Biosonar model for improved range accuracy in a noisy environment

Using the theory of optimal receivers the range accuracy of echolocating systems can be expressed as a function of receiver bandwidth and signal-to-noise ratio through the well-known Woodward equation. That equation however was developed in the limit of very high signal-to-noise ratios, and assumes that the correct peak of the crosscorrelation function is known a-priori. Echolocating animals such as dolphins and bats have developed a highly specialized receiver to optimize echolocation to different environments and conditions. In particular, they use a set of filters with different center frequencies but overlapping bands. We show that this structure can help in improving accuracy in the case of relatively low signal-to-noise ratios when the ambiguity in the choice of the main peak of the crosscorrelation function cannot be avoided.