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Proceedings Paper

Optimal inversions of uncertain matrices - an estimation and control perspective
Author(s): K. Mike Tao
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Paper Abstract

Many system and signal related problems involve matrix inversion of some kind. For example, in estimation and signal recovery applications, inversion of the channel response matrix is often required in order to estimate the source signals. In the control of multivariable systems, inverting a process gain matrix may be called for in order to deliver appropriate control actions. There are situations where these matrices should be considered as uncertain (or random): for example, when the process/channel environments vary randomly, or when significant uncertainties are involved in estimating these matrices. Based on a unified approach, this paper considers both the right inversion (for control) and the left inversion (for estimation) of random matrices. In both cases, minimizing a statistical error function leads to the determination of optimal or linear optimal inversion. Connections with related techniques, such as the total least squares (TLS), the ridge regression, the Levenberg-Marquardt algorithm and the regularization theory are discussed. A variant Kalman filtering problem with randomly varying measurement gain matrix is among the applications addressed. Monte Carlo simulation results show substantial benefits by taking process/model uncertainty into consideration.

Paper Details

Date Published: 24 December 2003
PDF: 15 pages
Proc. SPIE 5205, Advanced Signal Processing Algorithms, Architectures, and Implementations XIII, (24 December 2003); doi: 10.1117/12.504611
Show Author Affiliations
K. Mike Tao, SRI International (United States)

Published in SPIE Proceedings Vol. 5205:
Advanced Signal Processing Algorithms, Architectures, and Implementations XIII
Franklin T. Luk, Editor(s)

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