OpenCV的Sample分析：real_time_tracking(3)
我认为分析程序的主要原因不是弄清楚这个程序是怎样实现的，尽管这也很重要。最为重要的是，这段代码能不能给你解决一类问题的思路。比如上一讲的类RobustMatcher，学习它之后，如果我自己写一个PreciseMatcher，是不是可以从RobustMatcher中学到什么呢？
分析程序，从具体的解决方案开始，到一般性一类问题的解决结束
今天来看kalman滤波的初始化（说只前必须要说kalman到底估计什么，在这个例程中，kalman滤波器估计盒子的运动轨迹以及自身的转动，一共有18个变量，盒子的位置，速度，加速度，盒子的Euler角，角速度，角加速度）
void initKalmanFilter( KalmanFilter &KF, int nStates, int nMeasurements, int nInputs, double dt);
void updateKalmanFilter( KalmanFilter &KF, Mat &measurements,
Mat &translation_estimated, Mat &rotation_estimated );
void fillMeasurements( Mat &measurements,
const Mat &translation_measured, const Mat &rotation_measured);
先来看第一个函数initKalmanFiter()，首先需要了解类KalmanFilter的构成，
class CV_EXPORTS_W KalmanFilter
{
public:
/** @brief The constructors.
@note In C API when CvKalman\* kalmanFilter structure is not needed anymore, it should be released
with cvReleaseKalman(&kalmanFilter)
*/
CV_WRAP KalmanFilter();
/** @overload
@param dynamParams Dimensionality of the state.
@param measureParams Dimensionality of the measurement.
@param controlParams Dimensionality of the control vector.
@param type Type of the created matrices that should be CV_32F or CV_64F.
*/
CV_WRAP KalmanFilter( int dynamParams, int measureParams, int controlParams = 0, int type = CV_32F );
/** @brief Re-initializes Kalman filter. The previous content is destroyed.
@param dynamParams Dimensionality of the state.
@param measureParams Dimensionality of the measurement.
@param controlParams Dimensionality of the control vector.
@param type Type of the created matrices that should be CV_32F or CV_64F.
*/
void init( int dynamParams, int measureParams, int controlParams = 0, int type = CV_32F );
/** @brief Computes a predicted state.
@param control The optional input control
*/
CV_WRAP const Mat& predict( const Mat& control = Mat() );
/** @brief Updates the predicted state from the measurement.
@param measurement The measured system parameters
*/
CV_WRAP const Mat& correct( const Mat& measurement );
CV_PROP_RW Mat statePre; //!< predicted state (x'(k)): x(k)=A*x(k-1)+B*u(k)
CV_PROP_RW Mat statePost; //!< corrected state (x(k)): x(k)=x'(k)+K(k)*(z(k)-H*x'(k))
CV_PROP_RW Mat transitionMatrix; //!< state transition matrix (A)
CV_PROP_RW Mat controlMatrix; //!< control matrix (B) (not used if there is no control)
CV_PROP_RW Mat measurementMatrix; //!< measurement matrix (H)
CV_PROP_RW Mat processNoiseCov; //!< process noise covariance matrix (Q)
CV_PROP_RW Mat measurementNoiseCov;//!< measurement noise covariance matrix (R)
CV_PROP_RW Mat errorCovPre; //!< priori error estimate covariance matrix (P'(k)): P'(k)=A*P(k-1)*At + Q)*/
CV_PROP_RW Mat gain; //!< Kalman gain matrix (K(k)): K(k)=P'(k)*Ht*inv(H*P'(k)*Ht+R)
CV_PROP_RW Mat errorCovPost; //!< posteriori error estimate covariance matrix (P(k)): P(k)=(I-K(k)*H)*P'(k)
// temporary matrices
Mat temp1;
Mat temp2;
Mat temp3;
Mat temp4;
Mat temp5;
};
比较长，来看一下它的成员函数，以及成员变量。kalman滤波器的初始化，模型预测函数以及模型矫正函数。以及物体运动模型中的状态变量，观测值，噪声，以及相应的观测矩阵，系统矩阵，控制矩阵，噪声的方差矩阵等。以及
@param dynamParams Dimensionality of the state.
@param measureParams Dimensionality of the measurement.
@param controlParams Dimensionality of the control vector.
对kalman这个类熟悉以后，再来看initKalmanFiter
void initKalmanFilter(KalmanFilter &KF, int nStates, int nMeasurements, int nInputs, double dt)
{
KF.init(nStates, nMeasurements, nInputs, CV_64F); // init Kalman Filter
setIdentity(KF.processNoiseCov, Scalar::all(1e-5)); // set process noise
setIdentity(KF.measurementNoiseCov, Scalar::all(1e-2)); // set measurement noise
setIdentity(KF.errorCovPost, Scalar::all(1)); // error covariance
/** DYNAMIC MODEL **/
// [1 0 0 dt 0 0 dt2 0 0 0 0 0 0 0 0 0 0 0]
// [0 1 0 0 dt 0 0 dt2 0 0 0 0 0 0 0 0 0 0]
// [0 0 1 0 0 dt 0 0 dt2 0 0 0 0 0 0 0 0 0]
// [0 0 0 1 0 0 dt 0 0 0 0 0 0 0 0 0 0 0]
// [0 0 0 0 1 0 0 dt 0 0 0 0 0 0 0 0 0 0]
// [0 0 0 0 0 1 0 0 dt 0 0 0 0 0 0 0 0 0]
// [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
// [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]
// [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
// [0 0 0 0 0 0 0 0 0 1 0 0 dt 0 0 dt2 0 0]
// [0 0 0 0 0 0 0 0 0 0 1 0 0 dt 0 0 dt2 0]
// [0 0 0 0 0 0 0 0 0 0 0 1 0 0 dt 0 0 dt2]
// [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 dt 0 0]
// [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 dt 0]
// [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 dt]
// [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
// [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
// [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
// position
KF.transitionMatrix.at<double>(0,3) = dt;
KF.transitionMatrix.at<double>(1,4) = dt;
KF.transitionMatrix.at<double>(2,5) = dt;
KF.transitionMatrix.at<double>(3,6) = dt;
KF.transitionMatrix.at<double>(4,7) = dt;
KF.transitionMatrix.at<double>(5,8) = dt;
KF.transitionMatrix.at<double>(0,6) = 0.5*pow(dt,2);
KF.transitionMatrix.at<double>(1,7) = 0.5*pow(dt,2);
KF.transitionMatrix.at<double>(2,8) = 0.5*pow(dt,2);
// orientation
KF.transitionMatrix.at<double>(9,12) = dt;
KF.transitionMatrix.at<double>(10,13) = dt;
KF.transitionMatrix.at<double>(11,14) = dt;
KF.transitionMatrix.at<double>(12,15) = dt;
KF.transitionMatrix.at<double>(13,16) = dt;
KF.transitionMatrix.at<double>(14,17) = dt;
KF.transitionMatrix.at<double>(9,15) = 0.5*pow(dt,2);
KF.transitionMatrix.at<double>(10,16) = 0.5*pow(dt,2);
KF.transitionMatrix.at<double>(11,17) = 0.5*pow(dt,2);
/** MEASUREMENT MODEL **/
// [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
// [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
// [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
// [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
// [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
// [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
KF.measurementMatrix.at<double>(0,0) = 1; // x
KF.measurementMatrix.at<double>(1,1) = 1; // y
KF.measurementMatrix.at<double>(2,2) = 1; // z
KF.measurementMatrix.at<double>(3,9) = 1; // roll
KF.measurementMatrix.at<double>(4,10) = 1; // pitch
KF.measurementMatrix.at<double>(5,11) = 1; // yaw
}构建了系统的控制矩阵以及观测矩阵。
在建立系统控制矩阵的时候，有一点很奇怪，即少了单位阵，不知道为什么？
再来看updateKalmanFilter()函数，
void updateKalmanFilter( KalmanFilter &KF, Mat &measurement,
Mat &translation_estimated, Mat &rotation_estimated )
{
// First predict, to update the internal statePre variable
Mat prediction = KF.predict();
// The "correct" phase that is going to use the predicted value and our measurement
Mat estimated = KF.correct(measurement);
// Estimated translation
translation_estimated.at<double>(0) = estimated.at<double>(0);
translation_estimated.at<double>(1) = estimated.at<double>(1);
translation_estimated.at<double>(2) = estimated.at<double>(2);
// Estimated euler angles
Mat eulers_estimated(3, 1, CV_64F);
eulers_estimated.at<double>(0) = estimated.at<double>(9);
eulers_estimated.at<double>(1) = estimated.at<double>(10);
eulers_estimated.at<double>(2) = estimated.at<double>(11);
// Convert estimated quaternion to rotation matrix
rotation_estimated = euler2rot(eulers_estimated);
}
这个很好理解，最后看fillMeasurements，指获取观测数据，
void fillMeasurements( Mat &measurements,
const Mat &translation_measured, const Mat &rotation_measured)
{
// Convert rotation matrix to euler angles
Mat measured_eulers(3, 1, CV_64F);
measured_eulers = rot2euler(rotation_measured);
// Set measurement to predict
measurements.at<double>(0) = translation_measured.at<double>(0); // x
measurements.at<double>(1) = translation_measured.at<double>(1); // y
measurements.at<double>(2) = translation_measured.at<double>(2); // z
measurements.at<double>(3) = measured_eulers.at<double>(0); // roll
measurements.at<double>(4) = measured_eulers.at<double>(1); // pitch
measurements.at<double>(5) = measured_eulers.at<double>(2); // yaw
}到此为止，kalman的常用函数以及使用方式介绍到这里