An optimal volume ellipsoid algorithm for parameter set estimation

Abstract

A recursive ellipsoid algorithm is derived for estimating the parameter set of a single-input single-output linear time-invariant system with bounded noise. The algorithm's objective is to seek the minimal volume ellipsoid bounding the feasible parameter set. Cast in a recursive framework, where a minimal volume ellipsoid results at each recursion, the algorithm extends a result due to Khachian (see Aspvall and Stone, 1980) in which a technique was developed to solve a class of linear programming problems. This extension and application to the parameter set estimation problem have intuitive geometric appeal and are easy to implement. Comparisons are made to the optimal bounding ellipsoid algorithm of Fogel and Huang (1982), and the results are demonstrated through computer simulations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>