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In this paper we investigate some issues and solutions related to the design of a Data Warehouse (DW), storing several aggregate measures about trajectories of moving objects. First we discuss the loading phase of our DW which has to deal with overwhelming streams of trajectory observations, possibly produced at different rates, and arriving in an unpredictable and unbounded way. Then, we focus on the measure presence, the most complex measure stored in our DW. Such a measure returns the number of distinct trajectories that lie in a spatial region during a given temporal interval. We devise a novel way to compute an approximate, but very accurate, presence aggregate function, which algebraically combines a bounded amount of measures stored in the base cells of the data cube. We conducted many experiments to show the effectiveness of our method to compute such an aggregate function. In addition, the feasibility of our innovative trajectory DW was validated with an implementation based on Oracle. We investigated the most challenging issues in realizing our trajectory DW using standard DW technologies: namely, the preprocessing and loading phase, and the aggregation functions to support OLAP operations.