Bernard C. Levy, Albert Benveniste and Ramine Nikoukhah
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.
Keywords : estimation, smoothing, failure detection, descriptor systems, belief networks.