noise!
|
||||
const float PS0 = (q1) * (q1);
|
||||
const float PS1 = 0.25F * daxVar;
|
||||
const float PS2 = (q2) * (q2);
|
||||
const float PS3 = 0.25F * dayVar;
|
||||
const float PS4 = (q3) * (q3);
|
||||
const float PS5 = 0.25F * dazVar;
|
||||
const float PS6 = 0.5F * q1;
|
||||
const float PS7 = 0.5F * q2;
|
||||
const float PS8 = P(10, 11) * PS7;
|
||||
const float PS9 = 0.5F * q3;
|
||||
const float PS10 = P(10, 12) * PS9;
|
||||
const float PS11 = 0.5F * dax - 0.5F * dax_b;
|
||||
const float PS12 = 0.5F * day - 0.5F * day_b;
|
||||
const float PS13 = 0.5F * daz - 0.5F * daz_b;
|
||||
const float PS14 = P(0, 10) - P(1, 10) * PS11 + P(10, 10) * PS6 - P(2, 10) * PS12 - P(3, 10) * PS13 + PS10 + PS8;
|
||||
const float PS15 = P(10, 11) * PS6;
|
||||
const float PS16 = P(11, 12) * PS9;
|
||||
const float PS17 = P(0, 11) - P(1, 11) * PS11 + P(11, 11) * PS7 - P(2, 11) * PS12 - P(3, 11) * PS13 + PS15 + PS16;
|
||||
const float PS18 = P(10, 12) * PS6;
|
||||
const float PS19 = P(11, 12) * PS7;
|
||||
const float PS20 = P(0, 12) - P(1, 12) * PS11 + P(12, 12) * PS9 - P(2, 12) * PS12 - P(3, 12) * PS13 + PS18 + PS19;
|
||||
const float PS21 = P(1, 2) * PS12;
|
||||
const float PS22 = -P(1, 3) * PS13;
|
||||
const float PS23 = P(0, 1) - P(1, 1) * PS11 + P(1, 10) * PS6 + P(1, 11) * PS7 + P(1, 12) * PS9 - PS21 + PS22;
|
||||
const float PS24 = -P(1, 2) * PS11;
|
||||
const float PS25 = P(2, 3) * PS13;
|
||||
const float PS26 = P(0, 2) + P(2, 10) * PS6 + P(2, 11) * PS7 + P(2, 12) * PS9 - P(2, 2) * PS12 + PS24 - PS25;
|
||||
const float PS27 = P(1, 3) * PS11;
|
||||
const float PS28 = -P(2, 3) * PS12;
|
||||
const float PS29 = P(0, 3) + P(3, 10) * PS6 + P(3, 11) * PS7 + P(3, 12) * PS9 - P(3, 3) * PS13 - PS27 + PS28;
|
||||
const float PS30 = P(0, 1) * PS11;
|
||||
const float PS31 = P(0, 2) * PS12;
|
||||
const float PS32 = P(0, 3) * PS13;
|
||||
const float PS33 = P(0, 0) + P(0, 10) * PS6 + P(0, 11) * PS7 + P(0, 12) * PS9 - PS30 - PS31 - PS32;
|
||||
const float PS34 = 0.5F * q0;
|
||||
const float PS35 = q2 * q3;
|
||||
const float PS36 = q0 * q1;
|
||||
const float PS37 = q1 * q3;
|
||||
const float PS38 = q0 * q2;
|
||||
const float PS39 = q1 * q2;
|
||||
const float PS40 = q0 * q3;
|
||||
const float PS41 = 2 * PS2;
|
||||
const float PS42 = 2 * PS4 - 1;
|
||||
const float PS43 = PS41 + PS42;
|
||||
const float PS44 = P(0, 13) - P(1, 13) * PS11 + P(10, 13) * PS6 + P(11, 13) * PS7 + P(12, 13) * PS9 - P(2,
|
||||
13) * PS12 - P(3, 13) * PS13;
|
||||
const float PS45 = PS37 + PS38;
|
||||
const float PS46 = P(0, 15) - P(1, 15) * PS11 + P(10, 15) * PS6 + P(11, 15) * PS7 + P(12, 15) * PS9 - P(2,
|
||||
15) * PS12 - P(3, 15) * PS13;
|
||||
const float PS47 = 2 * PS46;
|
||||
const float PS48 = dvy - dvy_b;
|
||||
const float PS49 = PS48 * q0;
|
||||
const float PS50 = dvz - dvz_b;
|
||||
const float PS51 = PS50 * q1;
|
||||
const float PS52 = dvx - dvx_b;
|
||||
const float PS53 = PS52 * q3;
|
||||
const float PS54 = PS49 - PS51 + 2 * PS53;
|
||||
const float PS55 = 2 * PS29;
|
||||
const float PS56 = -PS39 + PS40;
|
||||
const float PS57 = P(0, 14) - P(1, 14) * PS11 + P(10, 14) * PS6 + P(11, 14) * PS7 + P(12, 14) * PS9 - P(2,
|
||||
14) * PS12 - P(3, 14) * PS13;
|
||||
const float PS58 = 2 * PS57;
|
||||
const float PS59 = PS48 * q2;
|
||||
const float PS60 = PS50 * q3;
|
||||
const float PS61 = PS59 + PS60;
|
||||
const float PS62 = 2 * PS23;
|
||||
const float PS63 = PS50 * q2;
|
||||
const float PS64 = PS48 * q3;
|
||||
const float PS65 = -PS64;
|
||||
const float PS66 = PS63 + PS65;
|
||||
const float PS67 = 2 * PS33;
|
||||
const float PS68 = PS50 * q0;
|
||||
const float PS69 = PS48 * q1;
|
||||
const float PS70 = PS52 * q2;
|
||||
const float PS71 = PS68 + PS69 - 2 * PS70;
|
||||
const float PS72 = 2 * PS26;
|
||||
const float PS73 = P(0, 4) - P(1, 4) * PS11 - P(2, 4) * PS12 - P(3, 4) * PS13 + P(4, 10) * PS6 + P(4, 11) * PS7 + P(4,
|
||||
12) * PS9;
|
||||
const float PS74 = 2 * PS0;
|
||||
const float PS75 = PS42 + PS74;
|
||||
const float PS76 = PS39 + PS40;
|
||||
const float PS77 = 2 * PS44;
|
||||
const float PS78 = PS51 - PS53;
|
||||
const float PS79 = -PS70;
|
||||
const float PS80 = PS68 + 2 * PS69 + PS79;
|
||||
const float PS81 = -PS35 + PS36;
|
||||
const float PS82 = PS52 * q1;
|
||||
const float PS83 = PS60 + PS82;
|
||||
const float PS84 = PS52 * q0;
|
||||
const float PS85 = PS63 - 2 * PS64 + PS84;
|
||||
const float PS86 = P(0, 5) - P(1, 5) * PS11 - P(2, 5) * PS12 - P(3, 5) * PS13 + P(5, 10) * PS6 + P(5, 11) * PS7 + P(5,
|
||||
12) * PS9;
|
||||
const float PS87 = PS41 + PS74 - 1;
|
||||
const float PS88 = PS35 + PS36;
|
||||
const float PS89 = 2 * PS63 + PS65 + PS84;
|
||||
const float PS90 = -PS37 + PS38;
|
||||
const float PS91 = PS59 + PS82;
|
||||
const float PS92 = PS69 + PS79;
|
||||
const float PS93 = PS49 - 2 * PS51 + PS53;
|
||||
const float PS94 = P(0, 6) - P(1, 6) * PS11 - P(2, 6) * PS12 - P(3, 6) * PS13 + P(6, 10) * PS6 + P(6, 11) * PS7 + P(6,
|
||||
12) * PS9;
|
||||
const float PS95 = (q0) * (q0);
|
||||
const float PS96 = -P(10, 11) * PS34;
|
||||
const float PS97 = P(0, 11) * PS11 + P(1, 11) + P(11, 11) * PS9 + P(2, 11) * PS13 - P(3, 11) * PS12 - PS19 + PS96;
|
||||
const float PS98 = P(0, 2) * PS13;
|
||||
const float PS99 = P(0, 3) * PS12;
|
||||
const float PS100 = P(0, 0) * PS11 + P(0, 1) - P(0, 10) * PS34 + P(0, 11) * PS9 - P(0, 12) * PS7 + PS98 - PS99;
|
||||
const float PS101 = P(0, 2) * PS11;
|
||||
const float PS102 = P(1, 2) - P(2, 10) * PS34 + P(2, 11) * PS9 - P(2, 12) * PS7 + P(2, 2) * PS13 + PS101 + PS28;
|
||||
const float PS103 = P(10, 11) * PS9;
|
||||
const float PS104 = P(10, 12) * PS7;
|
||||
const float PS105 = P(0, 10) * PS11 + P(1, 10) - P(10, 10) * PS34 + P(2, 10) * PS13 - P(3, 10) * PS12 + PS103 - PS104;
|
||||
const float PS106 = -P(10, 12) * PS34;
|
||||
const float PS107 = P(0, 12) * PS11 + P(1, 12) - P(12, 12) * PS7 + P(2, 12) * PS13 - P(3, 12) * PS12 + PS106 + PS16;
|
||||
const float PS108 = P(0, 3) * PS11;
|
||||
const float PS109 = P(1, 3) - P(3, 10) * PS34 + P(3, 11) * PS9 - P(3, 12) * PS7 - P(3, 3) * PS12 + PS108 + PS25;
|
||||
const float PS110 = P(1, 2) * PS13;
|
||||
const float PS111 = P(1, 3) * PS12;
|
||||
const float PS112 = P(1, 1) - P(1, 10) * PS34 + P(1, 11) * PS9 - P(1, 12) * PS7 + PS110 - PS111 + PS30;
|
||||
const float PS113 = P(0, 13) * PS11 + P(1, 13) - P(10, 13) * PS34 + P(11, 13) * PS9 - P(12, 13) * PS7 + P(2,
|
||||
13) * PS13 - P(3, 13) * PS12;
|
||||
const float PS114 = P(0, 15) * PS11 + P(1, 15) - P(10, 15) * PS34 + P(11, 15) * PS9 - P(12, 15) * PS7 + P(2,
|
||||
15) * PS13 - P(3, 15) * PS12;
|
||||
const float PS115 = 2 * PS114;
|
||||
const float PS116 = 2 * PS109;
|
||||
const float PS117 = P(0, 14) * PS11 + P(1, 14) - P(10, 14) * PS34 + P(11, 14) * PS9 - P(12, 14) * PS7 + P(2,
|
||||
14) * PS13 - P(3, 14) * PS12;
|
||||
const float PS118 = 2 * PS117;
|
||||
const float PS119 = 2 * PS112;
|
||||
const float PS120 = 2 * PS100;
|
||||
const float PS121 = 2 * PS102;
|
||||
const float PS122 = P(0, 4) * PS11 + P(1, 4) + P(2, 4) * PS13 - P(3, 4) * PS12 - P(4, 10) * PS34 + P(4, 11) * PS9 - P(4,
|
||||
12) * PS7;
|
||||
const float PS123 = 2 * PS113;
|
||||
const float PS124 = P(0, 5) * PS11 + P(1, 5) + P(2, 5) * PS13 - P(3, 5) * PS12 - P(5, 10) * PS34 + P(5, 11) * PS9 - P(5,
|
||||
12) * PS7;
|
||||
const float PS125 = P(0, 6) * PS11 + P(1, 6) + P(2, 6) * PS13 - P(3, 6) * PS12 - P(6, 10) * PS34 + P(6, 11) * PS9 - P(6,
|
||||
12) * PS7;
|
||||
const float PS126 = -P(11, 12) * PS34;
|
||||
const float PS127 = P(0, 12) * PS12 - P(1, 12) * PS13 + P(12, 12) * PS6 + P(2, 12) + P(3, 12) * PS11 - PS10 + PS126;
|
||||
const float PS128 = P(2, 3) - P(3, 10) * PS9 - P(3, 11) * PS34 + P(3, 12) * PS6 + P(3, 3) * PS11 + PS22 + PS99;
|
||||
const float PS129 = P(0, 1) * PS13;
|
||||
const float PS130 = P(0, 0) * PS12 - P(0, 10) * PS9 - P(0, 11) * PS34 + P(0, 12) * PS6 + P(0, 2) + PS108 - PS129;
|
||||
const float PS131 = P(11, 12) * PS6;
|
||||
const float PS132 = P(0, 11) * PS12 - P(1, 11) * PS13 - P(11, 11) * PS34 + P(2, 11) + P(3, 11) * PS11 - PS103 + PS131;
|
||||
const float PS133 = P(0, 10) * PS12 - P(1, 10) * PS13 - P(10, 10) * PS9 + P(2, 10) + P(3, 10) * PS11 + PS18 + PS96;
|
||||
const float PS134 = P(0, 1) * PS12;
|
||||
const float PS135 = -P(1, 1) * PS13 - P(1, 10) * PS9 - P(1, 11) * PS34 + P(1, 12) * PS6 + P(1, 2) + PS134 + PS27;
|
||||
const float PS136 = P(2, 3) * PS11;
|
||||
const float PS137 = -P(2, 10) * PS9 - P(2, 11) * PS34 + P(2, 12) * PS6 + P(2, 2) - PS110 + PS136 + PS31;
|
||||
const float PS138 = P(0, 13) * PS12 - P(1, 13) * PS13 - P(10, 13) * PS9 - P(11, 13) * PS34 + P(12, 13) * PS6 + P(2,
|
||||
13) + P(3, 13) * PS11;
|
||||
const float PS139 = P(0, 15) * PS12 - P(1, 15) * PS13 - P(10, 15) * PS9 - P(11, 15) * PS34 + P(12, 15) * PS6 + P(2,
|
||||
15) + P(3, 15) * PS11;
|
||||
const float PS140 = 2 * PS139;
|
||||
const float PS141 = 2 * PS128;
|
||||
const float PS142 = P(0, 14) * PS12 - P(1, 14) * PS13 - P(10, 14) * PS9 - P(11, 14) * PS34 + P(12, 14) * PS6 + P(2,
|
||||
14) + P(3, 14) * PS11;
|
||||
const float PS143 = 2 * PS142;
|
||||
const float PS144 = 2 * PS135;
|
||||
const float PS145 = 2 * PS130;
|
||||
const float PS146 = 2 * PS137;
|
||||
const float PS147 = P(0, 4) * PS12 - P(1, 4) * PS13 + P(2, 4) + P(3, 4) * PS11 - P(4, 10) * PS9 - P(4, 11) * PS34 + P(4,
|
||||
12) * PS6;
|
||||
const float PS148 = 2 * PS138;
|
||||
const float PS149 = P(0, 5) * PS12 - P(1, 5) * PS13 + P(2, 5) + P(3, 5) * PS11 - P(5, 10) * PS9 - P(5, 11) * PS34 + P(5,
|
||||
12) * PS6;
|
||||
const float PS150 = P(0, 6) * PS12 - P(1, 6) * PS13 + P(2, 6) + P(3, 6) * PS11 - P(6, 10) * PS9 - P(6, 11) * PS34 + P(6,
|
||||
12) * PS6;
|
||||
const float PS151 = P(0, 10) * PS13 + P(1, 10) * PS12 + P(10, 10) * PS7 - P(2, 10) * PS11 + P(3, 10) + PS106 - PS15;
|
||||
const float PS152 = P(1, 1) * PS12 + P(1, 10) * PS7 - P(1, 11) * PS6 - P(1, 12) * PS34 + P(1, 3) + PS129 + PS24;
|
||||
const float PS153 = P(0, 0) * PS13 + P(0, 10) * PS7 - P(0, 11) * PS6 - P(0, 12) * PS34 + P(0, 3) - PS101 + PS134;
|
||||
const float PS154 = P(0, 12) * PS13 + P(1, 12) * PS12 - P(12, 12) * PS34 - P(2, 12) * PS11 + P(3, 12) + PS104 - PS131;
|
||||
const float PS155 = P(0, 11) * PS13 + P(1, 11) * PS12 - P(11, 11) * PS6 - P(2, 11) * PS11 + P(3, 11) + PS126 + PS8;
|
||||
const float PS156 = P(2, 10) * PS7 - P(2, 11) * PS6 - P(2, 12) * PS34 - P(2, 2) * PS11 + P(2, 3) + PS21 + PS98;
|
||||
const float PS157 = P(3, 10) * PS7 - P(3, 11) * PS6 - P(3, 12) * PS34 + P(3, 3) + PS111 - PS136 + PS32;
|
||||
const float PS158 = P(0, 13) * PS13 + P(1, 13) * PS12 + P(10, 13) * PS7 - P(11, 13) * PS6 - P(12, 13) * PS34 - P(2,
|
||||
13) * PS11 + P(3, 13);
|
||||
const float PS159 = P(0, 15) * PS13 + P(1, 15) * PS12 + P(10, 15) * PS7 - P(11, 15) * PS6 - P(12, 15) * PS34 - P(2,
|
||||
15) * PS11 + P(3, 15);
|
||||
const float PS160 = 2 * PS159;
|
||||
const float PS161 = 2 * PS157;
|
||||
const float PS162 = P(0, 14) * PS13 + P(1, 14) * PS12 + P(10, 14) * PS7 - P(11, 14) * PS6 - P(12, 14) * PS34 - P(2,
|
||||
14) * PS11 + P(3, 14);
|
||||
const float PS163 = 2 * PS162;
|
||||
const float PS164 = 2 * PS152;
|
||||
const float PS165 = 2 * PS153;
|
||||
const float PS166 = 2 * PS156;
|
||||
const float PS167 = P(0, 4) * PS13 + P(1, 4) * PS12 - P(2, 4) * PS11 + P(3, 4) + P(4, 10) * PS7 - P(4, 11) * PS6 - P(4,
|
||||
12) * PS34;
|
||||
const float PS168 = 2 * PS158;
|
||||
const float PS169 = P(0, 5) * PS13 + P(1, 5) * PS12 - P(2, 5) * PS11 + P(3, 5) + P(5, 10) * PS7 - P(5, 11) * PS6 - P(5,
|
||||
12) * PS34;
|
||||
const float PS170 = P(0, 6) * PS13 + P(1, 6) * PS12 - P(2, 6) * PS11 + P(3, 6) + P(6, 10) * PS7 - P(6, 11) * PS6 - P(6,
|
||||
12) * PS34;
|
||||
const float PS171 = 2 * PS45;
|
||||
const float PS172 = 2 * PS56;
|
||||
const float PS173 = 2 * PS61;
|
||||
const float PS174 = 2 * PS66;
|
||||
const float PS175 = 2 * PS71;
|
||||
const float PS176 = 2 * PS54;
|
||||
const float PS177 = P(0, 13) * PS174 + P(1, 13) * PS173 + P(13, 13) * PS43 + P(13, 14) * PS172 - P(13,
|
||||
15) * PS171 + P(2, 13) * PS175 - P(3, 13) * PS176 + P(4, 13);
|
||||
const float PS178 = P(0, 15) * PS174 + P(1, 15) * PS173 + P(13, 15) * PS43 + P(14, 15) * PS172 - P(15,
|
||||
15) * PS171 + P(2, 15) * PS175 - P(3, 15) * PS176 + P(4, 15);
|
||||
const float PS179 = P(0, 3) * PS174 + P(1, 3) * PS173 + P(2, 3) * PS175 + P(3, 13) * PS43 + P(3, 14) * PS172 - P(3,
|
||||
15) * PS171 - P(3, 3) * PS176 + P(3, 4);
|
||||
const float PS180 = P(0, 14) * PS174 + P(1, 14) * PS173 + P(13, 14) * PS43 + P(14, 14) * PS172 - P(14,
|
||||
15) * PS171 + P(2, 14) * PS175 - P(3, 14) * PS176 + P(4, 14);
|
||||
const float PS181 = P(0, 1) * PS174 + P(1, 1) * PS173 + P(1, 13) * PS43 + P(1, 14) * PS172 - P(1, 15) * PS171 + P(1,
|
||||
2) * PS175 - P(1, 3) * PS176 + P(1, 4);
|
||||
const float PS182 = P(0, 0) * PS174 + P(0, 1) * PS173 + P(0, 13) * PS43 + P(0, 14) * PS172 - P(0, 15) * PS171 + P(0,
|
||||
2) * PS175 - P(0, 3) * PS176 + P(0, 4);
|
||||
const float PS183 = P(0, 2) * PS174 + P(1, 2) * PS173 + P(2, 13) * PS43 + P(2, 14) * PS172 - P(2, 15) * PS171 + P(2,
|
||||
2) * PS175 - P(2, 3) * PS176 + P(2, 4);
|
||||
const float PS184 = 4 * dvyVar;
|
||||
const float PS185 = 4 * dvzVar;
|
||||
const float PS186 = P(0, 4) * PS174 + P(1, 4) * PS173 + P(2, 4) * PS175 - P(3, 4) * PS176 + P(4, 13) * PS43 + P(4,
|
||||
14) * PS172 - P(4, 15) * PS171 + P(4, 4);
|
||||
const float PS187 = 2 * PS177;
|
||||
const float PS188 = 2 * PS182;
|
||||
const float PS189 = 2 * PS181;
|
||||
const float PS190 = 2 * PS81;
|
||||
const float PS191 = 2 * PS183;
|
||||
const float PS192 = 2 * PS179;
|
||||
const float PS193 = 2 * PS76;
|
||||
const float PS194 = PS43 * dvxVar;
|
||||
const float PS195 = PS75 * dvyVar;
|
||||
const float PS196 = P(0, 5) * PS174 + P(1, 5) * PS173 + P(2, 5) * PS175 - P(3, 5) * PS176 + P(4, 5) + P(5,
|
||||
13) * PS43 + P(5, 14) * PS172 - P(5, 15) * PS171;
|
||||
const float PS197 = 2 * PS88;
|
||||
const float PS198 = PS87 * dvzVar;
|
||||
const float PS199 = 2 * PS90;
|
||||
const float PS200 = P(0, 6) * PS174 + P(1, 6) * PS173 + P(2, 6) * PS175 - P(3, 6) * PS176 + P(4, 6) + P(6,
|
||||
13) * PS43 + P(6, 14) * PS172 - P(6, 15) * PS171;
|
||||
const float PS201 = 2 * PS83;
|
||||
const float PS202 = 2 * PS78;
|
||||
const float PS203 = 2 * PS85;
|
||||
const float PS204 = 2 * PS80;
|
||||
const float PS205 = -P(0, 14) * PS202 - P(1, 14) * PS204 - P(13, 14) * PS193 + P(14, 14) * PS75 + P(14,
|
||||
15) * PS190 + P(2, 14) * PS201 + P(3, 14) * PS203 + P(5, 14);
|
||||
const float PS206 = -P(0, 13) * PS202 - P(1, 13) * PS204 - P(13, 13) * PS193 + P(13, 14) * PS75 + P(13,
|
||||
15) * PS190 + P(2, 13) * PS201 + P(3, 13) * PS203 + P(5, 13);
|
||||
const float PS207 = -P(0, 0) * PS202 - P(0, 1) * PS204 - P(0, 13) * PS193 + P(0, 14) * PS75 + P(0, 15) * PS190 + P(0,
|
||||
2) * PS201 + P(0, 3) * PS203 + P(0, 5);
|
||||
const float PS208 = -P(0, 1) * PS202 - P(1, 1) * PS204 - P(1, 13) * PS193 + P(1, 14) * PS75 + P(1, 15) * PS190 + P(1,
|
||||
2) * PS201 + P(1, 3) * PS203 + P(1, 5);
|
||||
const float PS209 = -P(0, 15) * PS202 - P(1, 15) * PS204 - P(13, 15) * PS193 + P(14, 15) * PS75 + P(15,
|
||||
15) * PS190 + P(2, 15) * PS201 + P(3, 15) * PS203 + P(5, 15);
|
||||
const float PS210 = -P(0, 2) * PS202 - P(1, 2) * PS204 - P(2, 13) * PS193 + P(2, 14) * PS75 + P(2, 15) * PS190 + P(2,
|
||||
2) * PS201 + P(2, 3) * PS203 + P(2, 5);
|
||||
const float PS211 = -P(0, 3) * PS202 - P(1, 3) * PS204 + P(2, 3) * PS201 - P(3, 13) * PS193 + P(3, 14) * PS75 + P(3,
|
||||
15) * PS190 + P(3, 3) * PS203 + P(3, 5);
|
||||
const float PS212 = 4 * dvxVar;
|
||||
const float PS213 = -P(0, 5) * PS202 - P(1, 5) * PS204 + P(2, 5) * PS201 + P(3, 5) * PS203 - P(5, 13) * PS193 + P(5,
|
||||
14) * PS75 + P(5, 15) * PS190 + P(5, 5);
|
||||
const float PS214 = 2 * PS89;
|
||||
const float PS215 = 2 * PS91;
|
||||
const float PS216 = 2 * PS92;
|
||||
const float PS217 = 2 * PS93;
|
||||
const float PS218 = -P(0, 6) * PS202 - P(1, 6) * PS204 + P(2, 6) * PS201 + P(3, 6) * PS203 + P(5, 6) - P(6,
|
||||
13) * PS193 + P(6, 14) * PS75 + P(6, 15) * PS190;
|
||||
const float PS219 = P(0, 15) * PS216 + P(1, 15) * PS217 + P(13, 15) * PS199 - P(14, 15) * PS197 + P(15,
|
||||
15) * PS87 - P(2, 15) * PS214 + P(3, 15) * PS215 + P(6, 15);
|
||||
const float PS220 = P(0, 14) * PS216 + P(1, 14) * PS217 + P(13, 14) * PS199 - P(14, 14) * PS197 + P(14,
|
||||
15) * PS87 - P(2, 14) * PS214 + P(3, 14) * PS215 + P(6, 14);
|
||||
const float PS221 = P(0, 13) * PS216 + P(1, 13) * PS217 + P(13, 13) * PS199 - P(13, 14) * PS197 + P(13,
|
||||
15) * PS87 - P(2, 13) * PS214 + P(3, 13) * PS215 + P(6, 13);
|
||||
const float PS222 = P(0, 6) * PS216 + P(1, 6) * PS217 - P(2, 6) * PS214 + P(3, 6) * PS215 + P(6, 13) * PS199 - P(6,
|
||||
14) * PS197 + P(6, 15) * PS87 + P(6, 6);
|
||||
|
||||
|
||||
nextP(0, 0) = PS0 * PS1 - PS11 * PS23 - PS12 * PS26 - PS13 * PS29 + PS14 * PS6 + PS17 * PS7 + PS2 * PS3 + PS20 * PS9 +
|
||||
PS33 + PS4 * PS5;
|
||||
nextP(0, 1) = -PS1 * PS36 + PS11 * PS33 - PS12 * PS29 + PS13 * PS26 - PS14 * PS34 + PS17 * PS9 - PS20 * PS7 + PS23 + PS3
|
||||
* PS35 - PS35 * PS5;
|
||||
nextP(1, 1) = PS1 * PS95 + PS100 * PS11 + PS102 * PS13 - PS105 * PS34 - PS107 * PS7 - PS109 * PS12 + PS112 + PS2 * PS5 +
|
||||
PS3 * PS4 + PS9 * PS97;
|
||||
nextP(0, 2) = -PS1 * PS37 + PS11 * PS29 + PS12 * PS33 - PS13 * PS23 - PS14 * PS9 - PS17 * PS34 + PS20 * PS6 + PS26 - PS3
|
||||
* PS38 + PS37 * PS5;
|
||||
nextP(1, 2) = PS1 * PS40 + PS100 * PS12 + PS102 - PS105 * PS9 + PS107 * PS6 + PS109 * PS11 - PS112 * PS13 - PS3 * PS40 -
|
||||
PS34 * PS97 - PS39 * PS5;
|
||||
nextP(2, 2) = PS0 * PS5 + PS1 * PS4 + PS11 * PS128 + PS12 * PS130 + PS127 * PS6 - PS13 * PS135 - PS132 * PS34 - PS133 *
|
||||
PS9 + PS137 + PS3 * PS95;
|
||||
nextP(0, 3) = PS1 * PS39 - PS11 * PS26 + PS12 * PS23 + PS13 * PS33 + PS14 * PS7 - PS17 * PS6 - PS20 * PS34 + PS29 - PS3
|
||||
* PS39 - PS40 * PS5;
|
||||
nextP(1, 3) = -PS1 * PS38 + PS100 * PS13 - PS102 * PS11 + PS105 * PS7 - PS107 * PS34 + PS109 + PS112 * PS12 - PS3 * PS37
|
||||
+ PS38 * PS5 - PS6 * PS97;
|
||||
nextP(2, 3) = -PS1 * PS35 - PS11 * PS137 + PS12 * PS135 - PS127 * PS34 + PS128 + PS13 * PS130 - PS132 * PS6 + PS133 *
|
||||
PS7 + PS3 * PS36 - PS36 * PS5;
|
||||
nextP(3, 3) = PS0 * PS3 + PS1 * PS2 - PS11 * PS156 + PS12 * PS152 + PS13 * PS153 + PS151 * PS7 - PS154 * PS34 - PS155 *
|
||||
PS6 + PS157 + PS5 * PS95;
|
||||
nextP(0, 4) = PS43 * PS44 - PS45 * PS47 - PS54 * PS55 + PS56 * PS58 + PS61 * PS62 + PS66 * PS67 + PS71 * PS72 + PS73;
|
||||
nextP(1, 4) = PS113 * PS43 - PS115 * PS45 - PS116 * PS54 + PS118 * PS56 + PS119 * PS61 + PS120 * PS66 + PS121 * PS71 +
|
||||
PS122;
|
||||
nextP(2, 4) = PS138 * PS43 - PS140 * PS45 - PS141 * PS54 + PS143 * PS56 + PS144 * PS61 + PS145 * PS66 + PS146 * PS71 +
|
||||
PS147;
|
||||
nextP(3, 4) = PS158 * PS43 - PS160 * PS45 - PS161 * PS54 + PS163 * PS56 + PS164 * PS61 + PS165 * PS66 + PS166 * PS71 +
|
||||
PS167;
|
||||
nextP(4, 4) = -PS171 * PS178 + PS172 * PS180 + PS173 * PS181 + PS174 * PS182 + PS175 * PS183 - PS176 * PS179 + PS177 *
|
||||
PS43 + PS184 * (PS56) * (PS56) + PS185 * (PS45) * (PS45) + PS186 + (PS43) * (PS43) * dvxVar;
|
||||
nextP(0, 5) = PS47 * PS81 + PS55 * PS85 + PS57 * PS75 - PS62 * PS80 - PS67 * PS78 + PS72 * PS83 - PS76 * PS77 + PS86;
|
||||
nextP(1, 5) = PS115 * PS81 + PS116 * PS85 + PS117 * PS75 - PS119 * PS80 - PS120 * PS78 + PS121 * PS83 - PS123 * PS76 +
|
||||
PS124;
|
||||
nextP(2, 5) = PS140 * PS81 + PS141 * PS85 + PS142 * PS75 - PS144 * PS80 - PS145 * PS78 + PS146 * PS83 - PS148 * PS76 +
|
||||
PS149;
|
||||
nextP(3, 5) = PS160 * PS81 + PS161 * PS85 + PS162 * PS75 - PS164 * PS80 - PS165 * PS78 + PS166 * PS83 - PS168 * PS76 +
|
||||
PS169;
|
||||
nextP(4, 5) = PS172 * PS195 + PS178 * PS190 + PS180 * PS75 - PS185 * PS45 * PS81 - PS187 * PS76 - PS188 * PS78 - PS189 *
|
||||
PS80 + PS191 * PS83 + PS192 * PS85 - PS193 * PS194 + PS196;
|
||||
nextP(5, 5) = PS185 * (PS81) * (PS81) + PS190 * PS209 - PS193 * PS206 + PS201 * PS210 - PS202 * PS207 + PS203 * PS211 -
|
||||
PS204 * PS208 + PS205 * PS75 + PS212 * (PS76) * (PS76) + PS213 + (PS75) * (PS75) * dvyVar;
|
||||
nextP(0, 6) = PS46 * PS87 + PS55 * PS91 - PS58 * PS88 + PS62 * PS93 + PS67 * PS92 - PS72 * PS89 + PS77 * PS90 + PS94;
|
||||
nextP(1, 6) = PS114 * PS87 + PS116 * PS91 - PS118 * PS88 + PS119 * PS93 + PS120 * PS92 - PS121 * PS89 + PS123 * PS90 +
|
||||
PS125;
|
||||
nextP(2, 6) = PS139 * PS87 + PS141 * PS91 - PS143 * PS88 + PS144 * PS93 + PS145 * PS92 - PS146 * PS89 + PS148 * PS90 +
|
||||
PS150;
|
||||
nextP(3, 6) = PS159 * PS87 + PS161 * PS91 - PS163 * PS88 + PS164 * PS93 + PS165 * PS92 - PS166 * PS89 + PS168 * PS90 +
|
||||
PS170;
|
||||
nextP(4, 6) = -PS171 * PS198 + PS178 * PS87 - PS180 * PS197 - PS184 * PS56 * PS88 + PS187 * PS90 + PS188 * PS92 + PS189
|
||||
* PS93 - PS191 * PS89 + PS192 * PS91 + PS194 * PS199 + PS200;
|
||||
nextP(5, 6) = PS190 * PS198 - PS195 * PS197 - PS197 * PS205 + PS199 * PS206 + PS207 * PS216 + PS208 * PS217 + PS209 *
|
||||
PS87 - PS210 * PS214 + PS211 * PS215 - PS212 * PS76 * PS90 + PS218;
|
||||
nextP(6, 6) = PS184 * (PS88) * (PS88) - PS197 * PS220 + PS199 * PS221 + PS212 * (PS90) * (PS90) - PS214 * (P(0,
|
||||
2) * PS216 + P(1, 2) * PS217 + P(2, 13) * PS199 - P(2, 14) * PS197 + P(2, 15) * PS87 - P(2, 2) * PS214 + P(2,
|
||||
3) * PS215 + P(2, 6)) + PS215 * (P(0, 3) * PS216 + P(1, 3) * PS217 - P(2, 3) * PS214 + P(3, 13) * PS199 - P(3,
|
||||
14) * PS197 + P(3, 15) * PS87 + P(3, 3) * PS215 + P(3, 6)) + PS216 * (P(0, 0) * PS216 + P(0, 1) * PS217 + P(0,
|
||||
13) * PS199 - P(0, 14) * PS197 + P(0, 15) * PS87 - P(0, 2) * PS214 + P(0, 3) * PS215 + P(0, 6)) + PS217 * (P(0,
|
||||
1) * PS216 + P(1, 1) * PS217 + P(1, 13) * PS199 - P(1, 14) * PS197 + P(1, 15) * PS87 - P(1, 2) * PS214 + P(1,
|
||||
3) * PS215 + P(1, 6)) + PS219 * PS87 + PS222 + (PS87) * (PS87) * dvzVar;
|
||||
nextP(0, 7) = P(0, 7) - P(1, 7) * PS11 - P(2, 7) * PS12 - P(3, 7) * PS13 + P(7, 10) * PS6 + P(7, 11) * PS7 + P(7,
|
||||
12) * PS9 + PS73 * dt;
|
||||
nextP(1, 7) = P(0, 7) * PS11 + P(1, 7) + P(2, 7) * PS13 - P(3, 7) * PS12 - P(7, 10) * PS34 + P(7, 11) * PS9 - P(7,
|
||||
12) * PS7 + PS122 * dt;
|
||||
nextP(2, 7) = P(0, 7) * PS12 - P(1, 7) * PS13 + P(2, 7) + P(3, 7) * PS11 - P(7, 10) * PS9 - P(7, 11) * PS34 + P(7,
|
||||
12) * PS6 + PS147 * dt;
|
||||
nextP(3, 7) = P(0, 7) * PS13 + P(1, 7) * PS12 - P(2, 7) * PS11 + P(3, 7) + P(7, 10) * PS7 - P(7, 11) * PS6 - P(7,
|
||||
12) * PS34 + PS167 * dt;
|
||||
nextP(4, 7) = P(0, 7) * PS174 + P(1, 7) * PS173 + P(2, 7) * PS175 - P(3, 7) * PS176 + P(4, 7) + P(7, 13) * PS43 + P(7,
|
||||
14) * PS172 - P(7, 15) * PS171 + PS186 * dt;
|
||||
nextP(5, 7) = -P(0, 7) * PS202 - P(1, 7) * PS204 + P(2, 7) * PS201 + P(3, 7) * PS203 + P(5, 7) - P(7, 13) * PS193 + P(7,
|
||||
14) * PS75 + P(7, 15) * PS190 + dt * (-P(0, 4) * PS202 - P(1, 4) * PS204 + P(2, 4) * PS201 + P(3, 4) * PS203 - P(4,
|
||||
13) * PS193 + P(4, 14) * PS75 + P(4, 15) * PS190 + P(4, 5));
|
||||
nextP(6, 7) = P(0, 7) * PS216 + P(1, 7) * PS217 - P(2, 7) * PS214 + P(3, 7) * PS215 + P(6, 7) + P(7, 13) * PS199 - P(7,
|
||||
14) * PS197 + P(7, 15) * PS87 + dt * (P(0, 4) * PS216 + P(1, 4) * PS217 - P(2, 4) * PS214 + P(3, 4) * PS215 + P(4,
|
||||
13) * PS199 - P(4, 14) * PS197 + P(4, 15) * PS87 + P(4, 6));
|
||||
nextP(7, 7) = P(4, 7) * dt + P(7, 7) + dt * (P(4, 4) * dt + P(4, 7));
|
||||
nextP(0, 8) = P(0, 8) - P(1, 8) * PS11 - P(2, 8) * PS12 - P(3, 8) * PS13 + P(8, 10) * PS6 + P(8, 11) * PS7 + P(8,
|
||||
12) * PS9 + PS86 * dt;
|
||||
nextP(1, 8) = P(0, 8) * PS11 + P(1, 8) + P(2, 8) * PS13 - P(3, 8) * PS12 - P(8, 10) * PS34 + P(8, 11) * PS9 - P(8,
|
||||
12) * PS7 + PS124 * dt;
|
||||
nextP(2, 8) = P(0, 8) * PS12 - P(1, 8) * PS13 + P(2, 8) + P(3, 8) * PS11 - P(8, 10) * PS9 - P(8, 11) * PS34 + P(8,
|
||||
12) * PS6 + PS149 * dt;
|
||||
nextP(3, 8) = P(0, 8) * PS13 + P(1, 8) * PS12 - P(2, 8) * PS11 + P(3, 8) + P(8, 10) * PS7 - P(8, 11) * PS6 - P(8,
|
||||
12) * PS34 + PS169 * dt;
|
||||
nextP(4, 8) = P(0, 8) * PS174 + P(1, 8) * PS173 + P(2, 8) * PS175 - P(3, 8) * PS176 + P(4, 8) + P(8, 13) * PS43 + P(8,
|
||||
14) * PS172 - P(8, 15) * PS171 + PS196 * dt;
|
||||
nextP(5, 8) = -P(0, 8) * PS202 - P(1, 8) * PS204 + P(2, 8) * PS201 + P(3, 8) * PS203 + P(5, 8) - P(8, 13) * PS193 + P(8,
|
||||
14) * PS75 + P(8, 15) * PS190 + PS213 * dt;
|
||||
nextP(6, 8) = P(0, 8) * PS216 + P(1, 8) * PS217 - P(2, 8) * PS214 + P(3, 8) * PS215 + P(6, 8) + P(8, 13) * PS199 - P(8,
|
||||
14) * PS197 + P(8, 15) * PS87 + dt * (P(0, 5) * PS216 + P(1, 5) * PS217 - P(2, 5) * PS214 + P(3, 5) * PS215 + P(5,
|
||||
13) * PS199 - P(5, 14) * PS197 + P(5, 15) * PS87 + P(5, 6));
|
||||
nextP(7, 8) = P(4, 8) * dt + P(7, 8) + dt * (P(4, 5) * dt + P(5, 7));
|
||||
nextP(8, 8) = P(5, 8) * dt + P(8, 8) + dt * (P(5, 5) * dt + P(5, 8));
|
||||
nextP(0, 9) = P(0, 9) - P(1, 9) * PS11 - P(2, 9) * PS12 - P(3, 9) * PS13 + P(9, 10) * PS6 + P(9, 11) * PS7 + P(9,
|
||||
12) * PS9 + PS94 * dt;
|
||||
nextP(1, 9) = P(0, 9) * PS11 + P(1, 9) + P(2, 9) * PS13 - P(3, 9) * PS12 - P(9, 10) * PS34 + P(9, 11) * PS9 - P(9,
|
||||
12) * PS7 + PS125 * dt;
|
||||
nextP(2, 9) = P(0, 9) * PS12 - P(1, 9) * PS13 + P(2, 9) + P(3, 9) * PS11 - P(9, 10) * PS9 - P(9, 11) * PS34 + P(9,
|
||||
12) * PS6 + PS150 * dt;
|
||||
nextP(3, 9) = P(0, 9) * PS13 + P(1, 9) * PS12 - P(2, 9) * PS11 + P(3, 9) + P(9, 10) * PS7 - P(9, 11) * PS6 - P(9,
|
||||
12) * PS34 + PS170 * dt;
|
||||
nextP(4, 9) = P(0, 9) * PS174 + P(1, 9) * PS173 + P(2, 9) * PS175 - P(3, 9) * PS176 + P(4, 9) + P(9, 13) * PS43 + P(9,
|
||||
14) * PS172 - P(9, 15) * PS171 + PS200 * dt;
|
||||
nextP(5, 9) = -P(0, 9) * PS202 - P(1, 9) * PS204 + P(2, 9) * PS201 + P(3, 9) * PS203 + P(5, 9) - P(9, 13) * PS193 + P(9,
|
||||
14) * PS75 + P(9, 15) * PS190 + PS218 * dt;
|
||||
nextP(6, 9) = P(0, 9) * PS216 + P(1, 9) * PS217 - P(2, 9) * PS214 + P(3, 9) * PS215 + P(6, 9) + P(9, 13) * PS199 - P(9,
|
||||
14) * PS197 + P(9, 15) * PS87 + PS222 * dt;
|
||||
nextP(7, 9) = P(4, 9) * dt + P(7, 9) + dt * (P(4, 6) * dt + P(6, 7));
|
||||
nextP(8, 9) = P(5, 9) * dt + P(8, 9) + dt * (P(5, 6) * dt + P(6, 8));
|
||||
nextP(9, 9) = P(6, 9) * dt + P(9, 9) + dt * (P(6, 6) * dt + P(6, 9));
|
||||
nextP(0, 10) = PS14;
|
||||
nextP(1, 10) = PS105;
|
||||
nextP(2, 10) = PS133;
|
||||
nextP(3, 10) = PS151;
|
||||
nextP(4, 10) = P(0, 10) * PS174 + P(1, 10) * PS173 + P(10, 13) * PS43 + P(10, 14) * PS172 - P(10, 15) * PS171 + P(2,
|
||||
10) * PS175 - P(3, 10) * PS176 + P(4, 10);
|
||||
nextP(5, 10) = -P(0, 10) * PS202 - P(1, 10) * PS204 - P(10, 13) * PS193 + P(10, 14) * PS75 + P(10, 15) * PS190 + P(2,
|
||||
10) * PS201 + P(3, 10) * PS203 + P(5, 10);
|
||||
nextP(6, 10) = P(0, 10) * PS216 + P(1, 10) * PS217 + P(10, 13) * PS199 - P(10, 14) * PS197 + P(10, 15) * PS87 - P(2,
|
||||
10) * PS214 + P(3, 10) * PS215 + P(6, 10);
|
||||
nextP(7, 10) = P(4, 10) * dt + P(7, 10);
|
||||
nextP(8, 10) = P(5, 10) * dt + P(8, 10);
|
||||
nextP(9, 10) = P(6, 10) * dt + P(9, 10);
|
||||
nextP(10, 10) = P(10, 10);
|
||||
nextP(0, 11) = PS17;
|
||||
nextP(1, 11) = PS97;
|
||||
nextP(2, 11) = PS132;
|
||||
nextP(3, 11) = PS155;
|
||||
nextP(4, 11) = P(0, 11) * PS174 + P(1, 11) * PS173 + P(11, 13) * PS43 + P(11, 14) * PS172 - P(11, 15) * PS171 + P(2,
|
||||
11) * PS175 - P(3, 11) * PS176 + P(4, 11);
|
||||
nextP(5, 11) = -P(0, 11) * PS202 - P(1, 11) * PS204 - P(11, 13) * PS193 + P(11, 14) * PS75 + P(11, 15) * PS190 + P(2,
|
||||
11) * PS201 + P(3, 11) * PS203 + P(5, 11);
|
||||
nextP(6, 11) = P(0, 11) * PS216 + P(1, 11) * PS217 + P(11, 13) * PS199 - P(11, 14) * PS197 + P(11, 15) * PS87 - P(2,
|
||||
11) * PS214 + P(3, 11) * PS215 + P(6, 11);
|
||||
nextP(7, 11) = P(4, 11) * dt + P(7, 11);
|
||||
nextP(8, 11) = P(5, 11) * dt + P(8, 11);
|
||||
nextP(9, 11) = P(6, 11) * dt + P(9, 11);
|
||||
nextP(10, 11) = P(10, 11);
|
||||
nextP(11, 11) = P(11, 11);
|
||||
nextP(0, 12) = PS20;
|
||||
nextP(1, 12) = PS107;
|
||||
nextP(2, 12) = PS127;
|
||||
nextP(3, 12) = PS154;
|
||||
nextP(4, 12) = P(0, 12) * PS174 + P(1, 12) * PS173 + P(12, 13) * PS43 + P(12, 14) * PS172 - P(12, 15) * PS171 + P(2,
|
||||
12) * PS175 - P(3, 12) * PS176 + P(4, 12);
|
||||
nextP(5, 12) = -P(0, 12) * PS202 - P(1, 12) * PS204 - P(12, 13) * PS193 + P(12, 14) * PS75 + P(12, 15) * PS190 + P(2,
|
||||
12) * PS201 + P(3, 12) * PS203 + P(5, 12);
|
||||
nextP(6, 12) = P(0, 12) * PS216 + P(1, 12) * PS217 + P(12, 13) * PS199 - P(12, 14) * PS197 + P(12, 15) * PS87 - P(2,
|
||||
12) * PS214 + P(3, 12) * PS215 + P(6, 12);
|
||||
nextP(7, 12) = P(4, 12) * dt + P(7, 12);
|
||||
nextP(8, 12) = P(5, 12) * dt + P(8, 12);
|
||||
nextP(9, 12) = P(6, 12) * dt + P(9, 12);
|
||||
nextP(10, 12) = P(10, 12);
|
||||
nextP(11, 12) = P(11, 12);
|
||||
nextP(12, 12) = P(12, 12);
|
||||
nextP(0, 13) = PS44;
|
||||
nextP(1, 13) = PS113;
|
||||
nextP(2, 13) = PS138;
|
||||
nextP(3, 13) = PS158;
|
||||
nextP(4, 13) = PS177;
|
||||
nextP(5, 13) = PS206;
|
||||
nextP(6, 13) = PS221;
|
||||
nextP(7, 13) = P(4, 13) * dt + P(7, 13);
|
||||
nextP(8, 13) = P(5, 13) * dt + P(8, 13);
|
||||
nextP(9, 13) = P(6, 13) * dt + P(9, 13);
|
||||
nextP(10, 13) = P(10, 13);
|
||||
nextP(11, 13) = P(11, 13);
|
||||
nextP(12, 13) = P(12, 13);
|
||||
nextP(13, 13) = P(13, 13);
|
||||
nextP(0, 14) = PS57;
|
||||
nextP(1, 14) = PS117;
|
||||
nextP(2, 14) = PS142;
|
||||
nextP(3, 14) = PS162;
|
||||
nextP(4, 14) = PS180;
|
||||
nextP(5, 14) = PS205;
|
||||
nextP(6, 14) = PS220;
|
||||
nextP(7, 14) = P(4, 14) * dt + P(7, 14);
|
||||
nextP(8, 14) = P(5, 14) * dt + P(8, 14);
|
||||
nextP(9, 14) = P(6, 14) * dt + P(9, 14);
|
||||
nextP(10, 14) = P(10, 14);
|
||||
nextP(11, 14) = P(11, 14);
|
||||
nextP(12, 14) = P(12, 14);
|
||||
nextP(13, 14) = P(13, 14);
|
||||
nextP(14, 14) = P(14, 14);
|
||||
nextP(0, 15) = PS46;
|
||||
nextP(1, 15) = PS114;
|
||||
nextP(2, 15) = PS139;
|
||||
nextP(3, 15) = PS159;
|
||||
nextP(4, 15) = PS178;
|
||||
nextP(5, 15) = PS209;
|
||||
nextP(6, 15) = PS219;
|
||||
nextP(7, 15) = P(4, 15) * dt + P(7, 15);
|
||||
nextP(8, 15) = P(5, 15) * dt + P(8, 15);
|
||||
nextP(9, 15) = P(6, 15) * dt + P(9, 15);
|
||||
nextP(10, 15) = P(10, 15);
|
||||
nextP(11, 15) = P(11, 15);
|
||||
nextP(12, 15) = P(12, 15);
|
||||
nextP(13, 15) = P(13, 15);
|
||||
nextP(14, 15) = P(14, 15);
|
||||
nextP(15, 15) = P(15, 15);
|
||||
nextP(0, 16) = P(0, 16) - P(1, 16) * PS11 + P(10, 16) * PS6 + P(11, 16) * PS7 + P(12, 16) * PS9 - P(2, 16) * PS12 - P(3,
|
||||
16) * PS13;
|
||||
nextP(1, 16) = P(0, 16) * PS11 + P(1, 16) - P(10, 16) * PS34 + P(11, 16) * PS9 - P(12, 16) * PS7 + P(2,
|
||||
16) * PS13 - P(3, 16) * PS12;
|
||||
nextP(2, 16) = P(0, 16) * PS12 - P(1, 16) * PS13 - P(10, 16) * PS9 - P(11, 16) * PS34 + P(12, 16) * PS6 + P(2,
|
||||
16) + P(3, 16) * PS11;
|
||||
nextP(3, 16) = P(0, 16) * PS13 + P(1, 16) * PS12 + P(10, 16) * PS7 - P(11, 16) * PS6 - P(12, 16) * PS34 - P(2,
|
||||
16) * PS11 + P(3, 16);
|
||||
nextP(4, 16) = P(0, 16) * PS174 + P(1, 16) * PS173 + P(13, 16) * PS43 + P(14, 16) * PS172 - P(15, 16) * PS171 + P(2,
|
||||
16) * PS175 - P(3, 16) * PS176 + P(4, 16);
|
||||
nextP(5, 16) = -P(0, 16) * PS202 - P(1, 16) * PS204 - P(13, 16) * PS193 + P(14, 16) * PS75 + P(15, 16) * PS190 + P(2,
|
||||
16) * PS201 + P(3, 16) * PS203 + P(5, 16);
|
||||
nextP(6, 16) = P(0, 16) * PS216 + P(1, 16) * PS217 + P(13, 16) * PS199 - P(14, 16) * PS197 + P(15, 16) * PS87 - P(2,
|
||||
16) * PS214 + P(3, 16) * PS215 + P(6, 16);
|
||||
nextP(7, 16) = P(4, 16) * dt + P(7, 16);
|
||||
nextP(8, 16) = P(5, 16) * dt + P(8, 16);
|
||||
nextP(9, 16) = P(6, 16) * dt + P(9, 16);
|
||||
nextP(10, 16) = P(10, 16);
|
||||
nextP(11, 16) = P(11, 16);
|
||||
nextP(12, 16) = P(12, 16);
|
||||
nextP(13, 16) = P(13, 16);
|
||||
nextP(14, 16) = P(14, 16);
|
||||
nextP(15, 16) = P(15, 16);
|
||||
nextP(16, 16) = P(16, 16);
|
||||
nextP(0, 17) = P(0, 17) - P(1, 17) * PS11 + P(10, 17) * PS6 + P(11, 17) * PS7 + P(12, 17) * PS9 - P(2, 17) * PS12 - P(3,
|
||||
17) * PS13;
|
||||
nextP(1, 17) = P(0, 17) * PS11 + P(1, 17) - P(10, 17) * PS34 + P(11, 17) * PS9 - P(12, 17) * PS7 + P(2,
|
||||
17) * PS13 - P(3, 17) * PS12;
|
||||
nextP(2, 17) = P(0, 17) * PS12 - P(1, 17) * PS13 - P(10, 17) * PS9 - P(11, 17) * PS34 + P(12, 17) * PS6 + P(2,
|
||||
17) + P(3, 17) * PS11;
|
||||
nextP(3, 17) = P(0, 17) * PS13 + P(1, 17) * PS12 + P(10, 17) * PS7 - P(11, 17) * PS6 - P(12, 17) * PS34 - P(2,
|
||||
17) * PS11 + P(3, 17);
|
||||
nextP(4, 17) = P(0, 17) * PS174 + P(1, 17) * PS173 + P(13, 17) * PS43 + P(14, 17) * PS172 - P(15, 17) * PS171 + P(2,
|
||||
17) * PS175 - P(3, 17) * PS176 + P(4, 17);
|
||||
nextP(5, 17) = -P(0, 17) * PS202 - P(1, 17) * PS204 - P(13, 17) * PS193 + P(14, 17) * PS75 + P(15, 17) * PS190 + P(2,
|
||||
17) * PS201 + P(3, 17) * PS203 + P(5, 17);
|
||||
nextP(6, 17) = P(0, 17) * PS216 + P(1, 17) * PS217 + P(13, 17) * PS199 - P(14, 17) * PS197 + P(15, 17) * PS87 - P(2,
|
||||
17) * PS214 + P(3, 17) * PS215 + P(6, 17);
|
||||
nextP(7, 17) = P(4, 17) * dt + P(7, 17);
|
||||
nextP(8, 17) = P(5, 17) * dt + P(8, 17);
|
||||
nextP(9, 17) = P(6, 17) * dt + P(9, 17);
|
||||
nextP(10, 17) = P(10, 17);
|
||||
nextP(11, 17) = P(11, 17);
|
||||
nextP(12, 17) = P(12, 17);
|
||||
nextP(13, 17) = P(13, 17);
|
||||
nextP(14, 17) = P(14, 17);
|
||||
nextP(15, 17) = P(15, 17);
|
||||
nextP(16, 17) = P(16, 17);
|
||||
nextP(17, 17) = P(17, 17);
|
||||
nextP(0, 18) = P(0, 18) - P(1, 18) * PS11 + P(10, 18) * PS6 + P(11, 18) * PS7 + P(12, 18) * PS9 - P(2, 18) * PS12 - P(3,
|
||||
18) * PS13;
|
||||
nextP(1, 18) = P(0, 18) * PS11 + P(1, 18) - P(10, 18) * PS34 + P(11, 18) * PS9 - P(12, 18) * PS7 + P(2,
|
||||
18) * PS13 - P(3, 18) * PS12;
|
||||
nextP(2, 18) = P(0, 18) * PS12 - P(1, 18) * PS13 - P(10, 18) * PS9 - P(11, 18) * PS34 + P(12, 18) * PS6 + P(2,
|
||||
18) + P(3, 18) * PS11;
|
||||
nextP(3, 18) = P(0, 18) * PS13 + P(1, 18) * PS12 + P(10, 18) * PS7 - P(11, 18) * PS6 - P(12, 18) * PS34 - P(2,
|
||||
18) * PS11 + P(3, 18);
|
||||
nextP(4, 18) = P(0, 18) * PS174 + P(1, 18) * PS173 + P(13, 18) * PS43 + P(14, 18) * PS172 - P(15, 18) * PS171 + P(2,
|
||||
18) * PS175 - P(3, 18) * PS176 + P(4, 18);
|
||||
nextP(5, 18) = -P(0, 18) * PS202 - P(1, 18) * PS204 - P(13, 18) * PS193 + P(14, 18) * PS75 + P(15, 18) * PS190 + P(2,
|
||||
18) * PS201 + P(3, 18) * PS203 + P(5, 18);
|
||||
nextP(6, 18) = P(0, 18) * PS216 + P(1, 18) * PS217 + P(13, 18) * PS199 - P(14, 18) * PS197 + P(15, 18) * PS87 - P(2,
|
||||
18) * PS214 + P(3, 18) * PS215 + P(6, 18);
|
||||
nextP(7, 18) = P(4, 18) * dt + P(7, 18);
|
||||
nextP(8, 18) = P(5, 18) * dt + P(8, 18);
|
||||
nextP(9, 18) = P(6, 18) * dt + P(9, 18);
|
||||
nextP(10, 18) = P(10, 18);
|
||||
nextP(11, 18) = P(11, 18);
|
||||
nextP(12, 18) = P(12, 18);
|
||||
nextP(13, 18) = P(13, 18);
|
||||
nextP(14, 18) = P(14, 18);
|
||||
nextP(15, 18) = P(15, 18);
|
||||
nextP(16, 18) = P(16, 18);
|
||||
nextP(17, 18) = P(17, 18);
|
||||
nextP(18, 18) = P(18, 18);
|
||||
nextP(0, 19) = P(0, 19) - P(1, 19) * PS11 + P(10, 19) * PS6 + P(11, 19) * PS7 + P(12, 19) * PS9 - P(2, 19) * PS12 - P(3,
|
||||
19) * PS13;
|
||||
nextP(1, 19) = P(0, 19) * PS11 + P(1, 19) - P(10, 19) * PS34 + P(11, 19) * PS9 - P(12, 19) * PS7 + P(2,
|
||||
19) * PS13 - P(3, 19) * PS12;
|
||||
nextP(2, 19) = P(0, 19) * PS12 - P(1, 19) * PS13 - P(10, 19) * PS9 - P(11, 19) * PS34 + P(12, 19) * PS6 + P(2,
|
||||
19) + P(3, 19) * PS11;
|
||||
nextP(3, 19) = P(0, 19) * PS13 + P(1, 19) * PS12 + P(10, 19) * PS7 - P(11, 19) * PS6 - P(12, 19) * PS34 - P(2,
|
||||
19) * PS11 + P(3, 19);
|
||||
nextP(4, 19) = P(0, 19) * PS174 + P(1, 19) * PS173 + P(13, 19) * PS43 + P(14, 19) * PS172 - P(15, 19) * PS171 + P(2,
|
||||
19) * PS175 - P(3, 19) * PS176 + P(4, 19);
|
||||
nextP(5, 19) = -P(0, 19) * PS202 - P(1, 19) * PS204 - P(13, 19) * PS193 + P(14, 19) * PS75 + P(15, 19) * PS190 + P(2,
|
||||
19) * PS201 + P(3, 19) * PS203 + P(5, 19);
|
||||
nextP(6, 19) = P(0, 19) * PS216 + P(1, 19) * PS217 + P(13, 19) * PS199 - P(14, 19) * PS197 + P(15, 19) * PS87 - P(2,
|
||||
19) * PS214 + P(3, 19) * PS215 + P(6, 19);
|
||||
nextP(7, 19) = P(4, 19) * dt + P(7, 19);
|
||||
nextP(8, 19) = P(5, 19) * dt + P(8, 19);
|
||||
nextP(9, 19) = P(6, 19) * dt + P(9, 19);
|
||||
nextP(10, 19) = P(10, 19);
|
||||
nextP(11, 19) = P(11, 19);
|
||||
nextP(12, 19) = P(12, 19);
|
||||
nextP(13, 19) = P(13, 19);
|
||||
nextP(14, 19) = P(14, 19);
|
||||
nextP(15, 19) = P(15, 19);
|
||||
nextP(16, 19) = P(16, 19);
|
||||
nextP(17, 19) = P(17, 19);
|
||||
nextP(18, 19) = P(18, 19);
|
||||
nextP(19, 19) = P(19, 19);
|
||||
nextP(0, 20) = P(0, 20) - P(1, 20) * PS11 + P(10, 20) * PS6 + P(11, 20) * PS7 + P(12, 20) * PS9 - P(2, 20) * PS12 - P(3,
|
||||
20) * PS13;
|
||||
nextP(1, 20) = P(0, 20) * PS11 + P(1, 20) - P(10, 20) * PS34 + P(11, 20) * PS9 - P(12, 20) * PS7 + P(2,
|
||||
20) * PS13 - P(3, 20) * PS12;
|
||||
nextP(2, 20) = P(0, 20) * PS12 - P(1, 20) * PS13 - P(10, 20) * PS9 - P(11, 20) * PS34 + P(12, 20) * PS6 + P(2,
|
||||
20) + P(3, 20) * PS11;
|
||||
nextP(3, 20) = P(0, 20) * PS13 + P(1, 20) * PS12 + P(10, 20) * PS7 - P(11, 20) * PS6 - P(12, 20) * PS34 - P(2,
|
||||
20) * PS11 + P(3, 20);
|
||||
nextP(4, 20) = P(0, 20) * PS174 + P(1, 20) * PS173 + P(13, 20) * PS43 + P(14, 20) * PS172 - P(15, 20) * PS171 + P(2,
|
||||
20) * PS175 - P(3, 20) * PS176 + P(4, 20);
|
||||
nextP(5, 20) = -P(0, 20) * PS202 - P(1, 20) * PS204 - P(13, 20) * PS193 + P(14, 20) * PS75 + P(15, 20) * PS190 + P(2,
|
||||
20) * PS201 + P(3, 20) * PS203 + P(5, 20);
|
||||
nextP(6, 20) = P(0, 20) * PS216 + P(1, 20) * PS217 + P(13, 20) * PS199 - P(14, 20) * PS197 + P(15, 20) * PS87 - P(2,
|
||||
20) * PS214 + P(3, 20) * PS215 + P(6, 20);
|
||||
nextP(7, 20) = P(4, 20) * dt + P(7, 20);
|
||||
nextP(8, 20) = P(5, 20) * dt + P(8, 20);
|
||||
nextP(9, 20) = P(6, 20) * dt + P(9, 20);
|
||||
nextP(10, 20) = P(10, 20);
|
||||
nextP(11, 20) = P(11, 20);
|
||||
nextP(12, 20) = P(12, 20);
|
||||
nextP(13, 20) = P(13, 20);
|
||||
nextP(14, 20) = P(14, 20);
|
||||
nextP(15, 20) = P(15, 20);
|
||||
nextP(16, 20) = P(16, 20);
|
||||
nextP(17, 20) = P(17, 20);
|
||||
nextP(18, 20) = P(18, 20);
|
||||
nextP(19, 20) = P(19, 20);
|
||||
nextP(20, 20) = P(20, 20);
|
||||
nextP(0, 21) = P(0, 21) - P(1, 21) * PS11 + P(10, 21) * PS6 + P(11, 21) * PS7 + P(12, 21) * PS9 - P(2, 21) * PS12 - P(3,
|
||||
21) * PS13;
|
||||
nextP(1, 21) = P(0, 21) * PS11 + P(1, 21) - P(10, 21) * PS34 + P(11, 21) * PS9 - P(12, 21) * PS7 + P(2,
|
||||
21) * PS13 - P(3, 21) * PS12;
|
||||
nextP(2, 21) = P(0, 21) * PS12 - P(1, 21) * PS13 - P(10, 21) * PS9 - P(11, 21) * PS34 + P(12, 21) * PS6 + P(2,
|
||||
21) + P(3, 21) * PS11;
|
||||
nextP(3, 21) = P(0, 21) * PS13 + P(1, 21) * PS12 + P(10, 21) * PS7 - P(11, 21) * PS6 - P(12, 21) * PS34 - P(2,
|
||||
21) * PS11 + P(3, 21);
|
||||
nextP(4, 21) = P(0, 21) * PS174 + P(1, 21) * PS173 + P(13, 21) * PS43 + P(14, 21) * PS172 - P(15, 21) * PS171 + P(2,
|
||||
21) * PS175 - P(3, 21) * PS176 + P(4, 21);
|
||||
nextP(5, 21) = -P(0, 21) * PS202 - P(1, 21) * PS204 - P(13, 21) * PS193 + P(14, 21) * PS75 + P(15, 21) * PS190 + P(2,
|
||||
21) * PS201 + P(3, 21) * PS203 + P(5, 21);
|
||||
nextP(6, 21) = P(0, 21) * PS216 + P(1, 21) * PS217 + P(13, 21) * PS199 - P(14, 21) * PS197 + P(15, 21) * PS87 - P(2,
|
||||
21) * PS214 + P(3, 21) * PS215 + P(6, 21);
|
||||
nextP(7, 21) = P(4, 21) * dt + P(7, 21);
|
||||
nextP(8, 21) = P(5, 21) * dt + P(8, 21);
|
||||
nextP(9, 21) = P(6, 21) * dt + P(9, 21);
|
||||
nextP(10, 21) = P(10, 21);
|
||||
nextP(11, 21) = P(11, 21);
|
||||
nextP(12, 21) = P(12, 21);
|
||||
nextP(13, 21) = P(13, 21);
|
||||
nextP(14, 21) = P(14, 21);
|
||||
nextP(15, 21) = P(15, 21);
|
||||
nextP(16, 21) = P(16, 21);
|
||||
nextP(17, 21) = P(17, 21);
|
||||
nextP(18, 21) = P(18, 21);
|
||||
nextP(19, 21) = P(19, 21);
|
||||
nextP(20, 21) = P(20, 21);
|
||||
nextP(21, 21) = P(21, 21);
|
||||
nextP(0, 22) = P(0, 22) - P(1, 22) * PS11 + P(10, 22) * PS6 + P(11, 22) * PS7 + P(12, 22) * PS9 - P(2, 22) * PS12 - P(3,
|
||||
22) * PS13;
|
||||
nextP(1, 22) = P(0, 22) * PS11 + P(1, 22) - P(10, 22) * PS34 + P(11, 22) * PS9 - P(12, 22) * PS7 + P(2,
|
||||
22) * PS13 - P(3, 22) * PS12;
|
||||
nextP(2, 22) = P(0, 22) * PS12 - P(1, 22) * PS13 - P(10, 22) * PS9 - P(11, 22) * PS34 + P(12, 22) * PS6 + P(2,
|
||||
22) + P(3, 22) * PS11;
|
||||
nextP(3, 22) = P(0, 22) * PS13 + P(1, 22) * PS12 + P(10, 22) * PS7 - P(11, 22) * PS6 - P(12, 22) * PS34 - P(2,
|
||||
22) * PS11 + P(3, 22);
|
||||
nextP(4, 22) = P(0, 22) * PS174 + P(1, 22) * PS173 + P(13, 22) * PS43 + P(14, 22) * PS172 - P(15, 22) * PS171 + P(2,
|
||||
22) * PS175 - P(3, 22) * PS176 + P(4, 22);
|
||||
nextP(5, 22) = -P(0, 22) * PS202 - P(1, 22) * PS204 - P(13, 22) * PS193 + P(14, 22) * PS75 + P(15, 22) * PS190 + P(2,
|
||||
22) * PS201 + P(3, 22) * PS203 + P(5, 22);
|
||||
nextP(6, 22) = P(0, 22) * PS216 + P(1, 22) * PS217 + P(13, 22) * PS199 - P(14, 22) * PS197 + P(15, 22) * PS87 - P(2,
|
||||
22) * PS214 + P(3, 22) * PS215 + P(6, 22);
|
||||
nextP(7, 22) = P(4, 22) * dt + P(7, 22);
|
||||
nextP(8, 22) = P(5, 22) * dt + P(8, 22);
|
||||
nextP(9, 22) = P(6, 22) * dt + P(9, 22);
|
||||
nextP(10, 22) = P(10, 22);
|
||||
nextP(11, 22) = P(11, 22);
|
||||
nextP(12, 22) = P(12, 22);
|
||||
nextP(13, 22) = P(13, 22);
|
||||
nextP(14, 22) = P(14, 22);
|
||||
nextP(15, 22) = P(15, 22);
|
||||
nextP(16, 22) = P(16, 22);
|
||||
nextP(17, 22) = P(17, 22);
|
||||
nextP(18, 22) = P(18, 22);
|
||||
nextP(19, 22) = P(19, 22);
|
||||
nextP(20, 22) = P(20, 22);
|
||||
nextP(21, 22) = P(21, 22);
|
||||
nextP(22, 22) = P(22, 22);
|
||||
nextP(0, 23) = P(0, 23) - P(1, 23) * PS11 + P(10, 23) * PS6 + P(11, 23) * PS7 + P(12, 23) * PS9 - P(2, 23) * PS12 - P(3,
|
||||
23) * PS13;
|
||||
nextP(1, 23) = P(0, 23) * PS11 + P(1, 23) - P(10, 23) * PS34 + P(11, 23) * PS9 - P(12, 23) * PS7 + P(2,
|
||||
23) * PS13 - P(3, 23) * PS12;
|
||||
nextP(2, 23) = P(0, 23) * PS12 - P(1, 23) * PS13 - P(10, 23) * PS9 - P(11, 23) * PS34 + P(12, 23) * PS6 + P(2,
|
||||
23) + P(3, 23) * PS11;
|
||||
nextP(3, 23) = P(0, 23) * PS13 + P(1, 23) * PS12 + P(10, 23) * PS7 - P(11, 23) * PS6 - P(12, 23) * PS34 - P(2,
|
||||
23) * PS11 + P(3, 23);
|
||||
nextP(4, 23) = P(0, 23) * PS174 + P(1, 23) * PS173 + P(13, 23) * PS43 + P(14, 23) * PS172 - P(15, 23) * PS171 + P(2,
|
||||
23) * PS175 - P(3, 23) * PS176 + P(4, 23);
|
||||
nextP(5, 23) = -P(0, 23) * PS202 - P(1, 23) * PS204 - P(13, 23) * PS193 + P(14, 23) * PS75 + P(15, 23) * PS190 + P(2,
|
||||
23) * PS201 + P(3, 23) * PS203 + P(5, 23);
|
||||
nextP(6, 23) = P(0, 23) * PS216 + P(1, 23) * PS217 + P(13, 23) * PS199 - P(14, 23) * PS197 + P(15, 23) * PS87 - P(2,
|
||||
23) * PS214 + P(3, 23) * PS215 + P(6, 23);
|
||||
nextP(7, 23) = P(4, 23) * dt + P(7, 23);
|
||||
nextP(8, 23) = P(5, 23) * dt + P(8, 23);
|
||||
nextP(9, 23) = P(6, 23) * dt + P(9, 23);
|
||||
nextP(10, 23) = P(10, 23);
|
||||
nextP(11, 23) = P(11, 23);
|
||||
nextP(12, 23) = P(12, 23);
|
||||
nextP(13, 23) = P(13, 23);
|
||||
nextP(14, 23) = P(14, 23);
|
||||
nextP(15, 23) = P(15, 23);
|
||||
nextP(16, 23) = P(16, 23);
|
||||
nextP(17, 23) = P(17, 23);
|
||||
nextP(18, 23) = P(18, 23);
|
||||
nextP(19, 23) = P(19, 23);
|
||||
nextP(20, 23) = P(20, 23);
|
||||
nextP(21, 23) = P(21, 23);
|
||||
nextP(22, 23) = P(22, 23);
|
||||
nextP(23, 23) = P(23, 23);
|
||||
|
||||
// save output
|
||||
for (int col = 0; col <= 23; col++) {
|
||||
for (int row = 0; row <= col; row++) {
|
||||
nextP_sympy(row, col) = nextP(row, col);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
{
|
||||
Vector24f state_vector{};
|
||||
state_vector(0) = q0;
|
||||
state_vector(1) = q1;
|
||||
state_vector(2) = q2;
|
||||
state_vector(3) = q3;
|
||||
state_vector(10) = dax_b;
|
||||
state_vector(11) = day_b;
|
||||
state_vector(12) = daz_b;
|
||||
state_vector(13) = dvx_b;
|
||||
state_vector(14) = dvy_b;
|
||||
state_vector(15) = dvz_b;
|
||||
|
||||
const Vector3f d_vel(dvx, dvy, dvz);
|
||||
const Vector3f d_ang(dax, day, daz);
|
||||
|
||||
EXPECT_FLOAT_EQ(daxVar, dayVar);
|
||||
EXPECT_FLOAT_EQ(daxVar, dazVar);
|
||||
|
||||
const float d_ang_var = daxVar; // derivation assumes same variance on all gyro axes
|
||||
const Vector3f d_vel_var(dvxVar, dvyVar, dvzVar);
|
||||
|
||||
sym::PredictCovariance(state_vector, P, d_vel, d_vel_var, d_ang, d_ang_var, dt, &nextP_symforce);
|
||||
}
|
||||
|
||||
DiffRatioReport report = computeDiffRatioSquareMatrix24f(nextP_sympy, nextP_symforce);
|
||||
EXPECT_LT(report.max_diff_fraction, 2e-5f) << "Max diff fraction = " << report.max_diff_fraction <<
|
||||
" location index = " << report.max_row << " sympy = " << report.max_v1 << " symforce = " << report.max_v2;
|
||||
}
|
||||
|
|
@ -120,13 +120,13 @@ public:
|
|||
void learningCorrectAccelBias()
|
||||
{
|
||||
const Dcmf R_to_earth = Dcmf(_ekf->getQuaternion());
|
||||
const Vector3f dvel_bias_var = _ekf_wrapper.getDeltaVelBiasVariance();
|
||||
const Vector3f accel_bias_var = _ekf->getAccelBiasVariance();
|
||||
const Vector3f accel_bias = _ekf->getAccelBias();
|
||||
|
||||
for (int i = 0; i < 3; i++) {
|
||||
if (fabsf(R_to_earth(2, i)) > 0.8f) {
|
||||
// Highly observable, the variance decreases
|
||||
EXPECT_LT(dvel_bias_var(i), 4.0e-6f) << "axis " << i;
|
||||
EXPECT_LT(accel_bias_var(i), 4.0e-2f) << "axis " << i;
|
||||
}
|
||||
|
||||
EXPECT_LT(accel_bias(i), 4.0e-6f) << "axis " << i;
|
||||
|
|
|
|||
|
|
@ -42,8 +42,6 @@
|
|||
#include <vector>
|
||||
#include <mathlib/mathlib.h>
|
||||
|
||||
#include "EKF/utils.hpp"
|
||||
|
||||
TEST(eclPowfTest, compareToStandardImplementation)
|
||||
{
|
||||
std::vector<int> exponents = {-3, -2, -1, -0, 0, 1, 2, 3};
|
||||
|
|
@ -51,7 +49,7 @@ TEST(eclPowfTest, compareToStandardImplementation)
|
|||
|
||||
for (auto const exponent : exponents) {
|
||||
for (auto const basis : bases) {
|
||||
EXPECT_EQ(ecl::powf(basis, exponent),
|
||||
EXPECT_EQ(powf(basis, exponent),
|
||||
std::pow(basis, static_cast<float>(exponent)));
|
||||
}
|
||||
}
|
||||
|
|
|
|||
|
|
@ -74,9 +74,9 @@ void sympyYawEstUpdate(const SquareMatrix3f &P, float velObsVar, SquareMatrix<fl
|
|||
const float P22 = P(2, 2);
|
||||
|
||||
// optimized auto generated code from SymPy script src/lib/ecl/EKF/python/ekf_derivation/main.py
|
||||
const float t0 = ecl::powf(P01, 2);
|
||||
const float t0 = powf(P01, 2.f);
|
||||
const float t1 = -t0;
|
||||
const float t2 = P00 * P11 + P00 * velObsVar + P11 * velObsVar + t1 + ecl::powf(velObsVar, 2);
|
||||
const float t2 = P00 * P11 + P00 * velObsVar + P11 * velObsVar + t1 + powf(velObsVar, 2.f);
|
||||
|
||||
if (fabsf(t2) < 1e-6f) {
|
||||
return;
|
||||
|
|
@ -157,9 +157,9 @@ void sympyYawEstPrediction(const Vector3f &state, const SquareMatrix3f &P, const
|
|||
const float dazVar = d_ang_var;
|
||||
|
||||
const float S0 = cosf(psi);
|
||||
const float S1 = ecl::powf(S0, 2);
|
||||
const float S1 = powf(S0, 2.f);
|
||||
const float S2 = sinf(psi);
|
||||
const float S3 = ecl::powf(S2, 2);
|
||||
const float S3 = powf(S2, 2.f);
|
||||
const float S4 = S0 * dvy + S2 * dvx;
|
||||
const float S5 = P02 - P22 * S4;
|
||||
const float S6 = S0 * dvx - S2 * dvy;
|
||||
|
|
|
|||
Loading…
Reference in New Issue