A fast sequential algorithm for least-squares filtering and prediction

A new computationally efficient algorithm for sequential least-squares (LS) estimation is presented in this paper. This fast a posteriori error sequential technique (FAEST) requires 5p MADPR (multiplications and divisions per recursion) for AR modeling and 7p MADPR for LS FIR filtering, where p is the number of estimated parameters. In contrast the well-known fast Kalman algorithm requires 8p MADPR for AR modeling and 10p MADPR for FIR filtering. The increased computational speed of the introduced algorithm stems from an alternative definition of the so-called Kalman gain vector, which takes better advantage of the relationships between forward and backward linear prediction.