text: #include "FusionEKF.h"
  #include <iostream>
  #include "Eigen/Dense"
  #include "tools.h"
  
  using Eigen::MatrixXd;
  using Eigen::VectorXd;
  using std::cout;
  using std::endl;
  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.
     * TODO: Set the process and measurement noises
     */
    H_laser_ <<1,0,0,0,
            0,1,0,0;
    Hj_ <<1, 1, 0, 0,
        1, 1, 0, 0,
        1, 1, 1, 1; 
    
    //the initial transition matrix F_
    ekf_.F_ = MatrixXd(4, 4);
    ekf_.F_ << 1, 0, 1, 0,
           0, 1, 0, 1,
           0, 0, 1, 0,
           0, 0, 0, 1;
  
    //state covariance matrix P
    ekf_.P_ = MatrixXd(4, 4);
    ekf_.P_ << 1, 0, 0, 0,
           0, 1, 0, 0,
           0, 0, 1000, 0,
           0, 0, 0, 1000;
  
  }
  
  /**
   * Destructor.
   */
  FusionEKF::~FusionEKF() {}
  
  void FusionEKF::ProcessMeasurement(const MeasurementPackage &measurement_pack) {
    /**
     * Initialization
     */
    if (!is_initialized_) {
      /**
       * TODO: Initialize the state ekf_.x_ with the first measurement.
       * TODO: Create the covariance matrix.
       * 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 ro     = measurement_pack.raw_measurements_[0];
        float phi    = measurement_pack.raw_measurements_[1];
        float ro_dot = measurement_pack.raw_measurements_[2];
        ekf_.x_[0] = ro   * cos(phi);
        ekf_.x_[1] = ro   * sin(phi);      
        ekf_.x_[2] = ro_dot * cos(phi);
        ekf_.x_[3] = ro_dot * sin(phi);
      }
      else if (measurement_pack.sensor_type_ == MeasurementPackage::LASER) {
        // TODO: Initialize state.
        ekf_.x_ << measurement_pack.raw_measurements_[0], 
               measurement_pack.raw_measurements_[1], 
               0, 
               0;
      }
      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.
     * TODO: Update the process noise covariance matrix.
     * Use noise_ax = 9 and noise_ay = 9 for your Q matrix.
     */
    //compute the time elapsed between the current and previous measurements
    float dt = (measurement_pack.timestamp_ - previous_timestamp_) / 1000000.0;//dt - expressed 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 acceleration noise components
    float noise_ax = 9;
    float noise_ay = 9;
    
    //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
      Tools tools;
      Hj_ = tools.CalculateJacobian(ekf_.x_);
      ekf_.H_ = Hj_;
      ekf_.R_ = R_radar_;
      ekf_.UpdateEKF(measurement_pack.raw_measurements_);
    } else {
      // TODO: 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;
  }
  