Multiple-object estimation techniques for challenging scenarios

Abstract

A series of methods for solving the multi-object estimation problem in the context sequential Bayesian inference is presented. These methods concentrate on dealing with challenging scenarios of multiple target tracking, involving fundamental problems of nonlinearity and non-Gaussianity of processes, high state dimensionality, high number of targets, statistical dependence between target states, and degenerate cases of low signal-to-noise ratio, high uncertainty, lowly observable states or uninformative observations. These difficulties pose obstacles to most practical multi-object inference problems, lying at the heart of the shortcomings reported for state-of-the-art methods, and so elicit novel treatments to enable tackling a broader class of real problems. The novel algorithms offered as solutions in this dissertation address such challenges by acting on the root causes of the associated problems. Often this involves essential dilemmas commonly manifested in Statistics and Decision Theory, such as trading off estimation accuracy with algorithm complexity, soft versus hard decision, generality versus tractability, conciseness versus interpretativeness etc. All proposed algorithms constitute stochastic filters, each of which is formulated to address specific aspects of the challenges at hand while offering tools to achieve judicious compromises in the aforementioned dilemmas. Two of the filters address the weight degeneracy observed in sequential Monte Carlo filters, particularly for nonlinear processes. One of these filters is designed for nonlinear non-Gaussian high-dimensional problems, delivering representativeness of the uncertainty in high-dimensional states while mitigating part of the inaccuracies that arise from the curse of dimensionality. This filter is shown to cope well with scenarios of multimodality, high state uncertainty, uninformative observations and high number of false alarms. A multi-object filter deals with the problem of considering dependencies between target states in a way that is scalable to a large number of targets, by resorting to probabilistic graphical structures. Another multi-object filter treats the problem of reducing the computational complexity of a state-of-the-art cardinalized filter to deal with a large number of targets, without compromising accuracy significantly. Finally, a framework for associating measurements across observation sessions for scenarios of low state observability is proposed, with application to an important Space Surveillance task: cataloging of space debris in the geosynchronous/geostationary belt. The devised methods treat the considered challenges by bringing about rather general questions, and provide not only principled solutions but also analyzes the essence of the investigated problems, extrapolating the implemented techniques to a wider spectrum of similar problems in Signal Processing.