Bat's sonar signals and acceleration tolerance

Optimum parameter estimation in active SONAR techniques is deeply related to time estimation of the incoming echo. A new definition for time origin generates a well suited optimum time estimator. This estimator is related to the "non coupling time" defined by the signal's parameters. In such a case the result is thoroughly uncoupled with range rate effects. The high bandwidth duration product BT valued signals, with finite energy, define an optimum class related to this estimator. Among them the hyperbolic frequency modulated ones are such that they define an optimum subclass related to DOPPLER tolerance. Such results may be enlarged to acceleration effects. A waveform derived for target identification appears as a so called "non coupled estimation" signal. Bats are emitting various signals which are very close to the optimum ones defined above. During pursuit and cruise, bats emit Doppler tolerant signals with a very low acceleration bias.