Abstract
The use of carrier phase data is the main driver for high-precision Global Navigation Satellite Systems (GNSS) positioning solutions, such as Real-Time Kinematic (RTK). However, carrier phase observations are ambiguous by an unknown number of cycles, and their use in RTK relies on the process of mapping real-valued ambiguities to integer ones, so-called Integer Ambiguity Resolution (IAR). The main goal of IAR is to enhance the position solution by virtue of its correlation with the estimated integer ambiguities. With the deployment of new GNSS constellations and frequencies, a large number of observations is available. While this is generally positive, positioning in medium and long baselines is challenging due to the atmospheric residuals. In this context, the process of solving the complete set of ambiguities, so-called Full Ambiguity Resolution (FAR), is limiting and may lead to a decreased availability of precise positioning. Alternatively, Partial Ambiguity Resolution (PAR) relaxes the condition of estimating the complete vector of ambiguities and, instead, finds a subset of them to maximize the availability. This article reviews the state-of-the-art PAR schemes, addresses the analytical performance of a PAR estimator following a generalization of the Cramér–Rao Bound (CRB) for the RTK problem, and introduces Precision-Driven PAR (PD-PAR). The latter constitutes a new PAR scheme which employs the formal precision of the (potentially fixed) positioning solution as selection criteria for the subset of ambiguities to fix. Numerical simulations are used to showcase the performance of conventional FAR and FAR approaches, and the proposed PD-PAR against the generalized CRB associated with PAR problems. Real-data experimental analysis for a medium baseline complements the synthetic scenario. The results demonstrate that (i) the generalization for the RTK CRB constitutes a valid lower bound to assess the asymptotic behavior of PAR estimators, and (ii) the proposed PD-PAR technique outperforms existing FAR and PAR solutions as a non-recursive estimator for medium and long baselines.
Highlights
Even when a data-driven scheme offers a prominent approach in terms of mean squared error (MSE), a PD-Partial Ambiguity Resolution (PAR) scheme offers a major availability in having a correct Integer Ambiguity Resolution (IAR) satisfying the position precision criteria α and maximizes the Integer Least Squares (ILS) success rate
The Cramér–Rao Bound (CRB) for real/integer values presented in this work was used as a tool to verify the consistency and convergence of precision-aided PAR scheme
The bound was compared with the evaluated Root MSE (RMSE) together with its corresponding CRB, showing that precision-aided PAR scheme maps real-to-integer values in a consistent manner
Summary
This work focuses on PAR solutions for snapshot estimation, i.e., non-recursive estimation for which only the observations received at a time instant are considered This case is relevant for safety-critical vehicular applications, for which high availability of precise positioning is required in an instantaneous manner [7,8,9,10]. The results show that (i) the general CRB for the mixed PAR model is correct and there exist estimators which asymptotically attain it and (ii) PD-PAR is a promising subset selection criteria for PAR, attractive for applications requiring high availability of precise positioning in a snapshot manner (e.g., driverless vehicles or autonomous robots).
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