Backward linear predictor and overfit techniques for estimating rational impulse responses

Abstract

The authors present a fast and robust algorithm, based on Prony's method, which improves the identification of time invariant linear systems with pure real poles in the transfer functions. Previous investigations have more or less avoided this aspect of broad-band signals and the phenomenon of pole splitting. The authors supplement overfit techniques and backward predictor formulation with a new method (in this context), based on an inspection of the coefficients related to the stable poles in the sum of exponentials. The capabilities of the proposed algorithm are investigated by means of Monte Carlo simulation and compared with the widely used KT algorithm of Kumaresan and Tufts. For the purpose of on-line identification they assume the system order to be known, although they do comment on some order detection strategies. The modified identification tool yields improved robustness (for instance concerning the problem of pole splitting) and a smaller bias, as illustrated by a typical third order system.