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In this letter, we propose two algorithms for adaptive finite impulse response (FIR) filters as variants of the filtered gradient adaptive (FGA) algorithm. The proposed algorithms are formulated from the FGA by introducing an orthogonal constraint between the direction vectors. The algorithms employ the forgetting factor optimized on a sample-by-sample basis so that the direction vector is orthogonal to the previous direction vector, while the FGA algorithm uses a fixed one. It is shown through the computer simulations that the proposed algorithms are superior in terms of convergence and tracking capability to the FGA algorithm.