Static Precise Point Positioning Research Articles

Assessing the contribution of Galileo to GPS+GLONASS PPP: Towards full operational capability

By the end of 2018, the Galileo constellation consisted of four in-orbit validation (IOV) satellites and 22 full operational capability (FOC) satellites. Except for GPS and GLONASS, the FOC of Galileo has not been reached. In 2018, four Galileo FOC satellites were launched. With these launches, most of the Galileo FOC has been reached. In this paper, the latest contribution of the Galileo constellation to GPS+GLONASS combined Multi-GNSS precise point positioning (PPP) solutions is analyzed in terms of static/kinematic accuracy and convergence time. Three different elevation cut-off angles (5°,-15°,-30°) are chosen to simulate the ideal and restricted satellite visibilities. A two-month period and a one-week period in 2019 are chosen for conducting static and kinematic PPP, respectively, using the data of 20 Multi-GNSS Experiment (MGEX) stations. Non-overlapping sessions of 24, 12, 6, 3, 1, and 0.5 h within two months are processed for static PPP to analyze the effect of the Galileo contribution to static PPP for each observation length and cut-off angle. GipsyX scientific software developed by NASA’s Jet Propulsion Laboratory (JPL) is used for PPP processes. The statistical results show that the contribution of Galileo generally becomes higher as the observing sessions become shorter, but no significant correlation between the contribution of Galileo and observing session is found for each station. The largest horizontal and vertical accuracy improvements of Galileo are observed as 8 mm/11 mm (47%/61%) and 23 mm/30 mm (20%/48%) for static and kinematic PPP, respectively. The accuracy degradation is observed more in the vertical component for some stations when adding Galileo to GPS+GLONASS combined static and kinematic PPP. The Galileo contributions to minimum, maximum, and mean convergence times are also computed for both static and kinematic PPP. The largest improvement show that mean horizontal and vertical convergence times are shortened by 24 min/24 min (52%/45%) and 61 min/23 min (89%/62%) for static and kinematic PPP, respectively. The results also show that outliers can be reduced significantly for most of the stations by adding Galileo to the GPS+GLONASS combined PPP for short observation sessions.

GPS and BDS combined PPP model with inter-system differenced observations

This study proposes a combined precise point positioning (PPP) model, called the inter-system differenced PPP model, in which it formed the satellite-differenced observation between different satellite systems. Compared with the traditional combined PPP model, the inter-system differenced PPP model has the following characteristics: (1) The satellite difference between various systems can eliminate the receiver clock bias parameter, it enhances the strength of the PPP model. (2) Inter-satellite differences can eliminate some common model errors and reduce the impact of observation errors. (3) The system time difference can be calculated directly to provide the basis for time offset monitoring. In order to verify the positioning results of the inter-system differenced model, static PPP and dynamic PPP experiments were carried out to test the positioning accuracy and convergence time, and the results were compared with those of the traditional combination PPP model. In addition, the offset characteristics introduced by the inter-system differenced model were analysed, and the optimal estimation strategy was determined by dynamic PPP tests. Preliminary results are as follows: (1) For inter-system differenced static PPP, the convergence time of stations is less than 20 min. The standard deviation (STD) of the position bias for the East (E), North (N), and Up (U) components are better than 2.5 cm, 1.0 cm and 3.0 cm, respectively, and the corresponding root mean square deviation (RMS) are better than 3.0 cm, 1.5 cm and 6.0 cm, respectively. Compared with the traditional combined PPP model, the average convergence time of the inter-system differenced model is nearly the same, but its overall positioning accuracy is better. (2) For the inter-system differenced dynamic PPP model, the convergence time of stations is better than 30 min. The STD of the position bias for the E, N, and U components is better than 3.0 cm, 2.0 cm and 4.5 cm respectively, and the RMS is better than 4.0 cm, 2.5 cm and 7.0 cm respectively. Compared with the traditional combined PPP model, the convergence of the inter-system differenced model is slightly better, and the positioning accuracy does not differ significantly. Moreover, the inter-system differenced model is much better than the traditional model when fewer satellites are available. (3) The offset between GPS and BDS corresponding with the precise products of GFZ is related to the type of receiver, and the daily standard of offset is less than 0.5 ns. In addition, we determined optimum process noise of the offset parameter to be a 10-3/3(m2/s) random walk after comparing several options.

A Practical Adaptive Clock Offset Prediction Model for the Beidou-2 System

The predicted navigation satellite clock offsets are crucial to support real-time global navigation satellite system (GNSS) precise positioning applications, especially for those applications difficult to access the real-time data stream, such as the low earth orbit (LEO) autonomous precise orbit determination. Currently, the clock prediction for the Chinese BeiDou system is still challenging to meet the precise positioning requirement. The onboard clocks of BeiDou satellites are provided by different manufacturers, and the clocks’ switch events are more frequent. Considering the satellite-specified and temporal variation of the BeiDou clocks characteristics, we intend to use an adaptive model for BeiDou clock prediction. During clock prediction, we identify different models for BeiDou clocks’ characteristics, and then address the optimal model with a cross-validation procedure. The model achieving the minimum variance in the cross-validation procedure is used for the final clock prediction. We compared the prediction results of our method with two well-recognized BeiDou ultra-rapid clock products, named GBU-P and ISU-P, respectively. The comparison results indicate that the adaptive model achieves about 1-ns precision for 3-h prediction, which corresponds to 47.3% and 32.1% precision improvement compared to the GBU-P and ISU-P products, respectively. The efficiency of the predicted clocks is further validated with the precise point positioning (PPP) data processing. The results indicate that the static PPP solution precision is improved by 21.6%–30.0% compared to the current predicted clock product. The precision improvement in kinematic PPP is even more significant, which reaches 46.7%–53.9% with respect to these GBU-P and ISU-P products. Therefore, the proposed adaptive model is a practical and an efficient way to improve the BeiDou clock prediction.

Improving Short Term Clock Prediction for BDS-2 Real-Time Precise Point Positioning.

Although there are already several real-time precise positioning service providers, unfortunately, not all users can use the correction information due to either cost of the service and limitation of their equipment or out of the service coverage. An alternative way is to enhance the accuracy of the predicted satellite clocks for precise real-time positioning. Based on the study of existing prediction models, an improved model combing the spectrum analysis (SA) and the generalized regression neural network (GRNN) model is proposed especially for BeiDou satellite navigation system (BDS)-2 satellites. The periodic terms and GRNN-related parameters including length and interval of sample data, as well as a smooth factor, are optimized satellite by satellite to consider satellite-specific characteristics for all the fourteen BDS-2 satellites. The improved model is validated by comparing the predicted clocks of existing models and the improved model with precisely estimated ones. The bias of the predicted clock is within ±0.5 ns over three hours and better than that of the other models and can be used for several real-time precise applications. The clock prediction is further evaluated by applying clock corrections to precise point positioning (PPP) in both static and kinematic mode for eight IGS (International GNSS Service) MGEX (Multi-GNSS Experiment) stations in the Asia-Pacific region. In the static PPP, the improved model is validated to be effective, and position accuracies of some IGS MGEX stations achieve more than 30.0% improvements on average for each component, which enables us to obtain sub-decimeter positioning. In the kinematic PPP, the improved model performs much better than the others in terms of both the convergence time and the position accuracy. The convergence time can be shortened from 1–2 h to 0.5–1 h, while the position accuracy is enhanced by 15.4%, 21.6% and 19.3% on average in east, north and up component, respectively.

Assessment of BeiDou-3 and Multi-GNSS Precise Point Positioning Performance.

With the launch of BDS-3 and Galileo new satellites, the BeiDou navigation satellite system (BDS) has developed from the regional to global system, and the Galileo constellation will consist of 26 satellites in space. Thus, BDS, GPS, GLONASS, and Galileo all have the capability of global positioning services. It is meaningful to evaluate the ability of global precise point positioning (PPP) of the GPS, BDS, GLONASS, and Galileo. This paper mainly contributes to the assessment of BDS-2, BDS-2/BDS-3, GPS, GLONASS, and Galileo PPP with the observations that were provided by the international Global Navigation Satellite System (GNSS) Monitoring and Assessment System (iGMAS). The Position Dilution of Precision (PDOP) value was utilized to research the global coverage of GPS, BDS-2, BDS-2/BDS-3, GLONASS, and Galileo. In particular, GPS-only, BDS-2-only, BDS-2/BDS-3, GLONASS-only, Galileo-only, and multi-GNSS combined PPP solutions were analyzed to verify the capacity of the PPP performances in terms of positioning accuracy, convergence time, and zenith troposphere delay (ZTD) accuracy. In view of PDOP, the current BDS and Galileo are capable of global coverage. The BDS-2/BDS-3 and Galileo PDOP values are fairly evenly distributed around the world similar to GPS and GLONASS. The root mean square (RMS) of positioning errors for static BDS-2/BDS-3 PPP and Galileo-only PPP are 10.7, 19.5, 20.4 mm, and 6.9, 18.6, 19.6 mm, respectively, in the geographic area of the selected station, which is the same level as GPS and GLONASS. It is worth mentioning that, by adding BDS-3 observations, the positioning accuracy of static BDS PPP is improved by 17.05%, 24.42%, and 35.65%, and the convergence time is reduced by 27.15%, 27.87%, and 35.76% in three coordinate components, respectively. Similar to the static positioning, GPS, BDS-2/BDS-3, GLONASS, and Galileo have the basically same kinematic positioning accuracy. Multi-GNSS PPP significantly improves the positioning performances in both static and kinematic positioning. In terms of ZTD accuracy, the difference between GPS, BDS-2/BDS-3, GLONASS, and Galileo is less than 1 mm, and the BDS-2/BDS-3 improves ZTD accuracy by 20.48% over the BDS-2. The assessment of GPS, BDS-2, BDS-2/BDS-3, GLONASS, Galileo, and multi-GNSS global PPP performance are shown to make comments for the development of multi-GNSS integration, global precise positioning, and the construction of iGMAS.

Retrieving Precipitable Water Vapor From Shipborne Multi‐GNSS Observations

AbstractPrecipitable water vapor (PWV) is an important parameter for climate research and a crucial factor to achieve high accuracy in satellite geodesy and satellite altimetry. Currently Global Navigation Satellite System (GNSS) PWV retrieval using static Precise Point Positioning is limited to ground stations. We demonstrated the PWV retrieval using kinematic Precise Point Positioning method with shipborne GNSS observations during a 20‐day experiment in 2016 in Fram Strait, the region of the Arctic Ocean between Greenland and Svalbard. The shipborne GNSS PWV shows an agreement of ~1.1 mm with numerical weather model data and radiosonde observations, and a root‐mean‐square of ~1.7 mm compared to Satellite with ARgos and ALtiKa PWV. An improvement of 10% is demonstrated with the multi‐GNSS compared to the Global Positioning System solution. The PWV retrieval was conducted under different sea state from calm water up to gale. Such shipborne GNSS PWV has the promising potential to improve numerical weather forecasts and satellite altimetry.

Performance of Galileo: Global coverage, precise orbit determination, and precise positioning

As one of the major global navigation satellite systems (GNSSs), the performance of the Galileo Satellite Navigation System (Galileo) has been of pressing concern. By the end of June 2018, there were 17 operational satellites that provide navigation and positioning services. However, there is little research evaluating the performance of the Galileo single-system in terms of the average satellite coverage and precise positioning. To address this, this study firstly uses the number of visible satellites to analyze the global average satellite coverage of Galileo. Then different data processing strategies are used to evaluate the accuracy of the Galileo satellite orbit and clock. Finally, the performances of precise point positioning (PPP) and baseline solutions obtained using the Galileo single-system are analyzed. Results show that the number of visible Galileo satellites globally is between 6 and 7 and the time percentage where the number of visible Galileo satellites is greater than or equal to 4 is more than 90% globally. For the orbit determination of Galileo satellites, the Galileo/GPS combined solution is better than that of the Galileo single-system. Using the GeoForschungsZentrum Potsdam (GFZ) multi-GNSS orbit product (indicated by GBM) as a reference, the root mean squares (RMSs) of three-dimension and radial component of Galileo/GPS three-day combined solution are 4.4 cm and 1.8 cm, respectively. The accuracy of the Galileo/GPS single-day combined solution is almost the same as that of the Galileo/GPS three-day combined solution. For the Galileo satellite clock, the Galileo/GPS combined solution provides a better result than the Galileo single-system solution. The convergence times of the static and kinematic PPP solutions of the Galileo single-system are both about 2 h. The average the RMSs of the east (E), north (N), and up (U) components of the static Galileo-only PPP solution are 1.9 cm, 0.5 cm, and 2.0 cm, respectively. Those of the kinematic Galileo-only PPP solution are 2.1 cm, 1.4 cm, and 2.6 cm, respectively. Moreover, the baseline solution accuracy of the ultra-short baseline (48 m) of the Galileo single-system is comparable to GPS. For both static and kinematic solutions, the standard deviations (STDs) of the horizontal and vertical components are better than 6 mm and 8 mm, respectively. The accuracy of baseline solution results of the short baseline (1850 m) is poorer. For both static and kinematic solutions, the STDs of the horizontal and vertical components are better than 1.3 cm and 1.9 cm, respectively.

Real-Time Global Ionospheric Map and Its Application in Single-Frequency Positioning

The prevalence of real-time, low-cost, single-frequency, decimeter-level positioning has increased with the development of global navigation satellite systems (GNSSs). Ionospheric delay accounts for most errors in real-time single-frequency GNSS positioning. To eliminate ionospheric interference in real-time single-frequency precise point positioning (RT-SF-PPP), global ionospheric vertical total electron content (VTEC) product is designed in the next stage of the International GNSS Service (IGS) real-time service (RTS). In this study, real-time generation of a global ionospheric map (GIM) based on IGS RTS is proposed and assessed. There are three crucial steps in the process of generating a real-time global ionospheric map (RTGIM): estimating station differential code bias (DCB) using the precise point positioning (PPP) method, deriving slant total electron content (STEC) from PPP with raw observations, and modeling global vertical total electron content (VTEC). Experiments were carried out to validate the algorithm’s effectiveness. First, one month’s data from 16 globally distributed IGS stations were used to validate the performance of DCB estimation with the PPP method. Second, 30 IGS stations were used to verify the accuracy of static PPP with raw observations. Third, the modeling of residuals was assessed in high and quiet ionospheric activity periods. Afterwards, the quality of RTGIM products was assessed from two aspects: (1) comparison with the Center for Orbit Determination in Europe (CODE) global ionospheric map (GIM) products and (2) determination of the performance of RT-SF-PPP with the RTGIM. Experimental results show that DCB estimation using the PPP method can realize an average accuracy of 0.2 ns; static PPP with raw observations can achieve an accuracy of 0.7, 1.2, and 2.1 cm in the north, east, and up components, respectively. The average standard deviations (STDs) of the model residuals are 2.07 and 2.17 TEC units (TECU) for moderate and high ionospheric activity periods. Moreover, the average root-mean-square (RMS) error of RTGIM products is 2.4 TECU for the one-month moderate ionospheric period. Nevertheless, for the high ionospheric period, the RMS is greater than the RMS in the moderate period. A sub-meter-level horizontal accuracy and meter-level vertical accuracy can be achieved when the RTGIM is employed in RT-SF-PPP.

Evaluation of the GPS Precise Point Positioning technique during the 21 July 2017 Kos-Bodrum (East Aegean Sea) Mw 6.6 earthquake

Precise Point Positioning (PPP) algorithms have been widely used in the Global Positioning System (GPS)-based applications. A PPP technique with a single receiver provides effective solutions where accurate absolute positioning is required. This paper provides the performance assessment of GPS PPP for detecting the displacements caused by an earthquake. For this purpose, the earthquake that occurred on 21 July 2017 at Kos-Bodrum with the impact of Mw 6.6 was investigated by analyzing the data of the permanent GPS stations located around the related region with the PPP technique. The location distances of these GPS stations range from 10 to 89 km to the epicenter of this earthquake. GPS data provided from seven permanent stations from the Continuously Operating Reference Stations-Turkey (CORS-TR) and local Bodrum CORS networks were processed to determine the co-seismic displacements during the earthquake. The data of these stations for days of year (DOYs) 200, 201, 202, and 203 were analyzed with post-process static PPP and kinematic PPP methods. GIPSY-OASIS II v6.4 was used for processing the data and all of the solutions were performed in the ITRF2008 reference frame. Two strategies were followed on the post-process static solutions. In the first strategy, 4-day data with 24-h observations were separately analyzed day by day. In the second strategy, the 24-h data were divided into 3-h duration, which is the minimum duration for optimum PPP solutions, and then the analyses were performed. When the displacements between DOYs 200 and 203 are considered in the 24-h data analysis, significant displacements have been observed through northwest direction in the northern stations whereas MUG1 is excluded. Moreover, there is significant displacement through the southeast direction in the station DATC located in the south of the epicenter. When the 3-h solutions are examined, displacements, especially on n and e directions, are observed starting from the solutions, which include Mw 6.6 earthquake. According to the kinematic PPP solutions, the effects of the Mw 6.6 earthquake can be seen clearly in the stations DATC, ORTA, TRKB, and YALI. Considering all outcomes, the PPP technique with both static and kinematic solutions provides effective results for detecting the displacements during the earthquake.

Assessing the latest performance of Galileo-only PPP and the contribution of Galileo to Multi-GNSS PPP

By the end of 2016, the Galileo constellation had 4 in-orbit validation (IOV) satellites and 14 full operational capability (FOC) satellites, 17 of which were able to transmit signal in November 2017. Galileo has already had early operational capability (EOC). To assess the latest performance of the Galileo-only precise point positioning (PPP) and the contribution of Galileo to the Multi-GNSS PPP solutions, observations collected at 16 Multi-GNSS Experiment (MGEX) stations over ten days are used to realize the various PPP cases. The statistical results show that the three-dimensional positioning accuracy of Galileo static and kinematic PPP can reach centimeter level and decimeter level after convergence, respectively. The contribution of Galileo can improve the positioning accuracy by 29.49%, 29.96% and 23.70% for GPS kinematic PPP and 11.03%, 10.59% and 11.07% for GPS/GLONASS kinematic PPP solutions in the north, east and up components, respectively. The average convergence time can be reduced by 45.48% for GPS-only kinematic PPP and by 11.04% for GPS/GLONASS solutions by adding Galileo observations. Moreover, adding Galileo observations shortens the average convergence time by 30.45% and 7.8% for GPS-only and GPS/GLONASS static PPP solutions, respectively. Although the convergent positioning results of GPS and GPS/GLONASS static PPP solutions after the addition of Galileo measurements do not demonstrate as significant improvement as those of the kinematic PPP solutions, the positioning accuracy of the GPS/Galileo static PPP solutions compared to the GPS-only static PPP still demonstrates an improvement of approximately 25% on the east component. Furthermore, the GPS/Galileo internal system time bias (ISB) and observation residual are analyzed. The results show that the noise level of the GPS L1/L2 signals and the negative impact of multipath errors on the GPS pseudo-range observations for the L1/L2 signals are greater than those of Galileo E1/E5a signals, resulting in the residuals of GPS ionosphere-free code observations larger than those of Galileo code observations. However, the phase observation residuals of GPS and Galileo are of the same magnitude. Additionally, the one-day GPS/Galileo ISB is quite stable. Its stability described by standard deviation is approximately 0.34 ns.

Investigation of ionospheric scintillation effects on BDS precise point positioning at low-latitude regions

We present a study on the effects of ionospheric scintillation on BeiDou Navigation Satellite System (BDS) precise point positioning (PPP) at low-latitude regions. The analysis was carried out using BDS data collected by a newly installed ionospheric scintillation monitoring receiver located at Sha Tin of Hong Kong and 15 Hong Kong Satellite Positioning Reference Station Network (SatRef) stations from October 6, 2015, to November 17, 2015. The rate of total electron content index (ROTI) derived from BDS data is shown to be a good indicator in observing the ionospheric scintillation. The analysis indicates that the correlation coefficient between ROTI and $$S_{4}$$ / $$\sigma_{\varphi }$$ is about 0.7. Under scintillation activity, the time series of positioning results for BDS static PPP show a stable variation, but the irregularities are reflected in the time series of code and phase residuals with the maximum values as 7.096 and − 0.469 m, respectively. Further, under scintillation condition it is found that positioning results for BDS kinematic PPP vary significantly and the range can reach several meters in the east, north and up directions. The statistical results show that the three-dimensional root-mean-square of BDS PPP is 1.842 m under scintillation condition, which is much larger than that for non-scintillation condition as 0.155 m.

Study of ionospheric disturbances over the China mid- and low-latitude region with GPS observations

Abstract. Ionospheric disturbances constitute the main restriction factor for precise positioning techniques based on global positioning system (GPS) measurements. Simultaneously, GPS observations are widely used to determine ionospheric disturbances with total electron content (TEC). In this paper, we present an analysis of ionospheric disturbances over China mid- and low-latitude area before and during the magnetic storm on 17 March 2015. The work analyses the variation of magnetic indices, the amplitude of ionospheric irregularities observed with four arrays of GPS stations and the influence of geomagnetic storm on GPS positioning. The results show that significant ionospheric TEC disturbances occurred between 10:30 and 12:00 UT during the main phase of the large storm, and the static position reliability for this period are little affected by these disturbances. It is observed that the positive and negative disturbances propagate southward along the meridian from mid-latitude to low-latitude regions. The propagation velocity is from about 200 to 700 m s−1 and the amplitude of ionospheric disturbances is from about 0.2 to 0.9 TECU min−1. Moreover, the position dilution of precession (PDOP) with static precise point positioning (PPP) on storm and quiet days is 1.8 and 0.9 cm, respectively. This study is based on the analysis of ionospheric variability with differential rate of vertical TEC (DROVT) and impact of ionospheric storm on positioning with technique of GPS PPP. Keywords. Ionosphere (ionospheric disturbances)

Performance Analysis of Beidou-2/Beidou-3e Combined Solution with Emphasis on Precise Orbit Determination and Precise Point Positioning.

In 2015, the plan for global coverage by the Chinese BeiDou Navigation Satellite System was launched. Five global BeiDou experimental satellites (BeiDou-3e) are in orbit for testing. To analyze the performances of precise orbit determination (POD) and precise point positioning (PPP) of onboard BeiDou satellites, about two months of data from 24 tracking stations were used. According to quality analysis of BeiDou-2/BeiDou-3e data, there is no satellite-induced code bias in BeiDou-3e satellites, which has been found in BeiDou-2 satellites. This phenomenon indicates that the quality issues of pseudorange data in BeiDou satellites have been solved well. POD results indicate that the BeiDou-3e orbit precision is comparable to that of BeiDou-2 satellites. The ambiguity fixed solution improved the orbit consistency of inclined geosynchronous orbit satellites in along-track and cross-track directions, but had little effect in the radial direction. Satellite laser ranging of BeiDou-3e medium Earth orbit satellites (MEOs) achieved a standard deviation of about 4 cm. Differences in clock offset series after the removal of reference clock in overlapping arcs were used to assess clock quality, and standard deviation of clock offset could reach 0.18 ns on average, which was in agreement with the orbit precision. For static PPP, when BeiDou-3e satellites were included, the positioning performance for horizontal components was improved slightly. For kinematic PPP, when global positioning satellites (GPS) were combined with BeiDou-2 and BeiDou-3e satellites, the convergence time was 13.5 min with a precision of 2–3 cm for horizontal components, and 3–4 cm for the vertical component.

Undifferenced ionospheric-free ambiguity resolution using GLONASS data from inhomogeneous stations

GLONASS frequency division multiple access signals render ambiguity resolution (AR) rather difficult because: (1) Different wavelengths are used by different satellites, and (2) pseudorange inter-frequency biases (IFBs) cannot be precisely modeled by means of a simple function. In this study, an AR approach based on the ionospheric-free combination with a wavelength of about 5.3 cm is assessed for GLONASS precise point positioning (PPP). This approach simplifies GLONASS AR because pseudorange IFBs do not matter, and PPP-AR can be enabled across inhomogeneous receivers. One month of GLONASS data from 165 European stations were processed for different network size and different durations of observation periods. We find that 89.9% of the fractional parts of ionospheric-free ambiguities agree well within ± 0.15 cycles for a small network (radius = 500 km), while 77.6% for a large network (radius = 2000 km). In case of the 3-hourly GLONASS-only static PPP solutions for the small network, reliable AR can be achieved where the number of fixed GLONASS ambiguities account for 97.6% within all candidate ambiguities. Meanwhile, the RMS of the east, north and up components with respect to daily solutions is improved from 1.0, 0.6, 1.2 cm to 0.4, 0.4, 1.1 cm, respectively. When GPS PPP-AR is carried out simultaneously, the positioning performance can be improved significantly such that the GLONASS ambiguity fixing rate rises from 74.4 to 95.4% in case of hourly solutions. Finally, we introduce ambiguity-fixed GLONASS orbits to re-attempt GLONASS PPP-AR in contrast to the above solutions with ambiguity-float orbits. We find that ambiguity-fixed orbits lead to clearly better agreement among ionospheric-free ambiguity fractional parts in case of the large network, that is 80.5% of fractional parts fall in ± 0.15 cycles in contrast to 74.6% for the ambiguity-float orbits. We conclude that highly efficient GLONASS ionospheric-free PPP-AR is achievable in case of a few hours of data when GPS PPP-AR is also accomplished, and ambiguity-fixed GLONASS orbits will contribute significantly to PPP-AR over wide areas.

Precise Receiver Clock Offset Estimations According to Each Global Navigation Satellite Systems (GNSS) Timescales

Abstract Each GNSS constellation operates its own system times; namely, GPS system time (GPST), GLONASS system time (GLONASST), BeiDou system time (BDT) and Galileo system time (GST). They could be traced back to Coordinated Universal Time (UTC) scale and are aligned to GPST. This paper estimates the receiver clock offsets to three timescales: GPST, GLONASST and BDT. The two measurement scenarios use two identical multi-GNSS geodetic receivers connected to the same geodetic antenna through a splitter. One receiver is driven by its internal oscillators and another receiver is connected to the external frequency oscillators, caesium frequency standard, kept as the Thailand standard time scale at the National Institute of Metrology (Thailand) called UTC(NIMT). The three weeks data are observed at 30 seconds sample rate. The receiver clock offsets with respected to the three system time are estimated and analysed through the geodetic technique of static Precise Point Positioning (PPP) using a data processing software developed by Wuhan University - Positioning And Navigation Data Analyst (PANDA) software. The estimated receiver clock offsets are around 32, 33 and 18 nanoseconds from GPST, GLONASST and BDT respectively. This experiment is initially stated that each timescale is inter-operated with GPST and further measurements on receiver internal delay has to be determined for clock comparisons especially the high accuracy clock at timing laboratories.

Analysis of estimated satellite clock biases and their effects on precise point positioning

This study provides a systemic analysis to identify the biases in estimated satellite clocks and illustrates their effects in precise point positioning (PPP). First, the precise satellite clock estimation method considering pseudorange and carrier phase hardware delays is derived. Two methods for satellite clock estimation are compared, and their equivalency is discussed. The results show that apart from the well-known constant code hardware biases, the time-variant phase hardware biases are also absorbed by the estimated clocks. Also, the satellite clocks contain biases caused by modeling errors. To analyze the effects of these biases, they are grouped into initial clock biases (ICBs) and time-dependent biases (TDBs). Then, a detailed analysis of the impact of the biases on PPP-based troposphere and coordinate estimates is conducted. The experimental analysis demonstrates that TDBs affect positioning and tropospheric estimates, and their impacts are more significant in the static mode. The ICBs affect coordinate accuracy, zenith total delay mean bias, and its standard deviations only at the millimeter level for kinematic and static PPP, which is negligible. However, the ICBs affect the convergence period for both static and real kinematic PPP, and the magnitude of their impact largely depends on data quality. Note that satellites clocks are generally estimated with the P1/P2 and L1/L2 ionospheric-free combinations, and that hardware-specific parts of ICBs and TDBs cancel if users employ the same type of observables as the clock providers. Otherwise, the effects of biases cannot be ignored, especially for triple-frequency applications. Also, modeling-specific parts of ICBs and TDBs are significant in real-time clocks, which also affect user applications. Our conclusion is applicable for understanding the effects of these biases.

GPS Satellite Orbit Prediction at User End for Real-Time PPP System.

This paper proposed the high-precision satellite orbit prediction process at the user end for the real-time precise point positioning (PPP) system. Firstly, the structure of a new real-time PPP system will be briefly introduced in the paper. Then, the generation of satellite initial parameters (IP) at the sever end will be discussed, which includes the satellite position, velocity, and the solar radiation pressure (SRP) parameters for each satellite. After that, the method for orbit prediction at the user end, with dynamic models including the Earth’s gravitational force, lunar gravitational force, solar gravitational force, and the SRP, are presented. For numerical integration, both the single-step Runge–Kutta and multi-step Adams–Bashforth–Moulton integrator methods are implemented. Then, the comparison between the predicted orbit and the international global navigation satellite system (GNSS) service (IGS) final products are carried out. The results show that the prediction accuracy can be maintained for several hours, and the average prediction error of the 31 satellites are 0.031, 0.032, and 0.033 m for the radial, along-track and cross-track directions over 12 h, respectively. Finally, the PPP in both static and kinematic modes are carried out to verify the accuracy of the predicted satellite orbit. The average root mean square error (RMSE) for the static PPP of the 32 globally distributed IGS stations are 0.012, 0.015, and 0.021 m for the north, east, and vertical directions, respectively; while the RMSE of the kinematic PPP with the predicted orbit are 0.031, 0.069, and 0.167 m in the north, east and vertical directions, respectively.

Improved Short-Term Clock Prediction Method for Real-Time Positioning.

The application of real-time precise point positioning (PPP) requires real-time precise orbit and clock products that should be predicted within a short time to compensate for the communication delay or data gap. Unlike orbit correction, clock correction is difficult to model and predict. The widely used linear model hardly fits long periodic trends with a small data set and exhibits significant accuracy degradation in real-time prediction when a large data set is used. This study proposes a new prediction model for maintaining short-term satellite clocks to meet the high-precision requirements of real-time clocks and provide clock extrapolation without interrupting the real-time data stream. Fast Fourier transform (FFT) is used to analyze the linear prediction residuals of real-time clocks. The periodic terms obtained through FFT are adopted in the sliding window prediction to achieve a significant improvement in short-term prediction accuracy. This study also analyzes and compares the accuracy of short-term forecasts (less than 3 h) by using different length observations. Experimental results obtained from International GNSS Service (IGS) final products and our own real-time clocks show that the 3-h prediction accuracy is better than 0.85 ns. The new model can replace IGS ultra-rapid products in the application of real-time PPP. It is also found that there is a positive correlation between the prediction accuracy and the short-term stability of on-board clocks. Compared with the accuracy of the traditional linear model, the accuracy of the static PPP using the new model of the 2-h prediction clock in N, E, and U directions is improved by about 50%. Furthermore, the static PPP accuracy of 2-h clock products is better than 0.1 m. When an interruption occurs in the real-time model, the accuracy of the kinematic PPP solution using 1-h clock prediction product is better than 0.2 m, without significant accuracy degradation. This model is of practical significance because it solves the problems of interruption and delay in data broadcast in real-time clock estimation and can meet the requirements of real-time PPP.

Assessment of the accuracy and convergence period of Precise Point Positioning

Precise Point Positioning (PPP) is a well-known positioning method that removes, models, or estimates GNSS system errors to reach the optimal position accuracy from a single receiver. The accuracy of static PPP was tested for 523 daily observation files from 75 IGS globally distributed stations observed at the period from DOY 49 to 55 in 2012. Also, the convergence period was examined to reach different levels of the horizontal accuracy to serve two applications: precision agriculture and geodetic control surveying. The accuracy of static PPP was 4, 5 and 9mm in the north, east and vertical components, respectively. Static PPP needs 60min to reach five-centimeter horizontal accuracy at the 95% confidence level and 24h to achieve one-centimeter horizontal accuracy at the 95% confidence level.

Computational time reduction for sequential batch solutions in GNSS precise point positioning technique

Precise point positioning (PPP) is a well established Global Navigation Satellite System (GNSS) technique that only requires information from the receiver (or rover) to obtain high-precision position coordinates. This is a very interesting and promising technique because eliminates the need for a reference station near the rover receiver or a network of reference stations, thus reducing the cost of a GNSS survey.From a computational perspective, there are two ways to solve the system of observation equations produced by static PPP either in a single step (so-called batch adjustment) or with a sequential adjustment/filter. The results of each should be the same if they are both well implemented. However, if a sequential solution (that is, not only the final coordinates, but also those observed in previous GNSS epochs), is needed, as for convergence studies, finding a batch solution becomes a very time consuming task owing to the need for matrix inversion that accumulates with each consecutive epoch. This is not a problem for the filter solution, which uses information computed in the previous epoch for the solution of the current epoch. Thus filter implementations need extra considerations of user dynamics and parameter state variations between observation epochs with appropriate stochastic update parameter variances from epoch to epoch. These filtering considerations are not needed in batch adjustment, which makes it attractive.The main objective of this research is to significantly reduce the computation time required to obtain sequential results using batch adjustment. The new method we implemented in the adjustment process led to a mean reduction in computational time by 45%.