Precise Point Positioning (PPP), coupled with the ambiguity resolution (AR) method, has demonstrated substantial potential in fields like agricultural navigation and airborne mapping. However, there ...remains a notable deficiency in the comprehensive comparative evaluation of its performance when using rapid and real-time satellite products, especially for mass low-cost receivers. Stations equipped with geodetic and low-cost receivers are analyzed in kinematic and static mode. In the kinematic mode, the GPS+Galileo-combined PPP, employing ambiguity fixing with “WHU” rapid products, achieves the highest positioning accuracy of 0.9 cm, 0.9 cm, and 2.6 cm in the North, East, and Up components, respectively. Real-time PPP using “CNT” products attains accuracies of 2.1 cm, 2.7 cm, and 4.8 cm for these components, utilizing GPS ambiguity-fixed PPP. BDS positioning accuracy is inferior to standalone GPS, but improves when the number of visible BDS satellites exceeds 10. Convergence time analysis shows that approximately 38.2 min are required for single GPS or BDS PPP using the “WHU” products and geodetic receivers, which can be reduced to 18.5 min for dual-system combinations and further to 14.8 min for triple-system combinations. The time can be further reduced by ambiguity fixing. In the static mode, multi-GNSS combination does not significantly impact convergence times, which are more influenced by the precision of the products used. Real-time products require approximately 22 min to achieve horizontal accuracy below 0.1 m, while rapid products reach this accuracy within 10 min. For PPP using low-cost GNSS receivers, more than two hours are necessary to achieve an accuracy better than 0.1 m for kinematic PPP, which is considerably longer than the convergence time observed at MGEX stations. However, the accuracy achieved after convergence, as well as the performance of static PPP, is comparable to that of MGEX stations.
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Investigations have been focused on improving the precision of real-time GNSS satellite clock corrections. There is a little literature analyzing the characteristics and impacts of the clock datum ...and initial clock biases (ICBs). We illustrated the clock anomaly caused by the two factors and proposed a new strategy flexible for global and regional clock estimation based on the mixed-difference observation method. First, we analyzed the clock datum of the final and real-time clocks. Results show that the variation in the clock datum can be up to 500 ns per day depending on the datum definition strategy. The variations can lead to large inconsistencies in the datum for the re-convergence of estimated satellite clocks when using the mixed-difference clock estimation method. To resolve the problem, we propose a new method for the epoch-by-epoch datum definition, which can screen out any outliers in broadcast ephemeris in real time, and particularly suitable for the real-time clock estimation. Second, we analyzed ICB jumps in real-time clock corrections, which can degrade the accuracy of precise point positioning. We propose a short-term prediction of clock corrections for bridging ICBs with the precision better than 0.1 ns for stable satellite clocks within a gap of 1–3 min. The prediction can decrease the magnitude of ICB jumps and thus improve a user solution. Considering the prediction of clocks, high precision cannot be guaranteed for all conditions, we thus recommend broadcasting a discontinuity flag for real-time service, so the re-convergence of ICB can be identified by users for resetting carrier-phase ambiguities.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
The Galileo constellations are characterized by transmitting GNSS signals on multi-frequencies, which can benefit the robustness and accuracy of the solutions. However, the dual-frequency E1/E5a ...combinations are generally used for precise point positioning (PPP). In this paper, the performance of Galileo static and kinematic PPP using different dual- and multi-frequency combinations are assessed using observations from the European region. Overall, the accuracy of daily PPP achieved by the dual-frequency GPS, Galileo, and BDS is better than 5 mm in the horizontal direction and better than 10 mm in the vertical direction. Though the number of observed Galileo satellites is less than GPS, the horizontal accuracy can reach 1.6 mm/2.3 mm/5.7 mm on North/East/Up component, which is improved by 59.0% and 12.3% compared to the GPS in the north and up direction. Then, the accuracy of Galileo static PPP is analyzed using different dual- and multi-frequency combinations. Results indicate that the Galileo E1/E5b PPP can degrade the accuracy due to the inter-frequency clock biases between the E1/E5a and E1/E5b combinations. Best accuracy can be achieved for the triple- and four-frequency PPP, which is 4.8 mm in the up direction. The hourly accuracy for the static PPP can reach 5.6 mm/9.2 mm/12.6 mm in the north/east/up direction using the GPS/Galileo/GLONASS/BDS combinations. Finally, a positioning convergence ratio (PCR) indicator, which represents the accuracy of PPP over a period, is used to analyze the convergence time of kinematic PPP. Results indicated that the multi-frequency Galileo observations contribute minorly to the convergence of kinematic PPP. However, Galileo shows the best convergence performance for the single GNSS positioning, and the GPS/Galileo combined PPP achieved the best performance for the PPP using different GNSS combinations.
The tropospheric delays estimated from the Global Navigation Satellite System (GNSS) have been proven to be an efficient product for monitoring variations of water vapor, which plays an important ...role in meteorology applications. The operational GNSS water vapor monitoring system is currently based on the Global Positioning System (GPS) and GLObal NAvigation Satellite System(GLONASS) dual-frequency observations. The Galileo satellite navigation system has been evolving continuously, and on 11 February 2019, the constellation reached 22 active satellites, achieving a capability of standalone Precise Point Positioning (PPP) and tropospheric estimation that is global in scope. This enhancement shows a 37% improvement if the precision of the Galileo-only zenith tropospheric delay, while we may anticipate further benefits in terms of tropospheric gradients and slant delays in the future if an optimal multi-constellation and multi-frequency processing strategy is used. First, we analyze the performance of the multi-frequency troposphere estimates based on the PPP raw observation model by comparing it with the standard ionosphere-free model. The performance of the Galileo-only tropospheric solution is then validated with respect to GPS-only solution using 48 globally distributed Multi-GNSS Experiment (MGEX) stations. The averaged bias and standard deviations are −0.3 and 5.8 mm when only using GPS satellites, respectively, and 0.0 and 6.2 mm for Galileo, respectively, when compared to the International GNSS Service (IGS) final Zenith Troposphere Delay(ZTD) products. Using receiver antenna phase center corrections from the corresponding GPS dual-frequency observations does not affect the Galileo PPP ambiguity float troposphere solutions. These results demonstrate a comparable precision achieved for both Galileo-only and GPS-only ZTD solutions, however, horizontal tropospheric gradients, estimated from standalone GPS and Galileo solutions, still show larger discrepancies, mainly due to their being less Galileo satellites than GPS satellites. Including Galileo E1, E5a, E5b, and E5 signals, along with their proper observation weighting, show the benefit of multi-frequency observations, further improving the ZTD precision by 4% when compared to the dual-frequency raw observation model. Overall, the presented results demonstrate good prospects for the application of multi-frequency Galileo observations for the tropospheric parameter estimates.
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The water vapor content in the atmosphere is highly correlated with rainfall events, which can be used as a data source for rainfall prediction or drought monitoring. The GNSS PPP (Precise Point ...Positioning) technique can be used to estimate the troposphere ZWD (Zenith Wet Delay) parameter which can be converted into precipitable water vapor (PWV). In this study, we first investigate the impacts of the weighting strategies, observation noise settings, and gradient estimation on the accuracy of ZWD and positions. A refined strategy is proposed for the troposphere estimation with uncombined raw PPP model, down-weighting of Galileo/GLONASS/BDS code observation by a factor of 3, using a sine2-type elevation-dependent weighting function and estimating the horizontal gradients. Based on the strategy, the correlation of the estimated tropospheric parameters with the rainfall is analyzed based on the data from the “7.20” rainstorm in Henan Province, China. The PWV is first calculated based on the hourly global pressure and temperature (HGPT) model and compared with the results from ERA5 products. Results show their good consistency during the rainfall period or the normal period with a standard deviation of 3 mm. Then, the high correlation between the PWV and the heavy rain rainfall event is validated. Results show that the accumulated PWV maintains a high level before the rainstorm if a sustainable water supply is available, while it decreased rapidly after the rainfall. In comparison, the horizontal gradients and the satellite residuals are less correlated with the water vapor content. However, the gradients can be used to indicate the horizontal asymmetry of the water vapor in the atmosphere.
The Precise Point Positioning (PPP) with fast integer ambiguity resolution (PPP-RTK) is feasible only if the solution is augmented with precise ionospheric parameters. The vertical ionospheric delays ...together with the receiver hardware biases, are estimated simultaneously based on the uncombined PPP model. The performance of the ionospheric delays was evaluated and applied in the PPP-RTK demonstration during the low solar activity period. The processing was supported by precise products provided by Deutsches GeoForschungsZentrum Potsdam (GFZ) and also by real-time products provided by the National Centre for Space Studies (CNES). Since GFZ provides only precise orbits and clocks, other products needed for ambiguity resolution, such as phase biases, were estimated at the Geodetic Observatory Pecny (GOP). When ambiguity parameters were resolved as integer values in the GPS-only solution, the initial convergence period was reduced from 30 and 20 min to 24 and 13 min when using CNES and GFZ/GOP products, respectively. The accuracy of ionospheric delays derived from the ambiguity fixed PPP, and the CODE global ionosphere map were then assessed. Comparison of ambiguity fixed ionospheric delay obtained at two collocated stations indicated the accuracy of 0.15 TECU for different scenarios with more than 60% improvement compared to the ambiguity float PPP. However, a daily periodic variation can be observed from the multi-day short-baseline ionospheric residuals. The accuracy of the interpolated ionospheric delay from global maps revealed a dependency on the location of the stations, ranging from 1 to 3 TECU. Precise ionospheric delays derived from the EUREF permanent network with an inter-station distance larger than 73 km were selected for ionospheric modeling at the user location. Results indicated that the PPP ambiguity resolution could be achieved within three minutes. After enlarging the inter-station distance to 209 km, ambiguity resolution could also be achieved within several minutes.
We developed a new strategy for a synchronous generation of real-time (RT) and near real-time (NRT) tropospheric products. It exploits the precise point positioning method with Kalman filtering and ...backward smoothing, both supported by real-time orbit and clock products. The strategy can be optimized for the latency or the accuracy of NRT production. In terms of precision, it is comparable to the traditional NRT network solution using deterministic models in the least-square adjustment. Both RT and NRT solutions provide a consistent set of tropospheric parameters such as zenith total delays, horizontal tropospheric gradients and slant delays, all with a high resolution and optimally exploiting all observations from available GNSS multi-constellations. As the new strategy exploits RT processing, we assessed publicly precise RT products and results of RT troposphere monitoring. The backward smoothing applied for NRT solution, when using an optimal latency of 30 min, reached an improvement of 20% when compared to RT products. Additionally, multi-GNSS solutions provided more accurate (by 25%) tropospheric parameters, and the impact will further increase when constellations are complete and supported with precise models and products. The new strategy is ready to replace our NRT contribution to the EUMETNET EIG GNSS Water Vapour Programme (E-GVAP) and effectively support all modern multi-GNSS tropospheric products.
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Recently, multirotor UAVs have been widely used in high-precision terrain mapping, cadastral surveys and other fields due to their low cost, flexibility, and high efficiency. Indirect georeferencing ...of ground control points (GCPs) is often required to obtain highly accurate topographic products such as orthoimages and digital surface models. However, in practical projects, GCPs are susceptible to anomalies caused by external factors (GCPs covered by foreign objects such as crops and cars, vandalism, etc.), resulting in a reduced availability of UAV images. The errors associated with the loss of GCPs are apparent. The widely used solution of using natural feature points as ground control points often fails to meet the high accuracy requirements. For the problem of control point anomalies, this paper innovatively presents two new methods of completing data fusion by supplementing photos via UAV at a later stage. In this study, 72 sets of experiments were set up, including three control experiments for analysis. Two parameters were used for accuracy assessment: Root Mean Square Error (RMSE) and Multiscale Model to Model Cloud Comparison (M3C2). The study shows that the two new methods can meet the reference accuracy requirements in horizontal direction and elevation direction (RMSEX = 70.40 mm, RMSEY = 53.90 mm, RMSEZ = 87.70 mm). In contrast, the natural feature points as ground control points showed poor accuracy, with RMSEX = 94.80 mm, RMSEY = 68.80 mm, and RMSEZ = 104.40 mm for the checkpoints. This research considers and solves the problems of anomalous GCPs in the photogrammetry project from a unique perspective of supplementary photography, and proposes two new methods that greatly expand the means of solving the problem. In UAV high-precision projects, they can be used as an effective means to ensure accuracy when the GCP is anomalous, which has significant potential for application promotion. Compared with previous methods, they can be applied in more scenarios and have higher compatibility and operability. These two methods can be widely applied in cadastral surveys, geomorphological surveys, heritage conservation, and other fields.
The new generation of GNSS satellites, including BDS, Galileo, modernized GPS, and GLONASS, transmit navigation sdata at more frequencies. Multi-frequency signals open new prospects for precise ...positioning, but satellite code and phase inter-frequency biases (IFB) induced by the third frequency need to be handled. Satellite code IFB can be corrected using products estimated by different strategies, the theoretical and numerical compatibility of these methods need to be proved. Furthermore, a new type of phase IFB, which changes with the relative sun–spacecraft–earth geometry, has been observed. It is necessary to investigate the cause and possible impacts of phase Time-variant IFB (TIFB). Therefore, we present systematic analysis to illustrate the relevancy between satellite clocks and phase TIFB, and compare the handling strategies of the code and phase IFB in triple-frequency positioning. First, the un-differenced L1/L2 satellite clock corrections considering the hardware delays are derived. And IFB induced by the dual-frequency satellite clocks to triple-frequency PPP model is detailed. The analysis shows that estimated satellite clocks actually contain the time-variant phase hardware delays, which can be compensated in L1/L2 ionosphere-free combinations. However, the time-variant hardware delays will lead to TIFB if the third frequency is used. Then, the methods used to correct the code and phase IFB are discussed. Standard point positioning (SPP) and precise point positioning (PPP) using BDS observations are carried out to validate the improvement of different IFB correction strategies. Experiments show that code IFB derived from DCB or geometry-free and ionosphere-free combination show an agreement of 0.3ns for all satellites. Positioning results and error distribution with two different code IFB correcting strategies achieve similar tendency, which shows their substitutability. The original and wavelet filtered phase TIFB long-term series show significant periodical characteristic for most GEO and IGSO satellites, with the magnitude varies between – 5cm and 5cm. Finally, BDS L1/L3 kinematic PPP is conducted with code IFB corrected with DCB combinations, and TIFB corrected with filtered series. Results show that the IFB corrected L1/L3 PPP can achieve comparable convergence and positioning accuracy as L1/L2 combinations in static and kinematic mode.
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With the recovery of the triple-frequency clocks using satellite time-variant inter-frequency bias (TIFB) corrections, benefits of the third frequency observable on precise point positioning (PPP) ...have been investigated. But numerical investigations on the effects of the third frequency observable on precise network clock and troposphere solutions are inadequate. Besides, the current strategy used to estimate satellite TIFB differs from the strategy used for IGS standard satellite clocks estimation. Considering the inconsistency of the mathematical model, current TIFB estimation method cannot be directly used to investigate the effects of the third frequency observable. Therefore, we propose a unified method to estimate satellite clocks and TIFB simultaneously. The receiver TIFB corrections are also estimated as unknowns in the new model. The effects of the third frequency observable, as well characteristics of receiver TIFB, are investigated. Numerical experiment results indicate that the averaged standard deviation of satellite clock and troposphere estimated with triple-frequency model is within 0.1 ns and 0.08 ns, respectively. Compared to the dual-frequency estimation model, a slight improvement is observed for the troposphere precision. Analysis on the characteristic of receiver TIFB demonstrates that its time series show similar tendency over days and its precision is within 0.04 ns, suggesting that the receiver TIFB is stable and small. However, ignoring the receiver TIFB will degrade the precision of L1/L2 clocks by a level of 0.015 ns. Our results thus revealed that the third frequency observable contribute minor to the improvement of network solutions. Instead, it will degrade the estimation efficiency due to the receiver TIFB parameters.
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