The demand for outdoor precise location is increasing with the development of new applications such as autonomous vehicles, exploration robots and wireless sensor networks. Global Navigation Satellite System (GNSS) is the go-to system for outdoor localization. This thesis focuses on developing new methods for GNSS single-point positioning (SPP) model, where no access to a reference station or precise GNSS parameters is needed. We investigated the limitations of the standard method, least- squares adjustment (LSA), and we derived the Cramer-Rao bounds for the SPP estimation problem. We also investigated different techniques to formulate the positioning problem with the goal to increase the accuracy. A new method is developed by reformulating the problem as difference-of-convex program (DC program) and utilizing convex-concave procedure (CCCP) to solve the positioning problem without linearizing the observation equations. In addition, we examined the potential of multiple-receiver systems in increasing the accuracy. We formulated the multiple- receiver SPP estimation problem, and we proposed to configure the multiple receivers in a fixed equilateral triangle to exploit the symmetry and the geometrical constraints of the configuration. We extended the use of LSA in multiple-receiver system. We also developed a modification of LSA algorithm, named least-squares adjustment extension (LSAE), that utilizes attitude information and the constraints of the multiple-receiver system. In addition, we developed a new algorithm to optimizes the SPP estimates over the equilateral triangles Riemannian manifold, which enforces the geometrical constraints of the multiple-receiver system. Furthermore, we derived the constrained and the unconstrained Cramer-Rao bounds (CRB and CCRB) for the multiple-receiver SPP problem. Moreover, we investigated the influence of both attitude information and the equilateral triangle baseline length on the algorithms’ performances and the derived CCRB. Finally, we carried out a numerical analysis by implementing the algorithms and the bounds in MATLAB, where we tested the algorithms on simulated GNSS scenarios. The proposed multiple-receiver methods provide more precise estimates for the SPP problem in comparison to the single receiver methods.

Locating a radiating source based on range or range measurements obtained from a network of passive sensors has been a subject of research over the past two decades due to the problem’s importance in applications in wireless communications, surveillance, navigation, geosciences, and several other fields. In this thesis, we develop new solution methods for the problem of localizing a single radiating source based on range and range-difference measurements. Iterative re-weighting algorithms are developed for both range-based and range-difference-based least squares localization. Then we propose a penalty convex-concave procedure for finding an approximate solution to nonlinear least squares problems that are related to the range measurements. Finally, the sequential convex relaxation procedures are proposed to obtain the nonlinear least squares estimate of source coordinates. Localization in wireless sensor network, where the RF signals are used to derive the ranging measurements, is the primary application area of this work. However, the solution methods proposed are general and could be applied to range and range-difference measurements derived from other types of signals. / Graduate / 0544 / ismailds@uvic.ca