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记录一段卡尔曼滤波代码

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steelen 发表于 2020-6-24 11:39:09 | 显示全部楼层 |阅读模式
————————————————————kalman_filter.h————————————————————
/*
* FileName : kalman_filter.h
* Author   : xiahouzuoxin @163.com
* Version  : v1.0
* Date     : 2014/9/24 20:37:01
* Brief    :
*
* Copyright (C) MICL,USTB
*/
#ifndef  _KALMAN_FILTER_H
#define  _KALMAN_FILTER_H

/*
* NOTES: n Dimension means the state is n dimension,
* measurement always 1 dimension
*/

/* 1 Dimension */
typedef struct {
    float x;  /* state */
    float A;  /* x(n)=A*x(n-1)+u(n),u(n)~N(0,q) */
    float H;  /* z(n)=H*x(n)+w(n),w(n)~N(0,r)   */
    float q;  /* process(predict) noise convariance */
    float r;  /* measure noise convariance */
    float p;  /* estimated error convariance */
    float gain;
} kalman1_state;

/* 2 Dimension */
typedef struct {
    float x[2];     /* state: [0]-angle [1]-diffrence of angle, 2x1 */
    float A[2][2];  /* X(n)=A*X(n-1)+U(n),U(n)~N(0,q), 2x2 */
    float H[2];     /* Z(n)=H*X(n)+W(n),W(n)~N(0,r), 1x2   */
    float q[2];     /* process(predict) noise convariance,2x1 [q0,0; 0,q1] */
    float r;        /* measure noise convariance */
    float p[2][2];  /* estimated error convariance,2x2 [p0 p1; p2 p3] */
    float gain[2];  /* 2x1 */
} kalman2_state;                  

extern void kalman1_init(kalman1_state *state, float init_x, float init_p);
extern float kalman1_filter(kalman1_state *state, float z_measure);
extern void kalman2_init(kalman2_state *state, float *init_x, float (*init_p)[2]);
extern float kalman2_filter(kalman2_state *state, float z_measure);

#endif  /*_KALMAN_FILTER_H*/
————————————————————kalman_filter.c————————————————————
/*
* FileName : kalman_filter.c
* Author   : xiahouzuoxin @163.com
* Version  : v1.0
* Date     : 2014/9/24 20:36:51
* Brief    :
*
* Copyright (C) MICL,USTB
*/

#include "kalman_filter.h"

/*
* @brief   
*   Init fields of structure @kalman1_state.
*   I make some defaults in this init function:
*     A = 1;
*     H = 1;
*   and @q,@r are valued after prior tests.
*
*   NOTES: Please change A,H,q,r according to your application.
*
* @inputs  
*   state - Klaman filter structure
*   init_x - initial x state value   
*   init_p - initial estimated error convariance
* @outputs
* @retval  
*/
void kalman1_init(kalman1_state *state, float init_x, float init_p)
{
    state->x = init_x;
    state->p = init_p;
    state->A = 1;
    state->H = 1;
    state->q = 2e2;//10e-6;  /* predict noise convariance */
    state->r = 5e2;//10e-5;  /* measure error convariance */
}

/*
* @brief   
*   1 Dimension Kalman filter
* @inputs  
*   state - Klaman filter structure
*   z_measure - Measure value
* @outputs
* @retval  
*   Estimated result
*/
float kalman1_filter(kalman1_state *state, float z_measure)
{
    /* Predict */
    state->x = state->A * state->x;
    state->p = state->A * state->A * state->p + state->q;  /* p(n|n-1)=A^2*p(n-1|n-1)+q */

    /* Measurement */
    state->gain = state->p * state->H / (state->p * state->H * state->H + state->r);
    state->x = state->x + state->gain * (z_measure - state->H * state->x);
    state->p = (1 - state->gain * state->H) * state->p;

    return state->x;
}

/*
* @brief   
*   Init fields of structure @kalman1_state.
*   I make some defaults in this init function:
*     A = {{1, 0.1}, {0, 1}};
*     H = {1,0};
*   and @q,@r are valued after prior tests.
*
*   NOTES: Please change A,H,q,r according to your application.
*
* @inputs  
* @outputs
* @retval  
*/
void kalman2_init(kalman2_state *state, float *init_x, float (*init_p)[2])
{
    state->x[0]    = init_x[0];
    state->x[1]    = init_x[1];
    state->p[0][0] = init_p[0][0];
    state->p[0][1] = init_p[0][1];
    state->p[1][0] = init_p[1][0];
    state->p[1][1] = init_p[1][1];
    //state->A       = {{1, 0.1}, {0, 1}};
    state->A[0][0] = 1;
    state->A[0][1] = 0.1;
    state->A[1][0] = 0;
    state->A[1][1] = 1;
    //state->H       = {1,0};
    state->H[0]    = 1;
    state->H[1]    = 0;
    //state->q       = {{10e-6,0}, {0,10e-6}};  /* measure noise convariance */
    state->q[0]    = 10e-7;
    state->q[1]    = 10e-7;
    state->r       = 10e-7;  /* estimated error convariance */
}

/*
* @brief   
*   2 Dimension kalman filter
* @inputs  
*   state - Klaman filter structure
*   z_measure - Measure value
* @outputs
*   state->x[0] - Updated state value, Such as angle,velocity
*   state->x[1] - Updated state value, Such as diffrence angle, acceleration
*   state->p    - Updated estimated error convatiance matrix
* @retval  
*   Return value is equals to state->x[0], so maybe angle or velocity.
*/
float kalman2_filter(kalman2_state *state, float z_measure)
{
    float temp0 = 0.0f;
    float temp1 = 0.0f;
    float temp = 0.0f;

    /* Step1: Predict */
    state->x[0] = state->A[0][0] * state->x[0] + state->A[0][1] * state->x[1];
    state->x[1] = state->A[1][0] * state->x[0] + state->A[1][1] * state->x[1];
    /* p(n|n-1)=A^2*p(n-1|n-1)+q */
    state->p[0][0] = state->A[0][0] * state->p[0][0] + state->A[0][1] * state->p[1][0] + state->q[0];
    state->p[0][1] = state->A[0][0] * state->p[0][1] + state->A[1][1] * state->p[1][1];
    state->p[1][0] = state->A[1][0] * state->p[0][0] + state->A[0][1] * state->p[1][0];
    state->p[1][1] = state->A[1][0] * state->p[0][1] + state->A[1][1] * state->p[1][1] + state->q[1];

    /* Step2: Measurement */
    /* gain = p * H^T * [r + H * p * H^T]^(-1), H^T means transpose. */
    temp0 = state->p[0][0] * state->H[0] + state->p[0][1] * state->H[1];
    temp1 = state->p[1][0] * state->H[0] + state->p[1][1] * state->H[1];
    temp  = state->r + state->H[0] * temp0 + state->H[1] * temp1;
    state->gain[0] = temp0 / temp;
    state->gain[1] = temp1 / temp;
    /* x(n|n) = x(n|n-1) + gain(n) * [z_measure - H(n)*x(n|n-1)]*/
    temp = state->H[0] * state->x[0] + state->H[1] * state->x[1];
    state->x[0] = state->x[0] + state->gain[0] * (z_measure - temp);
    state->x[1] = state->x[1] + state->gain[1] * (z_measure - temp);

    /* Update @p: p(n|n) = [I - gain * H] * p(n|n-1) */
    state->p[0][0] = (1 - state->gain[0] * state->H[0]) * state->p[0][0];
    state->p[0][1] = (1 - state->gain[0] * state->H[1]) * state->p[0][1];
    state->p[1][0] = (1 - state->gain[1] * state->H[0]) * state->p[1][0];
    state->p[1][1] = (1 - state->gain[1] * state->H[1]) * state->p[1][1];

    return state->x[0];
}

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