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).
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