text: #include "kalman_filter.h"
  
  using Eigen::MatrixXd;
  using Eigen::VectorXd;
  
  /* 
   * Please note that the Eigen library does not initialize 
   *   VectorXd or MatrixXd objects with zeros upon creation.
   */
  
  KalmanFilter::KalmanFilter() {}
  
  KalmanFilter::~KalmanFilter() {}
  
  void KalmanFilter::Init(VectorXd &x_in, MatrixXd &P_in, MatrixXd &F_in,
                          MatrixXd &H_in, MatrixXd &R_in, MatrixXd &Q_in) {
    x_ = x_in;
    P_ = P_in;
    F_ = F_in;
    H_ = H_in;
    R_ = R_in;
    Q_ = Q_in;
  }
  
  void KalmanFilter::Predict() {
    /**
     * TODO: predict the state
     */
    DEBUGOUT("Getting new prediction.");
    x_ = F_ * x_;
    MatrixXd Ft = F_.transpose();
    P_ = F_ * P_ * Ft + Q_;
  }
  
  void KalmanFilter::Update(const VectorXd &z) {
    /**
     * update the state by using Kalman Filter equations
     */
    DEBUGOUT("Laser update.");
    VectorXd z_pred = H_ * x_;
    VectorXd y = z - z_pred;
    commonUpdate(y);
  }
  
  
  void KalmanFilter::UpdateEKF(const VectorXd &z) {
    /**
     * update the state by using Extended Kalman Filter equations
     */
    
    DEBUGOUT("Radar update.");
  
    double px = x_(0);
    double py = x_(1);
    double vx = x_(2);
    double vy = x_(3);
  
    double rho = sqrt(px*px + py*py);
    double theta = atan2(py, px);
    double rho_dot = (px*vx + py*vy) / rho;
    VectorXd h = VectorXd(3);
    h << rho, theta, rho_dot;
    VectorXd y = z - h;
  
    while ( y(1) > M_PI || y(1) < -M_PI ) {
      if ( y(1) > M_PI ) {
        y(1) -= (2*M_PI);
      } else {
        y(1) += (2*M_PI);
      }
    }
  
    commonUpdate(y);
  }
  
  
  
  
  void KalmanFilter::commonUpdate(const VectorXd& y){
  
    MatrixXd Ht = H_.transpose();
    MatrixXd S = H_ * P_ * Ht + R_;
    MatrixXd Si = S.inverse();
    MatrixXd PHt = P_ * Ht;
    MatrixXd K = PHt * Si;
  
    //new estimate
    x_ = x_ + (K * y);
    long x_size = x_.size();
    MatrixXd I = MatrixXd::Identity(x_size, x_size);
    P_ = (I - K * H_) * P_;
  }