Adaptive joint tracking of nonstationary system unknown parameters including the time delay

Abstract

The problem of joint parameters and time delay estimation or their tracking by processing of input-output observations arises, when LTI dynamical system has an unknown time delay. It is known that a mean-square error function is multiextremal for time delay even if the system parameters are known in advance. For this purpose an approach used to transform the multiextremal criterion into an unimodal function, in respect of the time delay, is developed and analyzed. Afterwards, it is possible to estimate unknown parameters and the time delay recursively by processing in each recursion pairs of input-output observation samples. The recursive approach based on the method of corrective operators is developed for the nonstationary dynamical systems with different excitations and additive noises, having the rational spectrum. Applicability of algorithms is supported by various simulation tests on a computer.