Refined instrumental variable methods of recursive time-series analysis Part III. Extensions

Abstract

This is the final paper in a series of three which have been concerned with the comprehensive evaluation of the refined instrumental variable (IV) method of recursive time-series analysis. The paper shows how the refined IV procedure can be extended in various important directions and how it can provide the basis for the synthesis of optimal generalized equation error (GEE) algorithms for a wide class of stochastic dynamic systems. The topics discussed include the estimation of parameters in continuous-time differential equation models from continuous or discrete data; the estimation of time-variable parameters in continuous or discrete-time models of dynamic systems ; the design of stochastic state reconstruction (Wiener-Kalman) filters direct from data ; the estimation of parameters in multi-input, single output (MISO) transfer function models ; the design of simple stochastic approximation (SA) implementations of the refined IV algorithms ; and the use of the recursive algorithms in self-adaptive (self tuning) control.