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;
  
    // State co-variance matrix
    ekf_.P_ = MatrixXd(4, 4);
    ekf_.P_ << 1, 0, 0, 0,
               0, 1, 0, 0,
               0, 0, 1000, 0,
               0, 0, 0, 1000;
  
    // Intialize transition matrix
    ekf_.F_ = MatrixXd(4, 4);
    ekf_.F_ << 1, 0, 1, 0,
               0, 1, 0, 1,
               0, 0, 1, 0,
               0, 0, 0, 1;
  }
  
  /**
   * 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_ << 0, 0, 0, 0;
  
      if (measurement_pack.sensor_type_ == MeasurementPackage::RADAR) {
        // TODO: Convert radar from polar to cartesian coordinates 
        //         and initialize state.
        double rho = measurement_pack.raw_measurements_(0);
        double phi = measurement_pack.raw_measurements_(1);
        double rhodot = measurement_pack.raw_measurements_(2);
  
        ekf_.x_ << rho * cos(phi), rho * sin(phi), rhodot * cos(phi), rhodot * 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.
     */
    float noise_ax = 9;
    float noise_ay = 9;
  
    float dt = (measurement_pack.timestamp_ - previous_timestamp_)/1000000.0;
    previous_timestamp_ = measurement_pack.timestamp_;
  
    float dt2 = dt * dt;
    float dt3 = dt2 * dt;
    float dt4 = dt3 * dt;
  
    // Update F with elapsed time
    ekf_.F_(0,2) = dt;
    ekf_.F_(1,3) = dt;
  
    //set the process covariance matrix Q
    ekf_.Q_ = MatrixXd(4,4);
    ekf_.Q_ << dt4*noise_ax/4, 0, dt3*noise_ax/2, 0,
               0, dt4*noise_ay/4, 0, dt3*noise_ay/2,
               dt3*noise_ax/2, 0, dt2*noise_ax, 0,
               0, dt3*noise_ay/2, 0, dt2*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) {
      // TODO: Radar updates
      Tools tools;
      ekf_.H_ = tools.CalculateJacobian(ekf_.x_);
      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;
  }