Optimal particle filters for tracking a time-varying harmonic or chirp signal

Efthimios E. Tsakonas, Nicholas D. Sidiropoulos, Ananthram Swami

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


We consider the problem of tracking the time-varying (TV) parameters of a harmonic or chirp signal using particle filtering (PF) tools. Similar to previous PF approaches to TV spectral analysis, we assume that the model parameters (complex amplitude, frequency, and frequency rate in the chirp case) evolve according to a Gaussian AR(1) model; but we concentrate on the important special case of a single TV harmonic or chirp. We show that the optimal importance function that minimizes the variance of the particle weights can be computed in closed form, and develop procedures to draw samples from it. We further employ Rao-Blackwellization to come up with reduced-complexity versions of the optimal filters. The end result is custom PF solutions that are considerably more efficient than generic ones, and can be used in a broad range of important applications that involve a single TV harmonic or chirp signal, e.g., TV Doppler estimation in communications, and radar.

Original languageEnglish (US)
Pages (from-to)4598-4610
Number of pages13
JournalIEEE Transactions on Signal Processing
Issue number10 I
StatePublished - Oct 8 2008


  • Carrier frequency offset
  • Chirp
  • Doppler
  • Particle filtering
  • Polynomial phase
  • Radar
  • Time-frequency analysis
  • Time-varying harmonic
  • Tracking

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