A Track-to-Track Fusion Method for Tracks With Unknown Correlations

This letter deals with the problem of track-totrack fusion under unknown correlations. We propose a novel method to construct the correlation terms between tracks from two sensors. We start by showing that the cross-covariance matrix of any two tracks can be expressed as the product of square roots of the tracks' covariance matrices and a contraction matrix. Then, we propose an optimization problem that obtains an estimate of this contraction matrix in a way that the fused track is less conservative than the one obtained by the well-known covariance intersection method but, at the same time, it is conservative in comparison with the optimal track obtained using the exact cross-covariance between the tracks. Through rigorous analysis we demonstrate our new fusion algorithm's properties. We also cast our design optimization problem as a difference of convex (DC) programming problem, which can be solved in an efficient manner using DC programming software solutions. We demonstrate our results through Monte Carlo simulations.