Continuous Time-Delay Estimation From Sampled Measurements

TL;DR

This paper introduces a novel continuous time-delay estimation algorithm from sampled data that accurately estimates subsample delays by leveraging Laguerre spectrum analysis, outperforming some existing methods.

Contribution

It presents a new two-step delay estimation method using Laguerre domain analysis, including bias modeling and comparison with state-of-the-art techniques.

Findings

Achieves comparable or higher accuracy than existing methods.

Effectively estimates subsample delays from noisy sampled data.

Provides a bias model for the delay estimation process.

Abstract

An algorithm for continuous time-delay estimation from sampled output data and known input of finite energy is presented. The continuous time-delay modeling allows for the estimation of subsample delays. The proposed estimation algorithm consists of two steps. First, the continuous Laguerre spectrum of the output signal is estimated from discrete-time (sampled) noisy measurements. Second, an estimate of the delay value is obtained in Laguerre domain given a continuous-time description of the input. The second step of the algorithm is shown to be intrinsically biased, the bias sources are established, and the bias itself is modeled. The proposed delay estimation approach is compared in a Monte-Carlo simulation with state-of-the-art methods implemented in time, frequency, and Laguerre domain demonstrating comparable or higher accuracy for the considered case.