Membership-Set Parameter Estimation via Optimal Bounding Ellipsoids.

摘要

In the last few years, there seems to have been a resurgence of interest in the membership-set-theoretic approach to parameter estimation. This report concentrates on the optimal bounding ellipsoid (OBE) approach to membership-set parameter estimation, with emphasis being placed on the performance of one particular OBE algorithm in nonideal conditions. It is first shown that OBE algorithms offer distinct advantages over commonly used recursive parameter estimation algorithms like the recursive least-squares (RLS) algorithm in some real-life environments. Then the extension of a particular OBE algorithm to the problem of parameter estimation with unobservable but bounded inputs (ARMA parameter estimation) is discussed in some detail. The problem is important because, in many signal processing applications, the inputs to the system under consideration are unknown. Analysis of the extended algorithm shows that under some conditions, the extended algorithm yields 100% confidence intervals for the parameters at every sampling instant. This feature does not appear to be present in any other existing ARMA parameter estimation algorithms. Furthermore, the transient performance of this algorithm is observed to be superior to that of the extended least-squares algorithm. Finite precision effects of one of the OBE algorithms are also studied via analysis of error propagation in the algorithm and through simulations. (KR)