Partial GNSS ambiguity resolution in coordinate domain

Traditionally, if full ambiguity resolution is not successful, partial ambiguity resolution (PAR) will be tried. However, identifying which subset of ambiguities to fix is not easy and is still an open problem. Since the actual purpose of most applications is positioning, rather than fixing all or part of the ambiguities, in this research, we are trying to bypass the problem of identifying which subset of ambiguities to fix and provide a partial solution in the coordinate domain for the bias-free case. The basic idea is that with a user-defined failure rate, we can find a group of ambiguity candidates and each will provide one position. The partial solution is constructed based on these positions together with an indicator to show its maximum positioning error with user-defined reliability. In order to meet various user requirements, different kinds of partial solutions in coordinate domain are proposed. Different from the traditional PAR methods, the new method still works with all the ambiguities (i.e. the complete vector), but works with the different possible values that the complete ambiguity vector may take. The validness and applicability of the proposed partial solution are demonstrated-based practical BeiDou triple-frequency observations. Numerical results show that some partial solutions can be more accurate, while others can meet higher reliability or integrity requirement.