Online Segmented Recursive Least-Squares for Multipath Doppler Tracking

Underwater communication signals typically suffer from distortion due to motion-induced Doppler. Especially in shallow water environments, recovering the signal is challenging due to the time-varying Doppler effects distorting each path differently. However, conventional Doppler estimation algorithms typically model uniform Doppler across all paths and often fail to provide robust Doppler tracking in multipath environments. In this paper, we propose a dynamic programming-inspired method, called online segmented recursive least-squares (OSRLS) to sequentially estimate the time-varying non-uniform Doppler across different multipath arrivals. By approximating the nonlinear time distortion as a piece-wise-linear Markov model, we formulate the problem in a dynamic programming framework known as segmented least-squares (SLS). In order to circumvent an ill-conditioned formulation, perturbations are added to the Doppler model during the linearization process. The successful operation of the algorithm is demonstrated in a simulation on a synthetic channel with time-varying non-uniform Doppler.