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Many novel spatio-temporal applications deal with moving objects. In such environments, a database typically maintains the initial position and the moving function for each object. Instead of updating the database whenever an object position changes (which is not manageable), updates are issued whenever the moving function deviates beyond a given threshold. For simplicity, we assume that objects move with linear trajectories. Maintaining the moving functions in a database introduces novel problems. For example, the database can answer queries about object positions in the future: "find all objects that will be in area A, 10 minutes from now". In this paper we present a thorough performance evaluation of techniques for estimating the selectivity of such queries. We consider various existing estimators that can be stored in main memory and are updated dynamically. Furthermore, we propose two new approaches, a technique that uses histograms and a secondary index based estimator. We run a diverse set of experiments to identify the strengths and weaknesses of every approach, using a wide variety of datasets.