实现你的kalman

本文结合opencv的Mat数据类型，实现了kalman跟踪，具体理论知识可以参考博客：http://blog.csdn.net/baimafujinji/article/details/50646814

#ifndef _KALMAN_H_
#define _KALMAN_H_#include <iostream>
#include <opencv2\opencv.hpp>
using namespace std;
using namespace cv;class KALMAN
{
public:KALMAN(int state_size, int mea_size);~KALMAN();public:Mat statePre;//预测状态矩阵(x'(k)) x(k) = A*x(k - 1) + B * u(k)Mat statePost;//状态估计修正矩阵(x(k)) x(k) = x'(k) + K(k)*(z(k) - H * x'(k)) ： 1 * 8Mat transitionMatrix;//转移矩阵(A)  ： 8 * 8Mat controMatrix;//控制矩阵(B)Mat measurementMatrix;//测量矩阵(H) ：4 * 8Mat processNoiseCov;//预测模型噪声协方差矩阵(Q) ：8 * 8Mat measurementNoiseCov;//测量噪声协方差矩阵(R)  ： 4 * 4Mat errorCovPre;//转移噪声矩阵(P'(k)) p'(k) = A * p(k - 1) * At + Q Mat K;//kalman增益矩阵 K = p'(k) * Ht * inv(H * p'(k) * Ht + R)Mat errorCovPost;//转移噪声修正矩阵(p(k)) p(k) = (I - K(k) * H) * p'(k)  ： 8 * 8public:void init();void update(Mat Y);Mat predicted(Mat Y);};#endif;

#include "kalman.h"KALMAN::KALMAN(int state_size,int mea_size)
{transitionMatrix = Mat::zeros(state_size,state_size,CV_32F);measurementMatrix = Mat::zeros(mea_size,state_size,CV_32F);processNoiseCov = Mat::zeros(state_size,state_size,CV_32F);measurementNoiseCov = Mat::zeros(mea_size,mea_size,CV_32F);errorCovPre = Mat::zeros(state_size, state_size, CV_32F);errorCovPost = Mat::zeros(state_size, state_size, CV_32F);statePost = Mat::zeros(state_size,1,CV_32F);statePre = Mat::zeros(state_size,1,CV_32F);K = Mat::zeros(state_size,mea_size,CV_32F);
}KALMAN::~KALMAN()
{}void KALMAN::init()
{setIdentity(measurementMatrix,Scalar::all(1));//观测矩阵的初始化;setIdentity(processNoiseCov,Scalar::all(1e-5));//模型本身噪声协方差矩阵初始化;setIdentity(measurementNoiseCov,Scalar::all(1e-1));//测量噪声的协方差矩阵初始化setIdentity(errorCovPost,Scalar::all(1));//转移噪声修正矩阵初始化randn(statePost,Scalar::all(0),Scalar::all(5));//kalaman状态估计修正矩阵初始化
}void KALMAN::update(Mat Y)
{K = errorCovPre * (measurementMatrix.t()) * ((measurementMatrix * errorCovPre * measurementMatrix.t() + measurementNoiseCov).inv());statePost = statePre + K * (Y - measurementMatrix * statePre);errorCovPost = errorCovPre - K * measurementMatrix * errorCovPre;
}Mat KALMAN::predicted(Mat Y)
{statePre = transitionMatrix * statePost;errorCovPre = transitionMatrix * errorCovPost * transitionMatrix.t() + processNoiseCov;update(Y);return statePost;
}

#include "kalman.h"const int winWidth = 800;
const int winHeight = 600;Point mousePosition = Point(winWidth >> 1, winHeight >> 1);//mouse call back
void mouseEvent(int event, int x, int y, int flags, void *param)
{if (event == CV_EVENT_MOUSEMOVE){mousePosition = Point(x, y);}
}void main()
{int state_size = 4;int mea_size = 2;KALMAN kalman(state_size,mea_size);kalman.init();kalman.transitionMatrix = *(Mat_<float>(4, 4) <<1, 0, 1, 0,0, 1, 0, 1,0, 0, 1, 0,0, 0, 0, 1);//元素导入矩阵，按行; Mat showImg(winWidth, winHeight, CV_8UC3);Mat measurement(mea_size,1,CV_32F);for (;;){setMouseCallback("Kalman", mouseEvent);showImg.setTo(0);Point statePt = Point((int)kalman.statePost.at<float>(0), (int)kalman.statePost.at<float>(1));//3.update measurement  measurement.at<float>(0) = (float)mousePosition.x;measurement.at<float>(1) = (float)mousePosition.y;//2.kalman prediction     Mat prediction = kalman.predicted(measurement);Point predictPt = Point((int)prediction.at<float>(0), (int)prediction.at<float>(1));//randn( processNoise, Scalar(0), Scalar::all(sqrt(KF.processNoiseCov.at<float>(0, 0))));  //state = KF.transitionMatrix*state + processNoise;  //draw  circle(showImg, statePt, 5, CV_RGB(255, 0, 0), 1);//former point  circle(showImg, predictPt, 5, CV_RGB(0, 255, 0), 1);//predict point  circle(showImg, mousePosition, 5, CV_RGB(0, 0, 255), 1);//ture point  //          CvFont font;//字体  //          cvInitFont(&font, CV_FONT_HERSHEY_SCRIPT_COMPLEX, 0.5f, 0.5f, 0, 1, 8);  char buf[256];sprintf_s(buf, 256, "Green:predicted position:(%3d,%3d)", predictPt.x, predictPt.y);//putText(showImg, "Red: Former Point", cvPoint(10, 30), FONT_HERSHEY_SIMPLEX, 1, Scalar::all(255));putText(showImg, buf, cvPoint(10, 60), FONT_HERSHEY_SIMPLEX, 1, Scalar::all(255));sprintf_s(buf, 256, "true position:(%3d,%3d)", mousePosition.x, mousePosition.y);putText(showImg, buf, cvPoint(10, 90), FONT_HERSHEY_SIMPLEX, 1, Scalar::all(255));imshow("Kalman", showImg);int key = waitKey(3);if (key == 27){break;}}
}

kalman论文看起来挺迷糊的，但是实现还是挺好实现的

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