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See detailKinematic precise point postioning at remote marine platforms
Geng, J.; Teferle, Felix Norman UL; Meng, X. et al

in GPS Solutions (2010), 14(4), 343-350

Precise kinematic differential positioning using the global positioning system (GPS) at a marine platform usually requires a relatively short distance (e.g. 500km) to a land-based reference station. As an ... [more ▼]

Precise kinematic differential positioning using the global positioning system (GPS) at a marine platform usually requires a relatively short distance (e.g. 500km) to a land-based reference station. As an alternative, precise point positioning (PPP) is normally considered free from this limiting requirement. However, due to the prerequisite of network-based satellite products, PPP at a remote marine platform may still be affected by its distance to the reference network. Hence, this paper investigates this scenario by configuring rings of reference stations with different radii centered on a to-be-positioned marine platform. Particularly, we applied ambiguity resolution at a single station to PPP by estimating uncalibrated phase delays (UPDs). We used three rings of reference stations centered on a vessel, with radii of roughly 900, 2,000 and 3,600 km, to determine satellite clocks and UPDs independently. For comparison, we also performed differential positioning based on a single reference station with baseline lengths of about 400, 1,700 and 2,800 km. We demonstrate that, despite the increasing ring-network radius to a few 1,000 km, the overall change in accuracy of the satellite clocks that are used at the vessel is smaller than 0.02 ns, and the RMS values of differences between the three sets of narrow-lane UPD estimates are around 0.05 cycles only. Moreover, the kinematic positioning accuracy of PPP is affected by the increasing ring-network radius, but can still achieve several centimeters after ambiguity resolution when the vessel is over a few 1,000 km away from the ring network, showing better performance than that of differential positioning. Therefore, we propose that ambiguity- fixed PPP can be used at remote marine platforms that support precise oceanographic and geophysical applications in open oceans. [less ▲]

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See detailPerformance of Precise Point Positioning with Ambiguity Resolution for 1- to 4- hour Observation Periods
Geng, J.; Meng, X.; Teferle, Felix Norman UL et al

in Survey Review (2010), 42(316), 155-165

Recent progress in integer ambiguity resolution at a single station has made it possible to achieve high positioning accuracy in static precise point positioning (PPP) using a short period of observations ... [more ▼]

Recent progress in integer ambiguity resolution at a single station has made it possible to achieve high positioning accuracy in static precise point positioning (PPP) using a short period of observations. In this paper, 12 stations across Europe are used to conduct short-period (i.e. one, two, three and four hours) static PPP with ambiguity resolution from Day 245 to 251 in 2007. It is demonstrated that, when over three hours of observations are used, PPP can achieve a success rate of 100% for ambiguity resolution, a 3D positioning accuracy of about 1.0 cm and an occurrence of less than 1.0% for degraded solutions. Moreover, for the fixed solutions, increasing the observation period hardly improves the horizontal positioning accuracy while still improving the vertical one. Therefore, it is proposed that at least three hours of observations should be used in the ambiguity-fixed static PPP if a reliable millimetre positioning accuracy is required in the engineering applications. [less ▲]

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See detailTowards PPP-RTK: Ambiguity Resolution in Real-Time Precise Point Positioning
Geng, J.; Teferle, Felix Norman UL; Meng, X. et al

in Advances in Space Research (2010)

Integer ambiguity resolution at a single station can be achieved by introducing predetermined uncalibrated phase delays (UPDs) into the float ambiguity estimates of precise point positioning (PPP). This ... [more ▼]

Integer ambiguity resolution at a single station can be achieved by introducing predetermined uncalibrated phase delays (UPDs) into the float ambiguity estimates of precise point positioning (PPP). This integer resolution technique has the potential of leading to a PPP-RTK (Real-Time Kinematic) model where PPP provides rapid convergence to a reliable centimeter-level positioning accuracy based on an RTK reference network. Nonetheless, implementing this model is technically subject to how rapidly we can fix wide-lane ambiguities, stabilize narrow-lane UPD estimates, and achieve the first ambiguity-fixed solution. To investigate these issues, we used seven days of 1-Hz sampling GPS data at 91 stations across Europe. We find that at least 10 minutes of observations are required for most receiver types to reliably fix about 90% of wide-lane ambiguities corresponding to high elevations, and over 20 minutes to fix about 90% of those corresponding to low elevations. Moreover, several tens of minutes are usually required for a regional network before a narrow-lane UPD estimate stabilizes to an accuracy of far better than 0.1 cycles. Finally, for hourly data, ambiguity resolution can significantly improve the accuracy of epoch-wise position estimates from 13.7, 7.1 and 11.4 cm to 0.8, 0.9 and 2.5 cm for the East, North and Up components, respectively, but a few tens of minutes is required to achieve the first ambiguity-fixed solution. Therefore, from the timeliness aspect, our PPP-RTK model currently cannot satisfy the critical requirement of instantaneous precise positioning where ambiguity-fixed solutions have to be achieved within at most a few seconds. However, this model can still be potentially applied to some near-real-time remote sensing applications, such as the GPS meteorology. [less ▲]

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See detailInteger ambiguity resolution in precise point poistioning: method comparison
Geng, J.; Meng, Xiaolin; Dodson, Alan H et al

in Journal of Geodesy (2010), 84(9), 569-581

Integer ambiguity resolution at a single receiver can be implemented by applying improved satellite products where the fractional-cycle biases (FCBs) have been separated from the integer ambiguities in a ... [more ▼]

Integer ambiguity resolution at a single receiver can be implemented by applying improved satellite products where the fractional-cycle biases (FCBs) have been separated from the integer ambiguities in a network solution. One method to achieve these products is to estimate the FCBs by averaging the fractional parts of the float ambiguity estimates, and the other is to estimate the integer-recovery clocks by fixing the undifferenced ambiguities to integers in advance. In this paper, we theoretically prove the equivalence of the ambiguity-fixed position estimates derived from these two methods by assuming that the FCBs are hardware-dependent and only they are assimilated into the clocks and ambiguities. To verify this equivalence, we implement both methods in the Position and Navigation Data Analyst software to process 1 year of GPS data from a global network of about 350 stations. The mean biases between all daily position estimates derived from these two methods are only 0.2, 0.1 and 0.0 mm, whereas the standard deviations of all position differences are only 1.3, 0.8 and 2.0 mm for the East, North and Up components, respectively. Moreover, the differences of the position repeatabilities are below 0.2 mm on average for all three components. The RMS of the position estimates minus those from the International GNSS Service weekly solutions for the former method differs by below 0.1 mm on average for each component from that for the latter method. Therefore, considering the recognized millimeter-level precision of current GPS-derived daily positions, these statistics empirically demonstrate the theoretical equivalence of the ambiguity-fixed position estimates derived from these two methods. In practice, we note that the former method is compatible with current official clock-generation methods, whereas the latter method is not, but can potentially lead to slightly better positioning quality. [less ▲]

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See detailRapid re-convergences to ambiguity-fixed solutions in precise point-positioning
Geng, J.; Meng, X.; Dodson, A. H. et al

in Journal of Geodesy (2010), 84(12), 705-714

Integer ambiguity resolution at a single station can be preformed if the fractional-cycle biases are separated from the ambiguity estimates in precise point positioning (PPP). Despite the improved ... [more ▼]

Integer ambiguity resolution at a single station can be preformed if the fractional-cycle biases are separated from the ambiguity estimates in precise point positioning (PPP). Despite the improved positioning accuracy by such integer resolutions, the convergence to an ambiguity-fixed solution normally requires at least a few tens of minutes. More importantly, such convergences can repeatedly occur on the occasion of losses of tracking locks for many satellites if an open sky-view is not constantly available, consequently totally destroying the practicability of real-time PPP. In this study, in case of such re-convergences, we develop a method in which ionospheric delays are precisely predicted to significantly accelerate integer ambiguity resolutions. The effectiveness of this method consists in two aspects: First, wide-lane ambiguities can be rapidly resolved using the ionosphere- corrected wide-lane measurements, instead of the noisy Melbourne-Wübbena combination measurements; second, narrow-lane ambiguity resolution can be accelerated under the tight constraints derived from the ionosphere-corrected unambiguous wide-lane measurements. In the tests at 90 static stations suffering from simulated total loss of tracking locks, 93.3% and 95.0% of re- convergences to wide-lane and narrow-lane ambiguity resolutions can be achieved within 5 s, respectively, even though the time latency for the predicted ionospheric delays is up to 180 s. In the tests at a mobile van moving in a GPS-adverse environment where satellite number significantly decreases and cycle slips frequently occur, only when the predicted ionospheric delays are applied can the rate of ambiguity-fixed epochs be dramatically improved from 7.7% to 93.6% of all epochs. Therefore, this method can potentially relieve the unrealistic requirement of a continuous open sky- view by most PPP applications and improve the practicability of real-time PPP. [less ▲]

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See detailAmbiguity resolution in precise point positioning with hourly data
Geng, J.; Teferle, Felix Norman UL; Shi, C. et al

in GPS Solutions (2009), 13(4), 263-270

Precise Point Positioning (PPP) has become a recognized and powerful tool for scientific analysis of Global Positioning System (GPS) measurements. Until recently, ambiguity resolution at a single station ... [more ▼]

Precise Point Positioning (PPP) has become a recognized and powerful tool for scientific analysis of Global Positioning System (GPS) measurements. Until recently, ambiguity resolution at a single station has been considered difficult, due to the non-integer uncalibrated hardware delays (UHD) originating in receivers and satellites. Fortunately, recent studies show that if these UHD can be determined precisely with a network in advance, then ambiguity resolution at a single station is possible. In this study, the method proposed by Ge et al (2007) is adopted with a refinement in which the fractional parts of single-difference narrow-lane UHD for a satellite pair are determined within each full pass over a regional network. This study uses the European Reference Frame Permanent Network (EPN) to determine these UHD from Day 245 to 251 in 2007, and 27 IGS stations inside and outside the EPN are used to conduct ambiguity resolution in hourly PPP. It is found that the total hourly position accuracy is improved from 3.8 cm, 1.5 cm and 2.8 cm to 0.5 cm, 0.5 cm and 1.4 cm in East, North and Up, respectively, for the stations inside the EPN. For the stations outside the EPN, some of which are even over 2000 km away from the EPN, their total hourly East, North and Up position accuracies still achieve 0.6 cm, 0.6 cm and 2.0 cm, respectively, when the EPN-based UHD are applied to the ambiguity resolution at these stations. Therefore, it is feasible and beneficial for the operators of GPS networks, such as the providers of PPP-based online services, to provide these UHD estimates as an additional product to allow users to conduct ambiguity resolution in PPP. [less ▲]

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