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Level Set Estimation of Spatial-Temporally Correlated Random Fields With Active Sparse Sensing

机译:具有主动稀疏感的时空相关随机场的水平集估计

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In this paper, we study the level set estimation of a spatial-temporally correlated random field by using a small number of spatially distributed sensors. The level sets of a random field are defined as regions where data values exceed a certain threshold. The identification of the boundaries of such sets is an important theoretical problem with a wide range of applications such as spectrum sensing, urban sensing, and environmental monitoring, etc. We propose a new active sparse sensing and inference scheme, which can achieve rapid and accurate extraction of level sets in a large random field by using a small number of data samples strategically and sparsely selected from the field. A Gaussian process (GP) prior model is used to capture the spatial-temporal correlations inherent in the random field. It is first shown that the optimal level set estimation can be achieved by performing a GP regression with all data samples and then thresholding the regression results. We then investigate the active sparse sensing scheme, where a central controller dynamically selects a small number of sensing locations according to the information revealed from past measurements, with the objective to minimize the expected level set estimation error probability. The expected estimation error probability is explicitly expressed as a function of the selected sensing locations, and the results are used to formulate the optimal sensing location selection problem as a combinatorial problem. Two low complexity greedy algorithms are developed by using analytical upper bounds of the expected estimation error probability. Both simulation and experiment results demonstrate that the greedy algorithms can achieve significant performance gains over baseline passive sensing algorithms and the GP upper confidence bound level set estimation algorithm.
机译:在本文中,我们通过使用少量空间分布的传感器来研究时空相关的随机场的水平集估计。随机字段的级别集定义为数据值超过某个阈值的区域。此类集合的边界的识别是一个重要的理论问题,具有广泛的应用,例如频谱感测,城市感测和环境监测等。我们提出了一种新的主​​动稀疏感测和推理方案,该方案可以实现快速,准确通过策略性地和稀疏地从现场选择的少量数据样本来提取大型随机场中的水平集。高斯过程(GP)先验模型用于捕获随机场中固有的时空相关性。首先表明,可以通过对所有数据样本执行GP回归,然后对回归结果进行阈值化来实现最佳水平集估计。然后,我们研究主动稀疏检测方案,其中中央控制器根据从过去的测量中揭示的信息动态选择少量的检测位置,目的是使预期的水平集估计误差概率最小化。预期估计误差概率明确表示为所选感应位置的函数,并且将结果用于将最佳感应位置选择问题公式化为组合问题。通过使用预期估计误差概率的解析上限,开发了两种低复杂度贪婪算法。仿真和实验结果均表明,相比于基线被动传感算法和GP上限置信水平集估计算法,贪婪算法可实现显着的性能提升。

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