Monte Carlo Optimization Approach for Decentralized Estimation Networks Under Communication Constraints

We consider designing decentralized estimation schemes over bandwidth limited communication links with a particular interest in the tradeoff between the estimation accuracy and the cost of communications due to, e.g., energy consumption. We take two classes of in–network processing strategies into account which yield graph representations through modeling the sensor platforms as the vertices and the communication links by edges as well as a tractable Bayesian risk that comprises the cost of transmissions and penalty for the estimation errors. This approach captures a broad range of possibilities for “online” processing of observations as well as the constraints imposed and enables a rigorous design setting in the form of a constrained optimization problem. Similar schemes as well as the structures exhibited by the solutions to the design problem has been studied previously in the context of decentralized detection. Under reasonable assumptions, the optimization can be carried out in a message passing fashion. We adopt this framework for estimation, however, the corresponding optimization schemes involve integral operators that cannot be evaluated exactly in general. We develop an approximation framework using Monte Carlo methods and obtain particle representations and approximate computational schemes for both classes of in–network processing strategies and their optimization. The proposed Monte Carlo optimization procedures operate in a scalable and efficient fashion and, owing to the non-parametric nature, can produce results for any distributions provided that samples can be produced from the marginals. In addition, this approach exhibits graceful degradation of the estimation accuracy asymptotically as the communication becomes more costly, through a parameterized Bayesian risk. Index Terms Decentralized estimation, communication constrained inference, random fields, message passing algorithms, graphical models, Monte Carlo methods, wireless sensor networks, in-network processing, collaborative signal and information processing. Murat Üney is with the Computer Vision and Pattern Analysis Lab., Signal and Information Processing Group, Sabancı University, OrhanlıTuzla 34956 İstanbul, Turkey ( e-mail: [email protected]). Müjdat Çetin is with the Faculty of Engineering and Natural Sciences, Sabancı University, Orhanlı-Tuzla 34956 İstanbul, Turkey ( e-mail: [email protected]). This work was partially supported by the Scientific and Technological Research Council of Turkey under grant 105E090, by the European Commission under grant MIRG-CT-2006-041919 and with a Turkish Academy of Sciences Young Scientist Award. TECHNICAL REPORT SABANCI UNIVERSITY 2