Efficient Bayesian spatial prediction with mobile sensor networks using Gaussian Markov random fields

Automatica ◽  
2013 ◽  
Vol 49 (12) ◽  
pp. 3520-3530 ◽  
Author(s):  
Yunfei Xu ◽  
Jongeun Choi ◽  
Sarat Dass ◽  
Tapabrata Maiti
Keyword(s):  
Sensor Networks ◽  
Random Fields ◽  
Markov Random Fields ◽  
Mobile Sensor Networks ◽  
Spatial Prediction ◽  
Mobile Sensor ◽  
Gaussian Markov Random Fields ◽  
Markov Random

Spatial Prediction With Mobile Sensor Networks Using Gaussian Process Regression Based on Gaussian Markov Random Fields

2011 ◽  
Author(s):  
Yunfei Xu ◽  
Jongeun Choi
Keyword(s):  
Sensor Networks ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Markov Random Fields ◽  
Mobile Sensor Networks ◽  
Spatial Prediction ◽  
Prediction Algorithm ◽  
Mobile Sensor ◽  
Covariance Functions ◽  
Wide Range

In this paper, a new class of Gaussian processes is proposed for resource-constrained mobile sensor networks. Such a Gaussian process builds on a GMRF with respect to a proximity graph over a surveillance region. The main advantages of using this class of Gaussian processes over standard Gaussian processes defined by mean and covariance functions are its numerical efficiency and scalability due to its built-in GMRF and its capability of representing a wide range of non-stationary physical processes. The formulas for Bayesian posterior predictive statistics such as prediction mean and variance are derived and a sequential field prediction algorithm is provided for sequentially sampled observations. For a special case using compactly supported kernels, we propose a distributed algorithm to implement field prediction by correctly fusing all observations in Bayesian statistics. Simulation results illustrate the effectiveness of our approach.

Sampling from Gaussian Markov random fields conditioned on linear constraints

2008 ◽  
Vol 48 ◽  
pp. 1041 ◽  
Author(s):  
Daniel Peter Simpson ◽  
Ian W. Turner ◽  
A. N. Pettitt
Keyword(s):  
Random Fields ◽  
Markov Random Fields ◽  
Linear Constraints ◽  
Gaussian Markov Random Fields ◽  
Markov Random
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