  Multipath time-delay estimation is commonly encountered in radar and sonar
signal processing. In some real-life environments, impulse noise is ubiquitous
and significantly degrades estimation performance. Here, we propose a Bayesian
approach to tailor the Bayesian Compressive Sensing (BCS) to mitigate impulsive
noises. In particular, a heavy-tail Laplacian distribution is used as a
statistical model for impulse noise, while Laplacian prior is used for sparse
multipath modeling. The Bayesian learning problem contains hyperparameters
learning and parameter estimation, solved under the BCS inference framework.
The performance of our proposed method is compared with benchmark methods,
including compressive sensing (CS), BCS, and Laplacian-prior BCS (L-BCS). The
simulation results show that our proposed method can estimate the multipath
parameters more accurately and have a lower root mean squared estimation error
(RMSE) in intensely impulsive noise.
