Predicted Mean and Covariance Assignment 1

Assignement Predicted Mean And Covariance

Predicted Mean and Covariance Assingment

Task Description:

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

Task Feedback:

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Helpful Equations

Weights

\Large w_i =\frac{\lambda}{\lambda+n_{a}}, i =1

\Large w_i =\frac{1}{2(\lambda+n_{a})}, i =2…n_{a}

Predicted Mean

\Large x_{k+1|k} = \sum_{i=1}^{n_\sigma} w_i X_{k+1|k,i}

Predicted Covariance

\Large P_{k+1|k} = \sum_{i=1}^{n_\sigma} w_i( X_{k+1|k,i} - x_{k+1|k})(X_{k+1|k,i} - x_{k+1|k})^T

Start Quiz:

main.cpp ukf.cpp ukf.h

#include <iostream>
#include "Dense"
#include <vector>
#include "ukf.h"

using namespace std;
using Eigen::MatrixXd;
using Eigen::VectorXd;
using std::vector;

int main() {

	//Create a UKF instance
	UKF ukf;

/*******************************************************************************
* Programming assignment calls
*******************************************************************************/
    
    VectorXd x_pred = VectorXd(5);
    MatrixXd P_pred = MatrixXd(5, 5);
    ukf.PredictMeanAndCovariance(&x_pred, &P_pred);

	return 0;
}

#include <iostream>
#include "ukf.h"

UKF::UKF() {
  //TODO Auto-generated constructor stub
  Init();
}

UKF::~UKF() {
  //TODO Auto-generated destructor stub
}

void UKF::Init() {

}


/*******************************************************************************
* Programming assignment functions: 
*******************************************************************************/

void UKF::PredictMeanAndCovariance(VectorXd* x_out, MatrixXd* P_out) {

  //set state dimension
  int n_x = 5;

  //set augmented dimension
  int n_aug = 7;

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

  //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 vector for weights
  VectorXd weights = VectorXd(2*n_aug+1);
  
  //create vector for predicted state
  VectorXd x = VectorXd(n_x);

  //create covariance matrix for prediction
  MatrixXd P = MatrixXd(n_x, n_x);


/*******************************************************************************
 * Student part begin
 ******************************************************************************/

  //set weights
  //predict state mean
  //predict state covariance matrix


/*******************************************************************************
 * Student part end
 ******************************************************************************/

  //print result
  std::cout << "Predicted state" << std::endl;
  std::cout << x << std::endl;
  std::cout << "Predicted covariance matrix" << std::endl;
  std::cout << P << std::endl;

  //write result
  *x_out = x;
  *P_out = P;
}

#ifndef UKF_H
#define UKF_H
#include "Dense"
#include <vector>

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

class UKF {
public:


  /**
	 * Constructor
	 */
	UKF();

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

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

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

};

#endif /* UKF_H */

expected result x:

x =

5.93637

1.49035

2.20528

0.536853

0.353577

expected result p:

P =

0.00543425 -0.0024053 0.00341576 -0.00348196 -0.00299378

-0.0024053 0.010845 0.0014923 0.00980182 0.00791091

0.00341576 0.0014923 0.00580129 0.000778632 0.000792973

-0.00348196 0.00980182 0.000778632 0.0119238 0.0112491

-0.00299378 0.00791091 0.000792973 0.0112491 0.0126972