Precise Point Positioning Applications Research Articles

Analysis of Galileo five-frequency precise satellite clock estimation models and its effect on multi-frequency PPP

The Global Navigation Satellite System (GNSS) multi-frequency observations are widely used in positioning applications, while precise orbit determination and precise clock estimation (PCE) techniques typically employ dual-frequency undifferenced (UD) ionospheric-free (IF) observations from global networks. To fully utilize the multi-frequency GNSS observations for generating satellite products at the server-end, we develop some new five-frequency PCE models based on Galileo data, which are five-frequency uncombined FFUC model, FFIF0 model combining the E1/E5a, E1/E5b, E1/E5 and E1/E6 IF observables, FFIF1 model combining E1/E5a and E1/E5a/E5b/E5/E6 IF observables, respectively. The traditional dual-frequency UD IF and triple-frequency PCE models are also introduced for comparison. The new multi-frequency PCE models can not only make full use of the modern GNSS multi-frequency observations, but also obtain satellite clock offsets and inter-frequency clock bias (IFCB) at the same time, which can better support multi-frequency precise point positioning (PPP) applications. The multi-frequency models can improve the stability of GNSS satellite clock estimation, the precision of satellite clock offsets can be improved by 8–12% for triple-frequency models, and 19–27% for five-frequency PCE models compared with the traditional dual-frequency IF model. The PPP positioning accuracy using only multi-frequency satellite clock offsets can be improved by 7–18% for dual-frequency PPP, 8–15% for triple-frequency PPP, 4–16% for five-frequency PPP. The positioning accuracy can be further improved by 11–28% for triple-frequency PPP and 7–20% for five-frequency PPP. Therefore, the new multi-frequency PCE models are demonstrated to support PPP applications with better performance.

Quasi-4-dimension ionospheric modeling and its application in PPP

Ionospheric delay modeling is not only important for Global Navigation Satellite System (GNSS) based space weather study and monitoring, but also an efficient tool to speed up the convergence time of Precise Point Positioning (PPP). In this study, a novel model, denoted as Quasi-4-Dimension Ionospheric Modeling (Q4DIM) is proposed for wide-area high precision ionospheric delay correction. In Q4DIM, the Line Of Sight (LOS) ionospheric delays from a GNSS station network are divided into different clusters according to not only the location of latitude and longitude, but also satellite elevation and azimuth. Both Global Ionosphere Map (GIM) and Slant Ionospheric Delay (SID) models that are traditionally used for wide-area and regional ionospheric delay modeling, respectively, can be regarded as the special cases of Q4DIM by defining proper grids in latitude, longitude, elevation, and azimuth. Thus, Q4DIM presents a resilient model that is capable for both wide-area coverage and high precision. Four different sets of clusters are defined to illustrate the properties of Q4DIM based on 200 EUREF Permanent Network (EPN) stations. The results indicate that Q4DIM is compatible with the GIM products. Moreover, it is proved that by inducting the elevation and azimuth angle dependent residuals, the precision of the 2-dimensional GIM-like model, i.e., Q4DIM 2-Dimensional (Q4DIM-2D), is improved from around 1.5 Total Electron Content Units (TECU) to better than 0.5 TECU. In addition, treating Q4DIM as a 4-dimensional matrix in latitude, longitude, elevation, and azimuth, whose sparsity is less than 5%, can result in its feasibility in a bandwidth-sensitive applications, e.g., satellite-based Precising Point Positioning Real-Time Kinematic (PPP-RTK) service. Finally, the advantages of Q4DIM in PPP over the 2-dimensional models are demonstrated with the one month's data from 30 EPN stations in both high solar activity year 2014 and low solar activity year 2020.

Investigation of Precise Single-Frequency Time and Frequency Transfer with Galileo E1/E5a/E5b/E5/E6 Observations

With the rapid upgrade of global navigation satellite system (GNSS) single-frequency (SF) receivers and the increasing market demand for low-cost hardware, SF precise point positioning (PPP) technology has been widely applied in the time and frequency field. The five-frequency signals provided by the whole constellation of Galileo bring more opportunities for the application of SF PPP in time and frequency transfer. In this contribution, using Galileo’s multi-frequency observations, three SF PPP time and frequency transfer models, i.e., the un-combined (UC) model, the ionosphere-free-half (IFH) model, and the ionosphere-weighted constraints (IWCs) model are established. SF PPP time and frequency transfer performance with Galileo E1, E5a, E5b, E5, and E6 multi-frequency observations is evaluated using four links (947.7 km to 1331.6 km) with five external high-precision atomic clocks stations. The results show that the time and frequency transfer performance of SF-UC and SF-IWC is better than that of SF-IFH, and the timing accuracy of SF-UC and SF-IWC is similar. SF PPP time and transfer performance with E5, E5a, E5b, and E6 signals is improved compared with traditional E1 signal. Among them, the frequency stability of E5 improves the most (about 58%), and that of E6 improves the least (about 14%). In addition, the difference in frequency stability between SF and double-frequency (DF) PPP decreases gradually with an increase in average time, and the frequency stability difference between SF and DF PPP can reach 2 × 10−16 in 120,000 s, indicating that SF PPP has the potential to achieve DF PPP frequency stability. Considering the possible frequency data loss during actual observation, the cost of the GNSS SF receiver, and the advantages of Galileo multi-frequency observations, SF PPP can also meet the long-time time and frequency transfer requirements, and the SF-IWC model based on Galileo E5 observations is more recommended.

Low-Cost GNSS and Real-Time PPP: Assessing the Precision of the u-blox ZED-F9P for Kinematic Monitoring Applications

With the availability of low-cost, mass-market dual-frequency GNSS (Global Navigation Satellite System) receivers, standalone processing methods such as Precise Point Positioning (PPP) are no longer restricted to geodetic-grade GNSS equipment only. However, with cheaper equipment, data quality is expected to degrade. This same principle also affects low-cost GNSS antennas, which usually suffer from poorer multipath mitigation and higher antenna noise compared to their geodetic-grade counterparts. This work assesses the quality of a particular piece of low-cost GNSS equipment for real-time PPP and high-rate dynamic monitoring applications, such as strong-motion seismology. We assembled the u-blox ZED-F9P chip in a small and light-weight data logger. With observational data from static experiments—which are processed under kinematic conditions—we assess the precision and stability of the displacement estimates. We tested the impact of different multi-band antenna types, including geodetic medium-grade helical-type (JAVAD GrAnt-G3T), as well as a low-cost helical (Ardusimple AS-ANT2B-CAL) and a patch-type (u-blox ANN-MB) antenna. Besides static tests for the assessment of displacement precision, strong-motion dynamic ground movements are simulated with a robot arm. For cross-validation, we collected measurements with a JAVAD SIGMA G3T geodetic-grade receiver. In terms of precision, we cross-compare the results of three different dual-frequency, real-time PPP solutions: (1) an ambiguity-float solution using the Centre National d’Études Spatiales (CNES) open-source software, (2) an ambiguity-float and an AR (ambiguity-resolved) solution using the raPPPid software from TU Vienna, and (3) and a PPP-RTK solution using the u-blox PointPerfect positioning service. We show that, even with low-cost GNSS equipment, it is possible to obtain a precision of one centimeter. We conclude that these devices provide an excellent basis for the densification of existing GNSS monitoring networks, as needed for strong-motion seismology and earthquake-early-warning.

Performance Evaluation of Near Real-time GNSS PPP Time Transfer with IGS Products

The GNSS time transfer technology is the high precision time transfer method based on the navigation satellite system and has been widely applied in time and frequency. Benefiting from the development of GNSS time transfer technology and the expansion of user needs for real-time time service applications, real-time time transfer technology has become an important research direction. GNSS Precise Point Positioning (PPP) is one of the most commonly used methods of GNSS time transfer technology. With the development of the many facilities, the application of the real-time GNSS PPP has become wider and wider. In this paper, we demonstrate and evaluate the performance of the international GNSS service (IGS) products in the near real-time PPP time transfer technology. A set of the PPP solutions were computed from the observed data from the timekeeping laboratories, and three types of products provided by IGS, including Ultra-Rapid (IGU), Rapid (IGR), and Final (IGS final) orbit and clock offset products. IGS final and IGR products have extremely high accuracy and stability and are used as a reference for the time transfer with IGU product. The near real time clock offset and the comparison link performed with the IGU product can provide a time comparison service with an accuracy of 0. 5ns for near real time applications.

Real-time GNSS precise point positioning with smartphones for vehicle navigation

The availability of raw Global Navigation Satellite System (GNSS) measurements from Android smart devices gives new possibilities for precise positioning solutions, e.g., Precise Point Positioning (PPP). However, the accuracy of the PPP with smart devices currently is a few meters due to the poor quality of the raw GNSS measurements in a kinematic scenario and in urban environments, particularly when the smart devices are placed inside vehicles. To promote the application of GNSS PPP for land vehicle navigation with smart devices, this contribution studies the real-time PPP with smartphones. For data quality analysis and positioning performance validation, two vehicle-based kinematic positioning tests were carried out using two Huawei Mate30 smartphones and two Huawei P40 smartphones with different installation modes: the vehicle-roof mode with smartphones mounted on the top roof outside the vehicle, and the dashboard mode with smartphones stabilized on the dashboard inside the vehicle. To realize high accuracy positioning, we proposed a real-time smartphone PPP method with the data processing strategies adapted for smart devices. Positioning results show that the real-time PPP can achieve the horizontal positioning accuracy of about 1–1.5 m in terms of root-mean-square and better than 2.5 m at the 95th percentile for the vehicle-based kinematic positioning with the experimental smartphones mounted on the dashboard inside the vehicle, which is the real scenario in vehicle navigation.

Modeling wide-area tropospheric delay corrections for fast PPP ambiguity resolution

The performance of precise point positioning (PPP) has been significantly improved thanks to the continuous improvements in satellite orbit, clock, and ambiguity resolution (AR) technologies, but the convergence speed remains a limiting factor in real-time PPP applications. To improve the PPP precision and convergence time, tropospheric delays from a regional network can be modeled to provide precise correction for users. We focus on the precise modeling of zenith wet delay (ZWD) over a wide area with large altitude variations for improving PPP-AR. By exploiting the water vapor exponential vertical decrease, we develop a modified optimal fitting coefficients (MOFC) model based on the traditional optimal fitting coefficients (OFC) model. The proposed MOFC model provides a precision better than 1.5 cm under sparse inter-station distances over the Europe region, with a significant improvement of 70% for high-altitude stations compared to the OFC model. The MOFC model with different densities of reference stations is further evaluated in GPS and Galileo kinematic PPP-AR solutions. Compared to the PPP-AR solutions without tropospheric delay augmentation, the positioning precision of those with 100-km inter-station spacing MOFC and OFC is improved by 25.7% and 17.8%, respectively, and the corresponding time to first fix (TTFF) is improved by 36.9% and 33.0% in the high-altitude areas. On the other hand, the OFC model only slightly improves the TTFF and positioning accuracy when using the 200 km inter-station spacing modeling and even degrades the positioning for high-altitude stations, whereas using the MOFC model, the PPP-AR solutions always improve. Moreover, the positioning precision improvement of MOFC compared with OFC is about 22.1%, 21.7%, and 25.7% for the Galileo-only, GPS-only, and GPS + Galileo PPP-AR solutions, respectively.

Prediction models of GNSS satellite clock errors: Evaluation and application in PPP

Satellite clock error prediction plays a key role in GNSS technology for Positioning, Navigation and Timing (PNT) service. However, due to the different types and quality of the space-borne atomic clocks, it is rather difficult to predict high-accuracy satellite clock errors by using one unique prediction model. In general, the performance of existing prediction models varies with different types of satellite clocks, lengths of fitting arcs and predicting arcs. In this article, three common-used prediction models e.g. polynomial model, grey model, and Auto-Regressive Integrated Moving Average (ARIMA) model are evaluated with GNSS precise satellite clock products provided by GFZ. The prediction precision of these models is calculated with respect to precise clock products, specified by different lengths of fitting arcs and prediction arcs respectively. Then, the clock errors predicted by these models are applied to kinematic Precise Point Positioning (PPP) separately and the corresponding positioning performance is discussed. The numerical results show that polynomial model performs the best compared to other two models. For 5-min prediction, the RMS values of predicted clock for GPS, Galileo, GLONASS, and BDS are 0.14 ns, 0.016 ns, 0.21 ns and 0.089 ns respectively. For kinematic PPP with 5-min predicted clock products, polynomial model has the minimum RMS values among three models, with 0.031 m, 0.026 m, and 0.068 m for east, north, and up components, respectively. Moreover, sub-decimeter can be reached for horizontal component with 1-hour predicted clock products. ARIMA model is comparable to polynomial model when the prediction arc is 5–15 min but becomes relatively worse with the increase of the length of prediction arc. Grey model is the worst among the three models, it can meet the requirement of sub-decimeter precision in kinematic PPP only if the prediction arc is shorter than 15 min.

Online algorithm for variance components estimation

In this study, we develop a new algorithm for online variance components estimation (Online-VCE) of geodetic data based on the batch expectation-maximization (EM) algorithm and stochastic approximation theory. The Online-VCE algorithm is then applied to the Kalman filter and least-squares method and validated using simulated kinematic precise point positioning (PPP) based on the global navigation satellite system as well as real-data PPP experiments. The Online-VCE algorithm is specifically designed to monitor and establish a stochastic model in real-time or high-rate data applications. Compared to other methods, the Online-VCE is faster and can estimate the stochastic model in real time because it does not need to store all data, but simply estimates the expected result and computes the gradient of the parameters using only one or a few observations. In future, the Online-VCE algorithm can be used to develop a real-time atmospheric stochastic model for PPP applications.

A variational Bayesian-based robust adaptive filtering for precise point positioning using undifferenced and uncombined observations

In the application of precise point positioning (PPP), especially in the dynamic mode, the classical Kalman filter (KF) usually produces a large number of estimation errors or diverges when there are gross errors in the observation data or unexpected turbulences occur in target motion state or both of them. For such problem, a variational Bayesian (VB)-based robust adaptive Kalman filtering (VB-RAKF) is proposed in this paper. This filter introduces a classification robust equivalent weight function to resist observation gross error and the inverse Wishart prior to model inaccurate process noise covariance matrix (PNCM). To improve the instantaneous accuracy of state estimation, the VB approach is used to obtain better estimations of inaccurate PNCM. Several sets of observation data collected by IGS reference stations and vehicles are employed to check the robustness and positioning accuracy of the VB-RAKF model. The results show that the VB-RAKF algorithm is more robust than the KF, and can effectively resist the gross error in observation data and control state disturbance. In the IGS reference station tests, when compared to the KF, the static positioning accuracies of the VB-RAKF in the north, east and up directions are improved by 13%, 8% and 22%, respectively, and the simulated dynamic positioning accuracies of the VB-RAKF in the north, east and up directions are improved by 19%, 9% and 21%, respectively. The in-vehicle dynamic test verifies that the VB-RAKF outperforms the KF, and shows that the VB-RAKF has better performance than the KF when dealing with observation data which has obvious gross errors, and similar performance as the KF when gross errors are small.

Long-term time-varying characteristics of UPD products generated by a global and regional network and their interoperable application in PPP

The quality and availability of Uncalibrated Phase Delay (UPD) solutions are crucial to the Precise Point Positioning (PPP) service, and the long-term temporal variability and its contributing factors should be better understood. In this paper, we comprehensively investigate the long-term time-varying characteristics of each UPD product respectively generated by a global and regional network and their interoperable application in PPP-AR (ambiguity resolution), the sampling of the WL and NL UPDs are daily and 30 s, respectively. Firstly, in terms of our 30 day Wide-Lane (WL) UPD products of 31 satellites, the Standard Deviation (STD) of each satellite WL UPDs ranges from 0.04 to 0.06 cycles, indicating that the long-term prediction accuracy of satellite WL UPD is sufficient for fixing Wide-Lane ambiguities. Secondly, when a satellite in eclipsing the discontinulity may corrupt the determination of Narrow-Lane (NL) UPD in form of offset, as a result of lacking or poor satellite attitude dynamic modeling. When the influence of discontinuity is removed, the STD of our estimated satellite NL UPDs is less than 0.05 cycles. Thirdly, the STD of our estimated receiver WL UPDs is mainly below 0.2 cycles, which implies that its stability is one order poorer that of the satellite. In addition, if they are used for stations in and around the network covered region, the stability of the UPD products from the CMONOC (Crustal Movement Observation Network of China) is better than that from a global network, benefit from the fact that all the CMONOC stations are equipped with the same receiver type. Finally, the PPP-AR results show that a rate of 82.9% for stations with a WL-ambiguity-fixed rate of over 90% while 69.5% for stations with an NL-ambiguity-fixed rate of over 80% can be achieved when using UPD from the global network, which is worse than that of using UPD from the CMONOC (85.7% for stations with a WL-ambiguity-fixed rate of over 90% while 75% for stations with an NL-ambiguity-fixed rate of over 80%). The results of the experiment on the UPD interoperable application in PPP show that the global network UPD products can provide a fast AR at any single station, and the convergence time is well below 25 min. Particularly, when the location of a station is in and around the regional network, our results show that the PPP results obtained using regional UPDs enable the consistent use of global UPDs. When the location of a station is far away from the regional network, using the regional UPDs can not achieve PPP-AR. Finally, the WL UPDs of the previous day is used for forecasting to estimate the NL UPDs, the stability analysis results of NL UPDs solution and positioning results are demonstrate the validity of forecasted UPD products.

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.

Regiomontan: A Regional High Precision Ionosphere Delay Model and Its Application in Precise Point Positioning

Propagation delays of GNSS signals caused by the ionosphere can range up to several meters in zenith direction and need to be corrected. Geodetic receivers observing at two or more frequencies allow the mitigation of the ionospheric effects by forming linear combinations. However, single frequency users depend on external information. The ionosphere delay model Regiomontan developed at TU Wien is a regional ionospheric delay model providing high accuracy information with a latency of only a few hours. The model is based on dual-frequency phase observations of a regional network operated by EPOSA (Echtzeit Positionierung Austria) and partners. The corrections cover a geographical extent for receiver positions within Austria and are provided in the standardized IONEX format. The performance of Regiomontan as well as its application in Precise Point Positioning (PPP) were tested with our in-house PPP software raPPPid using the so-called uncombined model with ionospheric constraint. Various tests, e.g., analyzing the coordinate convergence behavior or the difference between estimated and modeled ionospheric delay, proving the high level of accuracy provided with Regiomontan. We conclude that Regiomontan performs at a similar level of accuracy as IGS final TEC maps, but with explicitly reduced latency.

BDS/GPS/LEO triple-frequency uncombined precise point positioning and its performance in harsh environments

Precise point positioning (PPP) usually takes a few tens of minutes to achieve centimeter-level positioning accuracy, and reliable ambiguity resolution also requires a relatively long observation time. In addition, the time required will be longer in harsh environments such as urban and canyons. These problems limit the application of PPP. Currently, low earth orbit (LEO) enhanced Global Navigation Satellite System (GNSS) can increase the number of visible satellites and optimize observation structure, which is expected to improve the positioning performance of GNSS-only PPP under complex conditions. In this paper, the performance of LEO/GNSS combined PPP in harsh environments is evaluated initially. First, triple-frequency uncombined PPP model is developed. Then, a LEO constellation consisting of 180 polar-orbiting satellites is designed, and BDS-3 and current GPS constellation are also simulated for subsequent analysis. Besides, the corresponding observation simulation is also carried out. In order to better analyze the performance of LEO enhanced GNSS PPP in harsh environments, six sets of contrast experiments are designed. Both PPP float solution and fixed solution are processed. In term of float solution, it usually takes about 30 min for BDS-only to converge into 5 cm, while the BDS/LEO combination only takes about 10 min in extremely harsh environments. Compared with BDS-only, the accuracy of float solution of BDS/GPS, BDS/LEO, BDS/GPS/LEO combined PPP is improved by 42.44%, 73.77%, and 77.43%, respectively. In term of fixed solution, compared BDS-only, the average time to first fix (TTFF) of BDS/GPS, BDS/LEO, BDS/GPS/LEO combination can be shortened from 20.0 min to 10.3 min, 4.8 min and 4.0 min respectively. The fix rate of epochs increases from 83.8% to 91.6%. 96.1% and 96.7% in harsh environments, respectively. Compared with the float solution, the positioning accuracy of fixed solution in N, E, and U directions increases by 3.6%, 4.6%, and 3.2%, respectively.

Real-time clock prediction of multi-GNSS satellites and its application in precise point positioning

With the development of Global Navigation Satellite System (GNSS), multi-GNSS is expected to greatly benefit precise point positioning (PPP), especially during the outage of real time service (RTS). In this paper, we focus on the performance of multi-GNSS satellite clock prediction and its application in real-time PPP. Based on the statistical analysis of multi-system satellite clock products, a model consisting of polynomial and periodic terms is employed for multi-system satellite clock prediction. To evaluate the method proposed, both post-processed and real-time satellite clock products are employed in simulated real-time processing mode. The results show that the accuracy of satellite clock prediction is related to atomic clock type and satellite type. For GPS satellites, the average standard deviations (STDs) of Cs atomic clocks will reach as high as 0.65 ns while the STD of Rb atomic clocks is only about 0.15 ns. As for BDS and Galileo, the average STD of 2-hour satellite clock prediction are 0.30 ns and 0.06 ns, respectively. In addition, it is validated that real-time PPP can still achieve positioning accuracy of one to three decimeters by using products of 2-hour satellite clock prediction. Moreover, compared to the results of GPS-only PPP, multi-system can greatly enhance the accuracy of real-time PPP from 12.5% to 18.5% in different situations.

BeiDou Augmented Navigation from Low Earth Orbit Satellites.

Currently, the Global Navigation Satellite System (GNSS) mainly uses the satellites in Medium Earth Orbit (MEO) to provide position, navigation, and timing (PNT) service. The weak navigation signals limit its usage in deep attenuation environments, and make it easy to interference and counterfeit by jammers or spoofers. Moreover, being far away to the Earth results in relatively slow motion of the satellites in the sky and geometric change, making long time needed for achieved centimeter positioning accuracy. By using the satellites in Lower Earth Orbit (LEO) as the navigation satellites, these disadvantages can be addressed. In this contribution, the advantages of navigation from LEO constellation has been investigated and analyzed theoretically. The space segment of global Chinese BeiDou Navigation Satellite System consisting of three GEO, three IGSO, and 24 MEO satellites has been simulated with a LEO constellation with 120 satellites in 10 orbit planes with inclination of 55 degrees in a nearly circular orbit (eccentricity about 0.000001) at an approximate altitude of 975 km. With simulated data, the performance of LEO constellation to augment the global Chinese BeiDou Navigation Satellite System (BeiDou-3) has been assessed, as one of the example to show the promising of using LEO as navigation system. The results demonstrate that the satellite visibility and position dilution of precision have been significantly improved, particularly in mid-latitude region of Asia-Pacific region, once the LEO data were combined with BeiDou-3 for navigation. Most importantly, the convergence time for Precise Point Positioning (PPP) can be shorted from about 30 min to 1 min, which is essential and promising for real-time PPP application. Considering there are a plenty of commercial LEO communication constellation with hundreds or thousands of satellites, navigation from LEO will be an economic and promising way to change the heavily relay on GNSS systems.

A Simplified BDS Broadcast Ephemeris and State Space Representative (SSR) Matching Method for BDS-Only Real-Time Precise Point Positioning (PPP)

As opposed to the GPS real-time precise point positioning (PPP) with sophisticated orbit/clock recovery method, BDS real-time PPP applications were limited by the fact that no internationally recognized BDS issue of data (IOD) calculation and matching method was defined. This paper proposes a simplified BDS broadcast ephemeris and state space representative (SSR) matching method for the BDS precise orbit and clock recovery in real time. Unlike the existing method, the proposed method does not need to perform IOD calculation which involves several bitwise operations. Instead, it only needs to monitor the BDS SSR IOD updating status. Comparison result shows that the proposed method can reduce 6.97% computational time for the 24-hour real-time orbit/clock product recovery. Using the proposed matching method, Centre National d’Etudes Spatiales (CNES) BDS real-time orbit and clock product from day of year (DOY) 119 to 128 2018 were evaluated. By comparing the 10-day dataset with German Research Centre for Geosciences Potsdam (GFZ) final products, we could see that BDS real-time orbit accuracies were greatly improved, i.e. 1.644-6.143 m real-time precise orbit for Geosynchronous Earth Orbit (GEO) satellites, 0.059-0.286 m for Inclined Geosynchronous Satellite Orbit (IGSO)/Medium Earth Orbit (MEO) satellites. In the meantime, 0.12-2.32 ns real-time clock precision was obtained. Both static and kinematic tests were adopted to evaluate BDS-only real-time PPP using CNES real-time corrections. The results indicated that cm-level horizontal and < 0.1 m vertical precisions were obtained in static experiment. As for the kinematic test, < 0.1 m horizontal and dm-level vertical precisions were obtained in an unmanned aerial vehicle experiment.

Triple-Frequency Combining Observation Models and Performance in Precise Point Positioning Using Real BDS Data

Although precise point positioning (PPP) is a well-established and promising technique with the use of precise satellite orbit and clock products, it requires a long convergence time to reach a centimeter-level positioning accuracy. The availability of triple-frequency observations from a modernized global navigation satellite system (GNSS) constellations makes it possible to improve performance by formulating new observation models. The contribution of this paper is to propose two new observation models using triple-frequency data. The first model (UofC3) is the triple-frequency extension of dual-frequency University of Calgary model. The second model (UofB) is a combining observation model with five-dimensional observation equations. Thereafter, by theoretically analyzing the dimension of the triple-frequency observation models, all feasible triple-frequency observation models are systematically found out. Finally, the positioning experiments with 3-h observation period using real data at four BeiDou Navigation Satellite System (BDS) Asia-Pacific distributed reference stations on the day of the year (DOY) 42-48, 2018 are conducted to compare the performance of observation models. The results show that the triple-frequency models have less convergence time than the dual-frequency models. Meanwhile, most of the triple-frequency models have approximate convergence time in an experiment. Furthermore, UofB, which is one of the most stabilized observation models as well as uncombined observation model with the triple-frequency data (UC3), has less processing time than UC3. Compared with UofB, UofC3 has less processing time with sacrificing stability. These results show the significance of the UofB and UofC3 for future PPP applications in modernized GNSS.

Displacement monitoring performance of relative positioning and Precise Point Positioning (PPP) methods using simulation apparatus

Besides the classical geodetic methods, GPS (Global Positioning System) based positioning methods are widely used for monitoring crustal, structural, ground etc., deformations in recent years. Currently, two main GPS positioning methods are used: Relative and Precise Point Positioning (PPP) methods. It is crucial to know which amount of displacement can be detected with these two methods in order to inform their usability according to the types of deformation. Therefore, this study conducted to investigate horizontal and vertical displacement monitoring performance and capability of determining the direction of displacements of both methods using a developed displacement simulator apparatus. For this purpose, 20 simulated displacement tests were handled. Besides the 24 h data sets, 12 h, 8 h, 4 h and 2 h subsets were considered to examine the influence of short time spans. Each data sets were processed using GAMIT/GLOBK and GIPSY/OASIS scientific software for relative and PPP applications respectively and derived displacements were compared to the simulated (true) displacements. Then statistical significance test was applied. Results of the experiment show that using 24 h data sets, relative method can determine up to 6.0 mm horizontal displacement and 12.3 mm vertical displacement, while PPP method can detect 8.1 mm and 19.2 mm displacements in horizontal and vertical directions respectively. Minimum detected displacements are found to grow larger as time spans are shortened.

Measurements and Accuracy Evaluation of a Strapdown Marine Gravimeter Based on Inertial Navigation.

The strapdown gravimetry system uses the combination of an Inertial Measuring Unit (IMU) and a Global Navigation Satellite System (GNSS) to measure the Earth’s gravity field. Due to limited accuracies of IMU and GNSS, early strapdown gravimetry systems were more often used in airborne surveys, but less used in marine surveys. We developed a strapdown inertial navigation system (SINS), the Sea-Air Gravimeter-2Marine (SAG-2M), using novel IMU components, whose accuracy was further improved with the application of Precise Point Positioning (PPP) and enhanced algorithm, making it possible to be used in marine gravity survey. The testing results of the SAG-2M were compared to those of the Lacoste and Romberg S-129 gravimeter on the same ship in the South China Sea basin. The cruise lasted for 50 days, during which 134 effective gravity profiles were measured, resulting in 174 crossover points. The results showed that, for the SAG-2M, the root mean square (RMS) crossover points were 1.35 mGal before difference adjustment and 0.69 mGal after difference adjustment; for the S-129 gravimeter, they were 5.62 mGal and 0.95 mGal, correspondingly. In calm sea conditions, the results of the two systems were relatively consistent at all wavelengths. However, in rough sea conditions, since the SAG-2M was not affected by the cross-coupling effect, its data demonstrated less high-frequency jump. A physical platform adopted in SAG-2M can further make the transition data effective when the ship is turning around. Therefore, SAG-2M was able to improve the proportion of valid data and the efficiency of data post-processing for measurements taken during the cruise. The testing results indicate that in terms of accuracy and efficiency in the marine gravity survey, SAG-2M is better than S-129. In addition, as the miniaturization and precision of inertial components are developing continuously, SAG-2M also shows great potential in miniaturization.