Robust Kalman filtering for uncertain systems
Systems & Control Letters
Robust Filtering of Discrete-Time Linear Systems with Parameter Dependent Lyapunov Functions
SIAM Journal on Control and Optimization
Robust Filtering via Semidefinite Programming with Applications to Target Tracking
SIAM Journal on Optimization
Robust and reduced-order filtering: new LMI-based characterizationsand methods
IEEE Transactions on Signal Processing
Optimal linear filtering under parameter uncertainty
IEEE Transactions on Signal Processing
Robust discrete-time minimum-variance filtering
IEEE Transactions on Signal Processing
New approaches to robust minimum variance filter design
IEEE Transactions on Signal Processing
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In this paper a new approach to H"2 robust filter design is proposed. Both continuous- and discrete-time invariant systems subject to polytopic parameter uncertainty are considered. After a brief discussion on some of the most expressive methods available for H"2 robust filter design, a new one based on a performance certificate calculation is presented. The performance certificate is given in terms of the gap produced by the robust filter between lower and upper bounds of a minimax programming problem where the H"2 norm of the estimation error is maximized with respect to the feasible uncertainties and minimized with respect to all linear, rational and causal filters. The calculations are performed through convex programming methods developed to deal with linear matrix inequality (LMI). Many examples borrowed from the literature to date are solved and it is shown that the proposed method outperforms all other designs.