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

TL;DR

This paper presents a method for robust system identification using Toeplitz matrices to correct sparse errors and handle noise, with proven performance guarantees and error thresholds.

Contribution

It introduces a novel approach leveraging Toeplitz structured matrices for sparse error correction in system identification, providing theoretical performance guarantees.

Findings

Performance guarantee established for Toeplitz matrices in error correction

Thresholds for correctable errors are derived

Estimation error approaches zero with sufficient noise conditions

Abstract

In this paper, we consider robust system identification under sparse outliers and random noises. In our 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 also 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.