ins_ext_pose.c

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/*
 * Copyright (C) 2023 MAVLab
 *
 * This file is part of paparazzi.
 *
 * paparazzi is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2, or (at your option)
 * any later version.
 *
 * paparazzi is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with paparazzi; see the file COPYING.  If not, write to
 * the Free Software Foundation, 59 Temple Place - Suite 330,
 * Boston, MA 02111-1307, USA.
 */
 
#include <time.h>
 
#include "ins_ext_pose.h"
#include "state.h"
#include "math/pprz_algebra_float.h"
#include "modules/imu/imu.h"
#include "modules/ins/ins.h"
#include "generated/flight_plan.h"
#include "modules/core/abi.h"
 
#if 0
#include <stdio.h>
#define DEBUG_PRINT(...) printf(__VA_ARGS__)
#else
#define DEBUG_PRINT(...) {}
#endif
 
#ifdef INS_EXT_VISION_ROTATION
struct FloatQuat ins_ext_vision_rot;
#endif
 
struct InsExtPose {
  /* Inputs */
  struct FloatRates gyros_f;
  struct FloatVect3 accels_f;
  bool   has_new_gyro;
  bool   has_new_acc;
 
  struct FloatVect3 ev_pos;
  struct FloatVect3 ev_vel;
  struct FloatEulers ev_att;
  struct FloatQuat ev_quat;
  bool   has_new_ext_pose;
  float  ev_time;
 
  /* Origin */
  struct LtpDef_i  ltp_def;
 
  /* output LTP NED */
  struct NedCoor_i ltp_pos;
  struct NedCoor_i ltp_speed;
  struct NedCoor_i ltp_accel;
};
struct InsExtPose ins_ext_pos;
 
 
static void ins_ext_pose_init_from_flightplan(void)
{
 
  struct LlaCoor_i llh_nav0; /* Height above the ellipsoid */
  llh_nav0.lat = NAV_LAT0;
  llh_nav0.lon = NAV_LON0;
  /* NAV_ALT0 = ground alt above msl, NAV_MSL0 = geoid-height (msl) over ellipsoid */
  llh_nav0.alt = NAV_ALT0 + NAV_MSL0;
 
  struct EcefCoor_i ecef_nav0;
  ecef_of_lla_i(&ecef_nav0, &llh_nav0);
 
  ltp_def_from_ecef_i(&ins_ext_pos.ltp_def, &ecef_nav0);
  ins_ext_pos.ltp_def.hmsl = NAV_ALT0;
  stateSetLocalOrigin_i(MODULE_INS_EXT_POSE_ID, &ins_ext_pos.ltp_def);
  /* update local ENU coordinates of global waypoints */
  waypoints_localize_all();
}
 
 
#if PERIODIC_TELEMETRY
#include "modules/datalink/telemetry.h"
 
static void send_ins(struct transport_tx *trans, struct link_device *dev)
{
  pprz_msg_send_INS(trans, dev, AC_ID,
                    &ins_ext_pos.ltp_pos.x, &ins_ext_pos.ltp_pos.y, &ins_ext_pos.ltp_pos.z,
                    &ins_ext_pos.ltp_speed.x, &ins_ext_pos.ltp_speed.y, &ins_ext_pos.ltp_speed.z,
                    &ins_ext_pos.ltp_accel.x, &ins_ext_pos.ltp_accel.y, &ins_ext_pos.ltp_accel.z);
}
 
static void send_ins_z(struct transport_tx *trans, struct link_device *dev)
{
  static float fake_baro_z = 0.0;
  pprz_msg_send_INS_Z(trans, dev, AC_ID,
                      (float *)&fake_baro_z, &ins_ext_pos.ltp_pos.z,
                      &ins_ext_pos.ltp_speed.z, &ins_ext_pos.ltp_accel.z);
}
 
static void send_ins_ref(struct transport_tx *trans, struct link_device *dev)
{
  static float fake_qfe = 0.0;
  pprz_msg_send_INS_REF(trans, dev, AC_ID,
                        &ins_ext_pos.ltp_def.ecef.x, &ins_ext_pos.ltp_def.ecef.y, &ins_ext_pos.ltp_def.ecef.z,
                        &ins_ext_pos.ltp_def.lla.lat, &ins_ext_pos.ltp_def.lla.lon, &ins_ext_pos.ltp_def.lla.alt,
                        &ins_ext_pos.ltp_def.hmsl, (float *)&fake_qfe);
}
 
static void send_external_pose_down(struct transport_tx *trans, struct link_device *dev)
{ 
  pprz_msg_send_EXTERNAL_POSE_DOWN(trans, dev, AC_ID,
                        &ins_ext_pos.ev_time,
                        &ins_ext_pos.ev_pos.x, 
                        &ins_ext_pos.ev_pos.y, 
                        &ins_ext_pos.ev_pos.z,
                        &ins_ext_pos.ev_vel.x, 
                        &ins_ext_pos.ev_vel.y, 
                        &ins_ext_pos.ev_vel.z, 
                        &ins_ext_pos.ev_quat.qi, 
                        &ins_ext_pos.ev_quat.qx, 
                        &ins_ext_pos.ev_quat.qy, 
                        &ins_ext_pos.ev_quat.qz);
}
static void send_ahrs_bias(struct transport_tx *trans, struct link_device *dev)
{
  float dummy0 = 0.0;
  pprz_msg_send_AHRS_BIAS(trans, dev, AC_ID, 
                &ekf_X[9], 
                &ekf_X[10], 
                &ekf_X[11], 
                &ekf_X[12], 
                &ekf_X[13], 
                &ekf_X[14], 
                &dummy0, 
                &dummy0, 
                &dummy0);
}
#endif
 
 
#ifndef INS_EXT_POSE_IMU_ID
#define INS_EXT_POSE_IMU_ID ABI_BROADCAST
#endif
PRINT_CONFIG_VAR(INS_EXT_POSE_IMU_ID)
 
static abi_event accel_ev;
static abi_event gyro_ev;
 
static void accel_cb(uint8_t sender_id, uint32_t stamp, struct Int32Vect3 *accel);
static void gyro_cb(uint8_t sender_id, uint32_t stamp, struct Int32Rates *gyro);
 
 
 
static void gyro_cb(uint8_t sender_id __attribute__((unused)),
                    uint32_t stamp __attribute__((unused)),
                    struct Int32Rates *gyro)
{
  RATES_FLOAT_OF_BFP(ins_ext_pos.gyros_f, *gyro);
  ins_ext_pos.has_new_gyro = true;
}
 
static void accel_cb(uint8_t sender_id __attribute__((unused)),
                     uint32_t stamp __attribute__((unused)),
                     struct Int32Vect3 *accel)
{
  ACCELS_FLOAT_OF_BFP(ins_ext_pos.accels_f, *accel);
  ins_ext_pos.has_new_acc = true;
}
 
 
void ins_ext_pose_msg_update(uint8_t *buf)
{
  if (DL_EXTERNAL_POSE_ac_id(buf) != AC_ID) { return; } // not for this aircraft
  
  float enu_x  = DL_EXTERNAL_POSE_enu_x(buf);
  float enu_y  = DL_EXTERNAL_POSE_enu_y(buf);
  float enu_z  = DL_EXTERNAL_POSE_enu_z(buf);
  float enu_xd = DL_EXTERNAL_POSE_enu_xd(buf);
  float enu_yd = DL_EXTERNAL_POSE_enu_yd(buf);              
  float enu_zd = DL_EXTERNAL_POSE_enu_zd(buf);
  float quat_i = DL_EXTERNAL_POSE_body_qi(buf);
  float quat_x = DL_EXTERNAL_POSE_body_qx(buf);
  float quat_y = DL_EXTERNAL_POSE_body_qy(buf);
  float quat_z = DL_EXTERNAL_POSE_body_qz(buf);
 
  DEBUG_PRINT("EXT_UPDATE\n");
 
  struct FloatQuat orient;
  struct FloatEulers orient_eulers;
 
  // Transformation of External Pose. Optitrack motive 2.X Yup
  orient.qi = quat_i ;
  orient.qx = quat_y ; 
  orient.qy = quat_x ;                
  orient.qz = -quat_z;
 
#ifdef INS_EXT_VISION_ROTATION
  // Rotate the quaternion
  struct FloatQuat rot_q;
  float_quat_comp(&rot_q, &orient, &ins_ext_vision_rot);
  orient.qi = rot_q.qi;
  orient.qx = rot_q.qx;
  orient.qy = rot_q.qy;
  orient.qz = rot_q.qz;
#endif
 
  float_eulers_of_quat(&orient_eulers, &orient);
  
  ins_ext_pos.ev_time       = get_sys_time_usec(); 
  ins_ext_pos.ev_pos.x      = enu_y;                
  ins_ext_pos.ev_pos.y      = enu_x;                
  ins_ext_pos.ev_pos.z      = -enu_z;  
  ins_ext_pos.ev_vel.x      = enu_yd;
  ins_ext_pos.ev_vel.y      = enu_xd;
  ins_ext_pos.ev_vel.z      = -enu_zd;             
  ins_ext_pos.ev_att.phi    = orient_eulers.phi;
  ins_ext_pos.ev_att.theta  = orient_eulers.theta;
  ins_ext_pos.ev_att.psi    = orient_eulers.psi;
  ins_ext_pos.ev_quat.qi    = orient.qi;
  ins_ext_pos.ev_quat.qx    = orient.qx;
  ins_ext_pos.ev_quat.qy    = orient.qy;
  ins_ext_pos.ev_quat.qz    = orient.qz;
 
  ins_ext_pos.has_new_ext_pose = true;
 
  DEBUG_PRINT("Att = %f %f %f \n", ins_ext_pos.ev_att.phi, ins_ext_pos.ev_att.theta, ins_ext_pos.ev_att.psi);
}
 
static inline void ekf_init(void);
static inline void ekf_run(void);
 
void ins_ext_pose_init(void)
{
 
  // Initialize inputs
  ins_ext_pos.has_new_acc = false;
  ins_ext_pos.has_new_gyro = false;
  ins_ext_pos.has_new_ext_pose = false;
 
  // Get External Pose Origin From Flightplan
  ins_ext_pose_init_from_flightplan();
 
  // Provide telemetry
#if PERIODIC_TELEMETRY
  register_periodic_telemetry(DefaultPeriodic, PPRZ_MSG_ID_INS, send_ins);
  register_periodic_telemetry(DefaultPeriodic, PPRZ_MSG_ID_INS_Z, send_ins_z);
  register_periodic_telemetry(DefaultPeriodic, PPRZ_MSG_ID_INS_REF, send_ins_ref);
  register_periodic_telemetry(DefaultPeriodic, PPRZ_MSG_ID_EXTERNAL_POSE_DOWN, send_external_pose_down);
  register_periodic_telemetry(DefaultPeriodic, PPRZ_MSG_ID_AHRS_BIAS, send_ahrs_bias);
#endif
 
  // Get IMU through ABI
  AbiBindMsgIMU_ACCEL(INS_EXT_POSE_IMU_ID, &accel_ev, accel_cb);
  AbiBindMsgIMU_GYRO(INS_EXT_POSE_IMU_ID, &gyro_ev, gyro_cb);
  // Get External Pose through datalink message: setup in xml
 
  // Initialize EKF
  ekf_init();
}
 
void ins_ext_pose_run(void)
{
  ekf_run();
}
 
 
 
 
/***************************************************
 * Kalman Filter.
 */
 
 
 
static inline void ekf_f(const float X[EKF_NUM_STATES], const float U[EKF_NUM_INPUTS], float out[EKF_NUM_STATES]);
static inline void ekf_F(const float X[EKF_NUM_STATES], const float U[EKF_NUM_INPUTS],
                         float out[EKF_NUM_STATES][EKF_NUM_STATES]);
static inline void ekf_L(const float X[EKF_NUM_STATES], const float U[EKF_NUM_INPUTS],
                         float out[EKF_NUM_STATES][EKF_NUM_INPUTS]);
 
static inline void ekf_f_rk4(const float X[EKF_NUM_STATES], const float U[EKF_NUM_INPUTS], const float dt,
                             float out[EKF_NUM_STATES]);
 
static inline void ekf_step(const float U[EKF_NUM_INPUTS], const float Z[EKF_NUM_OUTPUTS], const float dt);
static inline void ekf_prediction_step(const float U[EKF_NUM_INPUTS], const float dt);
static inline void ekf_measurement_step(const float Z[EKF_NUM_OUTPUTS]);
 
 
 
float ekf_X[EKF_NUM_STATES];
float ekf_U[EKF_NUM_INPUTS];
float ekf_Z[EKF_NUM_OUTPUTS];
float ekf_P[EKF_NUM_STATES][EKF_NUM_STATES];
float ekf_Q[EKF_NUM_INPUTS][EKF_NUM_INPUTS];
float ekf_R[EKF_NUM_OUTPUTS][EKF_NUM_OUTPUTS];
 
float ekf_H[EKF_NUM_OUTPUTS][EKF_NUM_STATES] = {{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0}};
 
 
float t0;
float t1;
 
void ekf_set_diag(float **a, float *b, int n);
void ekf_set_diag(float **a, float *b, int n)
{
  int i, j;
  for (i = 0 ; i < n; i++) {
    for (j = 0 ; j < n; j++) {
      if (i == j) {
        a[i][j] = b[i];
      } else {
        a[i][j] = 0.0;
      }
    }
  }
}
 
 
 
static inline void ekf_init(void)
{
 
  DEBUG_PRINT("ekf init");
  float X0[EKF_NUM_STATES] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
  float U0[EKF_NUM_INPUTS] = {0, 0, 0, 0, 0, 0};
  float Z0[EKF_NUM_OUTPUTS] = {0, 0, 0, 0, 0, 0};
 
  float Pdiag[EKF_NUM_STATES] = {1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.};
  float Qdiag[EKF_NUM_INPUTS] = {1.0, 1.0, 1.0, 0.0173, 4.878e-4, 3.547e-4};//{0.0325, 0.4494, 0.5087, 0.0173, 4.878e-4, 3.547e-4};
 
  float Rdiag[EKF_NUM_OUTPUTS] = {8.372e-6, 3.832e-6, 4.761e-6, 2.830e-4, 8.684e-6, 7.013e-6};
 
  MAKE_MATRIX_PTR(ekf_P_, ekf_P, EKF_NUM_STATES);
  MAKE_MATRIX_PTR(ekf_Q_, ekf_Q, EKF_NUM_INPUTS);
  MAKE_MATRIX_PTR(ekf_R_, ekf_R, EKF_NUM_OUTPUTS);
 
  ekf_set_diag(ekf_P_, Pdiag, EKF_NUM_STATES);
  ekf_set_diag(ekf_Q_, Qdiag, EKF_NUM_INPUTS);
  ekf_set_diag(ekf_R_, Rdiag, EKF_NUM_OUTPUTS);
  float_vect_copy(ekf_X, X0, EKF_NUM_STATES);
  float_vect_copy(ekf_U, U0, EKF_NUM_INPUTS);
  float_vect_copy(ekf_Z, Z0, EKF_NUM_OUTPUTS);
}
 
static inline void ekf_f(const float X[EKF_NUM_STATES], const float U[EKF_NUM_INPUTS], float out[EKF_NUM_STATES])
{
  float x0 = cos(X[8]);
  float x1 = U[0] - X[9];
  float x2 = cos(X[7]);
  float x3 = x1 * x2;
  float x4 = U[2] - X[11];
  float x5 = sin(X[6]);
  float x6 = sin(X[8]);
  float x7 = x5 * x6;
  float x8 = sin(X[7]);
  float x9 = cos(X[6]);
  float x10 = x0 * x9;
  float x11 = U[1] - X[10];
  float x12 = x6 * x9;
  float x13 = x0 * x5;
  float x14 = tan(X[7]);
  float x15 = U[4] - X[13];
  float x16 = x15 * x5;
  float x17 = U[5] - X[14];
  float x18 = x17 * x9;
  float x19 = 1.0 / x2;
  out[0] = X[3];
  out[1] = X[4];
  out[2] = X[5];
  out[3] = x0 * x3 + x11 * (-x12 + x13 * x8) + x4 * (x10 * x8 + x7);
  out[4] = x11 * (x10 + x7 * x8) + x3 * x6 + x4 * (x12 * x8 - x13);
  out[5] = -x1 * x8 + x11 * x2 * x5 + x2 * x4 * x9 + 9.8100000000000005;
  out[6] = U[3] - X[12] + x14 * x16 + x14 * x18;
  out[7] = x15 * x9 - x17 * x5;
  out[8] = x16 * x19 + x18 * x19;
  out[9] = 0;
  out[10] = 0;
  out[11] = 0;
  out[12] = 0;
  out[13] = 0;
  out[14] = 0;
}
 
static inline void ekf_F(const float X[EKF_NUM_STATES], const float U[EKF_NUM_INPUTS],
                         float out[EKF_NUM_STATES][EKF_NUM_STATES])
{
  float x0 = U[1] - X[10];
  float x1 = sin(X[6]);
  float x2 = sin(X[8]);
  float x3 = x1 * x2;
  float x4 = sin(X[7]);
  float x5 = cos(X[6]);
  float x6 = cos(X[8]);
  float x7 = x5 * x6;
  float x8 = x4 * x7;
  float x9 = x3 + x8;
  float x10 = U[2] - X[11];
  float x11 = x2 * x5;
  float x12 = x1 * x6;
  float x13 = x12 * x4;
  float x14 = x11 - x13;
  float x15 = U[0] - X[9];
  float x16 = x15 * x4;
  float x17 = cos(X[7]);
  float x18 = x0 * x17;
  float x19 = x10 * x17;
  float x20 = x17 * x2;
  float x21 = x11 * x4;
  float x22 = x12 - x21;
  float x23 = -x3 * x4 - x7;
  float x24 = x17 * x6;
  float x25 = x17 * x5;
  float x26 = x1 * x17;
  float x27 = x4 * x5;
  float x28 = U[4] - X[13];
  float x29 = tan(X[7]);
  float x30 = x29 * x5;
  float x31 = U[5] - X[14];
  float x32 = x1 * x29;
  float x33 = pow(x29, 2) + 1;
  float x34 = x1 * x28;
  float x35 = 1.0 / x17;
  float x36 = x35 * x5;
  float x37 = x1 * x35;
  float x38 = pow(x17, -2);
  out[0][0] = 0;
  out[0][1] = 0;
  out[0][2] = 0;
  out[0][3] = 1;
  out[0][4] = 0;
  out[0][5] = 0;
  out[0][6] = 0;
  out[0][7] = 0;
  out[0][8] = 0;
  out[0][9] = 0;
  out[0][10] = 0;
  out[0][11] = 0;
  out[0][12] = 0;
  out[0][13] = 0;
  out[0][14] = 0;
  out[1][0] = 0;
  out[1][1] = 0;
  out[1][2] = 0;
  out[1][3] = 0;
  out[1][4] = 1;
  out[1][5] = 0;
  out[1][6] = 0;
  out[1][7] = 0;
  out[1][8] = 0;
  out[1][9] = 0;
  out[1][10] = 0;
  out[1][11] = 0;
  out[1][12] = 0;
  out[1][13] = 0;
  out[1][14] = 0;
  out[2][0] = 0;
  out[2][1] = 0;
  out[2][2] = 0;
  out[2][3] = 0;
  out[2][4] = 0;
  out[2][5] = 1;
  out[2][6] = 0;
  out[2][7] = 0;
  out[2][8] = 0;
  out[2][9] = 0;
  out[2][10] = 0;
  out[2][11] = 0;
  out[2][12] = 0;
  out[2][13] = 0;
  out[2][14] = 0;
  out[3][0] = 0;
  out[3][1] = 0;
  out[3][2] = 0;
  out[3][3] = 0;
  out[3][4] = 0;
  out[3][5] = 0;
  out[3][6] = x0 * x9 + x10 * x14;
  out[3][7] = x12 * x18 - x16 * x6 + x19 * x7;
  out[3][8] = x0 * x23 + x10 * x22 - x15 * x20;
  out[3][9] = -x24;
  out[3][10] = x14;
  out[3][11] = -x3 - x8;
  out[3][12] = 0;
  out[3][13] = 0;
  out[3][14] = 0;
  out[4][0] = 0;
  out[4][1] = 0;
  out[4][2] = 0;
  out[4][3] = 0;
  out[4][4] = 0;
  out[4][5] = 0;
  out[4][6] = x0 * (-x12 + x21) + x10 * x23;
  out[4][7] = x11 * x19 - x16 * x2 + x18 * x3;
  out[4][8] = x0 * (-x11 + x13) + x10 * x9 + x15 * x24;
  out[4][9] = -x20;
  out[4][10] = x23;
  out[4][11] = x22;
  out[4][12] = 0;
  out[4][13] = 0;
  out[4][14] = 0;
  out[5][0] = 0;
  out[5][1] = 0;
  out[5][2] = 0;
  out[5][3] = 0;
  out[5][4] = 0;
  out[5][5] = 0;
  out[5][6] = x0 * x25 - x10 * x26;
  out[5][7] = -x0 * x1 * x4 - x10 * x27 + x17 * (-U[0] + X[9]);
  out[5][8] = 0;
  out[5][9] = x4;
  out[5][10] = -x26;
  out[5][11] = -x25;
  out[5][12] = 0;
  out[5][13] = 0;
  out[5][14] = 0;
  out[6][0] = 0;
  out[6][1] = 0;
  out[6][2] = 0;
  out[6][3] = 0;
  out[6][4] = 0;
  out[6][5] = 0;
  out[6][6] = x28 * x30 - x31 * x32;
  out[6][7] = x31 * x33 * x5 + x33 * x34;
  out[6][8] = 0;
  out[6][9] = 0;
  out[6][10] = 0;
  out[6][11] = 0;
  out[6][12] = -1;
  out[6][13] = -x32;
  out[6][14] = -x30;
  out[7][0] = 0;
  out[7][1] = 0;
  out[7][2] = 0;
  out[7][3] = 0;
  out[7][4] = 0;
  out[7][5] = 0;
  out[7][6] = -x34 + x5 * (-U[5] + X[14]);
  out[7][7] = 0;
  out[7][8] = 0;
  out[7][9] = 0;
  out[7][10] = 0;
  out[7][11] = 0;
  out[7][12] = 0;
  out[7][13] = -x5;
  out[7][14] = x1;
  out[8][0] = 0;
  out[8][1] = 0;
  out[8][2] = 0;
  out[8][3] = 0;
  out[8][4] = 0;
  out[8][5] = 0;
  out[8][6] = x28 * x36 - x31 * x37;
  out[8][7] = x27 * x31 * x38 + x34 * x38 * x4;
  out[8][8] = 0;
  out[8][9] = 0;
  out[8][10] = 0;
  out[8][11] = 0;
  out[8][12] = 0;
  out[8][13] = -x37;
  out[8][14] = -x36;
  out[9][0] = 0;
  out[9][1] = 0;
  out[9][2] = 0;
  out[9][3] = 0;
  out[9][4] = 0;
  out[9][5] = 0;
  out[9][6] = 0;
  out[9][7] = 0;
  out[9][8] = 0;
  out[9][9] = 0;
  out[9][10] = 0;
  out[9][11] = 0;
  out[9][12] = 0;
  out[9][13] = 0;
  out[9][14] = 0;
  out[10][0] = 0;
  out[10][1] = 0;
  out[10][2] = 0;
  out[10][3] = 0;
  out[10][4] = 0;
  out[10][5] = 0;
  out[10][6] = 0;
  out[10][7] = 0;
  out[10][8] = 0;
  out[10][9] = 0;
  out[10][10] = 0;
  out[10][11] = 0;
  out[10][12] = 0;
  out[10][13] = 0;
  out[10][14] = 0;
  out[11][0] = 0;
  out[11][1] = 0;
  out[11][2] = 0;
  out[11][3] = 0;
  out[11][4] = 0;
  out[11][5] = 0;
  out[11][6] = 0;
  out[11][7] = 0;
  out[11][8] = 0;
  out[11][9] = 0;
  out[11][10] = 0;
  out[11][11] = 0;
  out[11][12] = 0;
  out[11][13] = 0;
  out[11][14] = 0;
  out[12][0] = 0;
  out[12][1] = 0;
  out[12][2] = 0;
  out[12][3] = 0;
  out[12][4] = 0;
  out[12][5] = 0;
  out[12][6] = 0;
  out[12][7] = 0;
  out[12][8] = 0;
  out[12][9] = 0;
  out[12][10] = 0;
  out[12][11] = 0;
  out[12][12] = 0;
  out[12][13] = 0;
  out[12][14] = 0;
  out[13][0] = 0;
  out[13][1] = 0;
  out[13][2] = 0;
  out[13][3] = 0;
  out[13][4] = 0;
  out[13][5] = 0;
  out[13][6] = 0;
  out[13][7] = 0;
  out[13][8] = 0;
  out[13][9] = 0;
  out[13][10] = 0;
  out[13][11] = 0;
  out[13][12] = 0;
  out[13][13] = 0;
  out[13][14] = 0;
  out[14][0] = 0;
  out[14][1] = 0;
  out[14][2] = 0;
  out[14][3] = 0;
  out[14][4] = 0;
  out[14][5] = 0;
  out[14][6] = 0;
  out[14][7] = 0;
  out[14][8] = 0;
  out[14][9] = 0;
  out[14][10] = 0;
  out[14][11] = 0;
  out[14][12] = 0;
  out[14][13] = 0;
  out[14][14] = 0;
}
 
static inline void ekf_L(const float X[EKF_NUM_STATES], __attribute__((unused))  const float U[EKF_NUM_INPUTS],
                         float out[EKF_NUM_STATES][EKF_NUM_INPUTS])
{
  float x0 = cos(X[7]);
  float x1 = cos(X[8]);
  float x2 = sin(X[8]);
  float x3 = cos(X[6]);
  float x4 = x2 * x3;
  float x5 = sin(X[7]);
  float x6 = sin(X[6]);
  float x7 = x1 * x6;
  float x8 = x2 * x6;
  float x9 = x1 * x3;
  float x10 = tan(X[7]);
  float x11 = 1.0 / x0;
  out[0][0] = 0;
  out[0][1] = 0;
  out[0][2] = 0;
  out[0][3] = 0;
  out[0][4] = 0;
  out[0][5] = 0;
  out[1][0] = 0;
  out[1][1] = 0;
  out[1][2] = 0;
  out[1][3] = 0;
  out[1][4] = 0;
  out[1][5] = 0;
  out[2][0] = 0;
  out[2][1] = 0;
  out[2][2] = 0;
  out[2][3] = 0;
  out[2][4] = 0;
  out[2][5] = 0;
  out[3][0] = -x0 * x1;
  out[3][1] = x4 - x5 * x7;
  out[3][2] = -x5 * x9 - x8;
  out[3][3] = 0;
  out[3][4] = 0;
  out[3][5] = 0;
  out[4][0] = -x0 * x2;
  out[4][1] = -x5 * x8 - x9;
  out[4][2] = -x4 * x5 + x7;
  out[4][3] = 0;
  out[4][4] = 0;
  out[4][5] = 0;
  out[5][0] = x5;
  out[5][1] = -x0 * x6;
  out[5][2] = -x0 * x3;
  out[5][3] = 0;
  out[5][4] = 0;
  out[5][5] = 0;
  out[6][0] = 0;
  out[6][1] = 0;
  out[6][2] = 0;
  out[6][3] = -1;
  out[6][4] = -x10 * x6;
  out[6][5] = -x10 * x3;
  out[7][0] = 0;
  out[7][1] = 0;
  out[7][2] = 0;
  out[7][3] = 0;
  out[7][4] = -x3;
  out[7][5] = x6;
  out[8][0] = 0;
  out[8][1] = 0;
  out[8][2] = 0;
  out[8][3] = 0;
  out[8][4] = -x11 * x6;
  out[8][5] = -x11 * x3;
  out[9][0] = 0;
  out[9][1] = 0;
  out[9][2] = 0;
  out[9][3] = 0;
  out[9][4] = 0;
  out[9][5] = 0;
  out[10][0] = 0;
  out[10][1] = 0;
  out[10][2] = 0;
  out[10][3] = 0;
  out[10][4] = 0;
  out[10][5] = 0;
  out[11][0] = 0;
  out[11][1] = 0;
  out[11][2] = 0;
  out[11][3] = 0;
  out[11][4] = 0;
  out[11][5] = 0;
  out[12][0] = 0;
  out[12][1] = 0;
  out[12][2] = 0;
  out[12][3] = 0;
  out[12][4] = 0;
  out[12][5] = 0;
  out[13][0] = 0;
  out[13][1] = 0;
  out[13][2] = 0;
  out[13][3] = 0;
  out[13][4] = 0;
  out[13][5] = 0;
  out[14][0] = 0;
  out[14][1] = 0;
  out[14][2] = 0;
  out[14][3] = 0;
  out[14][4] = 0;
  out[14][5] = 0;
}
 
 
 
static inline void ekf_f_rk4(const float X[EKF_NUM_STATES], const float U[EKF_NUM_INPUTS], const float dt,
                             float out[EKF_NUM_STATES])
{
  float k1[EKF_NUM_STATES];
  float k2[EKF_NUM_STATES];
  float k3[EKF_NUM_STATES];
  float k4[EKF_NUM_STATES];
 
  float Xtmp[EKF_NUM_STATES];
 
  // k1   = f(X,U)
  ekf_f(X, U, k1);
 
  // Xtmp = X+dt*k1/2
  float_vect_smul(Xtmp, k1, dt / 2, EKF_NUM_STATES);
  float_vect_add(Xtmp, X, EKF_NUM_STATES);
 
  // k2   = f(Xtmp,U)
  ekf_f(Xtmp, U, k2);
 
  // Xtmp = X+dt*k2/2
  float_vect_smul(Xtmp, k2, dt / 2, EKF_NUM_STATES);
  float_vect_add(Xtmp, X, EKF_NUM_STATES);
 
  // k3   = f(Xtmp,U)
  ekf_f(Xtmp, U, k3);
 
  // Xtmp = X+dt*k3
  float_vect_smul(Xtmp, k3, dt, EKF_NUM_STATES);
  float_vect_add(Xtmp, X, EKF_NUM_STATES);
 
  // k4   = f(Xtmp,U)
  ekf_f(Xtmp, U, k4);
 
  // out = k2+k3
  float_vect_sum(out, k2, k3, EKF_NUM_STATES);
  // out *= 2
  float_vect_scale(out, 2, EKF_NUM_STATES);
  // out += k1
  float_vect_add(out, k1, EKF_NUM_STATES);
  // out += k4
  float_vect_add(out, k4, EKF_NUM_STATES);
  // out *= dt/6
  float_vect_scale(out, dt / 6, EKF_NUM_STATES);
  // out += X
  float_vect_add(out, X, EKF_NUM_STATES);
}
 
 
static inline void ekf_step(const float U[EKF_NUM_INPUTS], const float Z[EKF_NUM_OUTPUTS], const float dt)
{
  // [1] Predicted (a priori) state estimate:
  float Xkk_1[EKF_NUM_STATES];
  ekf_f_rk4(ekf_X, U, dt, Xkk_1);
 
 
  // [2] Get matrices
  float F[EKF_NUM_STATES][EKF_NUM_STATES];
  float L[EKF_NUM_STATES][EKF_NUM_INPUTS];
  ekf_F(ekf_X, U, F);
  ekf_L(ekf_X, U, L);
 
 
  // [3] Continuous to discrete
  // Fd = eye(N) + F*dt + F*F*dt**2/2 = I + [I+F*dt/2]*F*dt
  // Ld = L*dt+F*L*dt**2/2            = [I+F*dt/2]*L*dt
  float Fd[EKF_NUM_STATES][EKF_NUM_STATES];
  float Ld[EKF_NUM_STATES][EKF_NUM_INPUTS];
  float tmp[EKF_NUM_STATES][EKF_NUM_STATES];
 
  MAKE_MATRIX_PTR(F_, F, EKF_NUM_STATES);
  MAKE_MATRIX_PTR(L_, L, EKF_NUM_STATES);
  MAKE_MATRIX_PTR(Fd_, Fd, EKF_NUM_STATES);
  MAKE_MATRIX_PTR(Ld_, Ld, EKF_NUM_STATES);
  MAKE_MATRIX_PTR(tmp_, tmp, EKF_NUM_STATES);
 
  // tmp = I+F*dt/2
  float_mat_diagonal_scal(tmp_, 1, EKF_NUM_STATES);
  float_mat_sum_scaled(tmp_, F_, dt / 2, EKF_NUM_STATES, EKF_NUM_STATES);
 
  // Ld = tmp*L*dt
  float_mat_mul(Ld_, tmp_, L_, EKF_NUM_STATES, EKF_NUM_STATES, EKF_NUM_INPUTS);
  float_mat_scale(Ld_, dt, EKF_NUM_STATES, EKF_NUM_INPUTS);
 
  // Fd = tmp*F*dt
  float_mat_mul(Fd_, tmp_, F_, EKF_NUM_STATES, EKF_NUM_STATES, EKF_NUM_STATES);
  float_mat_scale(Fd_, dt, EKF_NUM_STATES, EKF_NUM_STATES);
 
  // Fd += I
  int i;
  for (i = 0; i < EKF_NUM_STATES; i++) {
    Fd[i][i] += 1;
  }
 
 
  // [4] Predicted covariance estimate:
  // Pkk_1 = Fd*P*Fd.T + Ld*Q*Ld.T
  float Pkk_1[EKF_NUM_STATES][EKF_NUM_STATES];
  float LdT[EKF_NUM_INPUTS][EKF_NUM_STATES];
  float QLdT[EKF_NUM_INPUTS][EKF_NUM_STATES];
 
  MAKE_MATRIX_PTR(Pkk_1_, Pkk_1, EKF_NUM_STATES);
  MAKE_MATRIX_PTR(ekf_P_, ekf_P, EKF_NUM_STATES);
  MAKE_MATRIX_PTR(ekf_Q_, ekf_Q, EKF_NUM_STATES);
  MAKE_MATRIX_PTR(LdT_, LdT, EKF_NUM_INPUTS);
  MAKE_MATRIX_PTR(QLdT_, QLdT, EKF_NUM_INPUTS);
 
  // Fd = Fd.T
  float_mat_transpose_square(Fd_, EKF_NUM_STATES);
 
  // tmp = P*Fd
  float_mat_mul(tmp_, ekf_P_, Fd_, EKF_NUM_STATES, EKF_NUM_STATES, EKF_NUM_STATES);
 
  // Fd = Fd.T
  float_mat_transpose_square(Fd_, EKF_NUM_STATES);
 
  // Pkk_1 = Fd*tmp
  float_mat_mul(Pkk_1_, Fd_, tmp_, EKF_NUM_STATES, EKF_NUM_STATES, EKF_NUM_STATES);
 
  // LdT = Ld.T
  float_mat_transpose(LdT_, Ld_, EKF_NUM_STATES, EKF_NUM_INPUTS);
 
  // QLdT = Q*LdT
  float_mat_mul(QLdT_, ekf_Q_, LdT_, EKF_NUM_INPUTS, EKF_NUM_INPUTS, EKF_NUM_STATES);
 
  // tmp = Ld*QLdT
  float_mat_mul(tmp_, Ld_, QLdT_, EKF_NUM_STATES, EKF_NUM_INPUTS, EKF_NUM_STATES);
 
  // Pkk_1 += tmp
  float_mat_sum_scaled(Pkk_1_, tmp_, 1, EKF_NUM_STATES, EKF_NUM_STATES);
 
 
  // [5] Measurement residual:
  // yk = Z - H*Xkk_1
  float yk[EKF_NUM_OUTPUTS];
 
  MAKE_MATRIX_PTR(ekf_H_, ekf_H, EKF_NUM_OUTPUTS);
 
  float_mat_vect_mul(yk, ekf_H_, Xkk_1, EKF_NUM_OUTPUTS, EKF_NUM_STATES);
  float_vect_scale(yk, -1, EKF_NUM_OUTPUTS);
  float_vect_add(yk, Z, EKF_NUM_OUTPUTS);
 
 
  // [6] Residual covariance:
  // Sk = H*Pkk_1*H.T + R
  float Sk[EKF_NUM_OUTPUTS][EKF_NUM_OUTPUTS];
  float PHT[EKF_NUM_STATES][EKF_NUM_OUTPUTS];
 
  MAKE_MATRIX_PTR(Sk_, Sk, EKF_NUM_OUTPUTS);
  MAKE_MATRIX_PTR(PHT_, PHT, EKF_NUM_STATES);
  MAKE_MATRIX_PTR(ekf_R_, ekf_R, EKF_NUM_OUTPUTS);
 
  // PHT = Pkk_1*H.T
  float_mat_transpose(PHT_, ekf_H_, EKF_NUM_OUTPUTS, EKF_NUM_STATES);
  float_mat_mul_copy(PHT_, Pkk_1_, PHT_, EKF_NUM_STATES, EKF_NUM_STATES, EKF_NUM_OUTPUTS);
 
  // Sk = H*PHT
  float_mat_mul(Sk_, ekf_H_, PHT_, EKF_NUM_OUTPUTS, EKF_NUM_STATES, EKF_NUM_OUTPUTS);
 
  // Sk += R
  float_mat_sum_scaled(Sk_, ekf_R_, 1, EKF_NUM_OUTPUTS, EKF_NUM_OUTPUTS);
 
 
  // [7] Near-optimal Kalman gain:
  // K = Pkk_1*H.T*inv(Sk)
  float Sk_inv[EKF_NUM_OUTPUTS][EKF_NUM_OUTPUTS];
  float K[EKF_NUM_STATES][EKF_NUM_OUTPUTS];
 
  MAKE_MATRIX_PTR(Sk_inv_, Sk_inv, EKF_NUM_OUTPUTS);
  MAKE_MATRIX_PTR(K_, K, EKF_NUM_STATES);
 
  // Sk_inv = inv(Sk)
  float_mat_invert(Sk_inv_, Sk_, EKF_NUM_OUTPUTS);
 
  // K = PHT*Sk_inv
  float_mat_mul(K_, PHT_, Sk_inv_, EKF_NUM_STATES, EKF_NUM_OUTPUTS, EKF_NUM_OUTPUTS);
 
 
  // [8] Updated state estimate
  // Xkk = Xkk_1 + K*yk
  float_mat_vect_mul(ekf_X, K_, yk, EKF_NUM_STATES, EKF_NUM_OUTPUTS);
  float_vect_add(ekf_X, Xkk_1, EKF_NUM_STATES);
 
 
  // [9] Updated covariance estimate:
  // Pkk = (I - K*H)*Pkk_1
 
  // tmp = K*H
  float_mat_mul(tmp_, K_, ekf_H_, EKF_NUM_STATES, EKF_NUM_OUTPUTS, EKF_NUM_STATES);
 
  // tmp *= -1
  float_mat_scale(tmp_, -1, EKF_NUM_STATES, EKF_NUM_STATES);
 
  // tmp += I
  for (i = 0; i < EKF_NUM_STATES; i++) {
    tmp_[i][i] += 1;
  }
  // P = tmp*Pkk_1
  float_mat_mul(ekf_P_, tmp_, Pkk_1_, EKF_NUM_STATES, EKF_NUM_STATES, EKF_NUM_STATES);
}
 
static inline void ekf_prediction_step(const float U[EKF_NUM_INPUTS], const float dt)
{
  // [1] Predicted (a priori) state estimate:
  float Xkk_1[EKF_NUM_STATES];
  // Xkk_1 = f(X,U)
  ekf_f(ekf_X, U, Xkk_1);
  // Xkk_1 *= dt
  float_vect_scale(Xkk_1, dt, EKF_NUM_STATES);
  // Xkk_1 += X
  float_vect_add(Xkk_1, ekf_X, EKF_NUM_STATES);
 
 
  // [2] Get matrices
  float F[EKF_NUM_STATES][EKF_NUM_STATES];
  float Ld[EKF_NUM_STATES][EKF_NUM_INPUTS];
  ekf_F(ekf_X, U, F);
  ekf_L(ekf_X, U, Ld);
 
 
  // [3] Continuous to discrete
  // Fd = eye(N) + F*dt
  // Ld = L*dt
  float Fd[EKF_NUM_STATES][EKF_NUM_STATES];
 
  MAKE_MATRIX_PTR(F_, F, EKF_NUM_STATES);
  MAKE_MATRIX_PTR(Fd_, Fd, EKF_NUM_STATES);
  MAKE_MATRIX_PTR(Ld_, Ld, EKF_NUM_STATES);
 
  // Fd = I+F*dt/2
  float_mat_diagonal_scal(Fd_, 1, EKF_NUM_STATES);
  float_mat_sum_scaled(Fd_, F_, dt, EKF_NUM_STATES, EKF_NUM_STATES);
 
  // Ld = Ld*dt
  float_mat_scale(Ld_, dt, EKF_NUM_STATES, EKF_NUM_INPUTS);
 
 
  // [4] Predicted covariance estimate:
  // Pkk_1 = Fd*P*Fd.T + Ld*Q*Ld.T
  float Pkk_1[EKF_NUM_STATES][EKF_NUM_STATES];
  float LdT[EKF_NUM_INPUTS][EKF_NUM_STATES];
  float QLdT[EKF_NUM_INPUTS][EKF_NUM_STATES];
  float tmp[EKF_NUM_STATES][EKF_NUM_STATES];
 
  MAKE_MATRIX_PTR(Pkk_1_, Pkk_1, EKF_NUM_STATES);
  MAKE_MATRIX_PTR(ekf_P_, ekf_P, EKF_NUM_STATES);
  MAKE_MATRIX_PTR(ekf_Q_, ekf_Q, EKF_NUM_STATES);
  MAKE_MATRIX_PTR(LdT_, LdT, EKF_NUM_INPUTS);
  MAKE_MATRIX_PTR(QLdT_, QLdT, EKF_NUM_INPUTS);
  MAKE_MATRIX_PTR(tmp_, tmp, EKF_NUM_STATES);
 
  // Fd = Fd.T
  float_mat_transpose_square(Fd_, EKF_NUM_STATES);
 
  // tmp = P*Fd
  float_mat_mul(tmp_, ekf_P_, Fd_, EKF_NUM_STATES, EKF_NUM_STATES, EKF_NUM_STATES);
 
  // Fd = Fd.T
  float_mat_transpose_square(Fd_, EKF_NUM_STATES);
 
  // Pkk_1 = Fd*tmp
  float_mat_mul(Pkk_1_, Fd_, tmp_, EKF_NUM_STATES, EKF_NUM_STATES, EKF_NUM_STATES);
 
  // LdT = Ld.T
  float_mat_transpose(LdT_, Ld_, EKF_NUM_STATES, EKF_NUM_INPUTS);
 
  // QLdT = Q*LdT
  float_mat_mul(QLdT_, ekf_Q_, LdT_, EKF_NUM_INPUTS, EKF_NUM_INPUTS, EKF_NUM_STATES);
 
  // tmp = Ld*QLdT
  float_mat_mul(tmp_, Ld_, QLdT_, EKF_NUM_STATES, EKF_NUM_INPUTS, EKF_NUM_STATES);
 
  // Pkk_1 += tmp
  float_mat_sum_scaled(Pkk_1_, tmp_, 1, EKF_NUM_STATES, EKF_NUM_STATES);
 
  // X = Xkk_1
  float_vect_copy(ekf_X, Xkk_1, EKF_NUM_STATES);
 
  // P = Pkk_1
  float_mat_copy(ekf_P_, Pkk_1_, EKF_NUM_STATES, EKF_NUM_STATES);
}
 
static inline void ekf_measurement_step(const float Z[EKF_NUM_OUTPUTS])
{
  // Xkk_1 = X
  float Xkk_1[EKF_NUM_STATES];
  float_vect_copy(Xkk_1, ekf_X, EKF_NUM_STATES);
 
  // Pkk_1 = P
  float Pkk_1[EKF_NUM_STATES][EKF_NUM_STATES];
  MAKE_MATRIX_PTR(Pkk_1_, Pkk_1, EKF_NUM_STATES);
  MAKE_MATRIX_PTR(ekf_P_, ekf_P, EKF_NUM_STATES);
  float_mat_copy(Pkk_1_, ekf_P_, EKF_NUM_STATES, EKF_NUM_STATES);
 
  // [5] Measurement residual:
  // yk = Z - H*Xkk_1
  float yk[EKF_NUM_OUTPUTS];
 
  MAKE_MATRIX_PTR(ekf_H_, ekf_H, EKF_NUM_OUTPUTS);
 
  float_mat_vect_mul(yk, ekf_H_, Xkk_1, EKF_NUM_OUTPUTS, EKF_NUM_STATES);
  float_vect_scale(yk, -1, EKF_NUM_OUTPUTS);
  float_vect_add(yk, Z, EKF_NUM_OUTPUTS);
 
 
  // [6] Residual covariance:
  // Sk = H*Pkk_1*H.T + R
  float Sk[EKF_NUM_OUTPUTS][EKF_NUM_OUTPUTS];
  float PHT[EKF_NUM_STATES][EKF_NUM_OUTPUTS];
 
  MAKE_MATRIX_PTR(Sk_, Sk, EKF_NUM_OUTPUTS);
  MAKE_MATRIX_PTR(PHT_, PHT, EKF_NUM_STATES);
  MAKE_MATRIX_PTR(ekf_R_, ekf_R, EKF_NUM_OUTPUTS);
 
  // PHT = Pkk_1*H.T
  float_mat_transpose(PHT_, ekf_H_, EKF_NUM_OUTPUTS, EKF_NUM_STATES);
  float_mat_mul_copy(PHT_, Pkk_1_, PHT_, EKF_NUM_STATES, EKF_NUM_STATES, EKF_NUM_OUTPUTS);
 
  // Sk = H*PHT
  float_mat_mul(Sk_, ekf_H_, PHT_, EKF_NUM_OUTPUTS, EKF_NUM_STATES, EKF_NUM_OUTPUTS);
 
  // Sk += R
  float_mat_sum_scaled(Sk_, ekf_R_, 1, EKF_NUM_OUTPUTS, EKF_NUM_OUTPUTS);
 
 
  // [7] Near-optimal Kalman gain:
  // K = Pkk_1*H.T*inv(Sk)
  float Sk_inv[EKF_NUM_OUTPUTS][EKF_NUM_OUTPUTS];
  float K[EKF_NUM_STATES][EKF_NUM_OUTPUTS];
 
  MAKE_MATRIX_PTR(Sk_inv_, Sk_inv, EKF_NUM_OUTPUTS);
  MAKE_MATRIX_PTR(K_, K, EKF_NUM_STATES);
 
  // Sk_inv = inv(Sk)
  float_mat_invert(Sk_inv_, Sk_, EKF_NUM_OUTPUTS);
 
  // K = PHT*Sk_inv
  float_mat_mul(K_, PHT_, Sk_inv_, EKF_NUM_STATES, EKF_NUM_OUTPUTS, EKF_NUM_OUTPUTS);
 
 
  // [8] Updated state estimate
  // Xkk = Xkk_1 + K*yk
  float_mat_vect_mul(ekf_X, K_, yk, EKF_NUM_STATES, EKF_NUM_OUTPUTS);
  float_vect_add(ekf_X, Xkk_1, EKF_NUM_STATES);
 
 
  // [9] Updated covariance estimate:
  // Pkk = (I - K*H)*Pkk_1
  float tmp[EKF_NUM_STATES][EKF_NUM_STATES];
  MAKE_MATRIX_PTR(tmp_, tmp, EKF_NUM_STATES);
 
  // tmp = K*H
  float_mat_mul(tmp_, K_, ekf_H_, EKF_NUM_STATES, EKF_NUM_OUTPUTS, EKF_NUM_STATES);
 
  // tmp *= -1
  float_mat_scale(tmp_, -1, EKF_NUM_STATES, EKF_NUM_STATES);
 
  // tmp += I
  int i;
  for (i = 0; i < EKF_NUM_STATES; i++) {
    tmp_[i][i] += 1;
  }
  // P = tmp*Pkk_1
  float_mat_mul(ekf_P_, tmp_, Pkk_1_, EKF_NUM_STATES, EKF_NUM_STATES, EKF_NUM_STATES);
}
 
 
 
 
 
static inline void ekf_run(void)
{
  static bool start = false;
 
 
  // Time
  t1 = get_sys_time_float();
  float dt = t1 - t0;
  t0 = t1;
 
  // Only Start If External Pose is Available
  if (!start) {
    // ekf starts at the first ev update
    if (ins_ext_pos.has_new_ext_pose) {
      start = true;
 
      // initial guess
      ekf_X[0] = ins_ext_pos.ev_pos.x;
      ekf_X[1] = ins_ext_pos.ev_pos.y;
      ekf_X[2] = ins_ext_pos.ev_pos.z;
      ekf_X[6] = ins_ext_pos.ev_att.phi;
      ekf_X[7] = ins_ext_pos.ev_att.theta;
      ekf_X[8] = ins_ext_pos.ev_att.psi;
    }
  }
 
  // set input values
  if (ins_ext_pos.has_new_acc) {
    ekf_U[0] = ins_ext_pos.accels_f.x;
    ekf_U[1] = ins_ext_pos.accels_f.y;
    ekf_U[2] = ins_ext_pos.accels_f.z;
    ins_ext_pos.has_new_acc = false;
  } else {
    DEBUG_PRINT("ekf missing acc\n");
  }
  if (ins_ext_pos.has_new_gyro) {
    ekf_U[3] = ins_ext_pos.gyros_f.p;
    ekf_U[4] = ins_ext_pos.gyros_f.q;
    ekf_U[5] = ins_ext_pos.gyros_f.r;
    ins_ext_pos.has_new_gyro = false;
  } else {
    DEBUG_PRINT("ekf missing gyro\n");
  }
 
  if (start) {
 
    // prediction step
    DEBUG_PRINT("ekf prediction step U = %f, %f, %f, %f, %f, %f dt = %f \n", ekf_U[0], ekf_U[1], ekf_U[2], ekf_U[3],
                ekf_U[4], ekf_U[5], dt);
    ekf_prediction_step(ekf_U, dt);
 
    // measurement step
    if (ins_ext_pos.has_new_ext_pose) {
 
      //fix psi
      static float last_psi = 0;
      float delta_psi = ins_ext_pos.ev_att.psi - last_psi;
      last_psi = ins_ext_pos.ev_att.psi;
 
      if (delta_psi > M_PI) {
        delta_psi -= 2 * M_PI;
      } else if (delta_psi < -M_PI) {
        delta_psi += 2 * M_PI;
      }
 
 
      ekf_Z[0] = ins_ext_pos.ev_pos.x;
      ekf_Z[1] = ins_ext_pos.ev_pos.y;
      ekf_Z[2] = ins_ext_pos.ev_pos.z;
      ekf_Z[3] = ins_ext_pos.ev_att.phi;
      ekf_Z[4] = ins_ext_pos.ev_att.theta;
      ekf_Z[5] += delta_psi;
      ins_ext_pos.has_new_ext_pose = false;
 
      DEBUG_PRINT("ekf measurement step Z = %f, %f, %f, %f \n", ekf_Z[0], ekf_Z[1], ekf_Z[2], ekf_Z[3]);
      ekf_measurement_step(ekf_Z);
    }
  }
 
  // Export Results
  struct NedCoor_f ned_pos;
  ned_pos.x = ekf_X[0];
  ned_pos.y = ekf_X[1];
  ned_pos.z = ekf_X[2];
 
  struct NedCoor_f ned_speed;
  ned_speed.x  = ekf_X[3];
  ned_speed.y = ekf_X[4];
  ned_speed.z  = ekf_X[5];
 
  struct FloatEulers ned_to_body_eulers;
  ned_to_body_eulers.phi = ekf_X[6];
  ned_to_body_eulers.theta = ekf_X[7];
  ned_to_body_eulers.psi = ekf_X[8];
 
  struct FloatRates rates = { ekf_U[3] - ekf_X[12], ekf_U[4] - ekf_X[13], ekf_U[5] - ekf_X[14] };
 
  struct FloatVect3 accel;
  struct FloatVect3 accel_ned_f;
  accel.x = ekf_U[0] - ekf_X[9];
  accel.y = ekf_U[1] - ekf_X[10];
  accel.z = ekf_U[2] - ekf_X[11];
 
  // Export Body Accelerations (without bias)
  struct Int32Vect3 accel_i;
  ACCELS_BFP_OF_REAL(accel_i, accel);
  stateSetAccelBody_i(MODULE_INS_EXT_POSE_ID, &accel_i);
 
 
  struct FloatRMat *ned_to_body_rmat_f = stateGetNedToBodyRMat_f();
  float_rmat_transp_vmult(&accel_ned_f, ned_to_body_rmat_f, &accel);
  accel_ned_f.z += 9.81;
 
  stateSetPositionNed_f(MODULE_INS_EXT_POSE_ID, &ned_pos);
  stateSetSpeedNed_f(MODULE_INS_EXT_POSE_ID, &ned_speed);
  stateSetNedToBodyEulers_f(MODULE_INS_EXT_POSE_ID, &ned_to_body_eulers);
  stateSetBodyRates_f(MODULE_INS_EXT_POSE_ID, &rates);
  stateSetAccelNed_f(MODULE_INS_EXT_POSE_ID, (struct NedCoor_f *)&accel_ned_f);
 
}
 
 
 
void ins_ext_pos_log_header(FILE *file)
{
  fprintf(file,
          "ekf_X1,ekf_X2,ekf_X3,ekf_X4,ekf_X5,ekf_X6,ekf_X7,ekf_X8,ekf_X9,ekf_X10,ekf_X11,ekf_X12,ekf_X13,ekf_X14,ekf_X15,");
  fprintf(file, "ekf_U1,ekf_U2,ekf_U3,ekf_U4,ekf_U5,ekf_U6,");
  fprintf(file, "ekf_Z1,ekf_Z2,ekf_Z3,ekf_Z4,");
}
 
void ins_ext_pos_log_data(FILE *file)
{
  fprintf(file, "%f,%f,%f,%f,%f,%f,%f,%f,%f,%f,%f,%f,%f,%f,%f,", ekf_X[0], ekf_X[1], ekf_X[2], ekf_X[3], ekf_X[4],
          ekf_X[5], ekf_X[6], ekf_X[7], ekf_X[8], ekf_X[9], ekf_X[10], ekf_X[11], ekf_X[12], ekf_X[13], ekf_X[14]);
  fprintf(file, "%f,%f,%f,%f,%f,%f,", ekf_U[0], ekf_U[1], ekf_U[2], ekf_U[3], ekf_U[4], ekf_U[5]);
  fprintf(file, "%f,%f,%f,%f,", ekf_Z[0], ekf_Z[1], ekf_Z[2], ekf_Z[3]);
}