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, we show how reduced-order KBFs can be constructed

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... t 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. Efficient methods are presented to apply Pareto optimality to evaluate the tradeoffs between communication costs and RMS estimation error to select the best reduced-order KBF. The approach is illustrated with simulation results.