26. Predict Radar Measurement Assignment 1

Assignment Predict Radar Measurement

Predict Radar Measurements Assignment

Task Description:

You will be completing the missing code in ukf.cpp, PredictRadarMeasurement() function.

Task List:

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Helpful Equations

State Vector

x_{k+1|k}=\begin{bmatrix} p_x\\ p_y\\ v\\ \psi\\ \dot{\psi} \end{bmatrix}

Measurement Vector

z_{k+1|k}=\begin{bmatrix} \rho\\ \varphi\\ \dot{\rho} \end{bmatrix}

Measurement Model

z_{k+1|k}=h(x_{k+1}) + w_{k+1}
\rho = \sqrt{p_x^2+p_y^2}
\varphi =arctan(\frac{p_y}{p_x})
\dot{\rho}=\frac{p_xcos(\psi)v+p_ysin(\psi)v}{\sqrt{p_x^2+p_y^2}}

Predicted Measurement Mean

\large z_{k+1|k} = \sum_{i=1}^{n_\sigma} w_i Z_{k+1|k,i}

Predicted Covariance

\large S_{k+1|k} = \sum_{i=1}^{n_\sigma} w_i( Z_{k+1|k,i} - z_{k+1|k})(Z_{k+1|k,i} - z_{k+1|k})^T + R
\large R = E(w_k\cdot w_k^T) = \begin{bmatrix} \sigma_{\rho}^2 \qquad 0\qquad0\\ 0\qquad\sigma_{\varphi}^2 \qquad 0\\ 0\qquad0\qquad\sigma_{\dot{\rho}}^2 \end{bmatrix}

Start Quiz: 

#include "Dense"
#include "ukf.h"

using Eigen::MatrixXd;
using Eigen::VectorXd;

int main() {

  // Create a UKF instance
  UKF ukf;

  /**
   * Programming assignment calls
   */  
  VectorXd z_out = VectorXd(3);
  MatrixXd S_out = MatrixXd(3, 3);
  ukf.PredictRadarMeasurement(&z_out, &S_out);

  return 0;
}
#include <iostream>
#include "ukf.h"

using Eigen::MatrixXd;
using Eigen::VectorXd;

UKF::UKF() {
  Init();
}

UKF::~UKF() {

}

void UKF::Init() {

}

/**
 * Programming assignment functions: 
 */

void UKF::PredictRadarMeasurement(VectorXd* z_out, MatrixXd* S_out) {

  // set state dimension
  int n_x = 5;

  // set augmented dimension
  int n_aug = 7;

  // set measurement dimension, radar can measure r, phi, and r_dot
  int n_z = 3;

  // define spreading parameter
  double lambda = 3 - n_aug;

  // set vector for weights
  VectorXd weights = VectorXd(2*n_aug+1);
  double weight_0 = lambda/(lambda+n_aug);
  double weight = 0.5/(lambda+n_aug);
  weights(0) = weight_0;

  for (int i=1; i<2*n_aug+1; ++i) {  
    weights(i) = weight;
  }

  // radar measurement noise standard deviation radius in m
  double std_radr = 0.3;

  // radar measurement noise standard deviation angle in rad
  double std_radphi = 0.0175;

  // radar measurement noise standard deviation radius change in m/s
  double std_radrd = 0.1;

  // create example matrix with predicted sigma points
  MatrixXd Xsig_pred = MatrixXd(n_x, 2 * n_aug + 1);
  Xsig_pred <<
         5.9374,  6.0640,   5.925,  5.9436,  5.9266,  5.9374,  5.9389,  5.9374,  5.8106,  5.9457,  5.9310,  5.9465,  5.9374,  5.9359,  5.93744,
           1.48,  1.4436,   1.660,  1.4934,  1.5036,    1.48,  1.4868,    1.48,  1.5271,  1.3104,  1.4787,  1.4674,    1.48,  1.4851,    1.486,
          2.204,  2.2841,  2.2455,  2.2958,   2.204,   2.204,  2.2395,   2.204,  2.1256,  2.1642,  2.1139,   2.204,   2.204,  2.1702,   2.2049,
         0.5367, 0.47338, 0.67809, 0.55455, 0.64364, 0.54337,  0.5367, 0.53851, 0.60017, 0.39546, 0.51900, 0.42991, 0.530188,  0.5367, 0.535048,
          0.352, 0.29997, 0.46212, 0.37633,  0.4841, 0.41872,   0.352, 0.38744, 0.40562, 0.24347, 0.32926,  0.2214, 0.28687,   0.352, 0.318159;

  // create matrix for sigma points in measurement space
  MatrixXd Zsig = MatrixXd(n_z, 2 * n_aug + 1);

  // mean predicted measurement
  VectorXd z_pred = VectorXd(n_z);
  
  // measurement covariance matrix S
  MatrixXd S = MatrixXd(n_z,n_z);

  /**
   * Student part begin
   */

  // transform sigma points into measurement space
  
  // calculate mean predicted measurement
  
  // calculate innovation covariance matrix S

  /**
   * Student part end
   */

  // print result
  std::cout << "z_pred: " << std::endl << z_pred << std::endl;
  std::cout << "S: " << std::endl << S << std::endl;

  // write result
  *z_out = z_pred;
  *S_out = S;
}
#ifndef UKF_H
#define UKF_H

#include "Dense"

class UKF {
 public:
  /**
   * Constructor
   */
  UKF();

  /**
   * Destructor
   */
  virtual ~UKF();

  /**
   * Init Initializes Unscented Kalman filter
   */
  void Init();

  /**
   * Student assignment functions
   */
  void GenerateSigmaPoints(Eigen::MatrixXd* Xsig_out);
  void AugmentedSigmaPoints(Eigen::MatrixXd* Xsig_out);
  void SigmaPointPrediction(Eigen::MatrixXd* Xsig_out);
  void PredictMeanAndCovariance(Eigen::VectorXd* x_pred, 
                                Eigen::MatrixXd* P_pred);
  void PredictRadarMeasurement(Eigen::VectorXd* z_out, 
                               Eigen::MatrixXd* S_out);
  void UpdateState(Eigen::VectorXd* x_out, 
                   Eigen::MatrixXd* P_out);
};

#endif  // UKF_H

expected result z_out:

z_pred =

6.12155

0.245993

2.10313

expected result s_out:

S =

0.0946171 -0.000139448 0.00407016

-0.000139448 0.000617548 -0.000770652

0.00407016 -0.000770652 0.0180917

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