Probabilistic k-Nearest Neighbor Monitoring of Moving Gaussians

Abstract

We consider a centralized server that receives streaming updates from numerous moving objects regarding their current whereabouts. However, each object always relays its location cloaked into a broader uncertainty region under a Bivariate Gaussian model of varying densities. We wish to monitor a large number of continuous queries, each seeking k objects nearest to its own focal point with likelihood above a given threshold, e.g., "which of my friends are currently the k = 3 closest to our preferred cafe with probability over 75%". Since an exhaustive evaluation would be prohibitive, we develop heuristics based on spatial and probabilistic properties of the uncertainty model, and promptly issue approximate, yet reliable answers with confidence margins. We conducted a comprehensive empirical study to assess the performance and response quality of the proposed methodology, confirming that it can efficiently cope with large numbers of moving Gaussian objects under fluctuating uncertainty conditions, while also offering timely response with tolerable error to multiple queries of varying specifications.