Identification of Switched Autoregressive Systems from Large Noisy Data Sets

Abstract: The paper introduces a novel methodology for the identification of coefficients of switched autoregressive linear models. We consider the case when the system's outputs are contaminated by possibly large values of measurement noise. It is assumed that only partial information on the probability distribution of the noise is available. Given input-output data, we aim at identifying switched system coefficients and parameters of the distribution of the noise which are compatible with the collected data. System dynamics are estimated through expected values computation and by exploiting the strong law of large numbers. We demonstrate the efficiency of the proposed approach with several academic examples. The method is shown to be extremely effective in the situations where a large number of measurements is available; cases in which previous approaches based on polynomial or mixed-integer optimization cannot be applied due to very large computational burden.