Dynamic Programming Solution of State Estimation Problems with Constrained Disturbances

Authors:	Mare José, The University of Newcastle, Australia De Dona Jose, The University of Newcastle, Australia
Topic:	1.1 Modelling, Identification & Signal Processing
Session:	Advances in Systems Theory and Nonlinear Filtering
Keywords:	Constraint satisfaction problems, Dynamic programming, Estimators

Abstract

This paper is concerned with maximum a posteriori state estimation of linear systems in the presence of constrained scalar process noise. The goalof this work is to investigate closed form solutions aimed at reducing the online computations required by the estimationproblem. Dynamic programming is used to derive a closed form solution that can be precomputed offline. The optimal solution is given by a piece-wise affine function of the data (the mean value of the initial state and the sequence of measurement data). The data space is partitioned into a number of polyhedral regions, inside each of which a unique affine function is applied.