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

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

doi:10.1109/TSP.2008.927462

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

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

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	4598-4610
Number of pages	13
Journal	IEEE Transactions on Signal Processing
Volume	56
Issue number	10 I
DOIs	https://doi.org/10.1109/TSP.2008.927462
State	Published - 2008
Externally published	Yes

Bibliographical note

Funding 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.

Keywords

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

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10.1109/TSP.2008.927462

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abstract = "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.",

keywords = "Carrier frequency offset, Chirp, Doppler, Particle filtering, Polynomial phase, Radar, Time-frequency analysis, Time-varying harmonic, Tracking",

author = "Tsakonas, {Efthimios E.} and Sidiropoulos, {Nicholas D.} and Ananthram Swami",

note = "Funding 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.",

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PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - Carrier frequency offset

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KW - Polynomial phase

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KW - Time-frequency analysis

KW - Time-varying harmonic

KW - Tracking

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

Abstract

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Keywords

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