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In this paper, we consider robust system identification under sparse outliersand random noises. In our problem, system parameters are observed through aToeplitz matrix. All observations are subject to random noises and a few arecorrupted with outliers. We reduce this problem of system identification to asparse error correcting problem using a Toeplitz structured real-numberedcoding matrix. We prove the performance guarantee of Toeplitz structured matrixin sparse error correction. Thresholds on the percentage of correctable errorsfor Toeplitz structured matrices are also established. When both outliers andobservation noise are present, we have shown that the estimation error goes to0 asymptotically as long as the probability density function for observationnoise is not "vanishing" around 0.

Toeplitz Matrix Based Sparse Error Correction in System Identification: Outliers and Random Noises