An optimal volume ellipsoid algorithm for parameter set estimation

A recursive ellipsoid algorithm is derived for parameter set estimation of a single-input-single-output linear time-invariant system with bounded noise. The algorithm 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 in 1979 in which a technique was developed to solve a class of linear programming problems. This extension and application to the parameter set estimation problem has intuitive geometric appeal and is easy to implement. Comparisons are made to the optimal bounding ellipsoid algorithm of E. Fogel and Y.F. Huang, and the results are demonstrated via computer simulations