The problem of tracking a frequency-hopped signal without knowledge of its hopping pattern is considered. The problem is of interest in military communications, where, in addition to frequency, hop timing can also be randomly shifted to guard against unauthorized reception and jamming. A conceptually simple nonlinear and non-Gaussian stochastic state-space model is proposed to capture the randomness in carrier frequency and hop timing. This model is well-suited for the application of particle filtering tools: it is possible to compute the optimal (weight variance-minimizing) importance function in closed-form. A convenient mixture representation of the latter is employed together with Rao-Blackwellization to derive a very simple optimal sampling procedure. This is representative of the state-of-art in terms of systematic design of particle filters. A heuristic design approach is also developed, using the mode of the spectrogram to localize hop particles. Performance is assessed in a range of experiments using both simulated and measured data. Interestingly, the results indicate that the heuristic design approach can outperform the systematic one, and both are robust to model assumptions.
Bibliographical noteFunding Information:
Manuscript received September 10, 2008; accepted February 14, 2009. First published April 10, 2009; current version published July 15, 2009. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Zhengyuan (Daniel) Xu. This work was supported in part by the Army Research Laboratory (ARL) through the Collaborative Technology Alliance for Communications and Networks under Cooperative Agreement DADD19-01-2-0011, and in part by ERO Contract N62558-03-C-0012. Preliminary versions of parts of this work were presented at IEEE ICASSP, Toulouse, France, May 15–19, 2006, and in IEEE CAMSAP, St. Thomas, U.S. Virgin Islands, Dec. 12–14, 2007.
- Frequency hopping
- Particle filtering
- Random hop timing
- Timing jitter