Structured low-rank approximation and its applications

Markovsky, Ivan

doi:10.1016/j.automatica.2007.09.011

Cited by 233 publications

(195 citation statements)

References 31 publications

(29 reference statements)

Supporting

Mentioning

195

Contrasting

Order By: Relevance

“…These problems can be solved by existing methods, e.g., the prediction error (Söderström and Stoica 1989;Ljung 1999) and the low-rank approximation methods (Markovsky 2008;Markovsky and Usevich 2014). Deriving the the maximum likelihood estimator for the dynamic measurement problem with unknown dynamics is our second contribution.…”

Section: Novelty and Contributionsmentioning

confidence: 99%

An application of system identification in metrology

Markovsky

2015

Control Engineering Practice

Self Cite

View full text Add to dashboard Cite

Metrology is advancing by development of new measurement techniques and corresponding hardware. A given measurement technique, however, has fundamental speed and precision limitations. In order to overcome the hardware limitations, we develop signal processing methods based on the prior knowledge that the measurement process dynamics is linear time-invariant.Our approach is to model the measurement process as a step response of a dynamical system, where the input step level is the quantity of interest. The solution proposed is an algorithm that does real-time processing of the sensor's measurements. It is shown that when the measurement process dynamics is known, the input estimation problem is equivalent to state estimation. Otherwise, the input estimation problem can be solved as a system identification problem. The main underlying assumption is that the measured quantity is constant and the measurement process is a low-order linear time-invariant system. The methods are validated and compared on applications of temperature and weight measurement.

show abstract

Section: Novelty and Contributionsmentioning

confidence: 99%

An application of system identification in metrology

Markovsky

2015

Control Engineering Practice

Self Cite

View full text Add to dashboard Cite

show abstract

“…SLRA of a Hankel matrix with m = r + 1 rows and rank reduction by 1 is equivalent to identification of an autonomous linear-time-invariant system of order less than or equal to r [10].…”

Section: Identification Of Autonomous Systemsmentioning

confidence: 99%

“…(SLRA). For a given p ∈ R n p , structure S and natural number r < m minimize ∆p∈R np ∆p 2 subject to rank S (p − ∆p) ≤ r. (2) Many problems in system identification, signal processing and computer algebra can be posed and solved as SLRA problem [10,19]. A common case of an affine structure is…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Structured low-rank approximation as a rational function minimization

Usevich

Markovsky

2012

IFAC Proceedings Volumes

Self Cite

View full text Add to dashboard Cite

Many problems of system identification, model reduction and signal processing can be posed and solved as a structured low-rank approximation problem. In this paper a reformulation of the structured low-rank approximation problem as minimization of a multivariate rational function is considered. Using two different parametrizations, we show that the problem reduces to optimization over a compact manifold or to a set of optimization problems over bounded domains of Euclidean space. We make a review of methods of polynomial algebra for global optimization of the rational cost function.

show abstract

“…The method of Cadzow [6] alternates between these two steps until the algorithm converges to a solution that is indeed low-rank and structured. However, as Chu et al [8] and Markovsky [12] state, this solution can be far away from the initialization with no guarantees of finding an actually meaningful approximation to the data. Recently, Ishteva et al [11] have proposed a factorization approach with a cost function that joints the structural and low-rank constraint.…”

Section: Introductionmentioning

confidence: 99%

Robust Structured Low-Rank Approximation on the Grassmannian

Hage

Kleinsteuber

2015

Latent Variable Analysis and Signal Separation

View full text Add to dashboard Cite

Abstract. Over the past years Robust PCA has been established as a standard tool for reliable low-rank approximation of matrices in the presence of outliers. Recently, the Robust PCA approach via nuclear norm minimization has been extended to matrices with linear structures which appear in applications such as system identification and data series analysis. At the same time it has been shown how to control the rank of a structured approximation via matrix factorization approaches. The drawbacks of these methods either lie in the lack of robustness against outliers or in their static nature of repeated batch-processing. We present a Robust Structured Low-Rank Approximation method on the Grassmannian that on the one hand allows for fast re-initialization in an online setting due to subspace identification with manifolds, and that is robust against outliers due to a smooth approximation of the p -norm cost function on the other hand. The method is evaluated in online time series forecasting tasks on simulated and realworld data.

show abstract

Structured low-rank approximation and its applications

Cited by 233 publications

References 31 publications

An application of system identification in metrology

An application of system identification in metrology

Structured low-rank approximation as a rational function minimization

Robust Structured Low-Rank Approximation on the Grassmannian

Contact Info

Product

Resources

About