A Coalitional Game for Distributed Inference in Sensor Networks With Dependent Observations

Abstract

We consider the problem of collaborative inference in a sensor network with heterogeneous and statistically dependent sensor observations. Each sensor aims to maximize its inference performance by forming a coalition with other sensors and sharing information within the coalition. It is proved that the inference performance is a nondecreasing function of the coalition size. However, in an energy constrained network, the energy consumption of inter-sensor communication also increases with increasing coalition size, which discourages the formation of the grand coalition (the set of all sensors). In this paper, the formation of non-overlapping coalitions with statistically dependent sensors is investigated under a specific communication constraint. We apply a game theoretical approach to fully explore and utilize the information contained in the spatial dependence among sensors to maximize individual sensor performance. Before formulating the distributed inference problem as a coalition formation game, we first quantify the gain and loss in forming a coalition by introducing the concepts of diversity gain and redundancy loss for both estimation and detection problems. These definitions, enabled by the statistical theory of copulas, allow us to characterize the influence of statistical dependence among sensor observations on inference performance. An iterative algorithm based on merge-and-split operations is proposed for the solution and the stability of the proposed algorithm is analyzed. Numerical results are provided to demonstrate the superiority of our proposed game theoretical approach.

Representation Learning and Nature Encoded Fusion for Heterogeneous Sensor Networks

“…The application of copula theory for fusing correlated decisions has been recently considered in [10]. It has been shown that there is diversity gain and redundancy loss in the detection problem [11] and the influence of statistical dependence has been characterized. Previous fusion methods include the linear weighting methods [13], majority voting methods and product methods for the totally independent sensors.…”

“…In this paper, the two stage fusion framework is proposed, which exploits this kind of correlations between the sensor observations via belief propagation. Also in [11], it gives a proposition that the KLD is nondecreasing with the increased number of sensors. For any S ⊆ S, D(S ) ≤ D(S).…”

Distributed Estimation in Large Scale Wireless Sensor Networks via a Two Step Group-based Approach

“…However, handling of dependent sensor observations is a critical issue in distributed estimation. The underlying dependence can be both good and bad [12]- [14]. On the one hand, dependent sensors provide different viewpoints and aspects regarding the target parameter to be estimated.…”

“…Therefore, spatial dependence needs to be exploited properly to enhance the overall estimation efficiency. In [13], [14], the concepts of diversity gain and redundancy loss were introduced to characterize the influence of spatial dependence among sensor observations on estimation performance.…”

“…The copula based approach [17] is a flexible parametric dependence modeling methodology, where the joint distribution of multiple sensor observations can be modeled using marginal distributions and a multivariate (dependence) distribution, which is referred to as a multivariate copula. In the presence of collaboration, in [13], [14], a collaborative copula based distributed estimation scheme was proposed for large scale sensor networks, where spatial dependence was exploited to maximize the performance of non-overlapping coalitions under certain energy constraints, and non-linear sensor collaboration was conducted within coalitions.…”