We present an order-recursive lattice algorithm for H ∞ adaptive filtering. The standard H ∞ filter algorithm is expressed in an alternative formula that is closed in a relaxed sense. On the basis of this formula, the algorithm is reformulated as an indefinite least-squares problem that can be solved by a two-dimensional block recursive least-squares (RLS) algorithm. Then an H ∞ lattice filter is derived by transforming the block RLS algorithm into its multivariable least-squares lattice form. The resulting computational complexity is still proportional to the filter order, although 2 × 2 matrix computations are involved. The equivalence between the standard H ∞ filter and its lattice version is verified by numerical experiments. Keywords: adaptive filtering, H ∞ filter, lattice filter This paper is organized as follows. Section 2 introduces a typical H ∞ adaptive filtering problem and its recursive solution. Section 3 derives a pseudo-closed-form expression for the standard solution, which is used to reformulate H ∞ adaptive filtering as an indefinite least-squares problem. In Sec. 4, the indefinite least-squares problem is solved by employing a two-dimensional block RLS algo-

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This paper examines the problem of exponentially-weighted H ∞ adaptive filtering and shows that its suboptimal solution reduces to a recursive algorithm which is slightly different from the RLS algorithm. Based on this similarity, its fast array form is immediately obtained by following the derivation of the fast RLS array algorithm. Also a theoretical expression for its steady-state mean-square error is provided. Several numerical examples indicate that the exponentially-weighted H ∞ filter can achieve a proper balance between H ∞ and H 2 (least squares) filtering criteria.