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This paper concerns the problem of estimating a spatially distributed, time-varying random field from noisy measurements collected by a wireless sensor network. When the field dynamics are described by a linear, lumped-parameter model, the classical solution is the Kalman - Bucy Filter (KBF). Bandwidth and energy constraints can make it impractical to use all sensors to estimate the field at specific locations. Using graph-theoretic techniques, the authors show how reduced-order KBFs can be constructed that use only a subset of the sensors, thereby reducing energy consumption. This can lead to degraded performance, however, in terms of the Root Mean Squared (RMS) estimation error.
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