  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 non-linear
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.
