A New Formalism of the Sliding Window Recursive Least Squares Algorithm and Its Fast Version

A new compact form of the sliding window recursive least squares (SWRLS) algorithm, the I-SWRLS algorithm, is derived using an indefinite matrix. The resultant algorithm has a form similar to that of the traditional recursive least squares (RLS) algorithm, and is more computationally efficient than the conventional SWRLS algorithm including two Riccati equations. Furthermore, a computationally reduced version of the I-SWRLS algorithm is developed utilizing a shift property of the correlation matrix of input data. The resulting fast algorithm reduces the computational complexity from O(N-2) to O(N) per iteration when the filter length (tap number) is N. but retains the same tracking performance as the original algorithm. This fast algorithm is much easier to implement than the existing SWC FTF algorithms.