Abstract:
Tracking multiple objects is a challenging problem for an automated system,
with applications in many domains. Typically the system must be able to
represent the posterior distribution of the state of the targets, using a recursive
algorithm that takes information from noisy measurements. However, in
many important cases the number of targets is also unknown, and has also
to be estimated from data.
The Probability Hypothesis Density (PHD) filter is an effective approach
for this problem. The method uses a first-order moment approximation to
develop a recursive algorithm for the optimal Bayesian filter. The PHD
recursion can implemented in closed form in some restricted cases, and more
generally using Sequential Monte Carlo (SMC) methods. The assumptions
made in the PHD filter are appealing for computational reasons in real-time
tracking implementations. These are only justifiable when the signal to noise
ratio (SNR) of a single target is high enough that remediates the loss of
information from the approximation.
Although the original derivation of the PHD filter is based on functional
expansions of belief-mass functions, it can also be developed by exploiting elementary
constructions of Poisson processes. This thesis presents novel strategies
for improving the Sequential Monte Carlo implementation of PHD filter
using the point process approach. Firstly, we propose a post-processing state
estimation step for the PHD filter, using Markov Chain Monte Carlo methods
for mixture models. Secondly, we develop recursive Bayesian smoothing
algorithms using the approximations of the filter backwards in time. The
purpose of both strategies is to overcome the problems arising from the PHD
filter assumptions. As a motivating example, we analyze the performance of
the methods for the difficult problem of person tracking in crowded environments
