Kalman filter, particle filter, IMM, PDA, ITS, random sets... The number of useful object-tracking methods is exploding. But how are they related? How do they help track everything from aircraft, missiles and extra-terrestrial objects to people and lymphocyte cells? How can they be adapted to novel applications? Fundamentals of Object Tracking tells you how. Starting with the generic object-tracking problem, it outlines the generic Bayesian solution. It then shows systematically how to formulate the major tracking problems – maneuvering, multiobject, clutter, out-of-sequence sensors – within this Bayesian framework and how to derive the standard tracking solutions. This structured approach makes very complex object-tracking algorithms accessible to the growing number of users working on real-world tracking problems and supports them in designing their own tracking filters under their unique application constraints. The book concludes with a chapter on issues critical to successful implementation of tracking algorithms, such as track initialization and merging.

This paper is concerned with Gaussian approximations to the posterior probability density function (PDF) in the update step of Bayesian filtering with nonlinear measurements. In this setting, sigma-point approximations to the Kalman filter (KF) recursion are widely used due to their ease of implementation and relatively good performance. In the update step, these sigma-point KFs are equivalent to linearising the nonlinear measurement function by statistical linear regression (SLR) with respect to the prior PDF.In this paper, we argue that the measurement function should be linearised using SLR with respect to the posterior rather than the prior to take into account the information provided by the measurement. The resulting filter is referred to as the posterior linearisation filter (PLF). In practice, the exact PLF update is intractable but can be approximated by the iterated PLF (IPLF), which carries out iterated SLRs with respect to the best available approximation to the posterior. The IPLF can be seen as an approximate recursive Kullback-Leibler divergence minimisation procedure. We demonstrate the high performance of the IPLF in relation to other Gaussian filters in two numerical examples.

We propose a solution of the multiple target tracking (MTT) problem based on sets of trajectories and the random finite set framework. A full Bayesian approach to MTT should characterise the distribution of the trajectories given the measurements, as it contains all information about the trajectories. We attain this by considering multi-object density functions in which objects are trajectories. For the standard tracking models, we also describe a conjugate family of multitrajectory density functions.

Abstract-This paper considers the problem of simultaneously detecting and tracking multiple targets. The problem can be formulated in a Bayesian framework and solved, in principle, by computation of the joint multitarget probability density (JMPD). In practice, exact computation of the JMPD is impossible, and the predominant challenge is to arrive at a computationally tractable approximation. A particle filtering scheme is developed for this purpose in which each particle is a hypothesis on the number of targets present and the states of those targets. The importance density for the particle filter is designed in such a way that the measurements can guide sampling of both the target number and the target states. Simulation results, with measurements generated from real target trajectories, demonstrate the ability of the proposed procedure to simultaneously detect and track ten targets with a reasonable sample size.

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