基于9轴惯性运动传感器的三阶卡尔曼滤波器算法

基于9轴惯性运动传感器的三阶卡尔曼滤波器算法

最近在玩九轴的惯性传感器，很是有挑战性.九轴说的是三轴的加速度计、三轴的陀螺仪以及三轴的磁场传感器。但是只是单纯的测出九个轴的数据没什么用，关键是要能够融合这九轴数据得出我们想要的结果。这里就运用三阶卡尔曼滤波算法来融合这九轴运动数据为三轴的角度。运用这三个角度可以用来做自平衡车或者四轴飞行器.

个人原创，版权所有，转载请注明原文出处，并保留原文链接:

https://www.embbnux.com/2015/01/30/9_dof_imu_with_kalman_filter_on_avr/

参考: kalman wikipedia    KalmanFilteredIMU

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，具体意思可以看上面的wikipedia链接

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.c
float 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[m*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 + uk
matrix_add(xk,gyro_angle_mat,xk);
//pk = pk + Q
matrix_add(pk,Q,pk);
//yk =  xnew - xk
matrix_sub(am_angle_mat,xk,yk);
//S=Pk + R
matrix_add(pk,R,S);
//S求逆invert
sdet = 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_invert
matrix_multi(pk,S_invert,K);
//KxYk = K * Yk
matrix_multi(K,yk,KxYk);
//xk = xk + K * yk
matrix_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};
//8MS
ISR(TIMER0_OVF_vect){
//设置计数开始的初始值
TCNT0 = 130 ;  //8ms
sei();
//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]
}

实测可以准确的输出三轴的角度，为了获得更好的响应速度和跟踪精度还需调整参数.