Efficient frequencies estimation using Bayesian approach for parsimonious time-varying auto-regressions

Time-varying Auto-regressive (TVAR) modelling is one of the most important approaches to extracting spectral trajectories from non-stationary narrow-band signals. The parameters of such models can be estimated using sequential Bayesian methods (particle filters). In this paper, a new algorithm is presented to extract the frequency trajectories based on notch filters updated using sequential Monte Carlo techniques (particle filters). The formulation is parsimonious and instantaneous frequency is estimated directly. This eases interpretation of the results and parsimony reduces the computational load. Further, since the proposed method divides the signal using second order sections (one representing each of the narrow-band spectral components) then the algorithm can be designed in a cascade form, which means that the frequencies are estimated sequentially and independently. Experimental results from recordings of dolphin whistles are presented to demonstrate that the proposed method achieves good estimation accuracy in the presence of both single and multiple components or when the time-varying model order is unknown.