卡尔曼滤波简介算法实现代码

1、卡尔曼滤波简介 算法实现代码 程序匠人 发表于 2009-2-27 15:16:00 阅读全文(2640) | 回复(2) | 引用通告(0) | 编辑 卡尔曼滤波简介 算法实现代码 Posted on 2007-01-13 17:00 Jason.Jiang 阅读(10822) 评论(6) 编辑 收藏 网摘 所属分类: 信号处理 最佳线性滤波理论起源于40年代美国科学家Wiener和前苏联科学家等人的研究工作，后人统称为维纳滤波理论。从理论上说，维纳滤波的最大缺点是必须用到无限过去的数据，不适用于实时处理。为了克服这一缺点，60年代Kalman把状态空间模型引入滤波理论，并导出了一套递推估计

2、算法，后人称之为卡尔曼滤波理论。卡尔曼滤波是以最小均方误差为估计的最佳准则，来寻求一套递推估计的算法，其基本思想是：采用信号与噪声的状态空间模型，利用前一时刻地估计值和现时刻的观测值来更新对状态变量的估计，求出现时刻的估计值。它适合于实时处理和计算机运算。 现设线性时变系统的离散状态防城和观测方程为： X(k) = F(k,k-1)·X(k-1)+T(k,k-1)·U(k-1) Y(k) = H(k)·X(k)+N(k) 其中 X(k)和Y(k)分别是k时刻的状态矢量和观测矢量 F(k,k-1)为状态转移矩阵 U(k)为k时刻动态噪声 T(k,k-1)为系统控制矩

3、阵 H(k)为k时刻观测矩阵 N(k)为k时刻观测噪声 则卡尔曼滤波的算法流程为： 预估计X(k)= F(k,k-1)·X(k-1) 计算预估计协方差矩阵C(k)=F(k,k-1)×C(k)×F(k,k-1)'+T(k,k-1)×Q(k)×T(k,k-1)'Q(k) = U(k)×U(k)' 计算卡尔曼增益矩阵K(k) = C(k)×H(k)'×H(k)×C(k)×H(k)'+R(k)(-1)R(k) = N(k)×N(k)' 更新估计X

4、(k)=X(k)+K(k)×Y(k)-H(k)×X(k) 计算更新后估计协防差矩阵C(k) = I-K(k)×H(k)×C(k)×I-K(k)×H(k)'+K(k)×R(k)×K(k)' X(k+1) = X(k)C(k+1) = C(k)重复以上步骤 其c语言实现代码如下：i nclude "stdlib.h" i nclude "rinv.c" int lman(n,m,k,f,q,r,h,y,x,p,g) int n,m,k; double f,q,r,

5、h,y,x,p,g; int i,j,kk,ii,l,jj,js; double *e,*a,*b; e=malloc(m*m*sizeof(double); l=m; if (l<n) l=n; a=malloc(l*l*sizeof(double); b=malloc(l*l*sizeof(double); for (i=0; i<=n-1; i+) for (j=0; j<=n-1; j+) ii=i*l+j; aii=0.0; for (kk=0; kk<=n-1; kk+) aii=aii+pi*n+kk*fj*n+kk; for (i=0; i<=n-

6、1; i+) for (j=0; j<=n-1; j+) ii=i*n+j; pii=qii; for (kk=0; kk<=n-1; kk+) pii=pii+fi*n+kk*akk*l+j; for (ii=2; ii<=k; ii+) for (i=0; i<=n-1; i+) for (j=0; j<=m-1; j+) jj=i*l+j; ajj=0.0; for (kk=0; kk<=n-1; kk+) ajj=ajj+pi*n+kk*hj*n+kk; for (i=0; i<=m-1; i+) for (j=0; j<=m-1; j+

7、) jj=i*m+j; ejj=rjj; for (kk=0; kk<=n-1; kk+) ejj=ejj+hi*n+kk*akk*l+j; js=rinv(e,m); if (js=0) free(e); free(a); free(b); return(js); for (i=0; i<=n-1; i+) for (j=0; j<=m-1; j+) jj=i*m+j; gjj=0.0; for (kk=0; kk<=m-1; kk+) gjj=gjj+ai*l+kk*ej*m+kk; for (i=0; i<=n-1; i+) jj=(ii-1)*n+i; x

8、jj=0.0; for (j=0; j<=n-1; j+) xjj=xjj+fi*n+j*x(ii-2)*n+j; for (i=0; i<=m-1; i+) jj=i*l; bjj=y(ii-1)*m+i; for (j=0; j<=n-1; j+) bjj=bjj-hi*n+j*x(ii-1)*n+j; for (i=0; i<=n-1; i+) jj=(ii-1)*n+i; for (j=0; j<=m-1; j+) xjj=xjj+gi*m+j*bj*l; if (ii<k) for (i=0; i<=n-1; i+) for (j=0; j&

9、lt;=n-1; j+) jj=i*l+j; ajj=0.0; for (kk=0; kk<=m-1; kk+) ajj=ajj-gi*m+kk*hkk*n+j; if (i=j) ajj=1.0+ajj; for (i=0; i<=n-1; i+) for (j=0; j<=n-1; j+) jj=i*l+j; bjj=0.0; for (kk=0; kk<=n-1; kk+) bjj=bjj+ai*l+kk*pkk*n+j; for (i=0; i<=n-1; i+) for (j=0; j<=n-1; j+) jj=i*l+j; ajj=0.0; fo

10、r (kk=0; kk<=n-1; kk+) ajj=ajj+bi*l+kk*fj*n+kk; for (i=0; i<=n-1; i+) for (j=0; j<=n-1; j+) jj=i*n+j; pjj=qjj; for (kk=0; kk<=n-1; kk+) pjj=pjj+fi*n+kk*aj*l+kk; free(e); free(a); free(b); return(js); C+实现代码如下：=kalman.h=/ kalman.h: interface for the kalman class./#if !defined(AFX_KALMAN_H

11、_ED3D740F_01D2_4616_8B74_8BF57636F2C0_INCLUDED_)#define AFX_KALMAN_H_ED3D740F_01D2_4616_8B74_8BF57636F2C0_INCLUDED_#if _MSC_VER > 1000#pragma once#endif / _MSC_VER > 1000i nclude <math.h>i nclude "cv.h" class kalman public: void init_kalman(int x,int xv,int y,int yv); CvKalman*

12、 cvkalman; CvMat* state; CvMat* process_noise; CvMat* measurement; const CvMat* prediction; CvPoint2D32f get_predict(float x, float y); kalman(int x=0,int xv=0,int y=0,int yv=0); /virtual kalman();#endif / !defined(AFX_KALMAN_H_ED3D740F_01D2_4616_8B74_8BF57636F2C0_INCLUDED_)=kalman.cpp=i nclude &quo

13、t;kalman.h"i nclude <stdio.h>/* tester de printer toutes les valeurs des vecteurs*/* tester de changer les matrices du noises */* replace state by cvkalman->state_post ? */CvRandState rng;const double T = 0.1;kalman:kalman(int x,int xv,int y,int yv) cvkalman = cvCreateKalman( 4, 4, 0 )

14、; state = cvCreateMat( 4, 1, CV_32FC1 ); process_noise = cvCreateMat( 4, 1, CV_32FC1 ); measurement = cvCreateMat( 4, 1, CV_32FC1 ); int code = -1; /* create matrix data */ const float A = 1, T, 0, 0, 0, 1, 0, 0, 0, 0, 1, T, 0, 0, 0, 1 ; const float H = 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0

15、 ; const float P = pow(320,2), pow(320,2)/T, 0, 0, pow(320,2)/T, pow(320,2)/pow(T,2), 0, 0, 0, 0, pow(240,2), pow(240,2)/T, 0, 0, pow(240,2)/T, pow(240,2)/pow(T,2) ; const float Q = pow(T,3)/3, pow(T,2)/2, 0, 0, pow(T,2)/2, T, 0, 0, 0, 0, pow(T,3)/3, pow(T,2)/2, 0, 0, pow(T,2)/2, T ; const float R =

16、 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ; cvRandInit( &rng, 0, 1, -1, CV_RAND_UNI ); cvZero( measurement ); cvRandSetRange( &rng, 0, 0.1, 0 ); rng.disttype = CV_RAND_NORMAL; cvRand( &rng, state ); memcpy( cvkalman->transition_matrix->data.fl, A, sizeof(A); memcpy( cvkalman-

17、>measurement_matrix->data.fl, H, sizeof(H); memcpy( cvkalman->process_noise_cov->data.fl, Q, sizeof(Q); memcpy( cvkalman->error_cov_post->data.fl, P, sizeof(P); memcpy( cvkalman->measurement_noise_cov->data.fl, R, sizeof(R); /cvSetIdentity( cvkalman->process_noise_cov, cvR

18、ealScalar(1e-5) ); /cvSetIdentity( cvkalman->error_cov_post, cvRealScalar(1); /cvSetIdentity( cvkalman->measurement_noise_cov, cvRealScalar(1e-1) ); /* choose initial state */ state->data.fl0=x; state->data.fl1=xv; state->data.fl2=y; state->data.fl3=yv; cvkalman->state_post->

19、data.fl0=x; cvkalman->state_post->data.fl1=xv; cvkalman->state_post->data.fl2=y; cvkalman->state_post->data.fl3=yv; cvRandSetRange( &rng, 0, sqrt(cvkalman->process_noise_cov->data.fl0), 0 ); cvRand( &rng, process_noise ); CvPoint2D32f kalman:get_predict(float x, float

20、 y) /* update state with current position */ state->data.fl0=x; state->data.fl2=y; /* predict point position */ /* x'k=A鈥k+B鈥k P'k=A鈥k-1*AT + Q */ cvRandSetRange( &rng, 0, sqrt(cvkalman->measurement_noise_cov->data.fl0), 0 ); cvRand( &rng, measurement ); /* xk=A?xk-1+B?uk+wk */ cvMatMulAdd( cvkalman->transition_matrix, state, process_noise, cvkalman->state_post ); /* zk=H?xk+vk */ cvMatMulAdd( cvkalman->measurement_matrix, cvkalman->state_post, measurement, measurement ); /* adjust Kalman filter state */ /* Kk=P'k鈥T鈥?H鈥'k鈥T+R)-1 xk=x&#