卡尔曼滤波（2）

一、卡尔曼算法理解
其实如果不去考虑kalman算法是怎么来的，我们只需要知道有下面几个式子就可以了，具体意思可以看wikipedia

二　卡尔曼滤波算法的实现
这里我的算法是运行在avr单片机上的，所以采用的是c语言写的。下面的代码是要放到avr的定时器中断测试刷新的。用示波器测试了一下,这个算法在16M晶振下的运行时间需要0.35ms,而数据采集需要3ms左右,所以选定定时器时间为8ms.之前也写过一阶的kalman算法，运用在自平衡车上，这边是三阶的，主要是矩阵运算.

//kalman.cfloat dtTimer   = 0.008;float xk[9] = {0,0,0,0,0,0,0,0,0};float pk[9] = {1,0,0,0,1,0,0,0,0};float I[9]  = {1,0,0,0,1,0,0,0,1};float R[9]  = {0.5,0,0,0,0.5,0,0,0,0.01};float Q[9] = {0.005,0,0,0,0.005,0,0,0,0.001};void matrix_add(float* mata,float* matb,float* matc){    uint8_t i,j;    for (i=0; i<3; i++){       for (j=0; j<3; j++){          matc[i*3+j] = mata[i*3+j] + matb[i*3+j];       }    }}void matrix_sub(float* mata,float* matb,float* matc){    uint8_t i,j;    for (i=0; i<3; i++){       for (j=0; j<3; j++){          matc[i*3+j] = mata[i*3+j] - matb[i*3+j];       }    }}void matrix_multi(float* mata,float* matb,float* matc){  uint8_t i,j,m;  for (i=0; i<3; i++)  {    for (j=0; j<3; j++)   {      matc[i*3+j]=0.0;      for (m=0; m<3; m++)     {        matc[i*3+j] += mata[i*3+m] * matb[i*3+j];      }    } }}void KalmanFilter(float* am_angle_mat,float* gyro_angle_mat){uint8_t i,j;float yk[9];float pk_new[9];float K[9];float KxYk[9];float I_K[9];float S[9];float S_invert[9];float sdet;//xk = xk + ukmatrix_add(xk,gyro_angle_mat,xk);//pk = pk + Qmatrix_add(pk,Q,pk);//yk =  xnew - xkmatrix_sub(am_angle_mat,xk,yk);//S=Pk + Rmatrix_add(pk,R,S);//S求逆invertsdet = S[0] * S[4] * S[8]          + S[1] * S[5] * S[6]          + S[2] * S[3] * S[7]          - S[2] * S[4] * S[6]          - S[5] * S[7] * S[0]          - S[8] * S[1] * S[3];S_invert[0] = (S[4] * S[8] - S[5] * S[7])/sdet;S_invert[1] = (S[2] * S[7] - S[1] * S[8])/sdet;S_invert[2] = (S[1] * S[7] - S[4] * S[6])/sdet;S_invert[3] = (S[5] * S[6] - S[3] * S[8])/sdet;S_invert[4] = (S[0] * S[8] - S[2] * S[6])/sdet;S_invert[5] = (S[2] * S[3] - S[0] * S[5])/sdet;S_invert[6] = (S[3] * S[7] - S[4] * S[6])/sdet;S_invert[7] = (S[1] * S[6] - S[0] * S[7])/sdet;S_invert[8] = (S[0] * S[4] - S[1] * S[3])/sdet;//K = Pk * S_invertmatrix_multi(pk,S_invert,K);//KxYk = K * Ykmatrix_multi(K,yk,KxYk);//xk = xk + K * ykmatrix_add(xk,KxYk,xk);//pk = (I - K)*(pk)matrix_sub(I,K,I_K);matrix_multi(I_K,pk,pk_new);//update pk//pk = pk_new;for (i=0; i<3; i++){    for (j=0; j<3; j++){        pk[i*3+j] = pk_new[i*3+j];    }  }}

三　运用卡尔曼滤波器
这里的kalman滤波器是离散数字滤波器，需要迭代运算。这里把算法放到avr的定时器中断里面执行，进行递归运算.

//isr.c#include "kalman.h"float mpu_9dof_values[9]={0};float am_angle[3];float gyro_angle[3];float am_angle_mat[9]={0,0,0,0,0,0,0,0,0};float gyro_angle_mat[9]={0,0,0,0,0,0,0,0,0};//8MSISR(TIMER0_OVF_vect){//设置计数开始的初始值TCNT0 = 130 ;  //8mssei();//采集九轴数据//mpu_9dof_values 单位为g与度/s//加速度计和陀螺仪mpu_getValue6(&mpu_9dof_values[0],&mpu_9dof_values[1],&mpu_9dof_values[2],&mpu_9dof_values[3],&mpu_hmc_values[4],&mpu_hmc_values[5]);//磁场传感器compass_mgetValues(&mpu_9dof_values[6],&mpu_9dof_values[7],&mpu_9dof_values[8]);accel_compass2angle(&mpu_9dof_values[0],&mpu_9dof_values[6],am_angle);gyro2angle(&mpu_9dof_values[3],gyro_angle);am_angle_mat[0] = am_angle[0];am_angle_mat[4] = am_angle[1];am_angle_mat[8] = am_angle[2];gyro_angle_mat[0] = gyro_angle[1];gyro_angle_mat[4] = - gyro_angle[0];gyro_angle_mat[8] = - gyro_angle[2];//卡尔曼KalmanFilter(am_angle_mat,gyro_angle_mat);//输出三轴角度//xk[0] xk[4] xk[8]}