Random finite sets in Multi-object filtering

THE multi-object filtering problem is a logical and fundamental generalization of the ubiquitous single-object vector filtering problem. Multi-object filtering essentially concerns the joint detection and estimation of the unknown and time-varying number of objects present, and the dynamic state of each of these objects, given a sequence of observation sets. This problem is intrinsically challenging because, given an observation set, there is no knowledge of which object generated which measurement, if any, and the detected measurements are indistinguishable from false alarms. Multi-object filtering poses significant technical challenges, and is indeed an established area of research, with many applications in both military and commercial realms. The new and emerging approach to multi-object filtering is based on the formal theory of random finite sets, and is a natural, elegant and rigorous framework for the theory of multiobject filtering, originally proposed by Mahler. In contrast to traditional approaches, the random finite set framework is completely free of explicit data associations. The random finite set framework is adopted in this dissertation as the basis for a principled and comprehensive study of multi-object filtering. The premise of this framework is that the collection of object states and measurements at any time are treated namely as random finite sets. A random finite set is simply a finite-set-valued random variable, i.e. a random variable which is random in both the number of elements and the values of the elements themselves. Consequently, formulating the multiobject filtering problem using random finite set models precisely encapsulates the essence of the multi-object filtering problem, and enables the development of principled solutions therein. The central thesis of this dissertation is that the random finite set framework not only is a natural, elegant and rigorous foundation, but also leads to practical, efficient and reliable algorithms for Bayesian multi-object filtering. In support of this thesis, the following fundamental contributions are established within the random finite set framework. The first key contribution is a mathematically rigorous derivation and practical implementation of a novel algorithm for the important case of single-object Bayesian filtering, with multiple measurements generated by the object, state dependent sensor field of view and clutter. The performance of the proposed algorithm is demonstrated in simulated scenarios, and shown at least in simulation to dramatically outperform traditional single-object filtering in clutter approaches. The second iv key contribution is a mathematically principled derivation and practical implementation of a novel algorithm for multi-object Bayesian filtering, based on moment approximations to the posterior density of the random finite set state. The performance of the proposed algorithm is also demonstrated in practical scenarios, and shown to considerably outperform traditional multi-object filtering approaches. The third key contribution is a mathematically principled derivation and practical implementation of a novel algorithm for multi-object Bayesian filtering, based on functional approximations to the posterior density of the random finite set state. The performance of the proposed algorithm is compared with the previous, and shown to appreciably outperform the previous in certain classes of situations. The final key contribution is the definition of a consistent and efficiently computable metric for multi-object performance evaluation. It is shown that the finite set theoretic state space formulation permits a mathematically rigorous and physically intuitive construct for measuring the estimation error of a multi-object filter, in the form of a metric. This metric is used to evaluate and compare the multi-object filtering algorithms developed in this dissertation.