Parameter estimation on a fixed-point processor using the δ-operator

The delta (δ) operator has been proposed as an alternative to the shift (z) operator in the analysis of discrete systems. There has been little reportage in the literature on the practical real-time implementation of δ-based control or estimation algorithms, whose stated advantage lies in the area of numerical robustness. This paper examines this claim by assessing the problems associated with the real-time implementation of a recursive least squares (RLS) identification scheme based on the δ-operator. It is shown that implementation depends on the introduction of a stable polynomial operator F(δ) and a novel technique for optimising the choice of F(δ) is developed. Results are presented which clearly, show the advantage of the δ-operator over the z-operator in implementing the RLS algorithm on the TMS320C25 fixed point digital signal processor.