Wireless Sensor Networks

Wireless sensor networks (WSNs) [1] are massively distributed systems for sensing and processing of spatially dense data. They are composed of a large number of nodes deployed in harsh environments to execute challenging tasks including security/surveillance, environmental monitoring, health monitoring, industrial automation and disaster management, etc. Although the nodes only have limited resources, complicated tasks such as distributed detection and estimation [2] can be accomplished via nodes’ cooperation. The main argument is that a distributed sensor network can leverage its performance by aggregating information gathered by individual nodes, which is known as information fusion. The primary goal of sensor fusion is to process and progressively refine information from multiple nodes to eventually obtain situation awareness.

Recently, consensus based distributed estimation has attracted considerable attention from various fields to estimate deterministic parameters and track time-varying ones. In this chapter, the state-of-the-art of distributed consensus estimation is discussed.

This chapter focuses on exploiting the sensor fusion capability for situation monitoring applications over a kind of relay assisted sensor networks consisting of multiple kinds of SNs and RNs. SNs implement assimilation of new measurement and cooperation with other nodes. While for RNs, the main role is to aggregate their neighboring data. Moreover, SNs have different sensing modalities, which can only measure a part of the target parameter vector for situation monitoring. We propose a distributed consensus based unbiased estimation (DCUE) algorithm for this kind of sensor network. Different from existing algorithms, the DCUE algorithm explicitly takes the heterogeneity of responsibilities between SNs and RNs into account. By using algebraic graph theory in conjunction with Markov chain approach, we demonstrate how the distributed estimation method can be transformed to circumvent the challenges arisen from the heterogeneity. We analyze the performance of asymptotic unbiasedness and consistency of the DCUE algorithm in the presence of asymmetric communication, i.e., when a node can receive information from another node but not vice versa. Furthermore, a quantitative bound on the rate of convergence is established. Finally, simulation results are provided to validate the effectiveness of the DCUE algorithm. It is also demonstrated that the presence of RNs does contribute to the estimation accuracy and convergence rate compared with the homogeneous networks.

This chapter is concerned with the problem of filter design for target tracking over WSNs. Similar to Chap. 3, we also consider the relay assisted WSNs with SNs and RNs respectively. In Chap. 3, we deal with the parameter estimation in such networks. However, questions of how to deal with the heterogeneity of nodes and how to design filters for target tracking over such kind of networks remain largely unexplored. We propose in this chapter a novel distributed consensus filter to solve the target tracking problem. Two criteria, namely, unbiasedness and optimality are imposed for the filter design. The so-called sequential design scheme is then presented to tackle the heterogeneity of SNs and RNs. The minimum principle of Pontryagin is adopted for SNs to optimize the estimation errors. As for RNs, the Lagrange multiplier method coupled with the generalized inverse of matrices is then used for filter optimization. Furthermore, it is proven that convergence property is guaranteed for the proposed consensus filter in the presence of process and measurement noise. Simulation results have validated the performance of the proposed filter. It is also demonstrated that the relay assisted WSNs with the proposed filter outperform the homogeneous counterparts in light of reduction of the network cost with slight degradation of estimation performance.

This chapter deals with node deployment problem for distributed estimation of unknown signals in relay assisted WSNs. It is discovered that the network topology is closely related to the properties of the estimation algorithm. To satisfy the performance of the estimation algorithm, two node deployment algorithms are given. The first is concerned with the connectivity of network topology and the second illustrates a greedy approach to further optimize the network topology and the parameters of the estimation algorithms. Simulation results are provided to demonstrate the performance and effectiveness of the node deployment algorithms for solving distributed estimation problems in relay assisted WSNs.

In this chapter, we summarize the main results presented in this monograph and highlight future research directions.