Analysis of overshoot phenomena in initialisation stage of RLS algorithm

Abstract

The well-known recursive least-squares (RLS) algorithm experiences overshoot in the norm of the parameter error vector temporarily during the initialisation stage when the initial value of the input autocorrelation matrix is chosen very small. We have had no guide to choose a suitable initial value of the input autocorrelation matrix in order to cause the RLS algorithm not to fluctuate during the initialisation phase. In this paper, deriving the bound of parameter error norm square, we give a useful guide to choose the initial value in order to avoid the initial overshoot in the RLS algorithm. Besides, we show that what are the crucial factors of the overshoot phenomena. The ratio of the initial value to the input power should be chosen according to the signal-to-noise ratio of the system and the order of the filter. We present various simulation results to validate our analysis.