Numerical characteristics of fast recursive least squares transversal adaptation algorithms — A comparative study

Abstract

In this paper, eight known fast recursive least squares (FLRS) algorithms are compared with respect to computing effort and numerical stability. A uniform mathema tical notation makes the close affinity between the different algorithms transparent. For the exact FRLS algorithms (without additional stabilization measures) transformation equations are given which allow an unambiguous mutual conversion. Under certain conditions, FRLS algorithms with additional stabilization are equivalent to the exact ones. Consequently all FRLS algorithms examined should theoretically in each iteration step yield the same estimate values as the well-known recursive least squares (RLS) algorithm. As a result of unpredictable round-off errors, deviations or even instability may occur. Simulations demonstrate the different numerical sensitivity of the algorithms and the effects of stabilizing efforts.