MIT Department of Electrical Engineering & Computer Science

Observation Quantisation for Nonlinear Estimators

Dr. Nigel J. Newton
Department of Electronic Systems Engineering, Essex University, UK

Tuesday, December 14, 1999
4:00 PM (reception following)
Room 35-225
LIDS Colloquium

Abstract

The use of coarsely quantised observations with nonlinear estimators can substantially reduce the computational complexity of numerical implementations. For example, the nonlinear liklihood functions for quantised observations have finite support, and so can be pre-computed for each possible value of the observation and stored for rapid retrieval in real-time implementations.

The talk will concern the characterisation of the loss of information arising from the use of observation quantisation, and will consider estimators with both discrete- and continuous-time observations. In the former case, the loss of information for estimators with substantially noisy observations sequences will be quantified by means of a functional central-limit theorem. This quantification allows the optimisation of the quantisation parameters for such estimators, and shows that the loss of information is small, even for coarse quantisation schemes.

A related theorem for estimators with continuous-time observations will be discussed. This can be thought of as a `stochastic over-sampling theorem'. Its implications on numerical methods for continuous-time estimators will also be considered.