Analysis of the stabilized FTF algorithm with leakage correction

The O(7N) implementation of the fast transversal filter (FTF) for recursive least-squares (RLS) adaptive filtering is known to be numerically unstable. Stabilization methods for this algorithm employing error feedback can be difficult to tune and do not work for aggressive choices of the forgetting factor X. A numerically-stable FTF algorithm employing leakage correction has been introduced that overcomes many of these difficulties. In this paper, we analyze the stability characteristics of this new algorithm. Our analysis employs a linearized model of the errors in the states of the adaptive filter. Through our analysis, we prove that for positive leakage factors v/sub 1/ in the range 0/spl Lt/v/sub 1/\n\n\t\t