Nonlinear filtering with application to the bearings only measurement problem

Graham, Angus (1992) Nonlinear filtering with application to the bearings only measurement problem. University of Southampton, Doctoral Thesis.

Abstract

The general nonlinear filtering problem, and the application to bearings only measurements is considered. The problem may be formulated from a variety of perspectives: the discrete state space approach utilised for this research is set in context. The basic methods of solution then involve either modal filtering, or linearising the system by approximation. The methods are compared and contrasted, and the algorithms derived, including a novel implementation of the modal filter for a noisy process. This method circumvents the two point boundary value problem, and the consequent approximation schemes, usually associated with modal estimation of a random vector. As the modal filters carry a high computational cost, and the linearised approximation methods are prone to unstable, even divergent behaviour, many variants on the basic filters have been developed. These are reviewed, and derived where appropriate. Another source of practical difficulty in filtering applications is that it is often not possible to define the system as fully as the filter requires. Methods for coping with inaccuracy and uncertainty in the filter's model of the system are reviewed and algorithms derived. As these methods predominantly assume linearity, attention is paid in particular to their potential for extension to the nonlinear environment. A novel method for minimising the effect on the estimation error of the sudden onset of uncertainty in the process is presented. The application of these methods to, and bounds on their performance in the bearings only measurement problem is then discussed, together with filters developed specifically for this case. Addressed are both the standard formulation of the problem, in which the target is unaccelerated, and the case where the target is capable of manoeuvre, inducing error in the filter's model of the process. Extensive simulation studies of a selection of these filters and bounds, over a wide range of dynamical and filter initialisation parameter values, are presented and analysed.

This record has no associated files available for download.

Contributors

Download statistics