Identification of Linear Time-varying Systems Using Haar Basis Functions
نویسندگان
چکیده
Most of the physical systems exhibit some degree of time-varying behavior. Physical phenomena exhibit time-varying behavior for a number of reasons. Some of the systems are inherently time-varying and can not effectively be modeled using time invariant models. This paper deals with the identification of time-varying systems using Haar basis functions. Basis functions approach involves expanding the time-varying parameters onto a set of basis functions and then estimating the resulting expansion coefficients. In this paper we employed first order Time-Varying Auto-Regressive with eXogenous input (TVARX) model and its parameters are estimated using Haar basis functions with forgetting factor approach. The input to the time-varying system is chosen to be a Pseudo-Random Binary Sequence (PRBS) which is frequency rich signal and excites complete system. Results obtained from a simulation study of time-varying systems are presented to demonstrate the performance of the Haar basis functions approach. Parameters are estimated for noisy and noiseless conditions. Comparisons of Haar basis functions with Walsh, Cosine and Legendre basis functions, for estimation of the time-varying parameters are presented and it is found that Haar Basis functions produce best results. Key Words, Parameter estimation, Haar basis functions, System identification, Time-varying systems, TVARX model.
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