Subspace Identification for Linear Systems: Theory ― Implementation ― Applications

By P. Overschee, B. De Moor. 2011

2,350 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7a5b624ebbd7f4a6bd643daf15bf7dc763dc53ad

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Citations in the corpus

Hilbert Space Embeddings of Hidden Markov Models (2010, methodology): “…HMM to several alternative time series models including (I) linear dynamical systems (LDS) learned by Subspace Identification (Subspace ID) (Van Overschee & De Moor, 1996) with stability constraints (Siddiqi et al., 2008), (II) discrete HMMs learned by EM, and (III) the Reduced-rank HMM…”
Behavioral systems theory in data-driven analysis, signal processing, and control (2021, methodology): “…imarkovs@vub.be (Ivan Markovsky), dorfler@ethz.ch (Florian Dörfler) the global total least squares (Roorda and Heij, 1995), deterministic subspace (Van Overschee and De Moor, 1996), and structured low-rank approximation (Markovsky, 2013, 2019) approaches to system identification are motivated by…”
Learning GP-BayesFilters via Gaussian process latent variable models (2009, methodology): “…· System identification · Bayesian filtering · Time alignment · System control · Machine learning J. Ko ( ) · D. Fox Department of Computer Science & Engineering, University of Washington, Seattle, WA, USA e-mail: jonko@cs.washington.edu D. Fox Intel Labs Seattle, Intel Corp., Seattle, WA, USA”
Robust Spectral Filtering and Anomaly Detection (2018, background): “Across mathematics, statistics [29], artificial intelligence [25], and engineering [23, 36], much attention has been devoted to the identification of linear dynamical systems (LDS):”
Bayesian reasoning and machine learning (2012, unknown): “3 Subspace Methods An alternative to EM and Maximum Likelihood training of an LDS is to use a subspace method[281, 249].”
Closing the learning-planning loop with predictive state representations (2009, methodology): “The algorithm is closely related to subspace identification for learning Linear Dynamical Systems (LDSs) [23, 26] and spectral algorithms for learning Hidden Markov Models (HMMs) [6] and Reduced-Rank HMMs [19].”
Predictive-State Decoders: Encoding the Future into Recurrent Networks (2017, background): “In the controls literature, these approaches were developed as subspace identiﬁcation [51], and in the ML literature as spectral approaches for partially-observed systems [9, 8, 26, 56].”
Ergodic Theory, Dynamic Mode Decomposition, and Computation of Spectral Properties of the Koopman Operator (2016, background): “Singular Value Decomposition (SVD) is a central algorithm of linear algebra that lies at the heart of many data analysis techniques for dynamical systems including linear subspace identification methods [47] and DMD [38, 46].”
Identification of Hammerstein-Wiener models (2013, methodology): “The parameters of the noise filter state-space matrices (A⇠, C⌫ , Q) were initialised by using a subspace method [38] based on the measurements {y1, · · · , yN}.”