Analysis of a nonsmooth optimization approach to robust estimation

• Published in: Automatica (Oxford) Vol. 66; pp. 132 - 145
• Main Authors: Bako, Laurent, Ohlsson, Henrik
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.04.2016; Elsevier
• Subjects: Automatic; Combinatorial analysis; Engineering Sciences; Error analysis; Hybrid systems; Mathematical analysis; Nonsmooth optimization; Optimization; Outliers; Permissible error; Robust estimation; State estimation; System identification; Vectors (mathematics); Outliers; Robust estimation; Nonsmooth optimization; System identification; outliers; system identification; nonsmooth optimization; robust estimation
• ISSN: 0005-1098; 1873-2836; 1873-2836
• DOI: 10.1016/j.automatica.2015.12.024

In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitrarily large errors. This is a fundamental problem in many estimation-related applications such as fault detection, state estimation in lossy networks, hybrid system identification, robust estimation, etc. The problem is hard because it exhibits some intrinsic combinatorial features. Therefore, obtaining an effective solution necessitates relaxations that are both solvable at a reasonable cost and effective in the sense that they can return the true parameter vector. The current paper discusses a nonsmooth convex optimization approach and provides a new analysis of its behavior. In particular, it is shown that under appropriate conditions on the data, an exact estimate can be recovered from data corrupted by a large (even infinite) number of gross errors.