论文信息 - Optimization of the Window Shape in Weighted Least Squares Identification of a Class of Nonstationary Systems

Optimization of the Window Shape in Weighted Least Squares Identification of a Class of Nonstationary Systems

The problem of tracking of the coefficients of a time-varying linear stochastic system S is considered. Assuming that the coefficients of S are identified using the method of weighted least squares the effects of the window shape on the mean square tracking error are investigated. It is shown, using the method of variational calculus, that if the coefficients of S are evolving according to the “random-walk + jumps” model the exponential window is approximately the optimal one. In particular, it provides better results than the rectangular window of the “equivalent” width. The problem of matching the parameter trajectory of S is next stated. It is proved that the parameter-matching properties of the rectangular window are better than the corresponding properties of the exponential window.

M. Niedźwiecki

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