Abstract
Challenges of estimating broadband acoustic response functions at low signal to noise ratio (SNR) are due to both their varying sparsity and the varying spatio-temporal dynamics of each acoustic arrival. Acoustic responses can be quite sparse over the delay-Doppler-angle domain exhibiting large regions that are relatively quiet. The arrivals may share significant Doppler processes due to platform motion or may be driven independently by boundary interactions. Because of this estimation must be adaptive across delay-Doppler and angle with any single fixed estimator inadequate. One means of constructing such an estimator is to view each angle-Doppler-frequency slot as either ensonified or not. A mixture model can be employed for this purpose to describe the behavior of the acoustic response over received signal duration, aperture, and bandwidth. The posterior mean is derived and shown to be soft shrinkage operator of the conventional Wiener filtered coefficients under each of the components of the mixture. This estimator can be employed for bulk dilation estimation as an alternative to a phase locked loop. The posterior variance is derived and compared conventional Wiener filtering. The resulting adaptive structure is applied to M-ary orthogonal signaling sets taken in diverse shallow water environments at very low SNR. This work was supported by the Naval Innovative Science and Engineering Program and the Office of Naval Research.