An adaptive all-pass filter for time-varying delay estimation

Beth Jelfs*, Shuai Sun, Kamran Ghorbani, Christopher Gilliam

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


The focus of this letter is the estimation of a delay between two signals. Such a problem is common in signal processing and particularly challenging when the delay is non-stationary in nature. Our proposed solution is based on an all-pass filter framework comprising of two elements: a time delay is equivalent to all-pass filtering and an all-pass filter can be represented in terms of a ratio of a finite impulse response (FIR) filter and its time reversal. Using these elements, we propose an adaptive filtering algorithm with an LMS style update that estimates the FIR filter coefficients and the time delay. Specifically, at each time step, the algorithm updates the filter coefficients based on a gradient descent update and then extracts an estimate of the time delay from the filter. We validate our algorithm on synthetic data demonstrating that it is both accurate and capable of tracking time-varying delays.

Original languageEnglish
Article number9380457
Pages (from-to)628-632
Number of pages5
JournalIEEE Signal Processing Letters
Publication statusPublished - 17 Mar 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 1994-2012 IEEE.


  • Adaptive filter
  • all-pass filter
  • time-varying delay estimation

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics


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