Quasi-ML period estimation from incomplete timing data

Nicholas D. Sidiropoulos, Ananthram Swami, Brian M. Sadler

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


Given a noisy sequence of (possibly shifted) integer multiples of a certain period, it is often of interest to accurately estimate the period. With known integer regressors, the problem is classical linear regression. In many applications, however, the regressors are unknown integers, and only loose bounds on the period are available. Examples include hop period and timing estimation, wherein hops may be missed at the output of the frequency discriminator or the emitter may hop out of band; Pulse Repetition Interval (PRI) analysis; and passive rotating-beam radio scanning. We study several pertinent period estimators. Our emphasis is on a Quasi-Maximum Likelihood approach developed herein and an earlier method based on the Fourier Transform of a Dirac delta train representation of the data. Surprisingly, both are capable of attaining the clairvoyant Cramér-Rao Bound at moderate signal-to-noise ratios (SNRs), even for short (e.g., 10) samples. We carefully address parameter identifiability issues and corroborate our findings with extensive simulations.

Original languageEnglish (US)
Pages (from-to)733-739
Number of pages7
JournalIEEE Transactions on Signal Processing
Issue number2 I
StatePublished - Feb 2005

Bibliographical note

Funding Information:
Manuscript received July 10, 2003; revised February 23, 2004. This work was prepared through collaborative participation in the Collaborative Technology Alliance for Communications and Networks sponsored by the U.S. Army Research Laboratory under Cooperative Agreement DAAD19-01-2-0011. The associate editor coordinating the review of this paper and approving it for publication was Dr. Chong-Yung Chi.

Copyright 2008 Elsevier B.V., All rights reserved.


  • Fourier transform
  • Frequency estimation
  • Missing data
  • Period estimation
  • Pulse repetition interval analysis
  • Synchronization
  • Timing estimation


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