The effect of numerical stabilisation on AR spectral estimation

The paper considers the effect of the most successful stabilisation technique, first suggested by Botto (1989) on the windowed adaptive forward backward least squares algorithm when estimating AR spectra. The stabilisation technique depends on the availability of two different methods, precision arithmetic results in different values for each calculation. This difference can then be used to form an error signal and this can be used via feedback to maintain the numerical stability of the algorithm. It is shown that there is a price to be paid for the improved the numerical stability of the ABFLS algorithm. Each of the error feedback signals used to stabilise the algorithm has an associated gain and a major issue is the choice of these gains. The results of extensive simulations are used to illustrate how the stabilization techniques and selection of appropriate gains can adversely affect the quality of the spectral estimate