Efficient time-recursive least-squares algorithms for finite-memory adaptive filtering

This paper deals with efficient algorithms in the sense of minimization of the computational complexity for least-squares (LS) adaptive filters with finite memory. These filters obtain the current estimate of the desired response using only a fixed finite number of past data. First, two new fast recursive least-squares algorithms with computational complexities and multiplications and divisions per recursion (MADPR), respectively, are introduced ( is the filter order). Then a new estimation-error-oriented recursive modified Gram-Schmidt (RMGS) scheme with a complexity of MADPR is given. Finally, the learning characteristics of these algorithms are discussed and some simulation results are included.