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Accuracy Improvement in Least-Squares Estimation with Harmonic Regressor: New Preconditioning and Correction Methods

Alexander Stotsky (Institutionen för energi och miljö, Elteknik)
54th IEEE Conference on Decision and Control (CDC), Osaka, Japan, Dec 15-18, 2015 (2015)
[Konferensbidrag, refereegranskat]

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.

Nyckelord: Recursive Least-Squares Estimation with High Accuracy; Persistence of Excitation & Positive Definite Matrices



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Denna post skapades 2015-12-17. Senast ändrad 2016-12-14.
CPL Pubid: 228545

 

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Institutioner (Chalmers)

Institutionen för energi och miljö, Elteknik

Ämnesområden

Energi
Numerisk analys
Optimeringslära, systemteori

Chalmers infrastruktur