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 wellknown Woodward equation. That equation however was developed in the limit of very high signal-to-noise ratios, andassumes 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. . Introduction 'The theory of optimal receivers studies the design of pulses and receivers to obtain optimal detection in the presence of noise. In this paper we analyze the role of multiple -filters on the receiver side to improve detection accuracy with respect to a given wideband pulse design. In our analysis we have been inspired by the structure of pulses and receiver in echolocating animals such as bats and dolphins, as the capabilities of the their sonar are still significantly better that any man-made system. Considerable work on the theoretical accuracy of range measurements has been done in the past, and the Woodward equation has been derived using different methods. A comprehensive description can be found in [l]. However, it appears that interest in the mathematical aspects of the derivation of that equation has faded [2], while its use has become a standard in the field. In this letter we show that the validity of this equation .depends on various assumptions in particular the assumptions of very low signal-to-noise ratios (SNR), therefore it must be reexamined for the case of low SNR's. The theory of optimal receivers shows that the matched filter receiver maximizes the output peaksignal-to-mean-noise (power) ratio [2, 31, and is the optimum m,ethod for the detection of signals in noise. Information about the distance of the target i:; extracted by computing the time at which the crosscorrelation between the echo and a replica of the pulse is a ~