Principled Centroid Gating for Random Matrix Extended Object Tracking

Kurzfassung

Random matrix models are widely used approaches for extended object tracking, where the targets extent is described by a positive-definite matrix and combined with a conventional kinematic state-space model. While prediction and update formulas for the classical random matrix formulation are well established, a principled gating rule for the centroid measurements has been missing. In this paper, we derive a tractable gate for the sample mean of the measurements under the random matrix model with finite measurement noise. We start from the normal-inverse-Wishart hierarchy, marginalizing out the extent, and approximate the resulting predictive distribution of the sample mean by a multivariate t-distribution whose parameters are obtained by moment matching. This leads to a simple quadratic test statistic that follows an F-distribution and yields a closed-form ellipsoidal gate with prescribed coverage probability. This gate thus places existing practice on a solid mathematical footing and replaces an ad hoc construction by a fully justified, yet still simple, expression.