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

Weiyu Xu; Erwei Bai; Myung Cho

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

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

Weiyu Xu, Erwei Bai and Myung Cho

ArXiv.org

07/17/2012

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https://arxiv.org/abs/1207.4104View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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.

Details

Title: Subtitle: Outliers and Random Noises in System Identification: a Compressed Sensing Approach
Creators: Weiyu Xu
Erwei Bai
Myung Cho
Resource Type: Preprint
Publication Details: ArXiv.org
ISSN: 2331-8422
Number of pages: 10 pages
Language: English
Date posted: 07/17/2012
Academic Unit: Electrical and Computer Engineering
Record Identifier: 9984198011702771

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