Recursive Estimation of the Parameters of Linear Systems with Time Delay

Abstract

Abstract The problem of joint parameter and time delay estimation of linear discrete-time single-input single-output dynamic systems from input-output data is analysed in this paper. It is known that a mean-square error function is multiextremal for time delay even if the system parameters are known in advance. Therefore, it is a general problem to recursively estimate the time delay and that is why nonrecursive algorithms are used in this case. For this purpose a technique to transform the multiextremal criterion into a unimodal function for time delay is proposed here. Hence, it is possible to use recursive algorithms for time delay and parameter estimation. Moreover, a recursive method to define the efficiency of the identification scheme is presented. Applicability of the algorithms is supported by simulation tests and by experimental identification of the process in the hydraulic pipeline.