New adaptive filtering algorithms based on an orthogonal projection of gradient vectors

In this letter, we propose tno algorithms for adaptive finite impulse respo nse (FIR) filters as variants of the filtered gradient adaptive (FGA) algor ithm. 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 di rection vector is orthogonal to the previous direction vector, while the FG A algorithm uses a fixed one. It is shown through the computer simulations that the proposed algorithms are superior in terms of convergence and track ing capability to the FGA algorithm.