System identification in the presence of outliers and random noises: A compressed sensing approach

Xu, Weiyu; Bai, Er‐Wei; Cho, Myung‐Haing

doi:10.1016/j.automatica.2014.10.017

Cited by 23 publications

(32 citation statements)

References 17 publications

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“…It should be mentioned that the equivalence (i) ⇔ (ii) was also obtained in earlier papers, see e.g., [42,43].…”

Section: Worst-case Necessary and Sufficient Conditionssupporting

confidence: 71%

“…As a consequence, its minimizer is unique and equal to δ ⋆ = Ψϕ ⋆ . To see why the relation (46) holds, plug the expression (43) of θ ⋆ into (42). We get λs(ϕ ⋆ ) = Ψy − Ψϕ ⋆ .…”

Section: On the Treatment Of The Noise {E T }mentioning

confidence: 99%

“…The case when {f t } is zero and {e t } is a Gaussian process has been well-studied in linear system identification theory (see, e.g., the text books [23,38]). A less studied, but very relevant scenario in the system identification community, is when the additional perturbation {f t } in (1) is nonzero and contains intermittent and arbitrarily large errors [7,37,26,42]. It is worth noticing the difference with the problem studied in the field of compressive sensing [7,13,10].…”

Section: Introduction 1problem and Motivationsmentioning

confidence: 99%

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Analysis of a nonsmooth optimization approach to robust estimation

Bako

2016

Automatica

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In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily 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.

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“…It should be mentioned that the equivalence (i) ⇔ (ii) was also obtained in earlier papers, see e.g., [42,43].…”

Section: Worst-case Necessary and Sufficient Conditionssupporting

confidence: 71%

Section: On the Treatment Of The Noise {E T }mentioning

confidence: 99%

Section: Introduction 1problem and Motivationsmentioning

confidence: 99%

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Analysis of a nonsmooth optimization approach to robust estimation

Bako

2016

Automatica

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“…where we have used (27) and (9). This last inequality implies the negative definiteness of ∆V with respect to the origin for all states in M, which implies GES, therefore also GAS, of the origin for the dynamics restricted to M.…”

Section: Lemma 1 [21]mentioning

confidence: 99%

“…In [1] statistical tests are proposed that are less sensitive to abnormal noises. Identification based on an l 1 criterion is addressed in [16,27]. Instead of only attenuating the effect of outliers, a different approach is reported in [2], where a method based on a leave-one-out moving-horizon estimation strategy is proposed.…”

Section: Introductionmentioning

confidence: 99%

Stubborn state observers for linear time-invariant systems

Alessandri

Zaccarian

2018

Automatica

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For the purpose of estimating the state of a linear time-invariant system with measurements subject to outliers, we propose an observer with a saturated output injection in such a way to mitigate the effect of abnormal and isolated measurement noise on the error dynamics. Stability conditions in both the continuous-time and the discrete-time cases are derived, which ensure global exponential stability to the origin for the error dynamics. Such conditions can be expressed in terms of linear matrix inequalities, allowing for a viable design by using convex optimization. The effectiveness of the approach is illustrated by means of simulations in comparison with the Luenberger observer.

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Online continuous time system identification in the presence of impulsive terms

Belkoura

2022

Adaptive Control & Signal

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Online parameters estimation algorithms are proposed for continuous time systems subject to structured perturbations. Using a distribution framework, a matrix pencil structure, whose polynomial order is characterized by the nature of the singularities describing the impulsive effects, is proposed for the modeling of perturbed systems with different disturbance types. Then, using an appropriate projection subspace, the rectangular pencils are reformulated as square generalized eigenvalue problems subject to linear constraints, from which unperturbed regression are derived. This approach allows for the implementation of recursive estimation schemes, free of penalty terms. An identifiability analysis is also conducted, and theoretical results are illustrated with experimental and simulated data.

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System identification in the presence of outliers and random noises: A compressed sensing approach

Cited by 23 publications

References 17 publications

Analysis of a nonsmooth optimization approach to robust estimation

Analysis of a nonsmooth optimization approach to robust estimation

Stubborn state observers for linear time-invariant systems

Online continuous time system identification in the presence of impulsive terms

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