Continuous probabilistic nearest-neighbor queries for uncertain trajectories

Abstract

This work addresses the problem of processing continuous nearest neighbor (NN ) queries for moving objects trajectories when the exact position of a given object at a particular time instant is not known, but is bounded by an uncertainty region. As has already been observed in the literature, the answers to continuous NN-queries in spatio-temporal settings are time parameterized in the sense that the objects in the answer vary over time. Incorporating uncertainty in the model yields additional attributes that affect the semantics of the answer to this type of queries. In this work, we formalize the impact of uncertainty on the answers to the continuous probabilistic NN-queries, provide a compact structure for their representation and efficient algorithms for constructing that structure. We also identify syntactic constructs for several qualitative variants of continuous probabilistic NN-queries for uncertain trajectories and present efficient algorithms for their processing.

Nearest-neighbor searching under uncertainty

“…In this paper, we focus on the locational model of uncertainty to study the problem of nearest neighbor searching. When the data is uncertain but the query is exact, researchers have studied top-k probable nearest neighbor, ranking queries, probabilistic nearest neighbor, and superseding nearest neighbor [8,11,12,19,23,28,36,39]. Ljosa et al [28] investigated the expected k-NN under L1 metric using and obtained ε-approximation.…”

Indexing uncertain spatio-temporal data

“…Existing studies on modeling uncertain trajectories ( [23,25,24,26,15]) naively consider all possible trajectories bounded by a necklace equi-probable. However, given two consecutive observations o(ti) and o(tj) of object o, there are time dependencies between consecutive locations between o(ti) and o(tj), which render some locations in the corresponding diamond (e.g., those near the line segment that connects o(ti) and o(tj)) more probable to be visited by o than others (e.g., those near the boundary of the diamond).…”

“…The prevalent approach is to bound the possible positions of an object at each point of time by simple a spatial structure resulting in a spatio-temporal approximation. Examples include static ellipses [25,24,23], dynamic MBRs (Minimum Bounding Rectangles) [15] and dynamic ellipses [22,13] yielding skewed cylinders, diamonds and beads, respectively. To answer queries most of the existing works restrict the possible queries.…”

“…To answer queries most of the existing works restrict the possible queries. Often no specific assumption is made about the probability density function (pdf) of the object positions over time ( [17,25,24,23,22,28,7]). Thus quantifiers such as "always", "sometimes", "definitely" and "possibly" are used to indicate whether an object intersects a given spatio-temporal query window.…”

Uncertain Range Queries for Necklaces

“…Currently, we are working on quantitative range queries, where actual probabilistic value is assigned for the existing predicates, in a similar spirit to [3]. Concurrently, we are addressing the problems of uncertain spatio-temporal Nearest-Neighbor (NN) queries [12], [23] for beads/necklaces model. The beads appear to be an attractive uncertainty model for trajectories obtained by tracking via periodic sampling in wireless sensor networks.…”