Dynamic Sensor Coverage with Uncertainty Feedback : Analysis Using Iterated Maps

Abstract

This paper presents an analysis of the dynamic sensor coverage problem with uncertainty feedback. We consider a simple case of two spatially separate uncertain systems 1 and 2. In an earlier paper we introduced the dynamic sensor coverage problem and gave two stochastic sensor motion algorithms to solve the problem. We take a deterministic approach in this paper, the sensor decides to measure system 1 or 2 based on the relative uncertainty of its estimates of the states of the two systems. Error covariance is used as a metric for uncertainty of estimates. Based on the sensor measurements the error covariance evolves according to the Lyapunov or the Riccati map. The uncertainty space is partitioned and each partition has a different sensor motion decision associated with it. For a certain class of partitions we prove the existence and local stability of a unique periodic steady state orbit. We prove global stability for a scalar special case. We also show by way of an example that by changing certain parameters in these partitions stable orbits of higher periods can be obtained. Implications of this work and comparisons with existing work in the sensor scheduling and sensor coverage literature are also presented. In the end we present a discussion on future extensions of this work. Simulation examples are provided to illustrate the main concepts.

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