Bayesian Spatial Field Reconstruction with Unknown Distortions in Sensor Networks

44 Pages Posted: 25 Aug 2020

See all articles by Qikun Xiang

Qikun Xiang

Nanyang Technological University (NTU)

Ido Nevat

Heriot-Watt University - Department of Actuarial Mathematics and Statistics

Gareth Peters

University of California Santa Barbara; University of California, Santa Barbara

Date Written: July 20, 2020

Abstract

Spatial regression of random fields based on potentially biased sensing information is proposed in this paper. One major concern in such applications is that since it is not known a-priori what the accuracy of the collected data from each sensor is, the performance can be negatively affected if the collected information is not fused appropriately. For example, the data collector may measure the phenomenon inappropriately, or alternatively, the sensors could be out of calibration, thus introducing random gain and bias to the measurement process. Such readings would be systematically distorted, leading to incorrect estimation of the spatial field. To combat this detrimental effect, we develop a robust version of the spatial field model based on a mixture of Gaussian process experts. We then develop two different approaches for Bayesian spatial field reconstruction: the first algorithm is the Spatial Best Linear Unbiased Estimator (S-BLUE), in which one considers the quadratic loss function and restricts the estimator to the linear family of transformations; the second algorithm is based on empirical Bayes, which utilizes a two-stage estimation procedure to produce accurate predictive inference in the presence of “misbehaving” sensors. In addition, we develop the distributed version of these two approaches to drastically improve the computational efficiency in large-scale settings. We present extensive simulation results using both synthetic datasets and semi-synthetic datasets with real temperature measurements and simulated distortions to draw useful conclusions regarding the performance of each of the algorithms.

Keywords: Sensor Networks, Gaussian Process, Spatial Linear Unbiased Estimator (SBLUE), Empirical Bayes, Cross Entropy method (CEM), Iterated Conditional Modes (ICM)

Suggested Citation

Xiang, Qikun and Nevat, Ido and Peters, Gareth, Bayesian Spatial Field Reconstruction with Unknown Distortions in Sensor Networks (July 20, 2020). Available at SSRN: https://ssrn.com/abstract=3656297 or http://dx.doi.org/10.2139/ssrn.3656297

Qikun Xiang

Nanyang Technological University (NTU) ( email )

S3 B2-A28 Nanyang Avenue
Singapore, 639798
Singapore

Ido Nevat

Heriot-Watt University - Department of Actuarial Mathematics and Statistics ( email )

Edinburgh, Scotland EH14 4AS
United Kingdom

Gareth Peters (Contact Author)

University of California Santa Barbara ( email )

Santa Barbara, CA 93106
United States

University of California, Santa Barbara ( email )

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