Precision-Aided Partial Ambiguity Resolution Scheme for Instantaneous RTK Positioning

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.

A novel partial ambiguity method for multi-GNSS real-time kinematic positioning

Recent progress in using real-time kinematic (RTK) positioning has motivated the exploration of its application due to its high accuracy and efficiency. However, poorly-observed satellite data will cause unfixed ambiguities and markedly biased solutions. A novel partial ambiguity resolution method, named the irrespective of integer ambiguity resolution (IIAR) model, is proposed and applied to improve the reliability of ambiguity resolution. The proposed method contains initial ambiguity resolution and irrespective of integer ambiguity processes. The initial ambiguity resolution process applies an iterative partial ambiguity resolution method to obtain an approximate solution. The irrespective of integer ambiguity process transforms the approximate solution to a high-precision solution. Experiments show that the approximate solution is unreliable when the initial ambiguity resolution process has small redundancy, and the proposed method can obtain better results for those cases. The IIAR method showed about a 40% improvement of multi-GNSS ambiguity success rate and about a 25% improvement of standard deviation. Therefore, these results show that the proposed IIAR method can improve the results of multi-GNSS RTK positioning significantly.

GLONASS FDMA data for RTK positioning: a five-system analysis

The use of the GLONASS legacy signals for real-time kinematic positioning is considered. Due to the FDMA multiplexing scheme, the conventional CDMA observation model has to be modified to restore the integer estimability of the ambiguities. This modification has a strong impact on positioning capabilities. In particular, the ambiguity resolution performance of this model is clearly weaker than for CDMA systems, so that fast and reliable full ambiguity resolution is usually not feasible for standalone GLONASS, and adding GLONASS data in a multi-GNSS approach can reduce the ambiguity resolution performance of the combined model. Partial ambiguity resolution was demonstrated to be a suitable tool to overcome this weakness (Teunissen in GPS Solut 23(4):100, 2019). We provide an exhaustive formal analysis of the positioning precision and ambiguity resolution capabilities for short, medium, and long baselines in a multi-GNSS environment with GPS, Galileo, BeiDou, QZSS, and GLONASS. Simulations are used to show that with a difference test-based partial ambiguity resolution method, adding GLONASS data improves the positioning performance in all considered cases. Real data from different baselines are used to verify these findings. When using all five available systems, instantaneous centimeter-level positioning is possible on an 88.5 km baseline with the ionosphere weighted model, and on average, only 3.27 epochs are required for a long baseline with the ionosphere float model, thereby enabling near instantaneous solutions.

Partial Carrier-Phase Integer Ambiguity Resolution for High Accuracy GNSS Positioning

Global navigation satellite systems provide ranging based positioning and timing services. The use of the periodic carrier-phase signals is the key to fast and accurate solutions, given that the inherent ambiguities of the carrier-phase measurements are correctly resolved. The idea of partial ambiguity resolution is to resolve a subset of all ambiguities, which enables faster solutions but does not fully exploit the high precision of the carrier-phase measurements. Theory, methods, and algorithms for partial ambiguity resolution are discussed and analyzed with simulated and real data.

Ambiguity of Residual Constraint-Based Precise Point Positioning with Partial Ambiguity Resolution under No Real-Time Network Corrections Using Real Global Positioning System (GPS) Data

Although precise point positioning (PPP) is a well-established and promising technique with the use of precise satellite orbit and clock products, it costs a long convergence time to reach a centimeter-level positioning accuracy. The PPP with ambiguity resolution (PPP-AR) technique can improve convergence performance by resolving ambiguities after separating the fractional cycle bias (FCB). Now the FCB estimation is mainly realized by the regional or global operating reference station network. However, it does not work well in the areas where network resources are scarce. The contribution of this paper is to realize an ambiguity residual constraint-based PPP with partial ambiguity resolution (PPP-PARC) under no real-time network corrections to speed up the convergence, especially when the performance of the float solution is poor. More specifically, the update strategy of FCB estimation in a stand-alone receiver is proposed to realize the PPP-PAR. Thereafter, the solving process of FCB in a stand-alone receiver is summarized. Meanwhile, the influencing factors of the ambiguity success rate in the PPP-PAR without network corrections are analyzed. Meanwhile, the ambiguity residual constraint is added to adapt the particularity of the partial ambiguity-fixing without network corrections. Moreover, the positioning experiments with raw observation data at the Global Positioning System (GPS) globally distributed reference stations are conducted to determine the ambiguity residual threshold for post-processing and real-time scenarios. Finally, the positioning performance was verified by 22 GPS reference stations. The results show that convergence time is reduced by 15.8% and 26.4% in post-processing and real-time scenarios, respectively, when the float solution is unstable, compared with PPP using a float solution. However, if the float solution is stable, the PPP-PARC method has performance similar to the float solution. The method shows the significance of the PPP-PARC for future PPP applications in areas where network resource is deficient.

A Triple Checked Partial Ambiguity Resolution for GPS/BDS RTK Positioning

Reliable and accurate carrier phase ambiguity resolution is the key to high-precision Global Navigation Satellite System (GNSS) positioning and application. With the fast development of modern GNSS, the increased number of satellites and ambiguities makes it hard to fix all ambiguities completely and correctly. The partial ambiguity fixing technique, which selects a suitable subset of high-dimensional ambiguities to fix, is beneficial for improving the fixed success rate and reliability of ambiguity resolution. In this contribution, the bootstrapping success rate, bounded fixed-failure ratio test, and the new defined baseline precision defect are used for the selection of the ambiguity subset. Then a model and data dual-driven partial ambiguity resolution method is proposed with the above three checks imposed on it, which is named the Triple Checked Partial Ambiguity Resolution (TC-PAR). The comprehensive performance of TC-PAR compared to the full-fixed LAMBDA method is also analyzed based on several criteria including the fixed rate, the fixed success rate and correct fixed rate of ambiguity as well as the precision defect and RMS of the baseline solution. The results show that TC-PAR could significantly improve the fixed success rate of ambiguity, and it has a comparable baseline precision to the LAMBDA method, both of which are at centimeter level after ambiguities are fixed.