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//==================================================
//Atitude estimation (kalman filter)
//MPU board: mbed LPC1768
//Accelerometer +Gyro sensor : GY-521
//
//Matrix functions were derived from トランジスタ技術2019年7月号
//
//2019/12/30 A.Toda
//==================================================
#include "mbed.h"
#include "MPU6050.h"

//==================================================
#define RAD_TO_DEG          57.2957795f             // 180 / π
#define MAX_MEAN_COUNTER 100
#define ACC_X 1.3//offset of x-axi accelerometer  
#define FRQ 100//Hz
//==================================================

DigitalOut led1(LED1);

//Timer interrupt
Ticker flipper;

//Port Setting
MPU6050 mpu(p9, p10);  //Accelerometer + Gyro
                        //(SDA,SCLK)

Serial pc(USBTX, USBRX);    //UART

//==================================================
//Accelerometer and gyro data
//==================================================

double acc[3]; //variables for accelerometer
double gyro[3]; //variables for gyro

double offset_gyro_x=0.0;
double offset_gyro_y=0.0;

double sum_gyro_x=0.0;
double sum_gyro_y=0.0;

//==================================================
//Atitude data
//==================================================
double roll_and_pitch_acc[2][1];//atitude from accelerometer
double roll_and_pitch[2][1];    //atitude from gyro and accelerometer

double threshold_acc,threshold_acc_ini;

//==================================================
//Matrix definition
//==================================================
double MAT_A[2][2];
double inv_MAT_A[2][2];

double MAT_B[2][2];
double inv_MAT_B[2][2];

double MAT_C[2][2];
double inv_MAT_C[2][2];

double MAT_X_k[2][1];
double pre_MAT_X_k[2][1];

double COV_P[2][2];//covariance matrix of atitude angles
double pre_COV_P[2][2];//covariance matrix of atitude angles
double pre_COV_P_2[2][2];//covariance matrix of atitude angles
double pre_COV_P_3[2][2];//covariance matrix of atitude angles

double COV_Q[2][2];//covariance matrix of gyro inputs
double COV_R[2][2];//covariance matrix of atitude angles from accelerometer

//=========================================================
// Matrix common functions
//=========================================================
//Matrix addition
void mat_add(double *m1, double *m2, double *sol, int row, int column)
{
    for(int i=0; i<row; i++)
    {
        for(int j=0; j<column; j++)
        {
            sol[i*column + j] = m1[i*column + j] + m2[i*column + j];    
        }    
    }
    return;
}

//Matrix subtraction
void mat_sub(double *m1, double *m2, double *sol, int row, int column)
{
    for(int i=0; i<row; i++)
    {
        for(int j=0; j<column; j++)
        {
            sol[i*column + j] = m1[i*column + j] - m2[i*column + j];    
        }    
    }
    return;
}

//Matrix multiplication
void mat_mul(double *m1, double *m2, double *sol, int row1, int column1, int row2, int column2)
{
    for(int i=0; i<row1; i++)
    {
        for(int j=0; j<column2; j++)
        {
            sol[i*column2 + j] = 0;
            for(int k=0; k<column1; k++)
            {
                sol[i*column2 + j] += m1[i*column1 + k]*m2[k*column2 + j];    
            }
        }    
    }
    return;
}

//Matrix transposition
void mat_tran(double *m1, double *sol, int row_original, int column_original)
{
    for(int i=0; i<row_original; i++)
    {
        for(int j=0; j<column_original; j++)
        {
            sol[j*row_original + i] = m1[i*column_original + j];    
        }    
    }
    return;
}

//Matrix scalar maltiplication
void mat_mul_const(double *m1,double c, double *sol, int row, int column)
{
    for(int i=0; i<row; i++)
    {
        for(int j=0; j<column; j++)
        {
            sol[i*column + j] = c * m1[i*column + j];    
        }    
    }
    return;
}

//Matrix inversion (by Gaussian elimination)
void mat_inv(double *m, double *sol, int column, int row)
{
    //allocate memory for a temporary matrix
    double* temp = (double *)malloc( column*2*row*sizeof(double) );
    
    //make the augmented matrix
    for(int i=0; i<column; i++)
    {
        //copy original matrix
        for(int j=0; j<row; j++)
        {
            temp[i*(2*row) + j] = m[i*row + j];  
        }
        
        //make identity matrix
        for(int j=row; j<row*2; j++)
        {
            if(j-row == i)
            {
                temp[i*(2*row) + j] = 1;
            }    
            else
            {
                temp[i*(2*row) + j] = 0;    
            }
        }
    }

    //Sweep (down)
    for(int i=0; i<column; i++)
    {
        //pivot selection
        double pivot = temp[i*(2*row) + i];
        int pivot_index = i;
        double pivot_temp;
        for(int j=i; j<column;j++)
        {
            if( temp[j*(2*row)+i] > pivot )
            {
                pivot = temp[j*(2*row) + i];
                pivot_index = j;
            }    
        }  
        if(pivot_index != i)
        {
            for(int j=0; j<2*row; j++)
            {
                pivot_temp = temp[ pivot_index * (2*row) + j ];
                temp[pivot_index * (2*row) + j] = temp[i*(2*row) + j];
                temp[i*(2*row) + j] = pivot_temp;    
            }    
        }
        
        //division
        for(int j=0; j<2*row; j++)
        {
            temp[i*(2*row) + j] /= pivot;    
        }
        
        //sweep
        for(int j=i+1; j<column; j++)
        {
            double temp2 = temp[j*(2*row) + i];
            
            //sweep each row
            for(int k=0; k<row*2; k++)
            {
                temp[j*(2*row) + k] -= temp2 * temp[ i*(2*row) + k ];    
            }    
        }
    }
        
    //Sweep (up)
    for(int i=0; i<column-1; i++)
    {
        for(int j=i+1; j<column; j++)
        {
            double pivot = temp[ (column-1-j)*(2*row) + (row-1-i)];   
            for(int k=0; k<2*row; k++)
            {
                temp[(column-1-j)*(2*row)+k] -= pivot * temp[(column-1-i)*(2*row)+k];    
            }
        }    
    }     
    
    //copy result
    for(int i=0; i<column; i++)
    {
        for(int j=0; j<row; j++)
        {
            sol[i*row + j] = temp[i*(2*row) + (j+row)];    
        }    
    }
    free(temp);
    return;
}

//==================================================
//Gyro and accelerometer functions
//==================================================
//get data
void  aquisition_sensor_values(double *a,double *g){
    
    float ac[3],gy[3];
    
    mpu.getAccelero(ac);//get acceleration (Accelerometer)
                                //x_axis acc[0]
                                //y_axis acc[1]
                                //z_axis acc[2]
    mpu.getGyro(gy);   //get rate of angle(Gyro)
                      //x_axis gyro[0]
                      //y_axis gyro[1]
                      //z_axis gyro[2]
        
    //Invertion for direction of Accelerometer axis
    ac[0]*=(-1.0);
    ac[0]+=ACC_X;
    
    ac[2]*=(-1.0);
        
    //Unit convertion of rate of angle(radian to degree)
    gy[0]*=RAD_TO_DEG;
    gy[0]*=(-1.0);
        
    gy[1]*=RAD_TO_DEG;        
        
    gy[2]*=RAD_TO_DEG;
    gy[2]*=(-1.0);
  
    for(int i=0;i<3;i++){
        a[i]=double(ac[i]);
        g[i]=double(gy[i]);
        }
    g[0]-=offset_gyro_x;//offset rejection
    g[1]-=offset_gyro_y;//offset rejection
    
    return;
    
}

//calculate offset of gyro
void offset_calculation_for_gyro(){
    
    //Accelerometer and gyro setting 
    mpu.setAcceleroRange(0);//acceleration range is +-2G
    mpu.setGyroRange(1);//gyro rate is +-500degree per second(dps)
    
    //calculate offset of gyro
    for(int mean_counter=0; mean_counter<MAX_MEAN_COUNTER ;mean_counter++){
        aquisition_sensor_values(acc,gyro);
        sum_gyro_x+=gyro[0];
        sum_gyro_y+=gyro[1];
        wait(0.01);
        }
    
    offset_gyro_x=sum_gyro_x/MAX_MEAN_COUNTER;
    offset_gyro_y=sum_gyro_y/MAX_MEAN_COUNTER;
    
    return;
}

//atitude calculation from acceleromter
void atitude_estimation_from_accelerometer(double *a,double *roll_and_pitch){
    
    //roll_and_pitch[0] = atan2(a[1], a[2])*RAD_TO_DEG;//roll
    roll_and_pitch[0] = atan(a[1]/a[2])*RAD_TO_DEG;//roll
    //roll_and_pitch[1] = atan(a[0]/sqrt( a[1]*a[1]+a[2]*a[2] ) )*RAD_TO_DEG;//pitch
    roll_and_pitch[1] = atan2(a[0],sqrt( a[1]*a[1]+a[2]*a[2] ) )*RAD_TO_DEG;//pitch
            
    return;
}

//atitude calculation
void atitude_update(){
    
    
    aquisition_sensor_values(acc,gyro);//加速度、ジャイロの取得
    
    //入力の設定
    double MAT_IN[2][1]={};
    double pre_MAT_IN[2][1]={};
    
    MAT_IN[0][0]=gyro[0];
    MAT_IN[1][0]=gyro[1];
    
    /*--------------------Time update phase 時間更新フェーズ--------------------*/
    //A*x+B*u
    
    mat_mul(MAT_A[0], MAT_X_k[0],pre_MAT_X_k[0] ,2, 2, 2, 1);
    mat_mul(MAT_B[0], MAT_IN[0],pre_MAT_IN[0] ,2, 2, 2, 1);
    
    mat_add(pre_MAT_X_k[0],pre_MAT_IN[0], pre_MAT_X_k[0], 2, 1);
    
    //A*P*A^T+B*P*B^T
    double pre_COV_P_1[2][2]={};
    double pre_COV_P_1_2[2][2]={};
    
    double pre_COV_P_2[2][2]={};
    double pre_COV_P_2_2[2][2]={};
    
    mat_mul(MAT_A[0], COV_P[0],pre_COV_P_1[0] ,2, 2, 2, 2);
    mat_mul(pre_COV_P_1[0], inv_MAT_A[0] , pre_COV_P_1_2[0] ,2, 2, 2, 2);
    
    
    mat_mul(MAT_B[0], COV_Q[0],pre_COV_P_2[0] ,2, 2, 2, 2);
    mat_mul(pre_COV_P_2[0], inv_MAT_B[0] , pre_COV_P_2_2[0] ,2, 2, 2, 2);
    
    mat_add(pre_COV_P_1_2[0],pre_COV_P_2_2[0], pre_COV_P[0], 2, 2);
    
    //pc.printf("1;Roll=%f,Pitch=%f\r\n",pre_COV_P[0][0],pre_COV_P[1][1]);
    /*------------------------------------------------------------------------*/
    
    /*--------------------Measurement update phase 観測更新フェーズ--------------------*/  
      
    threshold_acc=sqrt(acc[0]*acc[0]+acc[1]*acc[1]+acc[2]*acc[2]);
    
    //加速度のノルムが9.8m/s^2付近かどうかの判定
    if((threshold_acc>=0.95*threshold_acc_ini)&&(threshold_acc<=1.05*threshold_acc_ini)){
              
              //pc.printf("corrected\r\n");
              led1=0;
              
              double GAIN_K[2][2]={};
              double pre_GAIN_K_1[2][2]={};
              double pre_GAIN_K_1_2[2][2]={};
              double pre_GAIN_K_1_3[2][2]={};
              double pre_GAIN_K_1_4[2][2]={};
              
              double pre_GAIN_K_2[2][2]={};
              
              //K=P*C^T*(C*P*C^T+R)^-1
              //(C*P*C^T+R)^-1
              mat_mul(MAT_C[0], pre_COV_P[0] , pre_GAIN_K_1[0] ,2, 2, 2, 2);
              mat_mul(pre_GAIN_K_1[0], inv_MAT_C[0] , pre_GAIN_K_1_2[0] ,2, 2, 2, 2);
              
              mat_add(pre_GAIN_K_1_2[0],COV_R[0], pre_GAIN_K_1_3[0], 2, 2);
              
              mat_inv(pre_GAIN_K_1_3[0], pre_GAIN_K_1_4[0], 2, 2);
              
              //P*C^T
              mat_mul(pre_COV_P[0], inv_MAT_C[0] , pre_GAIN_K_2[0] ,2, 2, 2, 2);
              
              //P*C^T*(C*P*C^T+R)^-1
              mat_mul(pre_GAIN_K_2[0], pre_GAIN_K_1_4[0] , GAIN_K[0] ,2, 2, 2, 2);
              
              double pre_MAT_X_k_2[2][1]={};
              double pre_MAT_X_k_2_2[2][1]={};
              
              //X=X+K(y-C*X)
              
              atitude_estimation_from_accelerometer(acc,roll_and_pitch_acc[0]);
              mat_sub(roll_and_pitch_acc[0], pre_MAT_X_k[0], pre_MAT_X_k_2[0], 2, 1);
              
              mat_mul(GAIN_K[0], pre_MAT_X_k_2[0] ,pre_MAT_X_k_2_2[0] ,2, 2, 2, 1);
              
              mat_add(pre_MAT_X_k[0], pre_MAT_X_k_2_2[0], MAT_X_k[0], 2, 1);
              
              //P=(I-K*C)*P
              double MAT_UNIT[2][2]={};
              /*initialize Unit matrix*/
              MAT_UNIT[0][0]=1.0;
              MAT_UNIT[0][1]=0.0;
              MAT_UNIT[1][0]=0.0;
              MAT_UNIT[1][1]=1.0;
              /*----------------------*/
              
              mat_sub(MAT_UNIT[0], GAIN_K[0], pre_COV_P_3[0], 2, 2);
              mat_mul(pre_COV_P_3[0], pre_COV_P[0], COV_P[0], 2, 2, 2, 2);
              
              
        }else{
            //pc.printf("Not corrected\r\n");
            led1=1;
            
            MAT_X_k[0][0]=pre_MAT_X_k[0][0];
            MAT_X_k[1][0]=pre_MAT_X_k[1][0];
            
            COV_P[0][0]=pre_COV_P[0][0];
            COV_P[1][1]=pre_COV_P[1][1];
            
            }
    
    pc.printf("%f,%f,Roll=%f,Pitch=%f\r\n",threshold_acc,threshold_acc_ini,MAT_X_k[0][0],MAT_X_k[1][0]);
    //pc.printf("2;Roll=%f,Pitch=%f\r\n",COV_P[0][0],COV_P[1][1]);
    
    /*--------------------------------------------------------------------*/
        
    return;

}


//==================================================
//Main
//==================================================
int main() {
    
    //UART initialization
    pc.baud(115200);
    
    //gyro and accelerometer initialization
    offset_calculation_for_gyro();
    
    //identify initilal atitude
    aquisition_sensor_values(acc,gyro);
    atitude_estimation_from_accelerometer(acc,MAT_X_k[0]);
    
    threshold_acc_ini=sqrt(acc[0]*acc[0]+acc[1]*acc[1]+acc[2]*acc[2]);
    
    /*Initialize MAT_A*/
    MAT_A[0][0]=1.0;
    MAT_A[0][1]=0.0;
    MAT_A[1][0]=0.0;
    MAT_A[1][1]=1.0;
    
    mat_tran(MAT_A[0], inv_MAT_A[0], 2, 2);
    /*----------------*/

    /*Initialize MAT_B*/
    MAT_B[0][0]=1.0/FRQ;
    MAT_B[0][1]=0.0;
    MAT_B[1][0]=0.0;
    MAT_B[1][1]=1.0/FRQ;
    
    mat_tran(MAT_B[0], inv_MAT_B[0], 2, 2);
    /*----------------*/

    /*Initialize MAT_C*/
    MAT_C[0][0]=1.0;
    MAT_C[0][1]=0.0;
    MAT_C[1][0]=0.0;
    MAT_C[1][1]=1.0;

    mat_tran(MAT_C[0], inv_MAT_C[0], 2, 2);
    /*----------------*/
    
    /*
    これら共分散の値は仮の値である。
    */
    /*Initialize COV_P*/
    COV_P[0][0]=1.0;
    COV_P[0][1]=0.0;
    COV_P[1][0]=0.0;
    COV_P[1][1]=1.0;
    /*----------------*/
    
    /*Initialize COV_Q*/
    COV_Q[0][0]=0.01;
    COV_Q[0][1]=0.0;
    COV_Q[1][0]=0.0;
    COV_Q[1][1]=0.01;
    /*----------------*/
    
    /*Initialize COV_R*/
    COV_R[0][0]=0.001;
    COV_R[0][1]=0.0;
    COV_R[1][0]=0.0;
    COV_R[1][1]=0.001;
    /*----------------*/
    
    pc.printf("Roll=%f,Pitch=%f\r\n",COV_P[0][0],COV_P[1][1]);
    
    //Ticker
    flipper.attach(&atitude_update, 0.01);
    
    while(1) {
        wait(0.01);
        
    }
}