text: #include "FusionEKF.h"
  #include "tools.h"
  #include "Eigen/Dense"
  #include <iostream>
  
  #define EPS 0.0001
  
  using namespace std;
  using Eigen::MatrixXd;
  using Eigen::VectorXd;
  using std::vector;
  
  /*
   * Constructor.
   */
  FusionEKF::FusionEKF() {
    is_initialized_ = false;
  
    previous_timestamp_ = 0;
  
    // initializing matrices
    R_laser_ = MatrixXd(2, 2);
    R_radar_ = MatrixXd(3, 3);
    H_laser_ = MatrixXd(2, 4);
    Hj_ = MatrixXd(3, 4);
  
    //measurement covariance matrix - laser
    R_laser_ << 0.0225, 0,
          0, 0.0225;
  
    //measurement covariance matrix - radar
    R_radar_ << 0.09, 0, 0,
          0, 0.0009, 0,
          0, 0, 0.09;
  
    /**
    TODO:
      * Finish initializing the FusionEKF.
      * Set the process and measurement noises
    */
      H_laser_ << 1, 0, 0, 0,
      0, 1, 0, 0;
      
      // initialize the kalman filter variables
      ekf_.P_ = MatrixXd(4, 4);
      ekf_.P_ << 1, 0, 0, 0,
      0, 1, 0, 0,
      0, 0, 1000, 0,
      0, 0, 0, 1000;
      
      ekf_.F_ = MatrixXd(4, 4);
      ekf_.F_ << 1, 0, 1, 0,
      0, 1, 0, 1,
      0, 0, 1, 0,
      0, 0, 0, 1;
      
      // set measurement noises
      noise_ax = 9;
      noise_ay = 11;
  }
  
  /**
  * Destructor.
  */
  FusionEKF::~FusionEKF() {}
  
  void FusionEKF::ProcessMeasurement(const MeasurementPackage &measurement_pack) {
  
  
    /*****************************************************************************
     *  Initialization
     ****************************************************************************/
    if (!is_initialized_) {
      /**
      TODO:
        * Initialize the state ekf_.x_ with the first measurement.
        * Create the covariance matrix.
        * Remember: you'll need to convert radar from polar to cartesian coordinates.
      */
      
      // first measurement
  //    cout << "EKF: " << endl;
      ekf_.x_ = VectorXd(4);
  //    ekf_.x_ << 1, 1, 1, 1;
  
      if (measurement_pack.sensor_type_ == MeasurementPackage::RADAR) {
        /**
        Convert radar from polar to cartesian coordinates and initialize state.
        */
          float rho = measurement_pack.raw_measurements_[0];      // range: radial distance from origin
          float phi = measurement_pack.raw_measurements_[1];      // bearing: angle between rho and x axis
          float rho_dot = measurement_pack.raw_measurements_[2];  // radial velocity: change of rho
          
  //        ekf_.x_ << rho * cos(phi), rho * sin(phi), rho_dot * cos(phi), rho_dot * sin(phi);
  //        phi is not the direction of the speed, it is better to set vx and vy to 0
          ekf_.x_ << rho * cos(phi), rho * sin(phi), 0, 0;  // x, y, vx, vy
  
      }
      else if (measurement_pack.sensor_type_ == MeasurementPackage::LASER) {
        /**
        Initialize state.
        */
          ekf_.x_ << measurement_pack.raw_measurements_[0], measurement_pack.raw_measurements_[1], 0, 0; // x, y, vx, vy
      }
      if (fabs(ekf_.x_(0)) < EPS and fabs(ekf_.x_(1)) < EPS){
            ekf_.x_(0) = EPS;
            ekf_.x_(1) = EPS;
      }
      previous_timestamp_ = measurement_pack.timestamp_;
      // done initializing, no need to predict or update
      is_initialized_ = true;
      return;
    }
  
    /*****************************************************************************
     *  Prediction
     ****************************************************************************/
  
    /**
     TODO:
       * Update the state transition matrix F according to the new elapsed time.
        - Time is measured in seconds.
       * Update the process noise covariance matrix.
       * Use noise_ax = 9 and noise_ay = 9 for your Q matrix.
     */
      float dt = (measurement_pack.timestamp_ - previous_timestamp_) / 1000000.0;  //  in seconds
      previous_timestamp_ = measurement_pack.timestamp_;
      
      float dt_2 = dt * dt;
      float dt_3 = dt_2 * dt;
      float dt_4 = dt_3 * dt;
      
      // Modify the F matrix so that the time is integrated
      ekf_.F_(0, 2) = dt;
      ekf_.F_(1, 3) = dt;
      
      //set the process covariance matrix Q
      ekf_.Q_ = MatrixXd(4, 4);
      ekf_.Q_ << dt_4/4*noise_ax,0,dt_3/2*noise_ax,0,
                 0,dt_4/4*noise_ay,0,dt_3/2*noise_ay,
                 dt_3/2*noise_ax,0,dt_2*noise_ax,0,
                 0,dt_3/2*noise_ay,0,dt_2*noise_ay;
  
    ekf_.Predict();
  
    /*****************************************************************************
     *  Update
     ****************************************************************************/
  
    /**
     TODO:
       * Use the sensor type to perform the update step.
       * Update the state and covariance matrices.
     */
  
      if (measurement_pack.sensor_type_ == MeasurementPackage::RADAR) {
          // Radar updates
          
          Hj_ = tools.CalculateJacobian(ekf_.x_);
          ekf_.H_ = Hj_;
          ekf_.R_ = R_radar_;
          ekf_.UpdateEKF(measurement_pack.raw_measurements_);
      }
      else {
          // Laser updates
          ekf_.H_ = H_laser_;
          ekf_.R_ = R_laser_;
          ekf_.Update(measurement_pack.raw_measurements_);
      }
  
    // print the output
    cout << "x_ = " << ekf_.x_ << endl;
    cout << "P_ = " << ekf_.P_ << endl;
  }
  