Implementation of Bayesian Parameter Estimation in Adaptive Control and Signal Processing

Abstract

Severe constraints are put on Bayesian estimation in adaptive control and signal processing. The sequential character of computations together with finite memory boundaries often require using a reduced rather than sufficient statistic. A fixed sampling period firmly limits the computational time. Under these conditions, the textbook scheme of Bayesian estimation may be impracticable. This paper asks: 'Does there exist a looser scheme that would meet the practical constraints and still be consistent in a certain sense with the Bayesian paradigm?' The key point appears to be the construction of a reduced data statistic. When the equivalence induced by the used statistic on the set of possible posteriors is compatible with the Bayes rule action, the true Bayesian inference can be performed recursively on the equivalence classes of posteriors. This fact opens a way towards a better-justified real-time implementation of Bayesian parameter estimation.