kalman filter 卡尔曼滤波的例子

因为在研究中使用了kalman 滤波，这是一个挺难理解的控制理论，我花了好长时间才了解一些基本的概念，opencv虽然提供了一个实例，但是这个例子基于c的，不容易看懂，也不好重用，后来我整理了一个简单的类来，期间在论坛上有一个handsome & romantic 的法国小伙也在研究这个滤波，后来我给了他程序，他修改后发给了我，所以这里的代码也有他的部分，算是中法合作产品 :)

对于kalman的初学者来讲，像我这样没什么数学功底的人，看教科书真是很累，说实在的，我觉得老外的基础理论的书都很评议近人，不像国内那些教授搞得那么悬虚，
初学者可以参考
http://bbs.matwav.com/index.jsp 研学论坛有几篇通俗易懂的中文解释
http://www.cs.unc.edu/~welch/kalman/ 这里是老外综合的kalman基地，很不错的。

代码示例:

============================kalman.h================================

// kalman.h: interface for the kalman class.
//
//////////////////////////////////////////////////////////////////////

#if !defined(AFX_KALMAN_H__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 > 1000

#include <math.h>
#include "cv.h"

class kalman
{
public:
void init_kalman(int x,int xv,int y,int yv);
CvKalman* 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================================

#include "kalman.h"
#include <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 );
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
};

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[] = {
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->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, cvRealScalar(1e-5) );
//cvSetIdentity( cvkalman->error_cov_post, cvRealScalar(1));
//cvSetIdentity( cvkalman->measurement_noise_cov, cvRealScalar(1e-1) );

/* choose initial state */

state->data.fl[0]=x;
state->data.fl[1]=xv;
state->data.fl[2]=y;
state->data.fl[3]=yv;
cvkalman->state_post->data.fl[0]=x;
cvkalman->state_post->data.fl[1]=xv;
cvkalman->state_post->data.fl[2]=y;
cvkalman->state_post->data.fl[3]=yv;

cvRandSetRange( &rng, 0, sqrt(cvkalman->process_noise_cov->data.fl[0]), 0 );
cvRand( &rng, process_noise );

}

CvPoint2D32f kalman::get_predict(float x, float y){

/* update state with current position */
state->data.fl[0]=x;
state->data.fl[2]=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.fl[0]), 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'k+Kk鈥?zk-H鈥'k)
Pk=(I-Kk鈥)鈥'k */
cvKalmanCorrect( cvkalman, measurement );
float measured_value_x = measurement->data.fl[0];
float measured_value_y = measurement->data.fl[2];

const CvMat* prediction = cvKalmanPredict( cvkalman, 0 );
float predict_value_x = prediction->data.fl[0];
float predict_value_y = prediction->data.fl[2];

return(cvPoint2D32f(predict_value_x,predict_value_y));
}

void kalman::init_kalman(int x,int xv,int y,int yv)
{
state->data.fl[0]=x;
state->data.fl[1]=xv;
state->data.fl[2]=y;
state->data.fl[3]=yv;
cvkalman->state_post->data.fl[0]=x;
cvkalman->state_post->data.fl[1]=xv;
cvkalman->state_post->data.fl[2]=y;
cvkalman->state_post->data.fl[3]=yv;
}

转载自：http://blog.csdn.net/hardVB/archive/2005/06/28/405582.aspx