fusecovunion

Covariance fusion using covariance union

Syntax

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

Description

[fusedState,fusedCov] = fusecovunion(trackState,trackCov) fuses the track states in trackState and their corresponding covariance matrices trackCov. The function estimates the fused state and covariance in a way that maintains consistency. For more details, see Consistent Estimator.

Examples

Covariance Union 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.

[fusedState,fusedCov] = fusecovunion(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('Covariance Union 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

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.

More About

Consistent Estimator

A consistent estimator is an estimator that converges in probability to the quantity being estimated as the sample size grows. In the case of tracking, a position estimate is consistent if its covariance (error) matrix is not smaller than the covariance of the actual distribution of the true state about the estimate. The covariance union method guarantees consistency by ensuring that all the individual means and covariances are bounded by the fused mean and covariance.

References

[1] Reece, Steven, and Stephen Rogers. "Generalised Covariance Union: A Unified Approach to Hypothesis Merging in Tracking." IEEE^® Transactions on Aerospace and Electronic Systems. Vol. 46, No. 1, Jan. 2010, pp. 207–221.

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

[3] Bochardt, Ottmar, et al. "Generalized information representation and compression using covariance union." Information Fusion, 2006 9th International Conference on. IEEE, 2006.

[4] Khachiyan, Leonid G. “Rounding of Polytopes in the Real Number Model of Computation.” Mathematics of Operations Research, vol. 21, no. 2, May 1996, pp. 307–20. DOI.org (Crossref), https://doi.org/10.1287/moor.21.2.307.

Extended Capabilities

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

Version History

Introduced in R2018b