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This paper deals with the problem of coordinating a team of mobile sensor platforms searching for a single mobile non-evading target. It follows the general Bayesian active sensor network approach introduced in  where each decision maker plans locally based on an equivalent representation of the target state probability density function (PDF). This paper focuses on the prediction stage of the decentralized Bayesian filter. It looks at how different types of realistic external constraints may affect the target motion and how they may be taken into account in the process model. Two general classes of constraints are identified soft and hard. A few constraint examples from each class are given to illustrate their impact on the evolution of the target state PDF. Multiple constraints of various types can be combined to increase the accuracy of the predicted PDF estimate, thus affecting the individual trajectories of the search platforms. The effectiveness of the framework is demonstrated for a team of airborne search vehicles looking for a drifting target lost in a storm at sea.