Fast Adaptive Identification of Stable Innovation Filters

TL;DR

This paper introduces a fast, adaptive method for identifying the impulse response of innovation filters by leveraging a square root algorithm with low displacement rank, enabling efficient updates especially with well-conditioned architectures.

Contribution

It presents a novel, low-rank, square root algorithm for adaptive identification of innovation filters with improved computational efficiency and stability.

Findings

Filter update complexity is O(n) with low displacement rank conditions.

Triangular input balanced architecture ensures well-conditioned estimation.

The method achieves efficient real-time adaptive identification.

Abstract

The adaptive identification of the impulse response of an innovation filter is considered. The impulse response is a finite sum of known basis functions with unknown coefficients. These unknown coefficients are estimated using a pseudolinear regression. This estimate is implemented using a square root algorithm based on a displacement rank structure. When the initial conditions have low displacement rank, the filter update is $O(n)$. If the filter architecture is chosen to be triangular input balanced, the estimation problem is well-conditioned and a simple, low rank initialization is available.