Fixed-point error analysis of the QR-recursive least square algorithm

Author

Diniz, Paulo S R ; Siqueira, Marcio G.

Author_Institution

Federal Univ. of Rio de Janeiro, Brazil

Volume

42

Issue

5

fYear

1995

fDate

5/1/1995 12:00:00 AM

Firstpage

334

Lastpage

348

Abstract

This paper presents a detailed analysis of the QR-RLS algorithm in finite and infinite precision environments. The mean squared values of all internal variables in steady state are derived. They are useful to dimension the wordlength of each variable of the algorithm. The recursive equations describing the quantization error propagation are derived and the stability conditions are presented. Then, we derive analytical expressions for the mean squared values of the deviations in the internal variables of the algorithm, for fixed-point arithmetic. In particular, new analytical expressions for the excess of mean squared error and for the variance of the deviation in the tap coefficients are derived. All the analytical results are confirmed to be accurate through computer simulations

Keywords

adaptive filters; digital arithmetic; error analysis; filtering theory; least squares approximations; numerical stability; recursive filters; QR-RLS algorithm; QR-recursive least squares algorithm; finite precision environment; fixed-point arithmetic; fixed-point error analysis; infinite precision environment; mean squared error; quantization error propagation; recursive equations; stability conditions; tap coefficients; Algorithm design and analysis; Analysis of variance; Computer errors; Equations; Error analysis; Fixed-point arithmetic; Least squares methods; Quantization; Stability; Steady-state;

fLanguage

English

Journal_Title

Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7130

Type

jour

DOI

10.1109/82.386173

Filename

386173