A Study on Particle Filters for Single-Tone Frequency Tracking

In this paper, we present an online approach for frequency tracking of a noisy sinusoid using sequential Monte Carlo (SMC) methods, also known as particle filters (PFs). In addition, apart from employing the classical Cartesian formulation model, we also develop two alternative dynamical models, namely, nearly constant frequency (NCF) and Singer, which are adapted from the maneuvering target tracking discipline, to describe the evolution of time-varying frequencies, and investigate their fitness to the frequency tracking application. When compared with conventional techniques whose performance is restricted to linear Gaussian models and/or to slowly varying frequencies, PFs are more flexible to handle situations where these conditions are violated. Extensive evaluations on the proposed new models and PF tracking algorithms are conducted with different sets of frequency inputs and levels of signal-to-noise ratio (SNR). According to the computer simulation results, it is found that PFs under all investigated models consistently outperform and are less sensitive to SNR levels than the extended Kalman filter (EKF). Furthermore, the results suggest that while none of the models perfectly fits all types of frequency inputs, NCF model is more suitable for moderately varying frequencies, whereas the Singer is more suitable for rapidly changing frequencies.