Understanding and mitigating the impact of passing ships on underwater environmental estimation from ambient sound

We investigate the impact of low-rank interference on the problem of distinguishing between two seabed types using ambient sound as an acoustic source. The resulting frequency-domain snapshots follow a zero-mean, circularly-symmetric Gaussian distribution, where each seabed type has a unique covariance matrix. Detecting changes in the seabed type across distinct spatial locations can be formulated as a two-sample hypothesis test for equality of covariance, for which Box's M-test is the classical solution. Interference sources such as passing ships result in additive noise with a low-rank covariance that can reduce the performance of hypothesis testing. We first present a method to construct a worst-case interference field, making hypothesis testing as difficult as possible. We then provide an alternating optimization procedure to recover the interference-free covariance matrix. Experiments on synthetic data show that the optimized interferer can greatly reduce hypothesis testing performance, while our recovery method perfectly eliminates this interference for a sufficiently small interference rank. On real data from the New England Shelf Break Acoustics experiment, we show that our approach successfully mitigates interference, allowing for accurate hypothesis testing and improving bottom loss estimation.