Localizing sources of physical quantities is often only possible in an indirect manner by observing the induced continuous phenomena, such as pollution loads of air or water. By employing model-based reconstruction methods, the task of localizing movable sources by distributed sensor measurements can be formulated as a non-linear stochastic parameter estimation problem. A computationally efficient state estimator is applied to this estimation problem for enabling real-time source localization. Furthermore, this paper proposes a novel approach to multistep sensor management for utilizing future sensors measurements in a most informative way. Here, predictive statistical linearization is employed for converting the given nonlinear non-Gaussian sensor management problem into a linear Gaussian one, which can be solved efficiently. By controlling a mobile sensor, it is demonstrated that the proposed method yields accurate source localization results.