Analysis of the Directivity Gain of a Synthetic Aperture in Active and Passive Modes

While synthetic aperture sonar is now a mature technology for active imaging of the sea floor, its use for improving passive detection or localisation of underwater acoustic sources is still a research issue. In the first part, we show that the phase shifts for passive synthetic aperture beamforming do not depend on the steering direction. Hence a passive synthetic aperture has the same directivity pattern like the real aperture that it originates from. The directivity gain of an active synthetic aperture is caused by the phase origin reset at each transmit time resulting in a phase discontinuity depending on the bearing angle. Model-based array processing (MBAP), which estimates a source state from the array vector signal, has been proposed as an alternative to passive synthetic aperture for improving source localization. In the second part, we propose a MBAP approach based on a hidden Markov model (HMM) where the signal phase is a third order polynomial. Numerical simulation shows that it does not improve the bearing angle accuracy with respect to an HMM tracker performing on the square magnitude output of real aperture beamforming. This result is in accordance with the fact that both estimators meet the same Cramer-Rao lower bound. But the new method has interesting detection potential