Energy Efficient Routing for Statistical Inference of Markov Random Fields

The problem of routing of sensor observations for optimal detection of a Markov random field (MRF) at a designated fusion center is analyzed. Assuming that the correlation structure of the MRF is defined by the nearest-neighbor dependency graph, routing schemes which minimize the total energy consumption are analyzed. It is shown that the optimal routing scheme involves data fusion at intermediate nodes and requires transmissions of two types viz., the raw sensor data and the aggregates of log-likelihood ratio (LLR). The raw data is transmitted among the neighbors in the dependency graph and local contributions to the LLR are computed. These local contributions are then aggregated and delivered to the fusion center. A 2-approximation routing algorithm (DFMRF) is proposed and it has a transmission multidigraph consisting of the dependency graph and the directed minimum spanning tree, with the directions toward the fusion center.