The KaGE RLS algorithm

A new fast recursive least squares (RLS) algorithm, the Kalman gain estimator (KaGE), is introduced. By making use of RLS interpolation as well as prediction, the algorithm generates the transversal filter weights without suffering the poor numerical attributes of the fast transversal filter (FTF) algorithm. The Kalman gain vector is generated at each time step in terms of interpolation residuals. The interpolation residuals are calculated in an order recursive manner. For an N^th-order problem, the procedure requires O(Nlog₂N) operations per iteration. This is achieved via a divide-and-conquer approach. Computer simulations suggest that the new algorithm is numerically robust, running successfully for many millions of iterations.