Time-Varying Systems

Abstract

A large number of physical systems are nonstationary. Identification of nonstationary processes have been widely studied in the literature for linear systems. Traditional techniques for identifying linear time-varying (LTV) systems are mostly based on the recursive weighted least squares methods (see [106], [22], [83], [34], [124]). The weights are dependent on time, in the sense that the most recent measurements should be privileged, while the oldest should have the smallest influence on the estimate. If the time horizon is too long, i.e. the weights decrease too slow, we obtain the bias connected with parameter changes. On the other hand, if the horizon is short, the estimate becomes sensitive on the noise and the variance error appears. The goal is thus to design a good compromise between bias and variance, i.e., we look for a good trade-off between tracking ability and noise rejection [84], [103], [82], [104]. Some of methods proposed in the literature use the Kalman filter approach [16], or expand jump changes of the coefficients in the wavelet series [137]. As regards the identification of time-varying nonlinear block-oriented (Hammerstein and Wiener) systems, comparatively little attention has been paid in the literature. It is commonly assumed that the nonlinear regression is quasi-stationary, i.e., that the system becomes stationary as the measurement index tends to infinity (see [51], [115], [116], [117]).