/// -*- tab-width: 4; Mode: C++; c-basic-offset: 4; indent-tabs-mode: nil -*-

#include <AP_Progmem.h>
#include "AP_InertialSensor.h"

#include <AP_Common.h>
#include <AP_HAL.h>
#include <AP_Notify.h>

extern const AP_HAL::HAL& hal;


#define SAMPLE_UNIT 1

// Class level parameters
const AP_Param::GroupInfo AP_InertialSensor::var_info[] PROGMEM = {
    // @Param: PRODUCT_ID
    // @DisplayName: IMU Product ID
    // @Description: Which type of IMU is installed (read-only). 
    // @User: Advanced
    // @Values: 0:Unknown,1:APM1-1280,2:APM1-2560,88:APM2,3:SITL,4:PX4v1,5:PX4v2,256:Flymaple,257:Linux
    AP_GROUPINFO("PRODUCT_ID",  0, AP_InertialSensor, _product_id,   0),

    // @Param: ACCSCAL_X
    // @DisplayName: Accelerometer scaling of X axis
    // @Description: Accelerometer scaling of X axis.  Calculated during acceleration calibration routine
    // @Range: 0.8 1.2
    // @User: Advanced

    // @Param: ACCSCAL_Y
    // @DisplayName: Accelerometer scaling of Y axis
    // @Description: Accelerometer scaling of Y axis  Calculated during acceleration calibration routine
    // @Range: 0.8 1.2
    // @User: Advanced

    // @Param: ACCSCAL_Z
    // @DisplayName: Accelerometer scaling of Z axis
    // @Description: Accelerometer scaling of Z axis  Calculated during acceleration calibration routine
    // @Range: 0.8 1.2
    // @User: Advanced
    AP_GROUPINFO("ACCSCAL",     1, AP_InertialSensor, _accel_scale[0],  0),

    // @Param: ACCOFFS_X
    // @DisplayName: Accelerometer offsets of X axis
    // @Description: Accelerometer offsets of X axis. This is setup using the acceleration calibration or level operations
    // @Units: m/s/s
    // @Range: -300 300
    // @User: Advanced

    // @Param: ACCOFFS_Y
    // @DisplayName: Accelerometer offsets of Y axis
    // @Description: Accelerometer offsets of Y axis. This is setup using the acceleration calibration or level operations
    // @Units: m/s/s
    // @Range: -300 300
    // @User: Advanced

    // @Param: ACCOFFS_Z
    // @DisplayName: Accelerometer offsets of Z axis
    // @Description: Accelerometer offsets of Z axis. This is setup using the acceleration calibration or level operations
    // @Units: m/s/s
    // @Range: -300 300
    // @User: Advanced
    AP_GROUPINFO("ACCOFFS",     2, AP_InertialSensor, _accel_offset[0], 0),

    // @Param: GYROFFS_X
    // @DisplayName: Gyro offsets of X axis
    // @Description: Gyro sensor offsets of X axis. This is setup on each boot during gyro calibrations
    // @Units: rad/s
    // @User: Advanced

    // @Param: GYROFFS_Y
    // @DisplayName: Gyro offsets of Y axis
    // @Description: Gyro sensor offsets of Y axis. This is setup on each boot during gyro calibrations
    // @Units: rad/s
    // @User: Advanced

    // @Param: GYROFFS_Z
    // @DisplayName: Gyro offsets of Z axis
    // @Description: Gyro sensor offsets of Z axis. This is setup on each boot during gyro calibrations
    // @Units: rad/s
    // @User: Advanced
    AP_GROUPINFO("GYROFFS",     3, AP_InertialSensor, _gyro_offset[0],  0),

    // @Param: MPU6K_FILTER
    // @DisplayName: MPU6000 filter frequency
    // @Description: Filter frequency to ask the MPU6000 to apply to samples. This can be set to a lower value to try to cope with very high vibration levels in aircraft. The default value on ArduPlane, APMrover2 and ArduCopter is 20Hz. This option takes effect on the next reboot or gyro initialisation
    // @Units: Hz
    // @Values: 0:Default,5:5Hz,10:10Hz,20:20Hz,42:42Hz,98:98Hz
    // @User: Advanced
    AP_GROUPINFO("MPU6K_FILTER", 4, AP_InertialSensor, _mpu6000_filter,  0),

#if INS_MAX_INSTANCES > 1
    // @Param: ACC2SCAL_X
    // @DisplayName: Accelerometer2 scaling of X axis
    // @Description: Accelerometer2 scaling of X axis.  Calculated during acceleration calibration routine
    // @Range: 0.8 1.2
    // @User: Advanced

    // @Param: ACC2SCAL_Y
    // @DisplayName: Accelerometer2 scaling of Y axis
    // @Description: Accelerometer2 scaling of Y axis  Calculated during acceleration calibration routine
    // @Range: 0.8 1.2
    // @User: Advanced

    // @Param: ACC2SCAL_Z
    // @DisplayName: Accelerometer2 scaling of Z axis
    // @Description: Accelerometer2 scaling of Z axis  Calculated during acceleration calibration routine
    // @Range: 0.8 1.2
    // @User: Advanced
    AP_GROUPINFO("ACC2SCAL",    5, AP_InertialSensor, _accel_scale[1],   0),

    // @Param: ACC2OFFS_X
    // @DisplayName: Accelerometer2 offsets of X axis
    // @Description: Accelerometer2 offsets of X axis. This is setup using the acceleration calibration or level operations
    // @Units: m/s/s
    // @Range: -300 300
    // @User: Advanced

    // @Param: ACC2OFFS_Y
    // @DisplayName: Accelerometer2 offsets of Y axis
    // @Description: Accelerometer2 offsets of Y axis. This is setup using the acceleration calibration or level operations
    // @Units: m/s/s
    // @Range: -300 300
    // @User: Advanced

    // @Param: ACC2OFFS_Z
    // @DisplayName: Accelerometer2 offsets of Z axis
    // @Description: Accelerometer2 offsets of Z axis. This is setup using the acceleration calibration or level operations
    // @Units: m/s/s
    // @Range: -300 300
    // @User: Advanced
    AP_GROUPINFO("ACC2OFFS",    6, AP_InertialSensor, _accel_offset[1],  0),

    // @Param: GYR2OFFS_X
    // @DisplayName: Gyro2 offsets of X axis
    // @Description: Gyro2 sensor offsets of X axis. This is setup on each boot during gyro calibrations
    // @Units: rad/s
    // @User: Advanced

    // @Param: GYR2OFFS_Y
    // @DisplayName: Gyro2 offsets of Y axis
    // @Description: Gyro2 sensor offsets of Y axis. This is setup on each boot during gyro calibrations
    // @Units: rad/s
    // @User: Advanced

    // @Param: GYR2OFFS_Z
    // @DisplayName: Gyro2 offsets of Z axis
    // @Description: Gyro2 sensor offsets of Z axis. This is setup on each boot during gyro calibrations
    // @Units: rad/s
    // @User: Advanced
    AP_GROUPINFO("GYR2OFFS",    7, AP_InertialSensor, _gyro_offset[1],   0),
#endif

#if INS_MAX_INSTANCES > 2
    // @Param: ACC3SCAL_X
    // @DisplayName: Accelerometer3 scaling of X axis
    // @Description: Accelerometer3 scaling of X axis.  Calculated during acceleration calibration routine
    // @Range: 0.8 1.2
    // @User: Advanced

    // @Param: ACC3SCAL_Y
    // @DisplayName: Accelerometer3 scaling of Y axis
    // @Description: Accelerometer3 scaling of Y axis  Calculated during acceleration calibration routine
    // @Range: 0.8 1.2
    // @User: Advanced

    // @Param: ACC3SCAL_Z
    // @DisplayName: Accelerometer3 scaling of Z axis
    // @Description: Accelerometer3 scaling of Z axis  Calculated during acceleration calibration routine
    // @Range: 0.8 1.2
    // @User: Advanced
    AP_GROUPINFO("ACC3SCAL",    8, AP_InertialSensor, _accel_scale[2],   0),

    // @Param: ACC3OFFS_X
    // @DisplayName: Accelerometer3 offsets of X axis
    // @Description: Accelerometer3 offsets of X axis. This is setup using the acceleration calibration or level operations
    // @Units: m/s/s
    // @Range: -300 300
    // @User: Advanced

    // @Param: ACC3OFFS_Y
    // @DisplayName: Accelerometer3 offsets of Y axis
    // @Description: Accelerometer3 offsets of Y axis. This is setup using the acceleration calibration or level operations
    // @Units: m/s/s
    // @Range: -300 300
    // @User: Advanced

    // @Param: ACC3OFFS_Z
    // @DisplayName: Accelerometer3 offsets of Z axis
    // @Description: Accelerometer3 offsets of Z axis. This is setup using the acceleration calibration or level operations
    // @Units: m/s/s
    // @Range: -300 300
    // @User: Advanced
    AP_GROUPINFO("ACC3OFFS",    9, AP_InertialSensor, _accel_offset[2],  0),

    // @Param: GYR3OFFS_X
    // @DisplayName: Gyro3 offsets of X axis
    // @Description: Gyro3 sensor offsets of X axis. This is setup on each boot during gyro calibrations
    // @Units: rad/s
    // @User: Advanced

    // @Param: GYR3OFFS_Y
    // @DisplayName: Gyro3 offsets of Y axis
    // @Description: Gyro3 sensor offsets of Y axis. This is setup on each boot during gyro calibrations
    // @Units: rad/s
    // @User: Advanced

    // @Param: GYR3OFFS_Z
    // @DisplayName: Gyro3 offsets of Z axis
    // @Description: Gyro3 sensor offsets of Z axis. This is setup on each boot during gyro calibrations
    // @Units: rad/s
    // @User: Advanced
    AP_GROUPINFO("GYR3OFFS",   10, AP_InertialSensor, _gyro_offset[2],   0),
#endif

    AP_GROUPEND
};

AP_InertialSensor::AP_InertialSensor() :
    _gyro_count(0),
    _accel_count(0),
    _backend_count(0),
    _accel(),
    _gyro(),
    _board_orientation(ROTATION_NONE),
    _hil_mode(false),
    _have_3D_calibration(false)
{
    AP_Param::setup_object_defaults(this, var_info);        
    for (uint8_t i=0; i<INS_MAX_BACKENDS; i++) {
        _backends[i] = NULL;
    }
    for (uint8_t i=0; i<INS_MAX_INSTANCES; i++) {
        _accel_error_count[i] = 0;
        _gyro_error_count[i] = 0;
    }
}


/*
  register a new gyro instance
 */
uint8_t AP_InertialSensor::register_gyro(void)
{
    if (_gyro_count == INS_MAX_INSTANCES) {
        hal.scheduler->panic(PSTR("Too many gyros"));
    }
    return _gyro_count++;
}

/*
  register a new accel instance
 */
uint8_t AP_InertialSensor::register_accel(void)
{
    if (_accel_count == INS_MAX_INSTANCES) {
        hal.scheduler->panic(PSTR("Too many accels"));
    }
    return _accel_count++;
}

void
AP_InertialSensor::init( Start_style style,
                         Sample_rate sample_rate)
{
    // remember the sample rate
    _sample_rate = sample_rate;

    if (_gyro_count == 0 && _accel_count == 0) {
        // detect available backends. Only called once
        _detect_backends();
    }

    _product_id = 0; // FIX

    // initialise accel scale if need be. This is needed as we can't
    // give non-zero default values for vectors in AP_Param
    for (uint8_t i=0; i<get_accel_count(); i++) {
        if (_accel_scale[i].get().is_zero()) {
            _accel_scale[i].set(Vector3f(1,1,1));
        }
    }

    // remember whether we have 3D calibration so this can be used for
    // AHRS health
    check_3D_calibration();

    if (WARM_START != style) {
        // do cold-start calibration for gyro only
        _init_gyro();
    }

    switch (sample_rate) {
    case RATE_50HZ:
        _sample_period_usec = 20000;
        break;
    case RATE_100HZ:
        _sample_period_usec = 10000;
        break;
    case RATE_200HZ:
        _sample_period_usec = 5000;
        break;
    case RATE_400HZ:
    default:
        _sample_period_usec = 2500;
        break;
    }

    // establish the baseline time between samples
    _delta_time = 0;
    _next_sample_usec = 0;
    _last_sample_usec = 0;
    _have_sample = false;
}

/*
  try to load a backend
 */
void AP_InertialSensor::_add_backend(AP_InertialSensor_Backend *(detect)(AP_InertialSensor &))
{
    if (_backend_count == INS_MAX_BACKENDS) {
        hal.scheduler->panic(PSTR("Too many INS backends"));
    }
    _backends[_backend_count] = detect(*this);
    if (_backends[_backend_count] != NULL) {
        _backend_count++;
    }
}


/*
  detect available backends for this board
 */
void 
AP_InertialSensor::_detect_backends(void)
{
#if HAL_INS_DEFAULT == HAL_INS_HIL
    _add_backend(AP_InertialSensor_HIL::detect);
#elif HAL_INS_DEFAULT == HAL_INS_MPU6000
    _add_backend(AP_InertialSensor_MPU6000::detect);
#elif HAL_INS_DEFAULT == HAL_INS_PX4 || HAL_INS_DEFAULT == HAL_INS_VRBRAIN
    _add_backend(AP_InertialSensor_PX4::detect);
#elif HAL_INS_DEFAULT == HAL_INS_OILPAN
    _add_backend(AP_InertialSensor_Oilpan::detect);
#elif HAL_INS_DEFAULT == HAL_INS_MPU9250
    _add_backend(AP_InertialSensor_MPU9250::detect);
#elif HAL_INS_DEFAULT == HAL_INS_FLYMAPLE
    _add_backend(AP_InertialSensor_Flymaple::detect);
#else
    #error Unrecognised HAL_INS_TYPE setting
#endif

#if 0 // disabled due to broken hardware on some PXF capes
#if CONFIG_HAL_BOARD_SUBTYPE == HAL_BOARD_SUBTYPE_LINUX_PXF
    // the PXF also has a MPU6000
    _add_backend(AP_InertialSensor_MPU6000::detect);
#endif
#endif

    if (_backend_count == 0 ||
        _gyro_count == 0 ||
        _accel_count == 0) {
        hal.scheduler->panic(PSTR("No INS backends available"));
    }

    // set the product ID to the ID of the first backend
    _product_id.set(_backends[0]->product_id());
}

void
AP_InertialSensor::init_accel()
{
    _init_accel();

    // save calibration
    _save_parameters();

    check_3D_calibration();
}

#if !defined( __AVR_ATmega1280__ )
// calibrate_accel - perform accelerometer calibration including providing user
// instructions and feedback Gauss-Newton accel calibration routines borrowed
// from Rolfe Schmidt blog post describing the method:
// http://chionophilous.wordpress.com/2011/10/24/accelerometer-calibration-iv-1-implementing-gauss-newton-on-an-atmega/
// original sketch available at
// http://rolfeschmidt.com/mathtools/skimetrics/adxl_gn_calibration.pde
bool AP_InertialSensor::calibrate_accel(AP_InertialSensor_UserInteract* interact,
                                        float &trim_roll,
                                        float &trim_pitch)
{
    uint8_t num_accels = min(get_accel_count(), INS_MAX_INSTANCES);
    Vector3f samples[INS_MAX_INSTANCES][6];
    Vector3f new_offsets[INS_MAX_INSTANCES];
    Vector3f new_scaling[INS_MAX_INSTANCES];
    Vector3f orig_offset[INS_MAX_INSTANCES];
    Vector3f orig_scale[INS_MAX_INSTANCES];
    uint8_t num_ok = 0;

    for (uint8_t k=0; k<num_accels; k++) {
        // backup original offsets and scaling
        orig_offset[k] = _accel_offset[k].get();
        orig_scale[k]  = _accel_scale[k].get();

        // clear accelerometer offsets and scaling
        _accel_offset[k] = Vector3f(0,0,0);
        _accel_scale[k] = Vector3f(1,1,1);
    }

    // capture data from 6 positions
    for (uint8_t i=0; i<6; i++) {
        const prog_char_t *msg;

        // display message to user
        switch ( i ) {
            case 0:
                msg = PSTR("level");
                break;
            case 1:
                msg = PSTR("on its LEFT side");
                break;
            case 2:
                msg = PSTR("on its RIGHT side");
                break;
            case 3:
                msg = PSTR("nose DOWN");
                break;
            case 4:
                msg = PSTR("nose UP");
                break;
            default:    // default added to avoid compiler warning
            case 5:
                msg = PSTR("on its BACK");
                break;
        }
        interact->printf_P(
                PSTR("Place vehicle %S and press any key.\n"), msg);

        // wait for user input
        if (!interact->blocking_read()) {
            //No need to use interact->printf_P for an error, blocking_read does this when it fails
            goto failed;
        }

        // clear out any existing samples from ins
        update();

        // average 32 samples
        for (uint8_t k=0; k<num_accels; k++) {
            samples[k][i] = Vector3f();
        }
        uint8_t num_samples = 0;
        while (num_samples < 32) {
            wait_for_sample();
            // read samples from ins
            update();
            // capture sample
            for (uint8_t k=0; k<num_accels; k++) {
                samples[k][i] += get_accel(k);
            }
            hal.scheduler->delay(10);
            num_samples++;
        }
        for (uint8_t k=0; k<num_accels; k++) {
            samples[k][i] /= num_samples;
        }
    }

    // run the calibration routine
    for (uint8_t k=0; k<num_accels; k++) {
        bool success = _calibrate_accel(samples[k], new_offsets[k], new_scaling[k]);

        interact->printf_P(PSTR("Offsets[%u]: %.2f %.2f %.2f\n"),
                           (unsigned)k,
                           new_offsets[k].x, new_offsets[k].y, new_offsets[k].z);
        interact->printf_P(PSTR("Scaling[%u]: %.2f %.2f %.2f\n"),
                           (unsigned)k,
                           new_scaling[k].x, new_scaling[k].y, new_scaling[k].z);
        if (success) num_ok++;
    }

    if (num_ok == num_accels) {
        interact->printf_P(PSTR("Calibration successful\n"));

        for (uint8_t k=0; k<num_accels; k++) {
            // set and save calibration
            _accel_offset[k].set(new_offsets[k]);
            _accel_scale[k].set(new_scaling[k]);
        }
        _save_parameters();

        check_3D_calibration();

        // calculate the trims as well from primary accels and pass back to caller
        _calculate_trim(samples[0][0], trim_roll, trim_pitch);

        return true;
    }

failed:
    interact->printf_P(PSTR("Calibration FAILED\n"));
    // restore original scaling and offsets
    for (uint8_t k=0; k<num_accels; k++) {
        _accel_offset[k].set(orig_offset[k]);
        _accel_scale[k].set(orig_scale[k]);
    }
    return false;
}
#endif

/*
  check if the accelerometers are calibrated in 3D. Called on startup
  and any accel cal
 */
void AP_InertialSensor::check_3D_calibration()
{
    _have_3D_calibration = false;
    // check each accelerometer has offsets saved
    for (uint8_t i=0; i<get_accel_count(); i++) {
        // exactly 0.0 offset is extremely unlikely
        if (_accel_offset[i].get().is_zero()) {
            return;
        }
        // exactly 1.0 scaling is extremely unlikely
        const Vector3f &scaling = _accel_scale[i].get();
        if (fabsf(scaling.x - 1.0f) < 0.00001f &&
            fabsf(scaling.y - 1.0f) < 0.00001f &&
            fabsf(scaling.z - 1.0f) < 0.00001f) {
            return;
        }
    }
    // if we got this far the accelerometers must have been calibrated
    _have_3D_calibration = true;
}

/*
  return true if we have 3D calibration values
 */
bool AP_InertialSensor::calibrated() const
{
    return _have_3D_calibration;
}

void
AP_InertialSensor::init_gyro()
{
    _init_gyro();

    // save calibration
    _save_parameters();
}

// get_gyro_health_all - return true if all gyros are healthy
bool AP_InertialSensor::get_gyro_health_all(void) const
{
    for (uint8_t i=0; i<get_gyro_count(); i++) {
        if (!get_gyro_health(i)) {
            return false;
        }
    }
    // return true if we have at least one gyro
    return (get_gyro_count() > 0);
}

// gyro_calibration_ok_all - returns true if all gyros were calibrated successfully
bool AP_InertialSensor::gyro_calibrated_ok_all() const
{
    for (uint8_t i=0; i<get_gyro_count(); i++) {
        if (!gyro_calibrated_ok(i)) {
            return false;
        }
    }
    return (get_gyro_count() > 0);
}

// get_accel_health_all - return true if all accels are healthy
bool AP_InertialSensor::get_accel_health_all(void) const
{
    for (uint8_t i=0; i<get_accel_count(); i++) {
        if (!get_accel_health(i)) {
            return false;
        }
    }
    // return true if we have at least one accel
    return (get_accel_count() > 0);
}

void
AP_InertialSensor::_init_accel()
{
    uint8_t num_accels = min(get_accel_count(), INS_MAX_INSTANCES);
    uint8_t flashcount = 0;
    Vector3f prev[INS_MAX_INSTANCES];
    Vector3f accel_offset[INS_MAX_INSTANCES];
    float total_change[INS_MAX_INSTANCES];
    float max_offset[INS_MAX_INSTANCES];

    memset(max_offset, 0, sizeof(max_offset));
    memset(total_change, 0, sizeof(total_change));

    // cold start
    hal.scheduler->delay(100);

    hal.console->print_P(PSTR("Init Accel"));

    // flash leds to tell user to keep the IMU still
    AP_Notify::flags.initialising = true;

    // clear accelerometer offsets and scaling
    for (uint8_t k=0; k<num_accels; k++) {
        _accel_offset[k] = Vector3f(0,0,0);
        _accel_scale[k] = Vector3f(1,1,1);

        // initialise accel offsets to a large value the first time
        // this will force us to calibrate accels at least twice
        accel_offset[k] = Vector3f(500, 500, 500);
    }

    // loop until we calculate acceptable offsets
    while (true) {
        // get latest accelerometer values
        update();

        for (uint8_t k=0; k<num_accels; k++) {
            // store old offsets
            prev[k] = accel_offset[k];

            // get new offsets
            accel_offset[k] = get_accel(k);
        }

        // We take some readings...
        for(int8_t i = 0; i < 50; i++) {

            hal.scheduler->delay(20);
            update();

            // low pass filter the offsets
            for (uint8_t k=0; k<num_accels; k++) {
                accel_offset[k] = accel_offset[k] * 0.9f + get_accel(k) * 0.1f;
            }

            // display some output to the user
            if(flashcount >= 10) {
                hal.console->print_P(PSTR("*"));
                flashcount = 0;
            }
            flashcount++;
        }

        for (uint8_t k=0; k<num_accels; k++) {
            // null gravity from the Z accel
            accel_offset[k].z += GRAVITY_MSS;

            total_change[k] = 
                fabsf(prev[k].x - accel_offset[k].x) + 
                fabsf(prev[k].y - accel_offset[k].y) + 
                fabsf(prev[k].z - accel_offset[k].z);
            max_offset[k] = (accel_offset[k].x > accel_offset[k].y) ? accel_offset[k].x : accel_offset[k].y;
            max_offset[k] = (max_offset[k] > accel_offset[k].z) ? max_offset[k] : accel_offset[k].z;
        }

        uint8_t num_converged = 0;
        for (uint8_t k=0; k<num_accels; k++) {
            if (total_change[k] <= AP_INERTIAL_SENSOR_ACCEL_TOT_MAX_OFFSET_CHANGE && 
                max_offset[k] <= AP_INERTIAL_SENSOR_ACCEL_MAX_OFFSET) {
                num_converged++;
            }
        }

        if (num_converged == num_accels) break;

        hal.scheduler->delay(500);
    }

    // set the global accel offsets
    for (uint8_t k=0; k<num_accels; k++) {
        _accel_offset[k] = accel_offset[k];
    }

    // stop flashing the leds
    AP_Notify::flags.initialising = false;

    hal.console->print_P(PSTR(" "));

}

void
AP_InertialSensor::_init_gyro()
{
    uint8_t num_gyros = min(get_gyro_count(), INS_MAX_INSTANCES);
    Vector3f last_average[INS_MAX_INSTANCES], best_avg[INS_MAX_INSTANCES];
    float best_diff[INS_MAX_INSTANCES];
    bool converged[INS_MAX_INSTANCES];

    // cold start
    hal.console->print_P(PSTR("Init Gyro"));

    // flash leds to tell user to keep the IMU still
    AP_Notify::flags.initialising = true;

    // remove existing gyro offsets
    for (uint8_t k=0; k<num_gyros; k++) {
        _gyro_offset[k] = Vector3f(0,0,0);
        best_diff[k] = 0;
        last_average[k].zero();
        converged[k] = false;
        _gyro_cal_ok[k] = true; // default calibration ok flag to true
    }

    for(int8_t c = 0; c < 5; c++) {
        hal.scheduler->delay(5);
        update();
    }

    // the strategy is to average 50 points over 0.5 seconds, then do it
    // again and see if the 2nd average is within a small margin of
    // the first

    uint8_t num_converged = 0;

    // we try to get a good calibration estimate for up to 30 seconds
    // if the gyros are stable, we should get it in 1 second
    for (int16_t j = 0; j <= 30*4 && num_converged < num_gyros; j++) {
        Vector3f gyro_sum[INS_MAX_INSTANCES], gyro_avg[INS_MAX_INSTANCES], gyro_diff[INS_MAX_INSTANCES];
        float diff_norm[INS_MAX_INSTANCES];
        uint8_t i;

        memset(diff_norm, 0, sizeof(diff_norm));

        hal.console->print_P(PSTR("*"));

        for (uint8_t k=0; k<num_gyros; k++) {
            gyro_sum[k].zero();
        }
        for (i=0; i<50; i++) {
            update();
            for (uint8_t k=0; k<num_gyros; k++) {
                gyro_sum[k] += get_gyro(k);
            }
            hal.scheduler->delay(5);
        }
        for (uint8_t k=0; k<num_gyros; k++) {
            gyro_avg[k] = gyro_sum[k] / i;
            gyro_diff[k] = last_average[k] - gyro_avg[k];
            diff_norm[k] = gyro_diff[k].length();
        }

        for (uint8_t k=0; k<num_gyros; k++) {
            if (converged[k]) continue;
            if (j == 0) {
                best_diff[k] = diff_norm[k];
                best_avg[k] = gyro_avg[k];
            } else if (gyro_diff[k].length() < ToRad(0.1f)) {
                // we want the average to be within 0.1 bit, which is 0.04 degrees/s
                last_average[k] = (gyro_avg[k] * 0.5f) + (last_average[k] * 0.5f);
                _gyro_offset[k] = last_average[k];
                converged[k] = true;
                num_converged++;
            } else if (diff_norm[k] < best_diff[k]) {
                best_diff[k] = diff_norm[k];
                best_avg[k] = (gyro_avg[k] * 0.5f) + (last_average[k] * 0.5f);
            }
            last_average[k] = gyro_avg[k];
        }
    }

    // stop flashing leds
    AP_Notify::flags.initialising = false;

    if (num_converged == num_gyros) {
        // all OK
        return;
    }

    // we've kept the user waiting long enough - use the best pair we
    // found so far
    hal.console->println();
    for (uint8_t k=0; k<num_gyros; k++) {
        if (!converged[k]) {
            hal.console->printf_P(PSTR("gyro[%u] did not converge: diff=%f dps\n"),
                                  (unsigned)k, ToDeg(best_diff[k]));
            _gyro_offset[k] = best_avg[k];
            // flag calibration as failed for this gyro
            _gyro_cal_ok[k] = false;
        }
    }
}

#if !defined( __AVR_ATmega1280__ )
// _calibrate_model - perform low level accel calibration
// accel_sample are accelerometer samples collected in 6 different positions
// accel_offsets are output from the calibration routine
// accel_scale are output from the calibration routine
// returns true if successful
bool AP_InertialSensor::_calibrate_accel( Vector3f accel_sample[6],
                                          Vector3f& accel_offsets, Vector3f& accel_scale )
{
    int16_t i;
    int16_t num_iterations = 0;
    float eps = 0.000000001;
    float change = 100.0;
    float data[3];
    float beta[6];
    float delta[6];
    float ds[6];
    float JS[6][6];
    bool success = true;

    // reset
    beta[0] = beta[1] = beta[2] = 0;
    beta[3] = beta[4] = beta[5] = 1.0f/GRAVITY_MSS;
    
    while( num_iterations < 20 && change > eps ) {
        num_iterations++;

        _calibrate_reset_matrices(ds, JS);

        for( i=0; i<6; i++ ) {
            data[0] = accel_sample[i].x;
            data[1] = accel_sample[i].y;
            data[2] = accel_sample[i].z;
            _calibrate_update_matrices(ds, JS, beta, data);
        }

        _calibrate_find_delta(ds, JS, delta);

        change =    delta[0]*delta[0] +
                    delta[0]*delta[0] +
                    delta[1]*delta[1] +
                    delta[2]*delta[2] +
                    delta[3]*delta[3] / (beta[3]*beta[3]) +
                    delta[4]*delta[4] / (beta[4]*beta[4]) +
                    delta[5]*delta[5] / (beta[5]*beta[5]);

        for( i=0; i<6; i++ ) {
            beta[i] -= delta[i];
        }
    }

    // copy results out
    accel_scale.x = beta[3] * GRAVITY_MSS;
    accel_scale.y = beta[4] * GRAVITY_MSS;
    accel_scale.z = beta[5] * GRAVITY_MSS;
    accel_offsets.x = beta[0] * accel_scale.x;
    accel_offsets.y = beta[1] * accel_scale.y;
    accel_offsets.z = beta[2] * accel_scale.z;

    // sanity check scale
    if( accel_scale.is_nan() || fabsf(accel_scale.x-1.0f) > 0.1f || fabsf(accel_scale.y-1.0f) > 0.1f || fabsf(accel_scale.z-1.0f) > 0.1f ) {
        success = false;
    }
    // sanity check offsets (3.5 is roughly 3/10th of a G, 5.0 is roughly half a G)
    if( accel_offsets.is_nan() || fabsf(accel_offsets.x) > 3.5f || fabsf(accel_offsets.y) > 3.5f || fabsf(accel_offsets.z) > 3.5f ) {
        success = false;
    }

    // return success or failure
    return success;
}

void AP_InertialSensor::_calibrate_update_matrices(float dS[6], float JS[6][6],
                                    float beta[6], float data[3])
{
    int16_t j, k;
    float dx, b;
    float residual = 1.0;
    float jacobian[6];
    
    for( j=0; j<3; j++ ) {
        b = beta[3+j];
        dx = (float)data[j] - beta[j];
        residual -= b*b*dx*dx;
        jacobian[j] = 2.0f*b*b*dx;
        jacobian[3+j] = -2.0f*b*dx*dx;
    }
    
    for( j=0; j<6; j++ ) {
        dS[j] += jacobian[j]*residual;
        for( k=0; k<6; k++ ) {
            JS[j][k] += jacobian[j]*jacobian[k];
        }
    }
}


// _calibrate_reset_matrices - clears matrices
void AP_InertialSensor::_calibrate_reset_matrices(float dS[6], float JS[6][6])
{
    int16_t j,k;
    for( j=0; j<6; j++ ) {
        dS[j] = 0.0f;
        for( k=0; k<6; k++ ) {
            JS[j][k] = 0.0f;
        }
    }
}

void AP_InertialSensor::_calibrate_find_delta(float dS[6], float JS[6][6], float delta[6])
{
    //Solve 6-d matrix equation JS*x = dS
    //first put in upper triangular form
    int16_t i,j,k;
    float mu;

    //make upper triangular
    for( i=0; i<6; i++ ) {
        //eliminate all nonzero entries below JS[i][i]
        for( j=i+1; j<6; j++ ) {
            mu = JS[i][j]/JS[i][i];
            if( mu != 0.0f ) {
                dS[j] -= mu*dS[i];
                for( k=j; k<6; k++ ) {
                    JS[k][j] -= mu*JS[k][i];
                }
            }
        }
    }

    //back-substitute
    for( i=5; i>=0; i-- ) {
        dS[i] /= JS[i][i];
        JS[i][i] = 1.0f;
        
        for( j=0; j<i; j++ ) {
            mu = JS[i][j];
            dS[j] -= mu*dS[i];
            JS[i][j] = 0.0f;
        }
    }

    for( i=0; i<6; i++ ) {
        delta[i] = dS[i];
    }
}

// _calculate_trim  - calculates the x and y trim angles (in radians) given a raw accel sample (i.e. no scaling or offsets applied) taken when the vehicle was level
void AP_InertialSensor::_calculate_trim(Vector3f accel_sample, float& trim_roll, float& trim_pitch)
{
    // scale sample and apply offsets
    Vector3f accel_scale = _accel_scale[0].get();
    Vector3f accel_offsets = _accel_offset[0].get();
    Vector3f scaled_accels_x( accel_sample.x * accel_scale.x - accel_offsets.x,
                              0,
                              accel_sample.z * accel_scale.z - accel_offsets.z );
    Vector3f scaled_accels_y( 0,
                              accel_sample.y * accel_scale.y - accel_offsets.y,
                              accel_sample.z * accel_scale.z - accel_offsets.z );

    // calculate x and y axis angle (i.e. roll and pitch angles)
    Vector3f vertical = Vector3f(0,0,-1);
    trim_roll = scaled_accels_y.angle(vertical);
    trim_pitch = scaled_accels_x.angle(vertical);

    // angle call doesn't return the sign so take care of it here
    if( scaled_accels_y.y > 0 ) {
        trim_roll = -trim_roll;
    }
    if( scaled_accels_x.x < 0 ) {
        trim_pitch = -trim_pitch;
    }
}

#endif // __AVR_ATmega1280__

// save parameters to eeprom
void AP_InertialSensor::_save_parameters()
{
    _product_id.save();
    for (uint8_t i=0; i<INS_MAX_INSTANCES; i++) {
        _accel_scale[i].save();
        _accel_offset[i].save();
        _gyro_offset[i].save();
    }
}


/*
  update gyro and accel values from backends
 */
void AP_InertialSensor::update(void)
{
    // during initialisation update() may be called without
    // wait_for_sample(), and a wait is implied
    wait_for_sample();

    if (!_hil_mode) {
        for (uint8_t i=0; i<INS_MAX_INSTANCES; i++) {
            // mark sensors unhealthy and let update() in each backend
            // mark them healthy via _rotate_and_offset_gyro() and
            // _rotate_and_offset_accel() 
            _gyro_healthy[i] = false;
            _accel_healthy[i] = false;
        }
        for (uint8_t i=0; i<_backend_count; i++) {
            _backends[i]->update();
        }

        // adjust health status if a sensor has a non-zero error count
        // but another sensor doesn't. 
        bool have_zero_accel_error_count = false;
        bool have_zero_gyro_error_count = false;
        for (uint8_t i=0; i<INS_MAX_INSTANCES; i++) {
            if (_accel_healthy[i] && _accel_error_count[i] == 0) {
                have_zero_accel_error_count = true;
            }
            if (_gyro_healthy[i] && _gyro_error_count[i] == 0) {
                have_zero_gyro_error_count = true;
            }
        }

        for (uint8_t i=0; i<INS_MAX_INSTANCES; i++) {
            if (_gyro_healthy[i] && _gyro_error_count[i] != 0 && have_zero_gyro_error_count) {
                // we prefer not to use a gyro that has had errors
                _gyro_healthy[i] = false;
            }
            if (_accel_healthy[i] && _accel_error_count[i] != 0 && have_zero_accel_error_count) {
                // we prefer not to use a accel that has had errors
                _accel_healthy[i] = false;
            }
        }

        // set primary to first healthy accel and gyro
        for (uint8_t i=0; i<INS_MAX_INSTANCES; i++) {
            if (_gyro_healthy[i]) {
                _primary_gyro = i;
                break;
            }
        }
        for (uint8_t i=0; i<INS_MAX_INSTANCES; i++) {
            if (_accel_healthy[i]) {
                _primary_accel = i;
                break;
            }
        }
    }

    _have_sample = false;
}

/*
  wait for a sample to be available. This is the function that
  determines the timing of the main loop in ardupilot. 

  Ideally this function would return at exactly the rate given by the
  sample_rate argument given to AP_InertialSensor::init(). 

  The key output of this function is _delta_time, which is the time
  over which the gyro and accel integration will happen for this
  sample. We want that to be a constant time if possible, but if
  delays occur we need to cope with them. The long term sum of
  _delta_time should be exactly equal to the wall clock elapsed time
 */
void AP_InertialSensor::wait_for_sample(void)
{
    if (_have_sample) {
        // the user has called wait_for_sample() again without
        // consuming the sample with update()
        return;
    }

    uint32_t now = hal.scheduler->micros();

    if (_next_sample_usec == 0 && _delta_time <= 0) {
        // this is the first call to wait_for_sample()
        _last_sample_usec = now - _sample_period_usec;
        _next_sample_usec = now + _sample_period_usec;
        goto check_sample;
    }

    // see how long it is till the next sample is due
    if (_next_sample_usec - now <=_sample_period_usec) {
        // we're ahead on time, schedule next sample at expected period
        uint32_t wait_usec = _next_sample_usec - now;
        if (wait_usec > 200) {
            hal.scheduler->delay_microseconds(wait_usec);
        }
        _next_sample_usec += _sample_period_usec;
    } else if (now - _next_sample_usec < _sample_period_usec/8) {
        // we've overshot, but only by a small amount, keep on
        // schedule with no delay
        _next_sample_usec += _sample_period_usec;
    } else {
        // we've overshot by a larger amount, re-zero scheduling with
        // no delay
        _next_sample_usec = now + _sample_period_usec;
    }

check_sample:
    if (!_hil_mode) {
        // we also wait for at least one backend to have a sample of both
        // accel and gyro. This normally completes immediately.
        bool gyro_available = false;
        bool accel_available = false;
        while (!gyro_available || !accel_available) {
            for (uint8_t i=0; i<_backend_count; i++) {
                gyro_available |= _backends[i]->gyro_sample_available();
                accel_available |= _backends[i]->accel_sample_available();
            }
            if (!gyro_available || !accel_available) {
                hal.scheduler->delay_microseconds(100);
            }
        }
    }

    now = hal.scheduler->micros();
    _delta_time = (now - _last_sample_usec) * 1.0e-6f;
    _last_sample_usec = now;

#if 0
    {
        static uint64_t delta_time_sum;
        static uint16_t counter;
        if (delta_time_sum == 0) {
            delta_time_sum = _sample_period_usec;
        }
        delta_time_sum += _delta_time * 1.0e6f;
        if (counter++ == 400) {
            counter = 0;
            hal.console->printf("now=%lu _delta_time_sum=%lu diff=%ld\n",
                                (unsigned long)now, 
                                (unsigned long)delta_time_sum,
                                (long)(now - delta_time_sum));
        }
    }
#endif

    _have_sample = true;
}

/*
  support for setting accel and gyro vectors, for use by HIL
 */
void AP_InertialSensor::set_accel(uint8_t instance, const Vector3f &accel)
{
    if (_accel_count == 0) {
        // we haven't initialised yet
        return;
    }
    if (instance < INS_MAX_INSTANCES) {
        _accel[instance] = accel;
        _accel_healthy[instance] = true;
        if (_accel_count <= instance) {
            _accel_count = instance+1;
        }
    }
}

void AP_InertialSensor::set_gyro(uint8_t instance, const Vector3f &gyro)
{
    if (_gyro_count == 0) {
        // we haven't initialised yet
        return;
    }
    if (instance < INS_MAX_INSTANCES) {
        _gyro[instance] = gyro;
        _gyro_healthy[instance] = true;
        if (_gyro_count <= instance) {
            _gyro_count = instance+1;
            _gyro_cal_ok[instance] = true;
        }
    }
}