Accuracy Improvement in Least-Squares Estimation with Harmonic Regressor: New Preconditioning and Correction Methods
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| Title: | Accuracy Improvement in Least-Squares Estimation with Harmonic Regressor: New Preconditioning and Correction Methods |
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| Authors: | Stotsky, Alexander, 1960 |
| Source: | Proceedings of the IEEE Conference on Decision and Control. 54rd IEEE Conference on Decision and Control,CDC 2015:4035-4040 |
| Subject Terms: | Persistence of Excitation & Positive Definite Matrices, Recursive Least-Squares Estimation with High Accuracy |
| Description: | Numerical aspects of least squares estimation have not been sufficiently studied in the literature. In particular, information matrix has a large condition number for systems with harmonic regressor in the initial steps of RLS (Recursive Least Squares) estimation. A large condition number indicates invertibility problems and necessitates the development of new algorithms with improved accuracy of estimation. Symmetric and positive definite information matrix is presented in a block diagonal form in this paper using transformation, which involves the Schur complement. Block diagonal sub-matrices have significantly smaller condition numbers and therefore can be easily inverted, forming a preconditioner for a large scale system. High order algorithms with controllable accuracy are used for solving least squares estimation problem. The second part of the paper is devoted to the performance improvement in classical RLS algorithm, which represents a feedforward estimation procedure with error accumulation. Two correction feedback terms originated from combined high order algorithms are introduced for performance improvement in classical RLS algorithms. Simulation results show significant performance improvement of modified algorithm compared to classical RLS algorithm in the presence of roundoff errors. |
| File Description: | electronic |
| Access URL: | https://research.chalmers.se/publication/228545 http://publications.lib.chalmers.se/records/fulltext/228545/local_228545.pdf |
| Database: | SwePub |
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Nájsť tento článok vo Web of Science | Abstract: | Numerical aspects of least squares estimation have not been sufficiently studied in the literature. In particular, information matrix has a large condition number for systems with harmonic regressor in the initial steps of RLS (Recursive Least Squares) estimation. A large condition number indicates invertibility problems and necessitates the development of new algorithms with improved accuracy of estimation. Symmetric and positive definite information matrix is presented in a block diagonal form in this paper using transformation, which involves the Schur complement. Block diagonal sub-matrices have significantly smaller condition numbers and therefore can be easily inverted, forming a preconditioner for a large scale system. High order algorithms with controllable accuracy are used for solving least squares estimation problem. The second part of the paper is devoted to the performance improvement in classical RLS algorithm, which represents a feedforward estimation procedure with error accumulation. Two correction feedback terms originated from combined high order algorithms are introduced for performance improvement in classical RLS algorithms. Simulation results show significant performance improvement of modified algorithm compared to classical RLS algorithm in the presence of roundoff errors. |
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| ISBN: | 1479978868 9781479978861 |
| ISSN: | 25762370 07431546 |
| DOI: | 10.1109/CDC.2015.7402847 |