Tim Bailey, Ben Upcroft and Hugh Durrant-Whyte

Validation Gating for Non-Linear Non-Gaussian Target Tracking

IEEE Conference on Information Fusion, 2006


 

Description

For target-tracking problems, validation gating is applied to cull very unlikely measurement-to-track associations before remaining association ambiguities are handled by a more comprehensive (and expensive) data association scheme. For linear Gaussian systems, the ellipsoidal validation gate is standard, but it has imprecise acceptance statistics for non-linear non-Gaussian systems. Defining a general gating measure is non-trivial because several different probabilistic measures are equivalent to the ellipsoidal gate for Gaussians, but make nonsensical decisions for more general distributions. This paper presents a fundamental measure for well-behaved gating.

NOTE 1: It is important to realise that this paper has one essential goal: to derive the general probabilistic form of a non-Gaussian validation gate. It is not concerned with practical gating solutions for real systems; our presented implementation is too expensive to be practical. However, for a real system, any practical gate must ensure that it approximates our measure: max p(x, z = z_i), otherwise it will not perform sensible gating. Thus, we are concerned with defining what constitutes the ideal gating measure, not how to implement it. For many non-Gaussian systems, a practical approximation of this ideal should be straightforward.

NOTE 2: The choice of a bearing-only likelihood is not to imply that this sort of validation gating scheme is well suited to the bearing-only problem. We state again: this is not a practical gating scheme. Rather, the bearing-only likelihood is chosen because it has interesting shape, particularly the pointy bit near the origin where we have high likelihood but low mass concentration. This shape provides a good intuition for non-Gaussian gating behaviour.

Abstract

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.

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