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.
Bibliographical noteFunding Information:
Manuscript received April 2, 2007; revised May 7, 2008. First published June 20, 2008; current version published September 17, 2008. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Antonio Napolitano. An earlier version of part of this work appears in conference form in the Proceedings of the IEEE Nonlinear Statistical Signal Processing Workshop (NSSPW), Corpus Christi College, Cambridge, U.K., September 13–15, 2006. Supported in part by the Army Research Laboratory (ARL) through participation in the ARL Collaborative Technology Alliance (ARL-CTA) for Communications and Networks under Cooperative Agreement DADD19-01-2-0011, and in part by ARO under ERO Contract N62558-03-C-0012.
Copyright 2008 Elsevier B.V., All rights reserved.
- Carrier frequency offset
- Particle filtering
- Polynomial phase
- Time-frequency analysis
- Time-varying harmonic