Membership Set Estimation – An Alternative Approach to System Identification

Abstract

Bounds on the magnitude of the noise or on the energy of the noise lend themselves to the formulation of system identification as a membership set estimation problem.In the case of energy bounded noise, a recursive algorithm for constructing a sequence of ellipsoids containing the true parameter vector is constructed. Convergence properties of the estimator are established. The relation between the convergence of the sequence of ellipsoids and convergence in the probabilistic sense is discussed. Furthermore, our approach demonstrates that the convergence of the unstable modes is superior to that of the stable modes (Fogel, 1979).The formulation of parameter set estimation in the bounded noise case yields algorithms which are capable of ignoring redundant data. A sequence of ellipsoids are updated with each measurement. Only data points which reduce the size of the ellipsoids are actually used in the update. Thus an efficient procedure for discarding redundant data in system identification is obtained (Fogel and Huang, 1982). Convergence analysis and identifiability condition in the set estimation context are obtained.