/**************************************************/
void Normalize(void)
{
  float error=0;
  float temporary[3][3];
  float renorm=0;
  boolean problem=FALSE;

  error= -Vector_Dot_Product(&DCM_Matrix[0][0],&DCM_Matrix[1][0])*.5; //eq.19

  Vector_Scale(&temporary[0][0], &DCM_Matrix[1][0], error); //eq.19
  Vector_Scale(&temporary[1][0], &DCM_Matrix[0][0], error); //eq.19

  Vector_Add(&temporary[0][0], &temporary[0][0], &DCM_Matrix[0][0]);//eq.19
  Vector_Add(&temporary[1][0], &temporary[1][0], &DCM_Matrix[1][0]);//eq.19

  Vector_Cross_Product(&temporary[2][0],&temporary[0][0],&temporary[1][0]); // c= a x b //eq.20

  renorm= Vector_Dot_Product(&temporary[0][0],&temporary[0][0]); 
  if (renorm < 1.5625f && renorm > 0.64f) {
    renorm= .5 * (3-renorm);                                                 //eq.21
  } else if (renorm < 100.0f && renorm > 0.01f) {
    renorm= 1. / sqrt(renorm);
#if PERFORMANCE_REPORTING == 1
    renorm_sqrt_count++;
#endif
  } else {
    problem = TRUE;
#if PERFORMANCE_REPORTING == 1
    renorm_blowup_count++;
#endif
  }
  Vector_Scale(&DCM_Matrix[0][0], &temporary[0][0], renorm);

  renorm= Vector_Dot_Product(&temporary[1][0],&temporary[1][0]); 
  if (renorm < 1.5625f && renorm > 0.64f) {
    renorm= .5 * (3-renorm);                                                 //eq.21
  } else if (renorm < 100.0f && renorm > 0.01f) {
    renorm= 1. / sqrt(renorm);  
#if PERFORMANCE_REPORTING == 1    
    renorm_sqrt_count++;
#endif
  } else {
    problem = TRUE;
#if PERFORMANCE_REPORTING == 1
    renorm_blowup_count++;
#endif
  }
  Vector_Scale(&DCM_Matrix[1][0], &temporary[1][0], renorm);

  renorm= Vector_Dot_Product(&temporary[2][0],&temporary[2][0]); 
  if (renorm < 1.5625f && renorm > 0.64f) {
    renorm= .5 * (3-renorm);                                                 //eq.21
  } else if (renorm < 100.0f && renorm > 0.01f) {
    renorm= 1. / sqrt(renorm);   
#if PERFORMANCE_REPORTING == 1 
    renorm_sqrt_count++;
#endif
  } else {
    problem = TRUE;  
#if PERFORMANCE_REPORTING == 1
    renorm_blowup_count++;
#endif
  }
  Vector_Scale(&DCM_Matrix[2][0], &temporary[2][0], renorm);

  if (problem) {                // Our solution is blowing up and we will force back to initial condition.  Hope we are not upside down!
    DCM_Matrix[0][0]= 1.0f;
    DCM_Matrix[0][1]= 0.0f;
    DCM_Matrix[0][2]= 0.0f;
    DCM_Matrix[1][0]= 0.0f;
    DCM_Matrix[1][1]= 1.0f;
    DCM_Matrix[1][2]= 0.0f;
    DCM_Matrix[2][0]= 0.0f;
    DCM_Matrix[2][1]= 0.0f;
    DCM_Matrix[2][2]= 1.0f;
    problem = FALSE;  
  }
}

/**************************************************/
void Drift_correction(void)
{
  //Compensation the Roll, Pitch and Yaw drift. 
  static float Scaled_Omega_P[3];
  static float Scaled_Omega_I[3];
  float Accel_magnitude;
  float Accel_weight;
  float Integrator_magnitude;
  float tempfloat;

  //*****Roll and Pitch***************

  // Calculate the magnitude of the accelerometer vector
  Accel_magnitude = sqrt(Accel_Vector[0]*Accel_Vector[0] + Accel_Vector[1]*Accel_Vector[1] + Accel_Vector[2]*Accel_Vector[2]);
  Accel_magnitude = Accel_magnitude / GRAVITY; // Scale to gravity.
  // Dynamic weighting of accelerometer info (reliability filter)
  // Weight for accelerometer info (<0.5G = 0.0, 1G = 1.0 , >1.5G = 0.0)
  Accel_weight = constrain(1 - 2*abs(1 - Accel_magnitude),0,1);  //  
  // Set to 0 if high_accel_flag is true
  if (high_accel_flag) Accel_weight = 0.;

#if PERFORMANCE_REPORTING == 1
  tempfloat = ((Accel_weight - 0.5) * 256.0f);    //amount added was determined to give imu_health a time constant about twice the time constant of the roll/pitch drift correction
  imu_health += tempfloat;
  imu_health = constrain(imu_health,129,65405);
#endif

  Vector_Cross_Product(&errorRollPitch[0],&Accel_Vector[0],&DCM_Matrix[2][0]); //adjust the ground of reference
  Vector_Scale(&Omega_P[0],&errorRollPitch[0],Kp_ROLLPITCH*Accel_weight);

  Vector_Scale(&Scaled_Omega_I[0],&errorRollPitch[0],Ki_ROLLPITCH*Accel_weight);
  Vector_Add(Omega_I,Omega_I,Scaled_Omega_I);     

  //*****YAW***************

  // Use GPS Ground course to correct yaw gyro drift
  if(ground_speed>=SPEEDFILT)
  {
    COGX = cos(ground_course);
    COGY = sin(ground_course);
    errorCourse=(DCM_Matrix[0][0]*COGY) - (DCM_Matrix[1][0]*COGX);  //Calculating YAW error
    Vector_Scale(errorYaw,&DCM_Matrix[2][0],errorCourse); //Applys the yaw correction to the XYZ rotation of the aircraft, depeding the position.

    Vector_Scale(&Scaled_Omega_P[0],&errorYaw[0],Kp_YAW);
    Vector_Add(Omega_P,Omega_P,Scaled_Omega_P);//Adding  Proportional.

    Vector_Scale(&Scaled_Omega_I[0],&errorYaw[0],Ki_YAW);
    Vector_Add(Omega_I,Omega_I,Scaled_Omega_I);//adding integrator to the Omega_I   
  }
  //  Here we will place a limit on the integrator so that the integrator cannot ever exceed half the saturation limit of the gyros
  Integrator_magnitude = sqrt(Vector_Dot_Product(Omega_I,Omega_I));
  if (Integrator_magnitude > ToRad(300)) {
    Vector_Scale(Omega_I,Omega_I,0.5f*ToRad(300)/Integrator_magnitude);
  }

}

/**************************************************/
void Accel_adjust(void)
{
  Accel_Vector[1] += Accel_Scale(speed_3d*Omega[2]);  // Centrifugal force on Acc_y = GPS_speed*GyroZ
  Accel_Vector[2] -= Accel_Scale(speed_3d*Omega[1]);  // Centrifugal force on Acc_z = GPS_speed*GyroY 
}

/**************************************************/
void Matrix_update(void)
{
  Gyro_Vector[0]=Gyro_Scaled_X(read_adc(0)); //gyro x roll
  Gyro_Vector[1]=Gyro_Scaled_Y(read_adc(1)); //gyro y pitch
  Gyro_Vector[2]=Gyro_Scaled_Z(read_adc(2)); //gyro Z yaw

  Accel_Vector[0]=read_adc(3); // acc x
  Accel_Vector[1]=read_adc(4); // acc y
  Accel_Vector[2]=read_adc(5); // acc z

  Vector_Add(&Omega[0], &Gyro_Vector[0], &Omega_I[0]);  //adding proportional term
  Vector_Add(&Omega_Vector[0], &Omega[0], &Omega_P[0]); //adding Integrator term

  Accel_adjust();    //Remove centrifugal acceleration.

  Update_Matrix[0][0]=0;
  Update_Matrix[0][1]=-G_Dt*Omega_Vector[2];//-z
  Update_Matrix[0][2]=G_Dt*Omega_Vector[1];//y
  Update_Matrix[1][0]=G_Dt*Omega_Vector[2];//z
  Update_Matrix[1][1]=0;
  Update_Matrix[1][2]=-G_Dt*Omega_Vector[0];//-x
  Update_Matrix[2][0]=-G_Dt*Omega_Vector[1];//-y
  Update_Matrix[2][1]=G_Dt*Omega_Vector[0];//x
  Update_Matrix[2][2]=0;

  Matrix_Multiply(DCM_Matrix,Update_Matrix,Temporary_Matrix); //a*b=c

  for(int x=0; x<3; x++) //Matrix Addition (update)
  {
    for(int y=0; y<3; y++)
    {
      DCM_Matrix[x][y]+=Temporary_Matrix[x][y];
    } 
  }
}

/**************************************************/
void Euler_angles(void)
{
  pitch = -asin(DCM_Matrix[2][0]);
  roll = atan2(DCM_Matrix[2][1],DCM_Matrix[2][2]);
  yaw = atan2(DCM_Matrix[1][0],DCM_Matrix[0][0]);
}

