Robust and reduced-order filtering: new LMI-based characterizations and methods

This paper addresses several challenging problems of robust filtering. We derive new linear matrix inequality (LMI) characterizations of minimum variance or H/sub 2/ performance and demonstrate that they allow the use of parameter-dependent Lyapunov functions while preserving tractability of the pro...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2001-12, Vol.49 (12), p.2975-2984
Main Authors: Tuan, H.D., Apkarian, P., Nguyen, T.Q.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Computational efficiency
Computing time
Density measurement
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Filtering
Filtering algorithms
Filters
Filtration
Helium
Information, signal and communications theory
Linear matrix inequalities
Linear systems
Lyapunov functions
Lyapunov method
Noise robustness
Optimization
Power measurement
Riccati equations
Signal and communications theory
Signal processing
Signal, noise
Telecommunications and information theory
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Summary:This paper addresses several challenging problems of robust filtering. We derive new linear matrix inequality (LMI) characterizations of minimum variance or H/sub 2/ performance and demonstrate that they allow the use of parameter-dependent Lyapunov functions while preserving tractability of the problem. The resulting conditions are less conservative than earlier techniques, which are restricted to fixed (not parameter-dependent) Lyapunov functions. The remainder of the paper discusses reduced-order filter problems. New LMI-based nonconvex optimization formulations are introduced for the existence of reduced-order filters, and several efficient optimization algorithms of local and global optimization are proposed. Nontrivial and less conservative relaxation techniques are presented as well. The viability and efficiency of the proposed approaches are then illustrated through computational experiments and comparisons with existing methods.
ISSN:1053-587X
1941-0476
DOI:10.1109/78.969506