kalman 滤波 演示与opencv代码

在机器视觉中追踪时常会用到预测算法，kalman是你一定知道的。它可以用来预测各种状态，比如说位置，速度等。关于它的理论有很多很好的文献可以参考。opencv给出了kalman filter的一个实现，而且有范例，但估计不少人对它的使用并不清楚，因为我也是其中一个。本文的应用是对二维坐标进行预测和平滑

 

使用方法：

1、初始化

const int stateNum=4;//状态数，包括（x，y，dx，dy）坐标及速度（每次移动的距离）
const int measureNum=2;//观测量，能看到的是坐标值，当然也可以自己计算速度，但没必要
Kalman* kalman = cvCreateKalman( stateNum, measureNum, 0 );//state(x,y,detaX,detaY)

转移矩阵或者说增益矩阵的值好像有点莫名其妙

float A[stateNum][stateNum] ={//transition matrix
        1,0,1,0,
        0,1,0,1,
        0,0,1,0,
        0,0,0,1
    };

看下图就清楚了

X1=X+dx，依次类推
所以这个矩阵还是很容易却确定的，可以根据自己的实际情况定制转移矩阵

同样的方法，三维坐标的转移矩阵可以如下

float A[stateNum][stateNum] ={//transition matrix
        1,0,0,1,0,0,
        0,1,0,0,1,0,
        0,0,1,0,0,1,
        0,0,0,1,0,0,
        0,0,0,0,1,0,
        0,0,0,0,0,1
    };

当然并不一定得是1和0

2.预测cvKalmanPredict，然后读出自己需要的值
3.更新观测矩阵 
4.更新CvKalman

 只有第一步麻烦些。上述这几步跟代码中的序号对应

 如果你在做tracking，下面的例子或许更有用些。

 

#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;
}

 

kalman filter 视频演示：

http://v.youku.com/v_show/id_XMjU4MzEyODky.html

 

demo snapshot：