fusexcov

Covariance fusion using cross-covariance

Syntax

[fusedState,fusedCov] = fusexcov(trackState,trackCov)

[fusedState,fusedCov] = fusexcov(trackState,trackCov,crossCovFactor)

Description

[fusedState,fusedCov] = fusexcov(trackState,trackCov) fuses the track states in trackState and their corresponding covariance matrices trackCov. The function estimates the fused state and covariance within a Bayesian framework in which the cross-correlation between tracks is unknown.

[fusedState,fusedCov] = fusexcov(trackState,trackCov,crossCovFactor) specifies a cross-covariance factor for the effective correlation coefficient when computing the cross-covariance.

Examples

Cross-Covariance Fusion Using Default Values

Define a state vector of tracks.

x(:,1) = [1;2;0];
x(:,2) = [2;2;0];
x(:,3) = [2;3;0];

Define the covariance matrices of the tracks.

p(:,:,1) = [10 5 0; 5 10 0;0 0 1];
p(:,:,2) = [10 -5 0; -5 10 0;0 0 1];
p(:,:,3) = [12 9 0; 9 12 0;0 0 1];

Estimate the fused state vector and its covariance.

[fusedState,fusedCov] = fusexcov(x,p);

Use trackPlotter to plot the results.

tPlotter = theaterPlot('XLim',[-10 10],'YLim',[-10 10],'ZLim',[-10 10]);
tPlotter1 = trackPlotter(tPlotter, ...
    'DisplayName','Input Tracks','MarkerEdgeColor',[0.000 0.447 0.741]);
tPlotter2 = trackPlotter(tPlotter, ...
    'DisplayName','Fused Track','MarkerEdgeColor',[0.850 0.325 0.098]);
plotTrack(tPlotter1,x',p)
plotTrack(tPlotter2, fusedState', fusedCov)
title('Cross-Covariance Fusion')

Cross-Covariance Fusion Using Cross-Covariance Factor

Define a state vector of tracks.

x(:,1) = [1;2;0];
x(:,2) = [2;2;0];
x(:,3) = [2;3;0];

Define the covariance matrices of the tracks.

p(:,:,1) = [10 5 0; 5 10 0;0 0 1];
p(:,:,2) = [10 -5 0; -5 10 0;0 0 1];
p(:,:,3) = [12 9 0; 9 12 0;0 0 1];

Estimate the fused state vector and its covariance. Specify a cross-covariance factor of 0.5.

[fusedState,fusedCov] = fusexcov(x,p,0.5);

Use trackPlotter to plot the results.

tPlotter = theaterPlot('XLim',[-10 10],'YLim',[-10 10],'ZLim',[-10 10]);
tPlotter1 = trackPlotter(tPlotter, ...
    'DisplayName','Input Tracks','MarkerEdgeColor',[0.000 0.447 0.741]);
tPlotter2 = trackPlotter(tPlotter, ...
    'DisplayName','Fused Track','MarkerEdgeColor',[0.850 0.325 0.098]);
plotTrack(tPlotter1,x',p)
plotTrack(tPlotter2, fusedState', fusedCov)
title('Cross-Covariance Fusion')

Input Arguments

trackState — Track states

N-by-M matrix

Track states, specified as an N-by-M matrix, where N is the dimension of the state and M is the number of tracks.

Data Types: single | double

trackCov — Track covariance matrices

N-by-N-by-M array

Track covariance matrices, specified as an N-by-N-by-M array, where N is the dimension of the state and M is the number of tracks.

Data Types: single | double

crossCovFactor — Cross-covariance factor

0.4 (default) | scalar

Cross-covariance factor, specified as a scalar.

Data Types: single | double

Output Arguments

fusedState — Fused state

N-by-1 vector

Fused state, returned as an N-by-1 vector, where N is the dimension of the state.

fusedCov — Fused covariance matrix

N-by-N matrix

Fused covariance matrix, returned as an N-by-N matrix, where N is the dimension of the state.

References

[1] Bar-Shalom, Yaakov, and Xiao-Rong Li. Multitarget-multisensor tracking: principles and techniques. Vol. 19. Storrs, CT: YBs, 1995.

[2] Weng, Zhiyuan, and Petar M. Djurić. "A bayesian approach to covariance estimation and data fusion." In 2012 Proceedings of the 20th European Signal Processing Conference , pp. 2352-2356. IEEE, 2012.

[3] Matzka, Stephan, and Richard Altendorfer. "A comparison of track-to-track fusion algorithms for automotive sensor fusion." In Multisensor Fusion and Integration for Intelligent Systems, pp. 69-81. Springer, Berlin, Heidelberg, 2009.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2018b