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In the context of the recent Maritime Rapid Environmental Assessment/Blue Planet 2007 sea trial (MREA/BP07), this paper presents a range-resolving tomography method based on ensemble Kalman filtering of full-field acoustic measurements, dedicated to the monitoring of environmental parameters in coastal waters. The inverse problem is formulated in a state-space form wherein the time-varying sound-speed field (SSF) is assumed to follow a random walk with known statistics and the acoustic measurements are a nonlinear function of the SSF and the bottom properties. The state-space form enables a straightforward implementation of a nonlinear Kalman filter, leading to a data assimilation problem. Surface measurements augment the measurement vector to constrain the range-dependent structure of the SSF. Realistic scenarios of vertical slice shallow-water tomography experiments are simulated with an oceanic model, based on the MREA/BP07 experiment. Prior geoacoustic inversion on the same location gives the bottom acoustic properties that are input to the propagation model. Simulation results show that the proposed scheme enables the continuous tracking of the range-dependent SSF parameters and their associated uncertainties assimilating new measurements each hour. It is shown that ensemble methods are required to properly manage the nonlinearity of the model. The problem of the sensitivity to the vertical array (VA) configuration is also addressed.