An analysis of robust recursive algorithms for dynamic system identification is presented. Problems related to the construction of optimal stochastic approximation algorithms in the min-max sense are demonstrated. Starting from the definition of one class of robustified recursive identification algorithms, several procedures are derived through convenient approximations and initial assumptions. A detailed Monte Carlo analysis gives an insight into the practical robustness of these procedures indicating the most reliable ones. Important relationships between parameters describing the algorithms are pointed out.
1. Introduction
NUMEROUS practical experiences have shown that optimal statistical estimation methods can become highly ineffective in cases when the parametric statistical description of the model is not ideally fulfilled. Many convincing examples can be found in areas such as flight control, electric power systems, telecommunications, industrial process control, econometrics etc. (e.g. see the surveys by Ershov, 1978 and Hrgg, 1979).Estimation algorithms based on the Gaussian model have been found to be especially inefficient when the real distribution belongs to the heavy-tailed variety, occasionally giving rise to very large outliers (Huber, 1972;Barnet and Lewis, 1978). Considerable efforts have been oriented towards the design of robust estimation algorithms possessing a low sensitivity to distribution changes, usually valid locally, within prespecified distribution classes (Huber, 1964;Hampel, 1971;Papantoni-Kazakos, 1977). Numerous robust algorithms have been proposed starting from simple ad hoc modifications of the parametric estimates, reducing the effect of extreme disturbances (Barnet and Lewis, 1978;Ershov, 1978; Hrgg, 1979). The fundamental contribution to the field of robust estimation has been given by Huber (1964), who introduced the concept of min-max robust estimation. Further developments of this idea and applications to different types of problems, including system identification and adaptive control, have led to many valuable achievements (Huber, 1972;Tsypkin, 1982). However, modest efforts have been oriented towards systematic practical verifications. The achievement of robustness in practice requires a more profound understanding of possible criteria and ways of *