Time-varying frequency analysis of bat echolocation signals using Monte Carlo methods
Echolocation in bats is a subject that has received much attention over the last few decades. Bat echolocation calls have evolved over millions of years and can be regarded as well suited to the task of active target-detection. In analysing the time-frequency structure of bat calls, it is hoped that some insight can be gained into their capabilities and limitations. Most analysis of calls is performed using non-parametric techniques such as the short time Fourier transform. The resulting time-frequency distributions are often ambiguous, leading to further uncertainty in any subsequent analysis which depends on the time-frequency distribution. There is thus a need to develop a method which allows improved time-frequency characterisation of bat echolocation calls. The aim of this work is to develop a parametric approach for signal analysis, specifically taking into account the varied nature of bat echolocation calls in the signal model. A time-varying harmonic signal model with a polynomial chirp basis is used to track the instantaneous frequency components of the signal. The model is placed within a Bayesian context and a particle filter is used to implement the filter. Marginalisation of parameters is considered, leading to the development of a new marginalised particle filter (MPF) which is used to implement the algorithm. Efficient reversible jump moves are formulated for estimation of the unknown (and varying) number of frequency components and higher harmonics. The algorithm is applied to the analysis of synthetic signals and the performance is compared with an existing algorithm in the literature which relies on the Rao-Blackwellised particle filter (RBPF) for online state estimation and a jump Markov system for estimation of the unknown number of harmonic components. A comparison of the relative complexity of the RBPF and the MPF is presented. Additionally, it is shown that the MPF-based algorithm performs no worse than the RBPF, and in some cases, better, for the test signals considered. Comparisons are also presented from various reversible jump sampling schemes for estimation of the time-varying number of tones and harmonics. The algorithm is subsequently applied to the analysis of bat echolocation calls to establish the improvements obtained from the new algorithm. The calls considered are both amplitude and frequency modulated and are of varying durations. The calls are analysed using polynomial basis functions of different orders and the performance of these basis functions is compared. Inharmonicity, which is deviation of overtones away from integer multiples of the fundamental frequency, is examined in echolocation calls from several bat species. The results conclude with an application of the algorithm to the analysis of calls from the feeding buzz, a sequence of extremely short duration calls emitted at high pulse repetition frequency, where it is shown that reasonable time-frequency characterisation can be achieved for these calls.