Approximate EM Algorithms for Parameter and State Estimation in Nonlinear Stochastic Models

Abstract—Due to the availability of rapidly improving com-puter speeds, industry is increasingly using nonlinear process models in calculations that appear further down the control hierarchy. Indeed, nonlinear models are now frequently used for real-time control calculations. This trend means that there is growing interest in the availability of high speed state and parameter estimation algorithms for nonlinear models. One family of algorithms that can be used for this purpose is based on the, so called, Expectation Maximization Scheme. Unfortunately, in its basic form, this algorithm requires large computational resources. In this paper we review the EM algorithm and propose several approximate schemes aimed at retaining the essential flavour of this class of algorithm whilst ensuring that the computations are tractable. We will also compare the EM algorithm with several simpler schemes via a number of examples and comment on the trade-offs that occur. I