text: #include "FusionEKF.h"
  #include "tools.h"
  #include "Eigen/Dense"
  #include <iostream>
  
  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
    */
    noise_ax = 9.0;
    noise_ay = 9.0;
  
  }
  
  /**
  * 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.
      */
      
      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];
  	  float phi = measurement_pack.raw_measurements_[1];
        float px = rho * cos(phi);
  	  float py = rho * sin(phi);
  	  ekf_.x_ << px, py, 0.f, 0.f;
      }
      else if (measurement_pack.sensor_type_ == MeasurementPackage::LASER) {
        /**
        Initialize state.
        */
        ekf_.x_ << measurement_pack.raw_measurements_[0], measurement_pack.raw_measurements_[1], 0.f, 0.f;
  
      }
  
  
        previous_timestamp_ = measurement_pack.timestamp_;
  
      H_laser_ << 1, 0, 0, 0,
              0, 1, 0, 0;
      ekf_.H_ = H_laser_;
  
    ekf_.F_ = MatrixXd(4, 4);       
    ekf_.F_ << 1, 0, 0, 0,
             0, 1, 0, 0,
             0, 0, 1, 0,
             0, 0, 0, 1;
  
    ekf_.P_ = MatrixXd(4, 4);     
    ekf_.P_ << 1, 0, 0, 0,
             0, 1, 0, 0,
             0, 0, 1000, 0,
             0, 0, 0, 1000;
      
      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;
    previous_timestamp_ = measurement_pack.timestamp_;
  
    float dt_2 = dt * dt;
    float dt_3 = dt_2 * dt;
    float dt_4 = dt_3 * dt;
    ekf_.F_(0,2) = dt;
      ekf_.F_(1,3) = dt;
      
      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) {
      
       ekf_.R_ = R_radar_;
      ekf_.UpdateEKF(measurement_pack.raw_measurements_);
  
    } else {
      
       ekf_.R_ = R_laser_;
      ekf_.Update(measurement_pack.raw_measurements_);
    }
  
    // print the output
    cout << "x_ = " << ekf_.x_ << endl;
    cout << "P_ = " << ekf_.P_ << endl;
  }
  