SYSTEM IDENTIFICATION USING LAGUERRE MODELS[专业论文].pdfVIP

System Identification Using Laguerre Models BO Wahlberg, Member, IEEE Abstract-The traditional approach of expanding transfer unstable poles, it follows that functions and noise models in the delay operator to obtain linear-in-the-parameters predictor models leads to approxima- tions of very high order in cases of rapid sampling and/or dispersion in time constants. BY using U priori information about the time constants of the system more appropriate expan- sions, related to Laguerre networks, are introduced and ana- lyzed. It is shown that the model order can be reduced, com- pared to ARX (FIR, AR) modeling, by using Laguerre models. By truncating these expansions at k = n and taking e = (a, Furthermore, the numerical accuracy of the corresponding lin- a,, b, * b,,)the well-known ARX model structure is ear regression estimation problem is improved by a suitable choice of Laguerre parameter. derived. Setting { ak} equal to zero corresponds to the special Consistency (error bounds), persistance of excitation condi- case of a finite impulse response (FIR) model structure, and tions, and asymptoticstatistical properties are investigated. This by taking { b k } equal to zero, we obtain an autoregressive analysis is based od the result that the covariance matrix of the (AR) time series model structure. regression vector of a Laguerre model has a Toeplitz structure. In [2]-[4], the consistency and convergence properties of estimated FIR, ARX, and AR models, respectively, are