An Echolocation Model for Range Discrimination of Multiple Closely Spaced Objects: Transformation of Spectrogram into the Reflected Intensity Distribution

Using frequency-modulated echolocation, bats can discriminate the range of objects with an accuracy of less than a millimeter. However, bats' echolocation mechanism is not well understood. The delay separation of three or more closely spaced objects can be determined through analysis of the echo spectrum. However, delay times cannot be properly correlated with objects using only the echo spectrum because the sequence of delay separations cannot be determined without information on temporal changes in the interference pattern of the echoes. To illustrate this, Gaussian chirplets with a carrier frequency compatible with bat emission sweep rates were used. The delay time for object 1, T1, can be estimated from the echo spectrum around the onset time. The delay time for object 2 is obtained by adding T1 to the delay separation between objects 1 and 2 (extracted from the first appearance of interference effects). Further objects can be located in sequence by this same procedure. This model can determine delay times for three or more closely spaced objects with an accuracy of about 1 micros, when all the objects are located within 30 micros of delay separation. This model is applicable for the range discrimination of objects having different reflected intensities and in a noisy environment (0-dB signal-to-noise ratio) while the cross-correlation method is hard to apply to these problems.