| Abstract | We introduce a realistic analysis for a framework for storing andprocessing 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.
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