Identification of Switched ARX Systems from Large Noisy Data Sets

The paper introduces a novel methodology for the identification of the coefficients of switched autoregressive exogenous (SARX) linear models. We consider the case when the system's outputs are contaminated by possibly large values of measurement noise. Partial information on the noise is available, in the form of the knowledge of a finite number of its moments (e.g. mean and variance). Given input-output data and the noise moments, we aim at identifying switched systems which are compatible with the collected data. System dynamics are estimated through expected values computation, by exploiting the strong law of large numbers. We demonstrate the efficiency of the proposed approach with several examples. The method is shown to be extremely effective in those situations where a large number of measurement is available, cases in which polynomial or mixed-integer optimization based methods encounter particular difficulties.

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