AN OPTIMAL VOLUME ELLIPSOID ALGORITHM FOR PARAMETER SET ESTIMATION

In this note, a recursive ellipsoid algorithm is derived for parameter set estimation of a SISO linear time-invariant system with bounded no ise. The algorithm objective is in seeking the minimal volume ellipsoi d bounding the feasible parameter set. Cast in a recursive framework, where a minimal volume ellipsoid results at each recursion, the algori thm extends a result due to Khachian in 1979 in which a technique was developed to solve a class of linear programming problems. This extens ion and application to the parameter set estimation problem has intuit ive geometric appeal and is easy to implement. Comparisons are made to the Optimal Bounding Ellipsoid (OBE) algorithm of Fogel and Huang, an d the results are demonstrated via computer simulations.