Precision-Aided Partial Ambiguity Resolution Technique for Short to Medium Baseline Positioning

Abstract

GNSS carrier phase observations are fundamental for safety-critical applications where the requirements of accuracy and availability are stringent. Unlike code observations, carrier phase measurements pose high precision at the cost of being ambiguous, since only their fractional part is measured by the receiver. The unknown number of integer cycles, the so-called ambiguities, is to be determined jointly to the dynamical parameters of the target and leads to the mixed real and integer parameter estimation problem. Although the mixed-integer estimation problem has been widely studied, its performance is subject to certain unresolved challenges. For instance, upon the deployment of new GNSS constellation and frequencies, the large number of observations can lead to a decreased probability of successfully mapping the real-valued carrier phase ambiguities to integer ones. In this regard, Partial Ambiguity Resolution (PAR) relaxes the condition of fixing the complete set of ambiguities and finds instead a subset of these based on the optimization of certain objective function (i.e., maximizing the probability of ambiguity resolution success rate). Existing PAR approaches prioritize the chance of finding an integer solution, regardless of whether the posterior positioning result presented a poor accuracy. Such phenomena occur when, for instance, solely a few ambiguities are fixed. To amend this common PAR-related issue, this work introduces the precision-aided PAR, for which the projection of the estimated ambiguities into the position domain is exploited to guide the PAR ambiguity selection process. The premise is straightforward: the covariance matrix for the (fixed) position solution is used to pose a constraint on the integer resolution minimization problem, based on a goal accuracy to achieve. Precision-guided PAR allows to efficiently working with large number of subsets, which makes the algorithm attractive for multi-GNSS multi-frequency applications with stringent availability and accuracy requirements. We leverage on the recently proposed Cramér Rao Bound (CRB) for the mixed-integer model to characterize what is the minimal achievable performance for a subset of observations. The experimentation comprises a synthetic scenario where the performance comparison for Full Ambiguity Resolution (FAR), classical PAR based on sequential observation elimination and the proposed precision-aided PAR is addressed. The evaluation employs multi-GNSS (GPS, Galileo and BeiDou) triple frequency observations and a variety of possible lengths.