Adaptive minimax filtering via recursive optimal quadratic approximations

This paper considers the minimax filtering problem in which the supremum norm of weighted error sequence is minimized. It is shown that the minimax solution is also the optimal Set-Membership Filtering (SMF) solution. An adaptive algorithm is derived that is based on approximating the minimax cost function at each time instant using an optimal quadratic lower bound. The proposed recursions are simple, and resemble weighted RLS recursions but with optimal data-dependent weighting. The proposed algorithm offers several advantages over other minimax algorithms, such as lower computational complexity and the discerning updating strategy which significantly reduces average computational burden. Aside from seeking the best attainable SMF solution, the proposed algorithm also offers certain key advantages over traditional algorithms for SMF and Set-Membership Identification (SMI), including automatic bound tuning and absence of divergence problems due to model violations.