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      Outliers and Random Noises in System Identification: a Compressed Sensing Approach

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          Abstract

          In this paper, we consider robust system identification under sparse outliers and random noises. In this problem, system parameters are observed through a Toeplitz matrix. All observations are subject to random noises and a few are corrupted with outliers. We reduce this problem of system identification to a sparse error correcting problem using a Toeplitz structured real-numbered coding matrix. We prove the performance guarantee of Toeplitz structured matrix in sparse error correction. Thresholds on the percentage of correctable errors for Toeplitz structured matrices are established. When both outliers and observation noise are present, we have shown that the estimation error goes to 0 asymptotically as long as the probability density function for observation noise is not "vanishing" around 0. No probabilistic assumptions are imposed on the outliers.

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          Author and article information

          Journal
          2012-07-17
          2013-05-27
          Article
          1207.4104
          3385cb42-0441-44f2-b43c-03d00f87c31a

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          10 pages, 5 figures
          cs.IT math.IT

          Numerical methods,Information systems & theory
          Numerical methods, Information systems & theory

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