摘抄自《统计信号处理》 叶中付
#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;//计算相对中心的坐标值 } 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);状态维数2，测量维数1，没有控制量 Mat state(2, 1, CV_32F); /* (phi, delta_phi) *///state(角度，△角度) Mat processNoise(2, 1, CV_32F); Mat measurement = Mat::zeros(1, 1, CV_32F); //定义测量值 char code = (char)-1; for(;;) { randn( state, Scalar::all(0), Scalar::all(0.1) );产生均值为0，标准差0.1的二维高斯列向量 KF.transitionMatrix = *(Mat_<float>(2, 2) << 1, 1, 0, 1);transitionMatrix为类KalmanFilter中的一个变量，Mat型，是Kalman模型中的状态转移矩阵 //转移矩阵为[1,1;0,1],2*2维的 setIdentity(KF.measurementMatrix); //setIdentity: 缩放的单位对角矩阵; //!< measurement matrix (H) 观测模型 setIdentity(KF.processNoiseCov, Scalar::all(1e-5)); //系统噪声方差矩阵Q setIdentity(KF.measurementNoiseCov, Scalar::all(1e-1)); //测量噪声方差矩阵R setIdentity(KF.errorCovPost, Scalar::all(1)); //后验错误估计协方差矩阵P randn(KF.statePost, Scalar::all(0), Scalar::all(0.1)); for(;;) { Point2f center(img.cols*0.5f, img.rows*0.5f); //图像中心点 float R = img.cols/3.f; //半径 double stateAngle = state.at<float>(0); Point statePt = calcPoint(center, R, stateAngle); //跟踪点坐标statePt Mat prediction = KF.predict(); //计算预测值，返回x' double predictAngle = prediction.at<float>(0); Point predictPt = calcPoint(center, R, predictAngle); //计算预测点 randn( measurement, Scalar::all(0), Scalar::all(KF.measurementNoiseCov.at<float>(0)));给measurement赋值N(0,R)的随机值,预测值的噪声模型 // 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)//调用kalman这个类的correct方法得到加入观察值校正后的状态变量值矩阵 KF.correct(measurement); randn( processNoise, Scalar(0), Scalar::all(sqrt(KF.processNoiseCov.at<float>(0, 0)))); state = KF.transitionMatrix*state + processNoise; //不加噪声的话就是匀速圆周运动，加了点噪声类似匀速圆周运动，因为噪声的原因，运动方向可能会改变 imshow( "Kalman", img ); code = (char)waitKey(100); if( code > 0 ) break; } if( code == 27 || code == 'q' || code == 'Q' ) break; } return 0; }
