Time-varying frequency analysis of bat echolocation signals using Monte Carlo methods

摘要

Echolocation in bats is a subject that has received much attention over the last few decades. Batudecholocation calls have evolved over millions of years and can be regarded as well suited to theudtask of active target-detection. In analysing the time-frequency structure of bat calls, it is hopedudthat some insight can be gained into their capabilities and limitations.udMost analysis of calls is performed using non-parametric techniques such as the short timeudFourier transform. The resulting time-frequency distributions are often ambiguous, leadingudto further uncertainty in any subsequent analysis which depends on the time-frequency distribution.udThere is thus a need to develop a method which allows improved time-frequencyudcharacterisation of bat echolocation calls.udThe aim of this work is to develop a parametric approach for signal analysis, specifically takingudinto account the varied nature of bat echolocation calls in the signal model. A time-varyingudharmonic signal model with a polynomial chirp basis is used to track the instantaneous frequencyudcomponents of the signal. The model is placed within a Bayesian context and a particleudfilter is used to implement the filter. Marginalisation of parameters is considered, leading toudthe development of a new marginalised particle filter (MPF) which is used to implement theudalgorithm. Efficient reversible jump moves are formulated for estimation of the unknown (andudvarying) number of frequency components and higher harmonics.udThe algorithm is applied to the analysis of synthetic signals and the performance is comparedudwith an existing algorithm in the literature which relies on the Rao-Blackwellised particle filterud(RBPF) for online state estimation and a jump Markov system for estimation of the unknownudnumber of harmonic components. A comparison of the relative complexity of the RBPF and theudMPF is presented. Additionally, it is shown that the MPF-based algorithm performs no worseudthan the RBPF, and in some cases, better, for the test signals considered. Comparisons are alsoudpresented from various reversible jump sampling schemes for estimation of the time-varyingudnumber of tones and harmonics.udThe algorithm is subsequently applied to the analysis of bat echolocation calls to establish theudimprovements obtained from the new algorithm. The calls considered are both amplitude andudfrequency modulated and are of varying durations. The calls are analysed using polynomialudbasis functions of different orders and the performance of these basis functions is compared.udInharmonicity, which is deviation of overtones away from integer multiples of the fundamentaludfrequency, is examined in echolocation calls from several bat species. The results concludeudwith an application of the algorithm to the analysis of calls from the feeding buzz, a sequenceudof extremely short duration calls emitted at high pulse repetition frequency, where it is shownudthat reasonable time-frequency characterisation can be achieved for these calls.