Fundamental frequency estimation, known as pitch estimation in speech signals is of interest both to the research community and to industry. Meanwhile, the particle filter is known to be a powerful Bayesian inference method to track dynamic parameters in nonlinear state-space models. In this paper, we propose a speech model under a time-varying source-filter speech model, and use variable rate particle filters (VRPF) to develop methods for estimation of pitch periods in speech signals. A Rao-Blackwellised variable rate particle filter (RBVRPF) is also implemented. The proposed VRPF and RBVRPF are compared with a state-of-the-art pitch estimation algorithm, the YIN algorithm. Simulation results show that more accurate estimation of pitch can be obtained by VRPF and RBVRPF even under strong background noise conditions.