Finite dimensional filters for ML estimation of discrete-time Gauss-Markov models

In this paper we derive a class of finite dimensional recursive filters for linear Gaussian state space systems. These finite dimensional filters can be used with the expectation maximization (EM) algorithm to yield maximum likelihood estimates of the parameters of a linear dynamical system. Important advantages of our filter-based EM algorithm compared with the standard smoother-based EM algorithm include: (i) substantially reduced memory requirements; (ii) ease of parallel implementation on a multiprocessor system. The algorithm has applications in multisensor signal enhancement of speech signals and also econometric modelling