A Hybrid Parametric, Non-parametric Approach to Bayesian Target Tracking

This article describes a versatile approach to non-linear, non-Gaussian noise target tracking which makes use of both parametric and non-parametric techniques within a Bayesian framework. It produces a Gaussian mixture model (GMM) of a track, but resorts to a sampling technique within the tracking process to handle non-linearity. GMMs are recovered from samples using the expectation-maximisation method. The approach has been implemented in PV-WAVE software and tested against a Kalman-lter tracker in a simulator with air-defence scenarios. Sample results are presented for a scenario with a single surveillance-radar and a single target following a weaving path. These show that the tracker produces signiicantly better position estimates and comparable heading and speed estimates. Computation times are about 30 times greater than for the Kalman-lter tracker, but there is scope for reducing that substantially by tolerating fewer samples. 1. BACKGROUND Multi-sensor, multi-target tracking is a very important and active research area, with major developments dating back to the mid-1950's 1]. Almost invariably, the objective has been to produce a best estimate of a track state vector-either a mean or a maximum likelihood. With the development of data fusion techniques, it is important to have the track probability distribution as well, but with a suitably economic representation allowing ready calculation and acceptably low bandwidth permission of the controller of Her Brittanic Majesty's Stationary OOce demands in the communication links of distributed systems. Gaussian mixture models (GMMs) are recog-nised as good candidates 2] and we use them in this work. They are a logical progression from the single Gaussian model associated with Kalman-lter tracking. The latter has been the workhorse in tracking for around two decades, but in principle it is limited to linear, Gaussian noise applications. These GMMs are parametric; the parameters are sets of means, covariances and weights. Unfortunately, while handling non-Gaussian noise, they do not propagate as GMMs in the prediction process of non-linear tracking which is a major current challenge. Approximate approaches have been developed to overcome the dii-culty, but they are not invariably satisfactory 3]. Recently , Gordon, Salmond and Smith 4] used a boot-strap sampling approach to solve the problem. Their track model is non-parametric in that it consists merely of random samples from the track distribution. All calculations are in terms of these samples and a mean is used as the best track estimate. 2. PRESENT APPROACH We have been much persuaded by the merits of both …