Abstract
The identification of AutoRegressive eXogenous (ARX) model by outliers is addressed in this paper. Shifted(non-centralized) asymmetric Laplace (SAL) distribution and expectation maximization (EM) algorithm are employed to estimate the unknown model parameters. Outliers are common in the signal acquisition process and have a serious impact on data-driven modeling method. In this paper, the probability method is used to solve the problem of outliers. When the noise parameter is regarded as a prior exponential distribution, the model output obeys the SAL distribution which is robust to outliers. The known statistical properties of SAL distribution are applied to calculate the M-step in the EM algorithm and get the iterative parametric formula. The accuracy of the proposed algorithm is verified by a numerical simulation example.
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