text: #include "kalman_filter.h"
  #include "tools.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
     */
    x_ = F_* x_ ;
    P_ = F_* P_* F_.transpose() + Q_;
  }
  
  void KalmanFilter::Update(const VectorXd &z) {
    /**
     * TODO: update the state by using Kalman Filter equations
     */
    VectorXd z_pred = H_ * x_;
    VectorXd y = z - z_pred;
    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_;
  }
  
  void KalmanFilter::UpdateEKF(const VectorXd &z) {
    /**
     * TODO: update the state by using Extended Kalman Filter equations
     */
    Tools tools;
    float rho_dot, prevoius_rho_dot;
  
    float rho = sqrt(x_(0)*x_(0) + x_(1)*x_(1));
    float phi = atan2(x_(1), x_(0));
    if(rho >0.0001)
    {
      rho_dot = (x_(0)*x_(2) + x_(1)*x_(3))/rho;
      prevoius_rho_dot = rho_dot;
    }
    else
      rho_dot = prevoius_rho_dot;
    
    VectorXd z_pred(3);
    z_pred << rho, phi, rho_dot;
    VectorXd y(3);
    y = z - z_pred;
    
    y(1) = tools.Angle_Norm(y(1));
    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_;
  }
  