fusexcov

Covariance fusion using cross-covariance

Syntax

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

Description

example

````[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.```

example

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

Examples

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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')```

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

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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`

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`

Cross-covariance factor, specified as a scalar.

Data Types: `single` | `double`

Output Arguments

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

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.

Version History

Introduced in R2018b