Precise Point Positioning with ambiguity resolution using multi-frequency multiconstellation GNSS measurements

This research aims to improve Precise Point Positioning (PPP) accuracy and solution convergence time by developing reliable PPP with ambiguity resolution (PPP-AR) methods and models using multi-frequency multi-Global Navigation Satellite System (GNSS) measurements. The convergence time is defined as when the position estimates and ambiguity parameters steadily approach to a defined accuracy level and maintain within the accuracy level. In particular the work focuses on the development of mathematical models to improve wide-lane (WL) and narrow-lane (NL or N1) ambiguity resolution methods. The prospects, effectiveness, as well as challenges in using triple-frequency GNSS measurements in a PPP model is presented. Specifically, using triple-frequency GPS measurements from eight Australian GPS stations, the performance of dual- and triple-frequency PPP has been assessed in the PPP static mode. It is indicated that the use of triple-frequency GPS-only measurements improves the 3D positioning accuracies as well as shortens solution convergence times compared with dual-frequency GPS-only PPP. The benefits of multi-frequency GNSS measurements in PPP-AR are investigated. The GNSS measurements include GPS L1, L2 and L5 signal; Galileo E1, E5a, E5b and E6 signal; and BeiDou B1, B2 and B3 signal. It is demonstrated that the quad-frequency Galileo combination of E1+E5a+E5b+E6 provides the most precise positioning and ambiguity solutions, and thus outperforms the triple-frequency GPS or BeiDou PPP solutions. Using real triple- and four-frequency GNSS measurements, it is concluded that the solution convergence time can be shortened compared with the triple-frequency GPS-only PPP case. A reliable WL ambiguity resolution method plays a significant role in reducing the solution convergence time in PPP. An optimal wide-lane ambiguity resolution (WL-AR) method is found by assessing two different PPP WL-AR methods, namely the geometry-based and ionospheric-free (GB-IF) linear combination method, and the geometry-free and ionospheric-free (GF-IF) method. It is concluded that an optimal WL-AR will be selected based on the ratio between the code and carrier phase measurement noise (RT). Specifically, the GF-IF WL-AR method should be used when RT<150. However, when RT>150, the GB-IF method should be selected instead. Depending on RT values used, 2 to 10 minutes is required to confidently resolve the WL ambiguities when using GNSS measurements with one-second sampling rate. An optimal ionospheric-free linear combination (LC) model for dual- and triple-frequency PPP, which can accelerate carrier-phase ambiguity and reduce the positioning solution convergence time, is proposed and investigated. To reduce computational complexity, a near-optimal LC model for triple-frequency PPP is also proposed. The proposed optimal and near-optimal LC models for dual- and triple-frequency GNSS PPP are compared with the uncombined observation (UC) model using both simulated and real GNSS data. It is found that ambiguity resolution is faster and positioning accuracy is improved using the optimal dual- and triple-frequency LC model. A new approach of partial ambiguity resolution method, namely the best integer equivariant estimator (BIE) using the t-distribution method (BIE-td), is proposed for fast and reliable solution convergence time in PPP-AR. This new method is then compared with two existing ambiguity resolution methods which are the partial ambiguity resolution based-Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method (PAR-Ps) and the iFlex method proposed by the Trimble Navigation Limited. The results suggest that the iFlex method outperforms the PAR-Ps method in the sense of minimising the position errors. In addition, the positioning convergence performance using the BIE-td and iFlex methods is comparable, with a similar positioning accuracy for both horizontal and vertical coordinate components.