A Sparse Kalman Filter with Application to Acoustic Communications Channel Estimation

A Sparse Bayesian Kalman filter (SB-KF) is developed for channel estimation in underwater acoustic communications. The SB-KF algorithm is based on parallel Kalman filtering, with each filter updated under a soft numerosity constraint. The soft constraint forces the one-step prediction of the channel to have fixed numerosity. The Bayesian framework yields both sparse channel estimates, and an estimate of the channel order (numerosity). Application of the SB-KF to an acoustic modem based on Walsh/m-sequence signaling is considered. A hybrid analysis/simulation approach is used to compute symbol error rates (SERs), which show that the sparse Bayesian algorithm significantly outperforms an unconstrained Kalman channel estimator