static void position_estimation_position_integration(position_estimator_t *pos_est)
{
	int32_t i;
	float dt = pos_est->ahrs->dt;
	
	quat_t qvel_bf,qvel; 

	qvel.s = 0;
	for (i = 0; i < 3; i++)
	{
		qvel.v[i] = pos_est->vel[i];
	}
	qvel_bf = quaternions_global_to_local(pos_est->ahrs->qe, qvel);
	for (i = 0; i < 3; i++)
	{
		pos_est->vel_bf[i] = qvel_bf.v[i];
		pos_est->vel_bf[i] = pos_est->vel_bf[i] * (1.0f - (VEL_DECAY * dt)) + pos_est->ahrs->linear_acc[i]  * dt;
	}
	
	// calculate velocity in global frame
	// vel = qe *vel_bf * qe - 1
	
	qvel_bf.s = 0.0f; 
	qvel_bf.v[0] = pos_est->vel_bf[0]; 	// TODO: replace this by quat_rotate_vector()
	qvel_bf.v[1] = pos_est->vel_bf[1]; 
	qvel_bf.v[2] = pos_est->vel_bf[2];
	
	qvel = quaternions_local_to_global(pos_est->ahrs->qe, qvel_bf);
	
	pos_est->vel[0] = qvel.v[0]; 
	pos_est->vel[1] = qvel.v[1]; 
	pos_est->vel[2] = qvel.v[2];	// TODO: replace this by quat_rotate_vector()
	
	for (i = 0; i < 3; i++)
	{
		pos_est->local_position.pos[i] = pos_est->local_position.pos[i] * (1.0f - (POS_DECAY * dt)) + pos_est->vel[i] * dt;

		pos_est->local_position.heading = coord_conventions_get_yaw(pos_est->ahrs->qe);
	}
	
}
예제 #2
0
void simulation_update(simulation_model_t *sim)
{
	int32_t i;
	quat_t qtmp1, qvel_bf,  qed;
	const quat_t front = {.s = 0.0f, .v = {1.0f, 0.0f, 0.0f}};
	const quat_t up = {.s = 0.0f, .v = {UPVECTOR_X, UPVECTOR_Y, UPVECTOR_Z}};
	
	
	uint32_t now = time_keeper_get_micros();
	sim->dt = (now - sim->last_update) / 1000000.0f;
	if (sim->dt > 0.1f)
	{
		sim->dt = 0.1f;
	}
	
	sim->last_update = now;
	// compute torques and forces based on servo commands
	forces_from_servos_diag_quad(sim);
	
	// integrate torques to get simulated gyro rates (with some damping)
	sim->rates_bf[0] = maths_clip((1.0f - 0.1f * sim->dt) * sim->rates_bf[0] + sim->dt * sim->torques_bf[0] / sim->vehicle_config.roll_pitch_momentum, 10.0f);
	sim->rates_bf[1] = maths_clip((1.0f - 0.1f * sim->dt) * sim->rates_bf[1] + sim->dt * sim->torques_bf[1] / sim->vehicle_config.roll_pitch_momentum, 10.0f);
	sim->rates_bf[2] = maths_clip((1.0f - 0.1f * sim->dt) * sim->rates_bf[2] + sim->dt * sim->torques_bf[2] / sim->vehicle_config.yaw_momentum, 10.0f);
	
	
	for (i = 0; i < 3; i++)
	{
			qtmp1.v[i] = 0.5f * sim->rates_bf[i];
	}
	
	qtmp1.s = 0;

	// apply step rotation 
	qed = quaternions_multiply(sim->ahrs.qe,qtmp1);

	// TODO: correct this formulas when using the right scales
	sim->ahrs.qe.s = sim->ahrs.qe.s + qed.s * sim->dt;
	sim->ahrs.qe.v[0] += qed.v[0] * sim->dt;
	sim->ahrs.qe.v[1] += qed.v[1] * sim->dt;
	sim->ahrs.qe.v[2] += qed.v[2] * sim->dt;

	sim->ahrs.qe = quaternions_normalise(sim->ahrs.qe);
	sim->ahrs.up_vec = quaternions_global_to_local(sim->ahrs.qe, up);
	
	sim->ahrs.north_vec = quaternions_global_to_local(sim->ahrs.qe, front);	

	// velocity and position integration
	
	// check altitude - if it is lower than 0, clamp everything (this is in NED, assuming negative altitude)
	if (sim->local_position.pos[Z] >0)
	{
		sim->vel[Z] = 0.0f;
		sim->local_position.pos[Z] = 0.0f;

		// simulate "acceleration" caused by contact force with ground, compensating gravity
		for (i = 0; i < 3; i++)
		{
			sim->lin_forces_bf[i] = sim->ahrs.up_vec.v[i] * sim->vehicle_config.total_mass * sim->vehicle_config.sim_gravity;
		}
				
		// slow down... (will make velocity slightly inconsistent until next update cycle, but shouldn't matter much)
		for (i = 0; i < 3; i++)
		{
			sim->vel_bf[i] = 0.95f * sim->vel_bf[i];
		}
		
		//upright
		sim->rates_bf[0] =  sim->ahrs.up_vec.v[1]; 
		sim->rates_bf[1] =  - sim->ahrs.up_vec.v[0];
		sim->rates_bf[2] = 0;
	}
	
	sim->ahrs.qe = quaternions_normalise(sim->ahrs.qe);
	sim->ahrs.up_vec = quaternions_global_to_local(sim->ahrs.qe, up);
	
	sim->ahrs.north_vec = quaternions_global_to_local(sim->ahrs.qe, front);	
	for (i = 0; i < 3; i++)
	{
			qtmp1.v[i] = sim->vel[i];
	}
	qtmp1.s = 0.0f;
	qvel_bf = quaternions_global_to_local(sim->ahrs.qe, qtmp1);
	
	float acc_bf[3];
	for (i = 0; i < 3; i++)
	{
		sim->vel_bf[i] = qvel_bf.v[i];
		
		// following the convention in the IMU, this is the acceleration due to force, as measured
		sim->ahrs.linear_acc[i] = sim->lin_forces_bf[i] / sim->vehicle_config.total_mass;
		
		// this is the "clean" acceleration without gravity
		acc_bf[i] = sim->ahrs.linear_acc[i] - sim->ahrs.up_vec.v[i] * sim->vehicle_config.sim_gravity;
		
		sim->vel_bf[i] = sim->vel_bf[i] + acc_bf[i] * sim->dt;
	}
	
	// calculate velocity in global frame
	// vel = qe *vel_bf * qe - 1
	qvel_bf.s = 0.0f; qvel_bf.v[0] = sim->vel_bf[0]; qvel_bf.v[1] = sim->vel_bf[1]; qvel_bf.v[2] = sim->vel_bf[2];
	qtmp1 = quaternions_local_to_global(sim->ahrs.qe, qvel_bf);
	sim->vel[0] = qtmp1.v[0]; sim->vel[1] = qtmp1.v[1]; sim->vel[2] = qtmp1.v[2];
	
	for (i = 0; i < 3; i++)
	{
		sim->local_position.pos[i] = sim->local_position.pos[i] + sim->vel[i] * sim->dt;
	}

	// fill in simulated IMU values
	for (i = 0;i < 3; i++)
	{
		sim->imu->raw_gyro.data[sim->imu->calib_gyro.axis[i]] = (sim->rates_bf[i] * sim->calib_gyro.scale_factor[i] + sim->calib_gyro.bias[i]) * sim->calib_gyro.orientation[i];
		sim->imu->raw_accelero.data[sim->imu->calib_accelero.axis[i]] = ((sim->lin_forces_bf[i] / sim->vehicle_config.total_mass / sim->vehicle_config.sim_gravity) * sim->calib_accelero.scale_factor[i] + sim->calib_accelero.bias[i]) * sim->calib_accelero.orientation[i];
		sim->imu->raw_compass.data[sim->imu->calib_compass.axis[i]] = ((sim->ahrs.north_vec.v[i] ) * sim->calib_compass.scale_factor[i] + sim->calib_compass.bias[i])* sim->calib_compass.orientation[i];
	}

	sim->local_position.heading = coord_conventions_get_yaw(sim->ahrs.qe);
}

void simulation_simulate_barometer(simulation_model_t *sim)
{
	sim->pressure->altitude = sim->local_position.origin.altitude - sim->local_position.pos[Z];
	sim->pressure->vario_vz = sim->vel[Z];
	sim->pressure->last_update = time_keeper_get_millis();
	sim->pressure->altitude_offset = 0;
}
	
void simulation_simulate_gps(simulation_model_t *sim)
{
	global_position_t gpos = coord_conventions_local_to_global_position(sim->local_position);
	
	sim->gps->altitude = gpos.altitude;
	sim->gps->latitude = gpos.latitude;
	sim->gps->longitude = gpos.longitude;
	sim->gps->time_last_msg = time_keeper_get_millis();
	sim->gps->time_last_posllh_msg = time_keeper_get_millis();
	sim->gps->time_last_velned_msg = time_keeper_get_millis();

	sim->gps->north_speed = sim->vel[X];
	sim->gps->east_speed = sim->vel[Y];
	sim->gps->vertical_speed = sim->vel[Z];

	sim->gps->status = GPS_OK;
	sim->gps->healthy = true;
}
예제 #3
0
void forces_from_servos_diag_quad(simulation_model_t* sim)
{
	float motor_command[4];
	float rotor_lifts[4], rotor_drags[4], rotor_inertia[4];
	float ldb;
	quat_t wind_gf = {.s = 0, .v = {sim->vehicle_config.wind_x, sim->vehicle_config.wind_y, 0.0f}};
	quat_t wind_bf = quaternions_global_to_local(sim->ahrs.qe, wind_gf);
	
	float sqr_lateral_airspeed = SQR(sim->vel_bf[0] + wind_bf.v[0]) + SQR(sim->vel_bf[1] + wind_bf.v[1]);
	float lateral_airspeed = sqrt(sqr_lateral_airspeed);
	
	float old_rotor_speed;
	
	for (int32_t i = 0; i < 4; i++)
	{
		motor_command[i] = (float)sim->mix->servos->servo[i].value - sim->vehicle_config.rotor_rpm_offset;
		if (motor_command[i] < 0.0f) 
		{
			motor_command[i] = 0;
		}
		
		// temporarily save old rotor speeds
		old_rotor_speed = sim->rotorspeeds[i];
		// estimate rotor speeds by low - pass filtering
		//sim->rotorspeeds[i] = (sim->vehicle_config.rotor_lpf) * sim->rotorspeeds[i] + (1.0f - sim->vehicle_config.rotor_lpf) * (motor_command[i] * sim->vehicle_config.rotor_rpm_gain);
		sim->rotorspeeds[i] = (motor_command[i] * sim->vehicle_config.rotor_rpm_gain);
		
		// calculate torque created by rotor inertia
		rotor_inertia[i] = (sim->rotorspeeds[i] - old_rotor_speed) / sim->dt * sim->vehicle_config.rotor_momentum;
		
		ldb = lift_drag_base(sim, sim->rotorspeeds[i], sqr_lateral_airspeed, -sim->vel_bf[Z]);
		//ldb = lift_drag_base(sim, sim->rotorspeeds[i], sqr_lateral_airspeed, 0.0f);
		
		rotor_lifts[i] = ldb * sim->vehicle_config.rotor_cl;
		rotor_drags[i] = ldb * sim->vehicle_config.rotor_cd;
	}
	
	float mpos_x = sim->vehicle_config.rotor_arm_length / 1.4142f;
	float mpos_y = sim->vehicle_config.rotor_arm_length / 1.4142f;

	// torque around x axis (roll)
	sim->torques_bf[ROLL] = ((rotor_lifts[sim->mix->motor_front_left]  + rotor_lifts[sim->mix->motor_rear_left]  ) 
						    	- (rotor_lifts[sim->mix->motor_front_right] + rotor_lifts[sim->mix->motor_rear_right] )) * mpos_y;;

	// torque around y axis (pitch)
	sim->torques_bf[PITCH] = ((rotor_lifts[sim->mix->motor_front_left]  + rotor_lifts[sim->mix->motor_front_right] )
								- (rotor_lifts[sim->mix->motor_rear_left]   + rotor_lifts[sim->mix->motor_rear_right] ))*  mpos_x;

	sim->torques_bf[YAW] = (sim->mix->motor_front_left_dir * (10.0f * rotor_drags[sim->mix->motor_front_left] + rotor_inertia[sim->mix->motor_front_left])
								+ sim->mix->motor_front_right_dir * (10.0f * rotor_drags[sim->mix->motor_front_right] + rotor_inertia[sim->mix->motor_front_right])
								+ sim->mix->motor_rear_left_dir * (10.0f * rotor_drags[sim->mix->motor_rear_left] + rotor_inertia[sim->mix->motor_rear_left])
								+ sim->mix->motor_rear_right_dir * (10.0f * rotor_drags[sim->mix->motor_rear_right] + rotor_inertia[sim->mix->motor_rear_right] ))*  sim->vehicle_config.rotor_diameter;

	sim->lin_forces_bf[X] = -(sim->vel_bf[X] - wind_bf.v[0]) * lateral_airspeed * sim->vehicle_config.vehicle_drag;  
	sim->lin_forces_bf[Y] = -(sim->vel_bf[Y] - wind_bf.v[1]) * lateral_airspeed * sim->vehicle_config.vehicle_drag;
	sim->lin_forces_bf[Z] = -(rotor_lifts[sim->mix->motor_front_left]+ rotor_lifts[sim->mix->motor_front_right] +rotor_lifts[sim->mix->motor_rear_left] +rotor_lifts[sim->mix->motor_rear_right]);

}


//------------------------------------------------------------------------------
// PUBLIC FUNCTIONS IMPLEMENTATION
//------------------------------------------------------------------------------

bool simulation_init(simulation_model_t* sim, const simulation_config_t* sim_config, ahrs_t* ahrs, imu_t* imu, position_estimation_t* pos_est, barometer_t* pressure, gps_t* gps, sonar_t* sonar, state_t* state, bool* waypoint_set, const servo_mix_quadcotper_diag_t* mix)
{
	bool init_success = true;
	
	//Init dependencies
	sim->vehicle_config = *sim_config;
	sim->imu = imu;
	sim->pos_est = pos_est;
	sim->pressure = pressure;
	sim->gps = gps;
	sim->sonar = sonar;
	sim->state = state;
	sim->nav_plan_active = &state->nav_plan_active;
	sim->mix = mix;
	
	// set initial conditions to a given attitude_filter
	sim->estimated_attitude = ahrs;
	sim->ahrs = *ahrs;

	print_util_dbg_print("Attitude:");
	print_util_dbg_print_num(sim->ahrs.qe.s*100,10);
	print_util_dbg_print(", ");
	print_util_dbg_print_num(sim->ahrs.qe.v[0]*100,10);
	print_util_dbg_print(", ");
	print_util_dbg_print_num(sim->ahrs.qe.v[1]*100,10);
	print_util_dbg_print(", ");
	print_util_dbg_print_num(sim->ahrs.qe.v[2]*100,10);
	print_util_dbg_print("\r\n");
	

	for (int32_t i = 0; i < ROTORCOUNT; i++)
	{
		sim->rotorspeeds[i] = 0.0f;			
	}
	sim->last_update = time_keeper_get_micros();
	sim->dt = 0.01f;
	
	simulation_reset_simulation(sim);
	simulation_calib_set(sim);
	
	print_util_dbg_print("[HIL SIMULATION] initialised.\r\n");
	
	return init_success;
}
void stabilisation_wing_cascade_stabilise(stabilisation_wing_t* stabilisation_wing)
{
    float rpyt_errors[4];
    control_command_t input;
    int32_t i;
    float feedforward[4];
    float nav_heading, current_heading, heading_error;
    float gps_speed_global[3], gps_speed_semi_local[3];
    float input_turn_rate;
    float input_roll_angle;
    aero_attitude_t attitude, attitude_yaw;
    quat_t q_rot;
    float airspeed_desired;
    float clipping_factor;

    // Get up vector in body frame
    quat_t up = {0.0f, {UPVECTOR_X, UPVECTOR_Y, UPVECTOR_Z}};
    quat_t up_vec = quaternions_global_to_local(stabilisation_wing->ahrs->qe,
                    up);

    // set the controller input
    input= *stabilisation_wing->controls;
    switch (stabilisation_wing->controls->control_mode) 
    {
    case VELOCITY_COMMAND_MODE:
        // Get current attitude
        attitude_yaw = coord_conventions_quat_to_aero(stabilisation_wing->ahrs->qe);
    
        /////////////
        // HEADING //
        /////////////
        // Compute the heading angle corresponding to the given input velocity vector (input from remote/vector field should be in semi-local frame).
        nav_heading = heading_from_velocity_vector(input.tvel);
        // Overwrite command if in remote
        if(stabilisation_wing->controls->yaw_mode == YAW_RELATIVE)
        {
            nav_heading = maths_calc_smaller_angle(input.rpy[YAW] - attitude_yaw.rpy[YAW]);
        }
        
        // Compute current heading
        gps_speed_global[X] = stabilisation_wing->gps->velocity_lf()[0];
        gps_speed_global[Y] = stabilisation_wing->gps->velocity_lf()[1];
        gps_speed_global[Z] = stabilisation_wing->pos_est->vel[Z];
        
        // Transform global to semi-local
        attitude_yaw.rpy[0] = 0.0f;
        attitude_yaw.rpy[1] = 0.0f;
        attitude_yaw.rpy[2] = -attitude_yaw.rpy[2];
        q_rot = coord_conventions_quaternion_from_aero(attitude_yaw);
        quaternions_rotate_vector(q_rot, gps_speed_global, gps_speed_semi_local);
        
        current_heading = heading_from_velocity_vector(gps_speed_semi_local);
        
        // Compute heading error
        heading_error = maths_calc_smaller_angle(nav_heading - current_heading);
        
        
        ///////////////
        // PID INPUT //
        ///////////////
        // Vector field normalize vector in plane x-y to cruise_speed value ==> airspeed should be done only on the x-y composants
        airspeed_desired = sqrtf(input.tvel[X]*input.tvel[X] + input.tvel[Y]*input.tvel[Y]);
        
        // Compute errors
        rpyt_errors[0] = heading_error;                                                             // Heading
        rpyt_errors[1] = input.tvel[Z] - gps_speed_global[Z];                                       // Vertical speed
        rpyt_errors[2] = 0.0f;
        rpyt_errors[3] = airspeed_desired - stabilisation_wing->airspeed_analog->get_airspeed();    // Airspeed
        
        // Compute the feedforward
        feedforward[0] = 0.0f;
        feedforward[1] = 0.0f;
        feedforward[2] = 0.0f;
        feedforward[3] = (airspeed_desired - 13.0f)/8.0f + 0.2f;
        
        // run PID update on all velocity controllers
        stabilisation_run_feedforward(&stabilisation_wing->stabiliser_stack.velocity_stabiliser, stabilisation_wing->ahrs->dt_s, rpyt_errors, feedforward);
        
        
        ////////////////
        // PID OUTPUT //
        ////////////////
        // Get turn rate command and transform it into a roll angle command for next layer
        input_turn_rate = stabilisation_wing->stabiliser_stack.velocity_stabiliser.output.rpy[0];
        // TODO: Fix this in case of bad airspeed readings...
        clipping_factor = stabilisation_wing->max_roll_angle / (PI/2.0f);
        if(clipping_factor == 0.0f)
        {
            input_roll_angle = 0.0f;
        }
        else
        {
            input_roll_angle = clipping_factor * atanf( (1.0f/clipping_factor) * (stabilisation_wing->airspeed_analog->get_airspeed() * input_turn_rate / 9.81f) );
        }
        
        // Set input for next layer
        input = stabilisation_wing->stabiliser_stack.velocity_stabiliser.output;
        input.rpy[0] = input_roll_angle;
        input.rpy[1] = - stabilisation_wing->stabiliser_stack.velocity_stabiliser.output.rpy[1];
        input.thrust = stabilisation_wing->stabiliser_stack.velocity_stabiliser.output.thrust;
        
        // Overwrite the commands during different key phases (take-off and landing)
        if(stabilisation_wing->navigation->internal_state_ == Navigation::NAV_TAKEOFF)
        {
            // Take-off: fixed 0 roll angle, fixed defined pitch angle and fixed defined constant thrust value.
            input.rpy[0] = 0.0f;
            input.rpy[1] = stabilisation_wing->take_off_pitch;
            input.thrust = stabilisation_wing->take_off_thrust;
        }
        else if(stabilisation_wing->navigation->internal_state_ == Navigation::NAV_LANDING)
        {
            // Landing: Limit the roll computed by the velocity layer (navigation), shut down the motor and impose a little pitch down to assure gliding without stall.
            if(input.rpy[0] > stabilisation_wing->landing_max_roll)
            {
                input.rpy[0] = stabilisation_wing->landing_max_roll;
            }
            else if(input.rpy[0] < -stabilisation_wing->landing_max_roll)
            {
                input.rpy[0] = -stabilisation_wing->landing_max_roll;
            }
            input.rpy[1] = stabilisation_wing->landing_pitch;
            input.thrust = -1.0f;
        }
        
    // -- no break here  - we want to run the lower level modes as well! -- 
    
    case ATTITUDE_COMMAND_MODE:
        // Add "a priori on the pitch" to fly horizontally and to compensate for roll angle
        attitude = coord_conventions_quat_to_aero(stabilisation_wing->ahrs->qe);
        input.rpy[1] += stabilisation_wing->pitch_angle_apriori;    // Constant compensation for horizontal
        if(maths_f_abs(attitude.rpy[ROLL]) < PI/2.0f)                       // Compensation for the roll bank angle
        {
            input.rpy[1] += stabilisation_wing->pitch_angle_apriori_gain * maths_f_abs(input.rpy[0]*input.rpy[0]*input.rpy[0]);
        }
        
        // run absolute attitude_filter controller
        rpyt_errors[0]= sinf(input.rpy[0]) + up_vec.v[1];                               // Roll
        rpyt_errors[1]= sinf(input.rpy[1]) - up_vec.v[0];                               // Pitch
        rpyt_errors[2]= 0.0f;                                                           // Yaw
        rpyt_errors[3]= input.thrust;       // no feedback for thrust at this level
        
        // run PID update on all attitude_filter controllers
        stabilisation_run(&stabilisation_wing->stabiliser_stack.attitude_stabiliser, stabilisation_wing->ahrs->dt_s, rpyt_errors);
        
        // use output of attitude_filter controller to set rate setpoints for rate controller 
        input = stabilisation_wing->stabiliser_stack.attitude_stabiliser.output;
    
    // -- no break here  - we want to run the lower level modes as well! -- 
    
    case RATE_COMMAND_MODE: // this level is always run
        // get rate measurements from IMU (filtered angular rates)
        for (i=0; i<3; i++)
        {
            rpyt_errors[i]= input.rpy[i]- stabilisation_wing->ahrs->angular_speed[i];
        }
        rpyt_errors[3] = input.thrust ;  // no feedback for thrust at this level
        
        // run PID update on all rate controllers
        stabilisation_run(&stabilisation_wing->stabiliser_stack.rate_stabiliser, stabilisation_wing->ahrs->dt_s, rpyt_errors);
    }

    stabilisation_wing->torque_command->xyz[0] = stabilisation_wing->stabiliser_stack.rate_stabiliser.output.rpy[ROLL];
    stabilisation_wing->torque_command->xyz[1] = stabilisation_wing->stabiliser_stack.rate_stabiliser.output.rpy[PITCH];
    stabilisation_wing->thrust_command->thrust = stabilisation_wing->stabiliser_stack.rate_stabiliser.output.thrust;
}
예제 #5
0
void qfilter_update(qfilter_t *qf)
{
	static uint32_t convergence_update_count = 0;
	float  omc[3], omc_mag[3] , tmp[3], snorm, norm, s_acc_norm, acc_norm, s_mag_norm, mag_norm;
	quat_t qed, qtmp1, up, up_bf;
	quat_t mag_global, mag_corrected_local;
	quat_t front_vec_global = 
	{
		.s = 0.0f, 
		.v = {1.0f, 0.0f, 0.0f}
	};

	float kp 	 = qf->kp;
	float kp_mag = qf->kp_mag;
	float ki 	 = qf->ki;
	float ki_mag = qf->ki_mag;

	// Update time in us
	float now_us 	= time_keeper_get_micros();
	
	// Delta t in seconds
	float dt     = 1e-6 * (float)(now_us - qf->ahrs->last_update);
	
	// Write to ahrs structure
	qf->ahrs->dt 		  = dt;
	qf->ahrs->last_update = now_us;

	
	// up_bf = qe^-1 *(0,0,0,-1) * qe
	up.s = 0; up.v[X] = UPVECTOR_X; up.v[Y] = UPVECTOR_Y; up.v[Z] = UPVECTOR_Z;
	up_bf = quaternions_global_to_local(qf->ahrs->qe, up);
	
	// calculate norm of acceleration vector
	s_acc_norm = qf->imu->scaled_accelero.data[X] * qf->imu->scaled_accelero.data[X] + qf->imu->scaled_accelero.data[Y] * qf->imu->scaled_accelero.data[Y] + qf->imu->scaled_accelero.data[Z] * qf->imu->scaled_accelero.data[Z];
	if ( (s_acc_norm > 0.7f * 0.7f) && (s_acc_norm < 1.3f * 1.3f) ) 
	{
		// approximate square root by running 2 iterations of newton method
		acc_norm = maths_fast_sqrt(s_acc_norm);

		tmp[X] = qf->imu->scaled_accelero.data[X] / acc_norm;
		tmp[Y] = qf->imu->scaled_accelero.data[Y] / acc_norm;
		tmp[Z] = qf->imu->scaled_accelero.data[Z] / acc_norm;

		// omc = a x up_bf.v
		CROSS(tmp, up_bf.v, omc);
	}
	else
	{
		omc[X] = 0;
		omc[Y] = 0;
		omc[Z] = 0;
	}

	// Heading computation
	// transfer 
	qtmp1 = quaternions_create_from_vector(qf->imu->scaled_compass.data); 
	mag_global = quaternions_local_to_global(qf->ahrs->qe, qtmp1);
	
	// calculate norm of compass vector
	//s_mag_norm = SQR(mag_global.v[X]) + SQR(mag_global.v[Y]) + SQR(mag_global.v[Z]);
	s_mag_norm = SQR(mag_global.v[X]) + SQR(mag_global.v[Y]);

	if ( (s_mag_norm > 0.004f * 0.004f) && (s_mag_norm < 1.8f * 1.8f) ) 
	{
		mag_norm = maths_fast_sqrt(s_mag_norm);

		mag_global.v[X] /= mag_norm;
		mag_global.v[Y] /= mag_norm;
		mag_global.v[Z] = 0.0f;   // set z component in global frame to 0

		// transfer magneto vector back to body frame 
		qf->ahrs->north_vec = quaternions_global_to_local(qf->ahrs->qe, front_vec_global);		
		
		mag_corrected_local = quaternions_global_to_local(qf->ahrs->qe, mag_global);		
		
		// omc = a x up_bf.v
		CROSS(mag_corrected_local.v, qf->ahrs->north_vec.v,  omc_mag);
		
	}
	else
	{
		omc_mag[X] = 0;
		omc_mag[Y] = 0;
		omc_mag[Z] = 0;
	}


	// get error correction gains depending on mode
	switch (qf->ahrs->internal_state)
	{
		case AHRS_UNLEVELED:
			kp = qf->kp * 10.0f;
			kp_mag = qf->kp_mag * 10.0f;
			
			ki = 0.5f * qf->ki;
			ki_mag = 0.5f * qf->ki_mag;
			
			convergence_update_count += 1;
			if( convergence_update_count > 2000 )
			{
				convergence_update_count = 0;
				qf->ahrs->internal_state = AHRS_CONVERGING;
				print_util_dbg_print("End of AHRS attitude initialization.\r\n");
			}
			break;
			
		case AHRS_CONVERGING:
			kp = qf->kp;
			kp_mag = qf->kp_mag;
			
			ki = qf->ki * 3.0f;
			ki_mag = qf->ki_mag * 3.0f;
			
			convergence_update_count += 1;
			if( convergence_update_count > 2000 )
			{
				convergence_update_count = 0;
				qf->ahrs->internal_state = AHRS_READY;
				print_util_dbg_print("End of AHRS leveling.\r\n");
			}
			break;

		case AHRS_READY:
			kp = qf->kp;
			kp_mag = qf->kp_mag;
			ki = qf->ki;
			ki_mag = qf->ki_mag;
			break;
	}

	// apply error correction with appropriate gains for accelerometer and compass

	for (uint8_t i = 0; i < 3; i++)
	{
		qtmp1.v[i] = 0.5f * (qf->imu->scaled_gyro.data[i] + kp * omc[i] + kp_mag * omc_mag[i]);
	}
	qtmp1.s = 0;

	// apply step rotation with corrections
	qed = quaternions_multiply(qf->ahrs->qe,qtmp1);

	// TODO: correct this formulas! 
	qf->ahrs->qe.s = qf->ahrs->qe.s + qed.s * dt;
	qf->ahrs->qe.v[X] += qed.v[X] * dt;
	qf->ahrs->qe.v[Y] += qed.v[Y] * dt;
	qf->ahrs->qe.v[Z] += qed.v[Z] * dt;

	snorm = qf->ahrs->qe.s * qf->ahrs->qe.s + qf->ahrs->qe.v[X] * qf->ahrs->qe.v[X] + qf->ahrs->qe.v[Y] * qf->ahrs->qe.v[Y] + qf->ahrs->qe.v[Z] * qf->ahrs->qe.v[Z];
	if (snorm < 0.0001f)
	{
		norm = 0.01f;
	}
	else
	{
		// approximate square root by running 2 iterations of newton method
		norm = maths_fast_sqrt(snorm);
	}
	qf->ahrs->qe.s /= norm;
	qf->ahrs->qe.v[X] /= norm;
	qf->ahrs->qe.v[Y] /= norm;
	qf->ahrs->qe.v[Z] /= norm;

	// bias estimate update
	qf->imu->calib_gyro.bias[X] += - dt * ki * omc[X] / qf->imu->calib_gyro.scale_factor[X];
	qf->imu->calib_gyro.bias[Y] += - dt * ki * omc[Y] / qf->imu->calib_gyro.scale_factor[Y];
	qf->imu->calib_gyro.bias[Z] += - dt * ki * omc[Z] / qf->imu->calib_gyro.scale_factor[Z];
	
	qf->imu->calib_gyro.bias[X] += - dt * ki_mag * omc_mag[X] / qf->imu->calib_compass.scale_factor[X];
	qf->imu->calib_gyro.bias[Y] += - dt * ki_mag * omc_mag[Y] / qf->imu->calib_compass.scale_factor[Y];
	qf->imu->calib_gyro.bias[Z] += - dt * ki_mag * omc_mag[Z] / qf->imu->calib_compass.scale_factor[Z];
	
	// set up-vector (bodyframe) in attitude
	qf->ahrs->up_vec.v[X] = up_bf.v[X];
	qf->ahrs->up_vec.v[Y] = up_bf.v[Y];
	qf->ahrs->up_vec.v[Z] = up_bf.v[Z];

	// Update linear acceleration
	qf->ahrs->linear_acc[X] = 9.81f * (qf->imu->scaled_accelero.data[X] - qf->ahrs->up_vec.v[X]) ;							// TODO: review this line!
	qf->ahrs->linear_acc[Y] = 9.81f * (qf->imu->scaled_accelero.data[Y] - qf->ahrs->up_vec.v[Y]) ;							// TODO: review this line!
	qf->ahrs->linear_acc[Z] = 9.81f * (qf->imu->scaled_accelero.data[Z] - qf->ahrs->up_vec.v[Z]) ;							// TODO: review this line!

	//update angular_speed.
	qf->ahrs->angular_speed[X] = qf->imu->scaled_gyro.data[X];
	qf->ahrs->angular_speed[Y] = qf->imu->scaled_gyro.data[Y];
	qf->ahrs->angular_speed[Z] = qf->imu->scaled_gyro.data[Z];
}