Distributional properties of adaptive estimators

Abstract

The robustness and performance of adaptive systems is strongly coupled to the behaviour of the adaptive estimation component of these systems. It is important for ensuring satisfactory performance that the parameter estimates remain with high probability for a significant length of time within a region of satisfactory behaviour, even with measurement noise present. We study in this paper methods for examining this property of estimators. Firstly, we develop bounded-output-moment/bounded-output-moment (BIMBOM) stability results for LMS-based stochastic adaptive estimators. This allows the analysis of the factors influencing the variability of the estimates and hence some quantification of tail effects in the stationary distribution. Secondly, we study the application of the theory of large deviations to such algorithms to gauge the design variables influencing the probability of escape of the parameters at finite times and develop estimates of expected time to escape. Show more