High-level primitives for linear estimation

This paper proposes a high level language constituted of only a few 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 (only the first case is considered here). The use of high level primitive allows the development of highly modular ML estimation algorithms based on only few numerical 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 ones, 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 considering the filtering and smoothing problems for linear descriptor systems, as well as failure detection and isolation