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The Impact of Quasi-Equally Spaced Sensor Topologies on Signal Reconstruction

机译：准等距传感器拓扑对信号重构的影响

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摘要

A wireless sensor network with randomly deployed nodes can be used to provide an irregular sampling of a physical field of interest. We assume that a sink node collects the data gathered by the sensors and uses a linear filter for the reconstruction of a bandlimited scalar field defined over a d -dimensional domain. Sensors' locations are assumed to be known at the sink node, up to a certain position error. We then take the mean square error (MSE) of the reconstructed field as performance metric, and evaluate the effect of both uniform and quasi-equally spaced sensor layouts on the quality of the reconstructed field. We define a parameter that provides a measure of the regularity of the sensors deployment, and, through asymptotic analysis, we derive the MSE in the case of different sensor spatial distributions. For two of them, an approximate closed formrnexpression is obtained. We validate our analysis through numerical results, and we show that an excellent match exists between analysis and simulation even for a small number of sensors.
机译：具有随机部署的节点的无线传感器网络可用于提供感兴趣的物理场的不规则采样。我们假设一个宿节点收集传感器收集的数据，并使用线性滤波器来重构在d维域上定义的带限标量场。假定传感器的位置在接收器节点处是已知的，直到某个位置误差为止。然后，我们将重建场的均方误差（MSE）作为性能指标，并评估均匀和准等距传感器布局对重建场质量的影响。我们定义了一个参数，该参数提供了传感器部署规律性的度量，并且通过渐近分析，我们得出了传感器空间分布不同时的MSE。对于其中两个，获得了近似的封闭式表达式。我们通过数值结果验证了我们的分析，并且表明即使对于少数传感器，分析与仿真之间也存在出色的匹配。

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