AbstractsMathematics

This PhD thesis considers the problem of locating some target nodes in different wireless infrastructures such as wireless cellular radio networks and wireless sensor networks. To be as realistic as possible, mixed line-of-sight and non-line-of-sight (LOS/NLOS) localization environment is introduced. Both the conventional non-cooperative localization and the new emerging cooperative localization have been studied thoroughly. Owing to the random nature of the measurements, probabilistic methods are more advanced as compared to the old-fashioned geometric methods. The gist behind the probabilistic methods is to infer the unknown positions of the target nodes in an estimation process, given a set of noisy position related measurements, a probabilistic measurement model, and a few known reference positions. In contrast to the majority of the existing methods, harsh but practical constraints are taken into account: neither offline calibration nor non-line-of-sight state identification is equipped in the desired localization system. This leads to incomplete knowledge about the measurement error statistics making the inference task extremely challenging. Two new classes of localization algorithms have been proposed to jointly estimate the positions and measurement error statistics. All unknown parameters are assumed to be deterministic, and maximum likelihood estimator is sought after throughout this thesis. The first class of algorithms assumes no knowledge about the measurement error distribution and adopts a nonparametric modeling. The idea is to alternate between a pdf estimation step, which approximates the exact measurement error pdf via adaptive kernel density estimation, and a parameter estimation step, which resolves a position estimate numerically from an approximated log-likelihood function. The computational complexity of this class of algorithms scales quadratically in the number of measurements. Hence, the first class of algorithms is applicable primarily for non-cooperative localization in wireless cellular radio networks. In order to reduce the computational complexity, a second class of algorithms resorts to approximate the measurement error distribution parametrically as a linear combination of Gaussian distributions. Iterative algorithms that alternate between updating the position(s) and other parameters have been developed with the aid of expectation-maximization (EM), expectation conditional maximization (ECM) and joint maximum a posterior-maximum likelihood (JMAP-ML) criteria. As a consequence, the computational complexity turns out to scale linearly in the number of measurements. Hence, the second class of algorithms is also applicable for cooperative localization in wireless sensor networks. Apart from the algorithm design, systematical analyses in terms of Cramer-Rao lower bound, computational complexity, and communication energy consumption have also been conducted for comprehensive algorithm evaluations. Simulation and experimental results have demonstrated that the proposed…