| Wireless sensor networks are defined as spatially distributed autonomous sensors to monitor certain physical or environmental conditions like temperature, pressure, sound, etc. and incorporate the collected data to pass to a central location through a network. Multifarious applications including cyber-physical systems, military, eHealth, environmental monitoring, weather forecasting, etc. make localization a crucial part of wireless sensor networks. Since accuracy and low computational time of the localization, in case of some applications like emergency police or medical services, is very important, the main objective of any localization algorithm should be to attain more accurate and less time consuming scheme.;This thesis presents a cooperative sensor network localization scheme that approximates measurement error statistics by Gaussian mixture. Expectation Maximization (EM) algorithm has been implemented to approximate maximum-likelihood estimator of the unknown sensor positions and Gaussian mixture model (GMM) parameters. To estimate the sensor positions we have adopted several algorithms including Broyden-Fletcher-Goldfarb-Shanno (BFGS) Quasi-Newton (QN), Davidon-Fletcher-Powell (DFP), and Cooperative Least Square (LS) algorithm. The distributive form of the algorithms meet the scalability requirements of sparse sensor networks. The algorithms have been analyzed for different number of network sizes. Cramer Rao Lower Bound (CRLB) has been presented and utilized to evaluate the performance of the algorithms. Through Monte Carlo simulation we show the superior performance of BFGS-QN over DFP and cooperative LS in terms of localization accuracy. Moreover the results demonstrate that Root Mean Square Error (RMSE) of BFGS-QN is closer to derived CRLB than both DFP and cooperative LS. |
