Realistic Compression of Kinetic Sensor Data

Abstract

We introduce a realistic analysis for a framework for storing and processing kinetic data observed by sensor networks. The massive data sets generated by these networks motivates a significant need for compression. We are interested in the kinetic data generated by a finite set of objects moving through space. Our previously introduced framework and accompanying compression algorithm assumed a given set of sensors, each of which continuously observes these moving objects in its surrounding region. The model relies purely on sensor observations; it allows points to move freely and requires no advance notification of motion plans. Here, we extend the initial theoretical analysis of this framework and compression scheme to a more realistic setting. We extend the current understanding of empirical entropy to introduce definitions for joint empirical entropy, conditional empirical entropy, and empirical independence. We also introduce a notion of limited independence between the outputs of the sensors in the system. We show that, even with this notion of limited independence and in both the statistical and empirical settings, the previously introduced compression algorithm achieves an encoding size on the order of the optimal.