Probabilistic Nearest Neighbor Queries on Uncertain Moving Object Trajectories

TL;DR

This paper develops probabilistic nearest neighbor query methods for uncertain moving object trajectories modeled by Markov chains, introducing exact algorithms for some cases and sampling-based approximations for others, supported by extensive experiments.

Contribution

It introduces a comprehensive framework for probabilistic NN queries on uncertain trajectories using Markov models, including exact algorithms and sampling methods with Bayesian inference.

Findings

Exact algorithms for polynomial-time solvable cases.

Sampling approach with Bayesian inference for complex cases.

Extensive experimental validation of methods.

Abstract

Nearest neighbor (NN) queries in trajectory databases have received significant attention in the past, due to their application in spatio-temporal data analysis. Recent work has considered the realistic case where the trajectories are uncertain; however, only simple uncertainty models have been proposed, which do not allow for accurate probabilistic search. In this paper, we fill this gap by addressing probabilistic nearest neighbor queries in databases with uncertain trajectories modeled by stochastic processes, specifically the Markov chain model. We study three nearest neighbor query semantics that take as input a query state or trajectory $q$ and a time interval. For some queries, we show that no polynomial time solution can be found. For problems that can be solved in PTIME, we present exact query evaluation algorithms, while for the general case, we propose a sophisticated sampling approach, which uses Bayesian inference to guarantee that sampled trajectories conform to the observation data stored in the database. This sampling approach can be used in Monte-Carlo based approximation solutions. We include an extensive experimental study to support our theoretical results.