Research On Multidimensional Scaling Localization Algorithm In Wireless Sensor Networks

As a new data collection technology, whether in state security or in every side of the country economy construction, wireless sensor networks(WSNs) have a broad application background. For most applications of WSNs, it is necessary to get the physical position of the sensor node, and it is usually no meaning for the data which has no position information; what is more, accurate position information is very important to routing protocol based on geographic position. However, the number of sensor nodes is huge, the distribution of nodes is random, and the resources of software and hardware are limited, it is need more efficient localization algorithm in WSNs, so to research efficient localization algorithm has important theoretical meaning and application value.In this paper, we first analyze kinds of localization algorithms of WSNs, especially summarize the advantages and disadvantages of various multidimensional scaling algorithms. Classical multidimensional scaling algorithms use the shortest paths to replace the real distance between the nodes, which leads to very high localization error in the anomalous networks, especially in sparse sensor networks. Then, as the distance matrix during the nodes is a low rank structural matrix, and for the sparse wireless sensor networks, we present a nonmetric weighted MDS localization algorithm based on virtual nodes and a MDS algorithm used low rank Hankel matrix approximation based on virtual nodes,they all use virtual nodes to increase the nodes density of the network. The main difference between two algorithms is to use different methods to carry out low rank approximating of the distance matrix, the first one uses the truncation singular value decomposition of matrix to construct the approximation matrix of dissimilarity matrix, which is not necessary for the structured matrix, so it must add the topology constraint condition; the second one use the low rank Hankel matrix approximation to construct the approximation matrix of dissimilarity matrix, which fully uses the feature that the distance matrix is the Hankel matrix, so that the computing result is certainly the structured matrix.At last, the paper evaluates the performance of the two localization algorithms from the theory analysis and simulation experiment, and compare with MA-MDS -MAP(P). The comparing result indicates that the two localization algorithms have high localization precision and good fault tolerance performance in sparse WSNs.