Rapid integer ambiguity resolution in GPS precise point positioning

Abstract

GPS precise point positioning (PPP) has been used in many scientific and commercial applications due to its high computational efficiency, no need for any synchronous measurements from a nearby reference receiver and homogeneous positioning quality on a global scale. However, these merits are devalued significantly by unresolved ambiguities and slow convergences of PPP. Therefore, this thesis aims at improving PPP’s performance by resolving ambiguities for a single receiver and accelerating the convergences to ambiguity-fixed solutions in order to achieve a centimeter-level positioning accuracy with only a few seconds of measurements. In recent years, ambiguity resolution for PPP has been developed by separating fractional cycle biases (FCBs) from single-receiver ambiguity estimates. One method is to estimate FCBs by averaging the fractional parts of single-difference ambiguity estimates between satellites, and the other is to assimilate FCBs into clocks by fixing undifferenced ambiguities to integers in advance. The first method suffers from a large number of redundant satellite-pair FCBs and unnecessary 15-minute narrow-lane FCBs. Therefore, this thesis suggests undifferenced FCBs and one narrow-lane FCB per satellite-pair pass over a regional area in order to reduce the size of FCB products and achieve comparable positioning quality with that of the original method. Typical tests show that ambiguity resolution dramatically reduces the RMS of differences between hourly and daily position estimates from 3.8, 1.5 and 2.8 cm in ambiguity-float solutions to 0.5, 0.5 and 1.4 cm in ambiguity-fixed solutions for the East, North and Up components, respectively. Likewise, the RMS for real-time position estimates are reduced drastically from 13.7, 7.1 and 11.4 cm to 0.8, 0.9 and 2.5 cm. Of particular note, this improvement can be achieved even at remote receivers which are over a few thousand kilometers from the reference receivers that are used to estimate FCBs. Furthermore, this thesis improves the accuracy of narrow-lane FCB estimates with integer constraints from double-difference ambiguities. In a one-year global network analysis, the RMS of differences for the East component between the daily and IGS weekly estimates is reduced from 2.6 mm in the solutions based on original FCBs to 2.2 mm in the solutions based on improved FCBs. Although small, this improvement is significant and critical to some geophysical studies, such as tectonic motions, sea level rise, and post-glacial rebound. More importantly, for the first time, this thesis provides a theoretical proof for the equivalence between the ambiguity-fixed position estimates derived from the aforementioned two methods. This equivalence is then empirically verified by the overall minimal discrepancies of the positioning qualities between the two methods. However, these discrepancies manifest a distribution of geographical pattern, i.e. the largest discrepancies correspond to sparse networks of reference receivers. This comparison can provide valuable reference for the GPS community to choose an appropriate method for their PPP ambiguity resolution. As the foremost contribution, an innovative method is originally developed in this thesis in order to effectively re-converge to ambiguity-fixed solutions with only a few seconds of measurements. Specifically, ionospheric delays at all ambiguity-fixed epochs are estimated and then predicted precisely to succeeding epochs in the case of re-convergences. The predicted ionospheric delays are first used to correct wide-lane measurements in order to rapidly resolve wide-lane ambiguities. The resulting ionosphere-corrected and ambiguity-fixed wide-lane measurements are then used to tightly constrain narrow-lane measurements and thus speed up narrow-lane ambiguity resolution significantly. As a result, the practicability of real-time PPP is greatly improved by eliminating the unrealistic requirement of a continuous open sky view in most PPP applications. Typical tests illustrate that over 90% of re-convergences can be achieved within five epochs of 1-Hz measurements, rather than the conventional 20 minutes, even if the latency for the predicted ionospheric delays is up to 180 s. Moreover, for a van-borne receiver moving in a GPS-adverse environment where satellite number decreases significantly and cycle slips occur frequently, only when the above rapid re-convergence technique is applied can the rate of ambiguity-fixed epochs dramatically rise from 7.7% to 93.6% of all epochs. Finally, a precise positioning service for the next-generation global RTK, characterized by both global coverage and regional augmentation, is originally proposed in this thesis based on real-time PPP enhanced by rapid (re-)convergences to ambiguity-fixed solutions. It is illustrated that a globally distributed network of 38 stations can ensure that the ambiguity-fixed epochs account for over 95% of all epochs