Bayesian methods for tracking
Neil Gordon · Spiral (Imperial College London) · 1993
Bayesian methods provide a rigorous general framework for dynamic state estimation and target tracking problems.The Bayesian approach is to construct the probability density function (pdf) of the state based on all available information.However, for situations where non-linear and/or non-Gaussian modelling is appropriate, in general, no analytic (closed form) expression for the required pdf exists.An example of this is the bearings-only tracking problem.This thesis is concerned with the development and analysis of techniques for the implementation of non-linear/non-Gaussian Bayesian recursive filters.Three distinct contributions are presented:1) A new recursive estimation procedure is proposed for the location of a dynamic linear model with non-normal errors.The procedure is a modification of a modal approximation algorithm, which is shown to be prone to instabilities.The modification is motivated by a notion of posterior modal consistency.2) An algorithm, which we call the bootstrap filter, is proposed for implementing general Bayesian recursive filters.The required pdf of the state is represented as a set of random samples, which are updated and propagated by the algorithm.The method is not restricted by assumptions of linearity or Gaussian noise.Simulation examples (including a bearings-only tracking problem) are presented to illustrate the efficacy and performance of the algorithm.Schemes are suggested for improving the efficiency of the basic algorithm.3) An algorithm is introduced for state estimation after group pattern distortion.This algorithm is based on a dependent motion model in which two processes act to move and distort the group.One is a bulk effect that acts equally on all members of the group, while the other is independent for each group member.The algorithm copes with missing and spurious measurements.