Research On Gossip Algorithms For Distributed Parameter Field Estimation In WSN

Nowadays, with the scale of wireless sensor network growing, the number o f nodes which are widely distributed increases rapidly. In such a large-scale distributed network, the tradit ional centralized communication mode is not appropriate compared to the d istributed signal processing technology, which has aroused wide attention to solve distributed problems. In pratical, people tend to know how a parameter in the monitored area varies and distributes, so as to understand the overall distribution of the parameter field. Recently, foreign research team have proposed a method combining gossip algorithm and compressed sensing techno logy. Using the compressed sensing algorithm, the discrete sampled values at nodes are sparse and compressed. Then the exchange and data update of the sparse signal between nodes is completed by gossip algorithm. Consequently, any user can recover and estimate the overall distributio n of the parameter by retrieving the data at any nodes.In this paper, we study the theory of gossip algorithm and compressed sensing technology. Firstly, three aspects, sparse transformation of signal, the construcution of measurement matrix and sparse signal reconstruction, invovled in compressed sensing are analysed respectively. The construction of transfomation matrix of the network data and the the gradient projection reconstruction algorithm are mainly considered. Then we analyze the consensus algorithms. Distributed averaging, network model and time model are dicussed firstly. The convergence o f the pairwise gossip algorithm is proved, and the upper bound as well as the lower bound of the convergence rate is also analyzed. In addit ion, the convergence in expectation and in the second moment of unbiased broadcast gossip algorithm, a faster algorithm is also studied. Based on above, an improved approach to distributed parameter field estimation based on the unbiased broadcast gossip algorithm is proposed. The new method uses the radio channel broadcast characteristic, improving the efficiency and saving the computation time. Moreover, in this paper we creatively apply these theories to the reconstruction o f the distribution of the received signal power. Finally, the simulation experiments are carried out to confirm the performances of method in different parameter fields.The simulat ion analysis shows that with the use of unbiased broadcast gossip algorithm, the computation time consumed by the improved algorithm is shorter. At the same time, the improved method can still reach the reconstruction accuracy requirement of parameter under a very small number of iterations. The reconstruction accuracy is not affected. Through theoretical analysis and simulation results, we come to the conclusion that it is feasible for the proposed method to solve the reconstruction and estimation problem in smooth field, filed with noise and the electromagnetic field, showing the advantages of high-speed and satisfing the requirement of application. The novel algorithm proposed in this paper can be used in applicat ions with requirements of both real-time and high accuracy.