先建立运动模型和观察模型，不是想用就能用的。如果不能建立运动模型，也就意味着你所要面对的问题不能用kalman滤波解决。
kalman.cpp这个例程来介绍一下如何在OpenCV中使用kalman滤波吧，OpenCV已经把Kalman滤波封装到一个类KalmanFilter中了。使用起来非常方便，但那繁多的各种矩阵还是容易让人摸不着头脑。这里要知道的一点是，想要用kalman滤波，要知道前一时刻的状态估计值x，当前的观测值y，还得建立状态方程和量测方程。有了这些就可以运用kalman滤波了。
OpenCV自带了例程里面是对一个1维点的运动跟踪，虽然这个点是在2维平面中运动，但由于它是在一个圆弧上运动，只有一个自由度，角度，所以还是1维的。还是一个匀速运动，建立匀速运动模型，
设定状态变量 x = [ x1, x2 ] = [ 角度，角速度 ]，
则运动模型为：
x1（k+1） = x1（k）+x2（k）*T
x2（k+1）= x2（k）
则状态转移方程为：
x* = Ax + w
这里设计的噪声是高斯随机噪声，则量测方程为：
z = Cx + v
看了代码，对应上以上各项：
状态估计值x --> state
当前观测值z --> measurement
KalmanFilter类内成员变量transitionMatrix就是状态转移方程中的矩阵A
KalmanFilter类内成员变量measurementMatrix就是量测方程中矩阵C
Mat statePre; //!< predicted state (x'(k)): x(k)=A*x(k-1)+B*u(k)
Mat statePost; //!< corrected state (x(k)): x(k)=x'(k)+K(k)*(z(k)-H*x'(k))
Mat transitionMatrix; //!< state transition matrix (A)
Mat controlMatrix; //!< control matrix (B) (not used if there is no control)
Mat measurementMatrix; //!< measurement matrix (H)
Mat processNoiseCov; //!< process noise covariance matrix (Q)
Mat measurementNoiseCov;//!< measurement noise covariance matrix (R)
Mat errorCovPre; //!< priori error estimate covariance matrix (P'(k)): P'(k)=A*P(k-1)*At + Q)*/
Mat gain; //!< Kalman gain matrix (K(k)): K(k)=P'(k)*Ht*inv(H*P'(k)*Ht+R)
Mat errorCovPost; //!< posteriori error estimate covariance matrix (P(k)): P(k)=(I-K(k)*H)*P'(k)processNoiseCov，measurementNoiseCov和errorCovPost。
第一步调用成员函数predict得到当前状态变量的估计值，第二步调用成员函数correct用观测值校正状态变量。再更新状态变量做下一次估计。
下面是OpenCV自带
samples\cpp\kalman.cpp中的源码：
#include "opencv2/video/tracking.hpp"
#include "opencv2/highgui/highgui.hpp"
#include <stdio.h>
using namespace cv;
static inline Point calcPoint(Point2f center, double R, double angle)
{
return center + Point2f((float)cos(angle), (float)-sin(angle))*(float)R;
}
static void help()
{
printf( "\nExamle of c calls to OpenCV's Kalman filter.\n"
" Tracking of rotating point.\n"
" Rotation speed is constant.\n"
" Both state and measurements vectors are 1D (a point angle),\n"
" Measurement is the real point angle + gaussian noise.\n"
" The real and the estimated points are connected with yellow line segment,\n"
" the real and the measured points are connected with red line segment.\n"
" (if Kalman filter works correctly,\n"
" the yellow segment should be shorter than the red one).\n"
"\n"
" Pressing any key (except ESC) will reset the tracking with a different speed.\n"
" Pressing ESC will stop the program.\n"
);
}
int main(int, char**)
{
help();
Mat img(500, 500, CV_8UC3);
KalmanFilter KF(2, 1, 0);
Mat state(2, 1, CV_32F); /* (phi, delta_phi) */
Mat processNoise(2, 1, CV_32F);
Mat measurement = Mat::zeros(1, 1, CV_32F);
char code = (char)-1;
for(;;)
{
randn( state, Scalar::all(0), Scalar::all(0.1) );
KF.transitionMatrix = *(Mat_<float>(2, 2) << 1, 1, 0, 1);
setIdentity(KF.measurementMatrix);
setIdentity(KF.processNoiseCov, Scalar::all(1e-5));
setIdentity(KF.measurementNoiseCov, Scalar::all(1e-1));
setIdentity(KF.errorCovPost, Scalar::all(1));
randn(KF.statePost, Scalar::all(0), Scalar::all(0.1));
for(;;)
{
Point2f center(img.cols*0.5f, img.rows*0.5f);
float R = img.cols/3.f;
double stateAngle = state.at<float>(0);
Point statePt = calcPoint(center, R, stateAngle);
Mat prediction = KF.predict();
double predictAngle = prediction.at<float>(0);
Point predictPt = calcPoint(center, R, predictAngle);
randn( measurement, Scalar::all(0), Scalar::all(KF.measurementNoiseCov.at<float>(0)));
// generate measurement
measurement += KF.measurementMatrix*state;
double measAngle = measurement.at<float>(0);
Point measPt = calcPoint(center, R, measAngle);
// plot points
#define drawCross( center, color, d ) \
line( img, Point( center.x - d, center.y - d ), \
Point( center.x + d, center.y + d ), color, 1, CV_AA, 0); \
line( img, Point( center.x + d, center.y - d ), \
Point( center.x - d, center.y + d ), color, 1, CV_AA, 0 )
img = Scalar::all(0);
drawCross( statePt, Scalar(255,255,255), 3 );
drawCross( measPt, Scalar(0,0,255), 3 );
drawCross( predictPt, Scalar(0,255,0), 3 );
line( img, statePt, measPt, Scalar(0,0,255), 3, CV_AA, 0 );
line( img, statePt, predictPt, Scalar(0,255,255), 3, CV_AA, 0 );
if(theRNG().uniform(0,4) != 0)
KF.correct(measurement);
randn( processNoise, Scalar(0), Scalar::all(sqrt(KF.processNoiseCov.at<float>(0, 0))));
state = KF.transitionMatrix*state + processNoise;
imshow( "Kalman", img );
code = (char)waitKey(100);
if( code > 0 )
break;
}
if( code == 27 || code == 'q' || code == 'Q' )
break;
}
return 0;
} 这里给出一个二维点跟踪的示例：
//#include "stdafx.h"
#include <cv.h>
#include <cxcore.h>
#include <highgui.h>
#include <cmath>
#include <vector>
#include <iostream>
using namespace std;
const int winHeight=600;
const int winWidth=800;
CvPoint mousePosition=cvPoint(winWidth>>1,winHeight>>1);
//mouse event callback
void mouseEvent(int event, int x, int y, int flags, void *param )
{
if (event==CV_EVENT_MOUSEMOVE) {
mousePosition=cvPoint(x,y);
}
}
int main (void)
{
//1.kalman filter setup
const int stateNum=4;
const int measureNum=2;
CvKalman* kalman = cvCreateKalman( stateNum, measureNum, 0 );//state(x,y,detaX,detaY)
CvMat* process_noise = cvCreateMat( stateNum, 1, CV_32FC1 );
CvMat* measurement = cvCreateMat( measureNum, 1, CV_32FC1 );//measurement(x,y)
CvRNG rng = cvRNG(-1);
float A[stateNum][stateNum] ={//transition matrix
1,0,1,0,
0,1,0,1,
0,0,1,0,
0,0,0,1
};
memcpy( kalman->transition_matrix->data.fl,A,sizeof(A));
cvSetIdentity(kalman->measurement_matrix,cvRealScalar(1) );
cvSetIdentity(kalman->process_noise_cov,cvRealScalar(1e-5));
cvSetIdentity(kalman->measurement_noise_cov,cvRealScalar(1e-1));
cvSetIdentity(kalman->error_cov_post,cvRealScalar(1));
//initialize post state of kalman filter at random
cvRandArr(&rng,kalman->state_post,CV_RAND_UNI,cvRealScalar(0),cvRealScalar(winHeight>winWidth?winWidth:winHeight));
CvFont font;
cvInitFont(&font,CV_FONT_HERSHEY_SCRIPT_COMPLEX,1,1);
cvNamedWindow("kalman");
cvSetMouseCallback("kalman",mouseEvent);
IplImage* img=cvCreateImage(cvSize(winWidth,winHeight),8,3);
while (1){
//2.kalman prediction
const CvMat* prediction=cvKalmanPredict(kalman,0);
CvPoint predict_pt=cvPoint((int)prediction->data.fl[0],(int)prediction->data.fl[1]);
//3.update measurement
measurement->data.fl[0]=(float)mousePosition.x;
measurement->data.fl[1]=(float)mousePosition.y;
//4.update
cvKalmanCorrect( kalman, measurement );
//draw
cvSet(img,cvScalar(255,255,255,0));
cvCircle(img,predict_pt,5,CV_RGB(0,255,0),3);//predicted point with green
cvCircle(img,mousePosition,5,CV_RGB(255,0,0),3);//current position with red
char buf[256];
sprintf_s(buf,256,"predicted position:(%3d,%3d)",predict_pt.x,predict_pt.y);
cvPutText(img,buf,cvPoint(10,30),&font,CV_RGB(0,0,0));
sprintf_s(buf,256,"current position :(%3d,%3d)",mousePosition.x,mousePosition.y);
cvPutText(img,buf,cvPoint(10,60),&font,CV_RGB(0,0,0));
cvShowImage("kalman", img);
int key=cvWaitKey(3);
if (key==27){//esc
break;
}
}
cvReleaseImage(&img);
cvReleaseKalman(&kalman);
return 0;
}本文章为转载内容，我们尊重原作者对文章享有的著作权。如有内容错误或侵权问题，欢迎原作者联系我们进行内容更正或删除文章。
