Collaborative localization with received signal strength in wireless sensor networks

In this paper, we present an in-depth study of two collaborative-localization methods, called the multidimensional scaling (MDS) and maximum-likelihood estimator (MLE), for wireless sensor networks. From theoretical analysis, it is shown that MLE is more appropriate than MDS, given the underlying assumption of statistical signal models of the received-signal -strength-based localization problem. We also show that MDS can approximately achieve asymptotic efficiency with appropriate weighting schemes in some scenarios. From extensive simulation results, it is noted that the nonlinear least square algorithms that are commonly used to determine MLE are not as efficient as the iterative MDS algorithms. Thus, we propose a new integrated method MDS-MLE to effectively benefit from the strength of both methods. In the new method, MDS is used as an initialization method for MLE. With the solution of MDS as an initial value, MLE converges much faster and achieves significantly better performance than with random initial values. Superior performance of the new method is clearly demonstrated through simulation results. The effects of the deployment density of sensor nodes and reference nodes (RNs), as well as the deployment structure of RNs, are also studied through various simulations.