我正在尝试使用速度加速度模型来实现基于卡尔曼滤波器的鼠标跟踪（首先作为测试）。
我想试试这个简单的模型，我的状态转移方程是：
X(k) = [x(k), y(k)]' (Position)
V(k) = [vx(k), vy(k)]' (Velocity)
X(k) = X(k-1) + dt*V(k-1) + 0.5*dt*dt*a(k-1)
V(k) = V(k-1) + t*a(k-1)
a(k) = a(k-1)
使用它，我基本上写下了以下代码：
#include <iostream>
#include <vector>
#include <cstdio>
#include <opencv2/core/core.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <opencv2/video/tracking.hpp>
using namespace cv;
using namespace std;
struct mouse_info_struct { int x,y; };
struct mouse_info_struct mouse_info = {-1,-1}, last_mouse;
void on_mouse(int event, int x, int y, int flags, void* param)
{
//if (event == CV_EVENT_LBUTTONUP)
{
last_mouse = mouse_info;
mouse_info.x = x;
mouse_info.y = y;
}
}
void printmat(const cv::Mat &__mat, std::string __str)
{
std::cout << "--------" << __str << "----------\n";
for (int i=0 ; i<__mat.rows ; ++i)
{
for (int j=0 ; j<__mat.cols ; ++j)
std::cout << __mat.at<double>(i,j) << " ";
std::cout << std::endl;
}
std::cout << "-------------------------------------\n";
}
int main (int argc, char * const argv[])
{
int nStates = 5, nMeasurements = 2, nInputs = 1;
Mat img(500, 900, CV_8UC3);
KalmanFilter KF(nStates, nMeasurements, nInputs, CV_64F);
Mat state(nStates, 1, CV_64F); /* (x, y, Vx, Vy, a) */
Mat measurement(nMeasurements,1,CV_64F); measurement.setTo(Scalar(0));
Mat prevMeasurement(nMeasurements,1,CV_64F); prevMeasurement.setTo(Scalar(0));
int key = -1, dt=100, T=1000;
float /*a=100, acclErrMag = 0.05,*/ measurementErrVar = 100, noiseVal=0.001, covNoiseVal=0.9e-4;
namedWindow("Mouse-Kalman");
setMouseCallback("Mouse-Kalman", on_mouse, 0);
//while ( (char)(key=cv::waitKey(100)) != 'q' )
{
/// A
KF.transitionMatrix.at<double>(0,0) = 1;
KF.transitionMatrix.at<double>(0,1) = 0;
KF.transitionMatrix.at<double>(0,2) = (dt/T);
KF.transitionMatrix.at<double>(0,3) = 0;
KF.transitionMatrix.at<double>(0,4) = 0.5*(dt/T)*(dt/T);
KF.transitionMatrix.at<double>(1,0) = 0;
KF.transitionMatrix.at<double>(1,1) = 1;
KF.transitionMatrix.at<double>(1,2) = 0;
KF.transitionMatrix.at<double>(1,3) = (dt/T);
KF.transitionMatrix.at<double>(1,4) = 0.5*(dt/T)*(dt/T);
KF.transitionMatrix.at<double>(2,0) = 0;
KF.transitionMatrix.at<double>(2,1) = 0;
KF.transitionMatrix.at<double>(2,2) = 1;
KF.transitionMatrix.at<double>(2,3) = 0;
KF.transitionMatrix.at<double>(2,4) = (dt/T);
KF.transitionMatrix.at<double>(3,0) = 0;
KF.transitionMatrix.at<double>(3,1) = 0;
KF.transitionMatrix.at<double>(3,2) = 0;
KF.transitionMatrix.at<double>(3,3) = 1;
KF.transitionMatrix.at<double>(3,4) = (dt/T);
KF.transitionMatrix.at<double>(4,0) = 0;
KF.transitionMatrix.at<double>(4,1) = 0;
KF.transitionMatrix.at<double>(4,2) = 0;
KF.transitionMatrix.at<double>(4,3) = 0;
KF.transitionMatrix.at<double>(4,4) = 1;
/// Initial estimate of state variables
KF.statePost = cv::Mat::zeros(nStates, 1,CV_64F);
KF.statePost.at<double>(0) = mouse_info.x;
KF.statePost.at<double>(1) = mouse_info.y;
KF.statePost.at<double>(2) = 0;
KF.statePost.at<double>(3) = 0;
KF.statePost.at<double>(4) = 0;
KF.statePre = KF.statePost;
/// Ex or Q
setIdentity(KF.processNoiseCov, Scalar::all(noiseVal));
/// Initial covariance estimate Sigma_bar(t) or P'(k)
setIdentity(KF.errorCovPre, Scalar::all(1000));
/// Sigma(t) or P(k)
setIdentity(KF.errorCovPost, Scalar::all(1000));
/// B
KF.controlMatrix = cv::Mat(nStates, nInputs,CV_64F);
KF.controlMatrix.at<double>(0,0) = 0;
KF.controlMatrix.at<double>(1,0) = 0;
KF.controlMatrix.at<double>(2,0) = 0;
KF.controlMatrix.at<double>(3,0) = 0;
KF.controlMatrix.at<double>(4,0) = 1;
/// H
KF.measurementMatrix = cv::Mat::eye(nMeasurements, nStates, CV_64F);
/// Ez or R
setIdentity(KF.measurementNoiseCov, Scalar::all(measurementErrVar*measurementErrVar));
printmat(KF.controlMatrix, "KF.controlMatrix");
printmat(KF.transitionMatrix, "KF.transitionMatrix");
printmat(KF.statePre,"KF.statePre");
printmat(KF.processNoiseCov, "KF.processNoiseCov");
printmat(KF.measurementMatrix, "KF.measurementMatrix");
printmat(KF.measurementNoiseCov, "KF.measurementNoiseCov");
printmat(KF.errorCovPost,"KF.errorCovPost");
printmat(KF.errorCovPre,"KF.errorCovPre");
printmat(KF.statePost,"KF.statePost");
while (mouse_info.x < 0 || mouse_info.y < 0)
{
imshow("Mouse-Kalman", img);
waitKey(30);
continue;
}
while ( (char)key != 's' )
{
/// MAKE A MEASUREMENT
measurement.at<double>(0) = mouse_info.x;
measurement.at<double>(1) = mouse_info.y;
/// MEASUREMENT UPDATE
Mat estimated = KF.correct(measurement);
/// STATE UPDATE
Mat prediction = KF.predict();
cv::Mat u(nInputs,1,CV_64F);
u.at<double>(0,0) = 0.0 * sqrt(pow((prevMeasurement.at<double>(0) - measurement.at<double>(0)),2)
+ pow((prevMeasurement.at<double>(1) - measurement.at<double>(1)),2));
/// STORE ALL DATA
Point predictPt(prediction.at<double>(0),prediction.at<double>(1));
Point estimatedPt(estimated.at<double>(0),estimated.at<double>(1));
Point measuredPt(measurement.at<double>(0),measurement.at<double>(1));
/// PLOT POINTS
#define drawCross( center, color, d ) \
line( img, Point( center.x - d, center.y - d ), \
Point( center.x + d, center.y + d ), color, 2, CV_AA, 0); \
line( img, Point( center.x + d, center.y - d ), \
Point( center.x - d, center.y + d ), color, 2, CV_AA, 0 )
/// DRAW ALL ON IMAGE
img = Scalar::all(0);
drawCross( predictPt, Scalar(255,255,255), 9 ); //WHITE
drawCross( estimatedPt, Scalar(0,0,255), 6 ); //RED
drawCross( measuredPt, Scalar(0,255,0), 3 ); //GREEN
line( img, estimatedPt, measuredPt, Scalar(100,255,255), 3, CV_AA, 0 );
line( img, estimatedPt, predictPt, Scalar(0,255,255), 3, CV_AA, 0 );
prevMeasurement = measurement;
imshow( "Mouse-Kalman", img );
key=cv::waitKey(10);
}
}
return 0;
}
这是代码的输出：http ://www.youtube.com/watch?v=9_xd4HSz8_g
如您所见，跟踪非常非常慢。我不明白模型有什么问题以及为什么估计如此缓慢。我不希望有任何控制输入。
谁能解释一下？