TY - JOUR
T1 - Optimum distributed estimation of a spatially correlated random field
AU - Wang, Zuoen
AU - Wu, Jingxian
AU - Yang, Jing
AU - Cao, Yingli
N1 - Funding Information:
Manuscript received September 9, 2018; revised April 1, 2019 and August 6, 2019; accepted August 12, 2019. Date of publication September 18, 2019; date of current version October 22, 2019. The work of Z. Wang and J. Wu was supported by National Science Foundation under Grants ECCS-1405403 and ECCS-1711087. The work of J. Yang was supported by National Science Foundation under Grant ECCS-1454471. The work for Y. Cao was supported by the National Key R&D Program of China under Grant 2017YFD0300700. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Marcelo G.S. Bruno. (Corresponding author: Jingxian Wu.) Z. Wang and J. Wu are with the Department of Electrical Engineering, University of Arkansas, Fayetteville, AR 72701 USA (e-mail: zw002@email.uark.edu; wuj@uark.edu).
Publisher Copyright:
© 2015 IEEE.
PY - 2019/12
Y1 - 2019/12
N2 - The distributed estimation of a spatially correlated random field with decentralized sensor networks is studied in this paper. Nodes in the network take spatial samples of the random field, then each node estimates the values of arbitrary points on the random field by iteratively exchanging information with each other. The objective is to minimize the estimation mean squared error (MSE) while ensuring all nodes reach a distributed consensus on the estimation results. We propose a distributed iterative linear minimum mean squared error (LMMSE) algorithm that contains a state consensus stage and a local estimation stage in each iteration. The proposed algorithm requires the knowledge of the second-order statistics of the random field, and they are estimated by using a distributed learning algorithm with the help of distributed consensus. The key parameters of the algorithm, including an edge weight matrix and a sample weight matrix, are designed to minimize an MSE upper bound at all nodes when the number of iterations is large. It is shown that the optimum performance can be achieved by distributively mapping the high dimension measurement samples from all nodes into a low dimension subspace related to the covariance matrices of data and noise samples. The low-dimension mapping is achieved in a distributed manner through iterative information propagation. The low dimension mapping can significantly reduce the amount of data exchanged in the network, thus improve the convergence speed of the iterative algorithm.
AB - The distributed estimation of a spatially correlated random field with decentralized sensor networks is studied in this paper. Nodes in the network take spatial samples of the random field, then each node estimates the values of arbitrary points on the random field by iteratively exchanging information with each other. The objective is to minimize the estimation mean squared error (MSE) while ensuring all nodes reach a distributed consensus on the estimation results. We propose a distributed iterative linear minimum mean squared error (LMMSE) algorithm that contains a state consensus stage and a local estimation stage in each iteration. The proposed algorithm requires the knowledge of the second-order statistics of the random field, and they are estimated by using a distributed learning algorithm with the help of distributed consensus. The key parameters of the algorithm, including an edge weight matrix and a sample weight matrix, are designed to minimize an MSE upper bound at all nodes when the number of iterations is large. It is shown that the optimum performance can be achieved by distributively mapping the high dimension measurement samples from all nodes into a low dimension subspace related to the covariance matrices of data and noise samples. The low-dimension mapping is achieved in a distributed manner through iterative information propagation. The low dimension mapping can significantly reduce the amount of data exchanged in the network, thus improve the convergence speed of the iterative algorithm.
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U2 - 10.1109/TSIPN.2019.2942192
DO - 10.1109/TSIPN.2019.2942192
M3 - Article
AN - SCOPUS:85072728460
SN - 2373-776X
VL - 5
SP - 739
EP - 752
JO - IEEE Transactions on Signal and Information Processing over Networks
JF - IEEE Transactions on Signal and Information Processing over Networks
IS - 4
M1 - 8844851
ER -