High-level primitives for recursive maximum likelihood estimation

This paper proposes a high-level language constituted of a small number of primitives and macros for describing recursive maximum likelihood (ML) estimation algorithms. This language is applicable to estimation problems involving linear Gaussian models or processes taking values in a finite set. The use of high-level primitives allows the development of highly modular ML estimation algorithms based on simple numerical building blocks. The primitives, which correspond to the combination of different measurements, the extraction of sufficient statistics, and the conversion of the status of a variable from unknown to observed, or vice versa, are first defined for linear Gaussian relations specifying mixed deterministic/stochastic information about the system variables. These primitives are used to define other macros and are illustrated by deriving new filtering and smoothing algorithms for linear descriptor systems. The primitives are then extended to finite state processes and used to implement the Viterbi ML state sequence estimator for a hidden Markov model.