Validation Gating for Non-Linear Non-Gaussian Target Tracking

This paper develops a general theory of validation gating for non-linear non-Gaussian models. Validation gates are used in target tracking to cull very unlikely measurement-to-track associations, before remaining association ambiguities are handled by a more comprehensive (and expensive) data association scheme. The essential property of a gate is to accept a high percentage of correct associations, thus maximising track accuracy, but provide a sufficiently tight bound to minimise the number of ambiguous associations. For linear Gaussian systems, the ellipsoidal validation gate is standard, and possesses the statistical property whereby a given threshold will accept a certain percentage of true associations. This property does not hold for non-linear non-Gaussian models. As a system departs from linear-Gaussian, the ellipsoid gate tends to reject a higher than expected proportion of correct associations and permit an excess of false ones. In this paper, the concept of the ellipsoidal gate is extended to permit correct statistics for the non-linear non-Gaussian case. The new gate is demonstrated by a bearing-only tracking example