Characterization of the diversity in bat biosonar beampatterns with spherical harmonics power spectra

An assessment of the direction-finding accuracy of bat biosonar beampatterns

In the biosonar systems of bats, emitted acoustic energy and receiver sensitivity are distributed over direction and frequency through beampattern functions that have diverse and often complicated geometries. This complexity could be used by the animals to determine the direction of incoming sounds based on spectral signatures. The present study has investigated how well bat biosonar beampatterns are suited for direction finding using a measure of the smallest estimator variance that is possible for a given direction [Cramér-Rao lower bound (CRLB)]. CRLB values were estimated for numerical beampattern estimates derived from 330 individual shape samples, 157 noseleaves (used for emission), and 173 outer ears (pinnae). At an assumed 60 dB signal-to-noise ratio, the average value of the CRLB was 3.9°, which is similar to previous behavioral findings. Distribution for the CRLBs in individual beampatterns had a positive skew indicating the existence of regions where a given beampattern does not support a high accuracy. The highest supported accuracies were for direction finding in elevation (with the exception of phyllostomid emission patterns). No large, obvious differences in the CRLB (greater 2° in the mean) were found between the investigated major taxonomic groups, suggesting that different bat species have access to similar direction-finding information.

Eigenbeam analysis of the diversity in bat biosonar beampatterns

A quantitative analysis of the interspecific variability in bat biosonar beampatterns has been carried out on 267 numerical predictions of emission and reception beampatterns from 98 different species. Since these beampatterns did not share a common orientation, an alignment was necessary to analyze the variability in the shape of the patterns. To achieve this, beampatterns were aligned using a pairwise optimization framework based on a rotation-dependent cost function. The sum of the p-norms between beam-gain functions across frequency served as a figure of merit. For a representative subset of the data, it was found that all pairwise beampattern alignments resulted in a unique global minimum. This minimum was found to be contained in a subset of all possible beampattern rotations that could be predicted by the overall beam orientation. Following alignment, the beampatterns were decomposed into principal components. The average beampattern consisted of a symmetric, positionally static single lobe that narrows and became progressively asymmetric with increasing frequency. The first three "eigenbeams" controlled the beam width of the beampattern across frequency while higher rank eigenbeams account for symmetry and lobe motion. Reception and emission beampatterns could be distinguished (85% correct classification) based on the first 14 eigenbeams.