Noise reduction in Laguerre-domain discrete delay estimation

TL;DR

This paper develops a stochastic framework for Laguerre-domain discrete delay estimation, introducing a new disturbance model and a noise reduction method that improves accuracy when noise is correlated.

Contribution

It proposes a novel Laguerre domain disturbance model and a noise reduction technique that enhances delay estimation accuracy in noisy environments.

Findings

Significant reduction in delay estimation error with correlated noise.

The disturbance model is applicable to various Laguerre-domain problems.

Improved noise robustness in delay estimation methods.

Abstract

This paper introduces a stochastic framework for a recently proposed discrete-time delay estimation method in Laguerre-domain, i.e. with the delay block input and output signals being represented by the corresponding Laguerre series. A novel Laguerre domain disturbance model is devised, which allows the involved signals to be square-summable sequences and is suitable in a number of important applications. The relation to two commonly used time-domain disturbance models is clarified. Furthermore, by forming the input signal in a certain way, the signal shape of an additive output disturbance can be estimated and utilized for noise reduction. It is demonstrated that a significant improvement in the delay estimation error is achieved when the noise sequence is correlated. The noise reduction approach is applicable to other Laguerre-domain problems than pure delay estimation.