The Infinite-Dimensional Optimal Filtering Problem with Mobile and Stationary Sensor Networks |
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Authors: | John A. Burns |
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Affiliation: | Interdisciplinary Center for Applied Mathematics , Virginia Tech , Blacksburg , Virginia , USA |
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Abstract: | In this article, we introduce a framework to address filtering and smoothing with mobile sensor networks for distributed parameter systems. The main problem is formulated as the minimization of a functional involving the trace of the solution of a Riccati integral equation with constraints given by the trajectory of the sensor network. We prove existence and develop approximation of the solution to the Riccati equation in certain trace-class spaces. We also consider the corresponding optimization problem. Finally, we employ a Galerkin approximation scheme and implement a descent algorithm to compute optimal trajectories of the sensor network. Numerical examples are given for both stationary and moving sensor networks. |
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Keywords: | Filtering Optimal sensor networks Riccati integral equations |
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