8

JOINT BAYESIAN STATE/PARAMETRIC PROCESSORS

**8.1 INTRODUCTION**

In this chapter we develop the Bayesian approach to the parameter estimation/system identification problem [1–4] which is based on the decomposition of the joint posterior distributions that incorporates *both* dynamic state and parameter variables. From this formulation the following problems evolve: (1) joint state/parameter estimation; (2) state estimation; and (3) parameter (fixed and/or dynamic) estimation. The state estimation problem is thoroughly discussed in the previous chapters. However, the most common problem found in the current literature is the parameter estimation problem which can be solved “off line” using batch approaches (maximum entropy, maximum likelihood, minimum variance, least squares, etc.) or “on-line” using the expectation-maximization (*EM*) technique (see Chapter 2), the stochastic Monte Carlo approach and for that matter almost any (deterministic) optimization technique [5, 6]. These on-line approaches follow the classical (*EKF*), modern (*UKF*)and the sequential Monte Carlo or particle filter (PF). However, it still appears that there is *no* universally accepted approach to solving this problem especially for fixed parameters [7–9]. From the pragmatic perspective, the most useful problem is the *joint* state/parameter estimation problem, since it evolves quite naturally from the fact that a model is developed to solve the basic state estimation problem and it is found that its inherent parameters ...