Abstract
We introduce a theoretical framework for the dynamic sensor coverage problem for the case with multiple discrete time linear stochastic systems placed at spacially separate locations. The objective is to keep an appreciable estimate of the states of the systems at all times by deploying a few limited range mobile sensors. The sensors implement a Kalman filter to estimate the states of all the systems. In this paper we present results for a single sensor executing two different random motion strategies. Under the first strategy the sensor motion is an independent and identically distributed random process and a discrete time discrete state ergodic Markov chain under the second strategy. For both these strategies we give conditions under which a single sensor fails or succeeds to solve the dynamic coverage problem. We also demonstrate that the conditions for the first strategy are a special case of the main result for the second strategy.
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