Bias-Bounded Estimation of AmbiguiTy: A Method for Radio Interferometric Positioning
Amir Khodabandeh
Abstract
Carrier phase signals form the basis of various interferometric measurement models and estimation techniques that have parameters of which some are integer. In this paper, integer least-squares estimation theory is extended and applied to bias-bounded mixed-integer models. This extension accommodates the presence of bounded real-valued parameters in mixed-integer models through incorporating prior knowledge of a set, in which the parameters reside, into the estimation process. This enables one to jointly estimate the ambiguous phase cycles and the parameters of interest. To compute such mixed-integer estimates, a fast search strategy is developed that makes use of a dual-ellipsoid encompassing region. The volume of the stated region is quantified and its links to existing ellipsoidal search spaces are highlighted. Simulated and real-world data are employed to illustrate the theory. It is then, for the first time, shown that the proposed method makes <i>single-epoch</i>, <i>phase-only</i> positioning feasible with Global Navigation Satellite Systems (GNSS).