Global total least squares modeling of multivariable time series

Roorda, Berend; Heij, Christiaan

doi:10.1109/9.362900

Cited by 67 publications

(25 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Total least squares is applied in computer vision [58], image reconstruction [65,54,22], speech and audio processing [39,29], modal and spectral analysis [89,93], linear system theory [14,13], system identification [66,37,63,52], and astronomy [8]. An overview of errors-in-variables methods in system identification is given by Söderström in [75].…”

Section: Applicationsmentioning

confidence: 99%

Overview of total least-squares methods

2007

View full text Add to dashboard Cite

We review the development and extensions of the classical total least squares method and describe algorithms for its generalization to weighted and structured approximation problems. In the generic case, the classical total least squares problem has a unique solution, which is given in analytic form in terms of the singular value decomposition of the data matrix. The weighted and structured total least squares problems have no such analytic solution and are currently solved numerically by local optimization methods. We explain how special structure of the weight matrix and the data matrix can be exploited for efficient cost function and first derivative computation. This allows to obtain computationally efficient solution methods. The total least squares family of methods has a wide range of applications in system theory, signal processing, and computer algebra. We describe the applications for deconvolution, linear prediction, and errors-in-variables system identification.

show abstract

Section: Applicationsmentioning

confidence: 99%

Overview of total least-squares methods

2007

View full text Add to dashboard Cite

show abstract

“…The behavioral approach to system theory put forward by Willems (1986Willems ( , 1987) is a manifestation of the representation free thinking. Deriving dynamic models from data, i.e., system identification, has been considered in the behavioral setting in Roorda and Heij (1995), Roorda (1995), and Markovsky, Willems, Van Huffel, De Moor, and Pintelon (2005).…”

Section: Contributions Of the Paper And Related Workmentioning

confidence: 99%

Structured low-rank approximation and its applications

2008

View full text Add to dashboard Cite

Fitting data by a bounded complexity linear model is equivalent to low-rank approximation of a matrix constructed from the data. The data matrix being Hankel structured is equivalent to the existence of a linear time-invariant system that fits the data and the rank constraint is related to a bound on the model complexity. In the special case of fitting by a static model, the data matrix and its low-rank approximation are unstructured.We outline applications in system theory (approximate realization, model reduction, output error, and errors-in-variables identification), signal processing (harmonic retrieval, sum-of-damped exponentials, and finite impulse response modeling), and computer algebra (approximate common divisor). Algorithms based on heuristics and local optimization methods are presented. Generalizations of the low-rank approximation problem result from different approximation criteria (e.g., weighted norm) and constraints on the data matrix (e.g., nonnegativity). Related problems are rank minimization and structured pseudospectra. ᭧

show abstract

“…The noisy I/O state estimation problem is treated implicitly in Roorda and Heij (1995) and Fagnani and Willems (1997), where the behavioral setting is adopted. In the behavioral setting, the observations are not partitioned into inputs and outputs and in this respect all observation channels are treated symmetrically.…”

Section: Introductionmentioning

confidence: 99%

“…In the behavioral setting, the observations are not partitioned into inputs and outputs and in this respect all observation channels are treated symmetrically. The global total least-squares problem of Roorda and Heij (1995) has as a subproblem the computation of the closest trajectory in the behavior of a given system to a given time series. This is a deterministic estimation problem, the recursive solution of which corresponds to the Kalman filter.…”

Section: Introductionmentioning

confidence: 99%

Linear Dynamic Filtering with Noisy Input and Output

Markovsky

Moor

2003

IFAC Proceedings Volumes

View full text Add to dashboard Cite

State estimation problems for linear time-invariant systems with noisy inputs and outputs are considered. An efficient recursive algorithm for the smoothing problem is presented. The equivalence between the optimal filter and an appropriately modified Kalman filter is established. The optimal estimate of the input signal is derived from the optimal state estimate. The result shows that the noisy input/output filtering problem is not fundamentally different from the classical Kalman filtering problem.

show abstract

Global total least squares modeling of multivariable time series

Cited by 67 publications

References 7 publications

Overview of total least-squares methods

Overview of total least-squares methods

Structured low-rank approximation and its applications

Linear Dynamic Filtering with Noisy Input and Output

Contact Info

Product

Resources

About