本帖最后由 真爱有你 于 2020-6-24 18:40 编辑
转自：https://blog.csdn.net/baidu_31872269/article/details/71426301?utm_source=blogxgwz3
—————————————————————————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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