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Complex queries on trajectory data are increasingly common in applications involving moving objects. MBR or grid-cell approximations on trajectories perform suboptimally since they do not capture the smoothness and lack of internal area of trajectories. We describe a parametric space indexing method for historical trajectory data, approximating a sequence of movement functions with single continuous polynomial. Our approach works well, yielding much finer approximation quality than MBRs. We present the PA-tree, a parametric index that uses this method, and show through extensive experiments that PA-trees have excellent performance for offline and online spatio-temporal range queries. Compared to MVR-trees, PA-trees are an order of magnitude faster to construct and incur I/O cost for spatio-temporal range queries lower by a factor of 2-4. SETI is faster than our method for index construction and timestamp queries, but incurs twice the I/O cost for time interval queries, which are much more expensive and are the bottleneck in online processing. Therefore, the PA-tree is an excellent choice for both offline and online processing of historical trajectories.
Access methods, spatio-temporal databases.

C. V. Ravishankar and J. Ni, "Indexing Spatio-Temporal Trajectories with Efficient Polynomial Approximations," in IEEE Transactions on Knowledge & Data Engineering, vol. 19, no. , pp. 663-678, 2007.
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