Array shape estimation tracking using active sonar reverberation

This paper concerns the problem of array shape estimation and tracking for towed active sonar arrays, using received reverberation returns from a single transmitted CW pulse. Uniform linear arrays (ULAs) deviate from their nominal geometry while being towed due to ship maneuvers as well as ocean currents. In such scenarios, conventional beamforming performed under the assumption of a ULA can sometimes lead to unacceptably high spatial sidelobes. The reverberation leaking through the sidelobes can potentially mask weak targets in Doppler, especially when the target Doppler is close to that of the mainlobe reverberation and the reverberation-to-target ratio (RTR) is very high. Although heading sensors located along the array can be used to provide shape estimates, they may not be sufficiently available or accurate to provide the required sidelobe levels. We propose an array shape calibration algorithm using multipath reverberation returns from each ping as a distributed source of opportunity. More specifically, a maximum likelihood (ML) array shape calibration algorithm is developed, which exploits a deterministic relationship between the reverberation spatial and Doppler frequencies causing it to be low rank in the space-time vector space formed across a single coherent processing interval (CPI). In this application, a sequence of overlapped CPI length snapshots of duration less than the CW pulse is used. The ML estimates obtained for each snapshot are tracked using a Kalman filter with a state equation corresponding to the water pulley model for array dynamics. Simulations performed using real heading sensor data in conjunction with simulated reverberation suggest that 8-10 dB improvement in sidelobe level may be possible using the proposed array shape tracking algorithm versus an algorithm that uses only the available heading information.