Towards PPP-RTK: Ambiguity resolution in real-time precise point positioning

Integer ambiguity resolution at a single station can be achieved by introducing predetermined uncalibrated phase delays (UPDs) into the float ambiguity estimates of precise point positioning (PPP). This integer resolution technique has the potential of leading to a PPP-RTK (real-time kinematic) model where PPP provides rapid convergence to a reliable centimeter-level positioning accuracy based on an RTK reference network. Nonetheless, implementing this model is technically subject to how rapidly we can fix wide-lane ambiguities, stabilize narrow-lane UPD estimates, and achieve the first ambiguity-fixed solution. To investigate these issues, we used 7 days of 1-Hz sampling GPS data at 91 stations across Europe. We find that at least 10 min of observations are required for most receiver types to reliably fix about 90% of wide-lane ambiguities corresponding to high elevations, and over 20 min to fix about 90% of those corresponding to low elevations. Moreover, several tens of minutes are usually required for a regional network before a narrow-lane UPD estimate stabilizes to an accuracy of far better than 0.1 cycles. Finally, for hourly data, ambiguity resolution can significantly improve the accuracy of epoch-wise position estimates from 13.7, 7.1 and 11.4 cm to 0.8, 0.9 and 2.5 cm for the East, North and Up components, respectively, but a few tens of minutes is required to achieve the first ambiguity-fixed solution. Therefore, from the timeliness aspect, our PPP-RTK model currently cannot satisfy the critical requirement of instantaneous precise positioning where ambiguity-fixed solutions have to be achieved within at most a few seconds. However, this model can still be potentially applied to some near-real-time remote sensing applications, such as the GPS meteorology.     

Performance improvement of real-time PPP ambiguity resolution using a regional integer clock

Obtaining reliable GNSS uncalibrated phase delay (UPD) or integer clock products is the key to achieving ambiguity-fixed solutions for real-time (RT) precise point positioning (PPP) users. However, due to the influence of RT orbit errors, the quality of UPD/integer clock products estimated with a globally distributed GNSS network is difficult to ensure, thereby affecting the ambiguity resolution (AR) performance of RT-PPP. In this contribution, by fully utilising the consistency of orbital errors in regional GNSS network coverage areas, a method is proposed for estimating regional integer clock products to compensate for RT orbit errors. Based on Centre National d’Études Spatiales (CNES) RT precise products, the regional GPS/BDS integer clock was estimated with a CORS network in the west of China. Results showed that the difference between the estimated regional and CNES global integer clock/bias products was generally less than 5 cm for GPS, whereas clock differences of greater than 10 cm were observed for BDS due to the large RT orbit error. Compared with PPP using global integer clock/bias products, the AR performance of PPP using the regional integer clock was obviously improved for four rover stations. For single GPS, the horizontal and vertical accuracies of ambiguity-fixed PPP solutions were improved by 56.2% and 45.3% on average, respectively, whereas improvements of 67.5% and 50.5% in the horizontal and vertical directions, respectively, were observed for the combined GPS/BDS situation. Based on a regional integer clock, the RMS error of a kinematic ambiguity-fixed PPP solution in the horizontal direction could reach 0.5 cm. In terms of initialisation time, the average time to first fix (TTFF) in combined GPS/BDS PPP was shortened from 18.2 min to 12.7 min. In view of the high AR performance realised with the use of regional integer clocks, this method can be applied to scenarios that require high positioning accuracy, such as deformation monitoring.     

Using only observation station data for PPP ambiguity resolution by UPD estimation

This article proposes a new method for uncalibrated phase delay (UPD) estimation to improve the accuracy of precise point positioning (PPP), which uses only observation station data. This means that the station used to generate the UPDs is the same station to which they are applied. First, dual-frequency observation equations based on a raw PPP model are developed. Then, the UPDs are calculated from integer linear combinations of float ambiguities. Third, with the UPD corrections, the least-squares ambiguity decorrelation adjustment (LAMBDA) method is utilized to obtain the integer ambiguities. Since only observation station data are used for UPD estimation, the partial ambiguity resolution (PAR) method is adopted to increase the possibility of finding a subset of integer ambiguities. The UPD estimation and ambiguity resolution are performed in each epoch. To obtain the correct integer ambiguity, the ratio test and success rate (bootstrapping) are used to evaluate the estimated integer ambiguity. Finally, by treating the integer ambiguities as constants, fixed solutions can be obtained. Quality control is also applied throughout the entire data processing procedure to obtain high quality float and fixed solutions. Data from 22 stations of the International Global Navigation Satellite System (GNSS) Service (IGS) in East Asia on day of year (DOY) 206, 2017, are used to verify the feasibility of this method. The experimental results show that compared with the float solution, the proposed method can significantly improve the accuracy in the east, north and up directions by 24%, 21% and 18% for static PPP and 36%, 18% and 34% for dynamic PPP, respectively. However, the accuracy of the proposed method is still lower than that of the fixed solutions obtained by the PRIDE-PPPAR software, in which the fractional cycle bias is computed based on reference network data. These findings sufficiently show that the proposed method can offer better solution accuracy than the float solution. However, the quality of the UPDs estimated only from observation station data is not as good as that of the estimates obtained based on reference network data.     

The GFZ real-time GNSS precise positioning service system and its adaption for COMPASS

Motivated by the IGS real-time Pilot Project, GFZ has been developing its own real-time precise positioning service for various applications. An operational system at GFZ is now broadcasting real-time orbits, clocks, global ionospheric model, uncalibrated phase delays and regional atmospheric corrections for standard PPP, PPP with ambiguity fixing, single-frequency PPP and regional augmented PPP. To avoid developing various algorithms for different applications, we proposed a uniform algorithm and implemented it into our real-time software. In the new processing scheme, we employed un-differenced raw observations with atmospheric delays as parameters, which are properly constrained by real-time derived global ionospheric model or regional atmospheric corrections and by the empirical characteristics of the atmospheric delay variation in time and space. The positioning performance in terms of convergence time and ambiguity fixing depends mainly on the quality of the received atmospheric information and the spatial and temporal constraints. The un-differenced raw observation model can not only integrate PPP and NRTK into a seamless positioning service, but also syncretize these two techniques into a unique model and algorithm. Furthermore, it is suitable for both dual-frequency and sing-frequency receivers. Based on the real-time data streams from IGS, EUREF and SAPOS reference networks, we can provide services of global precise point positioning (PPP) with 5–10 cm accuracy, PPP with ambiguity-fixing of 2–5 cm accuracy, PPP using single-frequency receiver with accuracy of better than 50 cm and PPP with regional augmentation for instantaneous ambiguity resolution of 1–3 cm accuracy. We adapted the system for current COMPASS to provide PPP service. COMPASS observations from a regional network of nine stations are used for precise orbit determination and clock estimation in simulated real-time mode, the orbit and clock products are applied for real-time precise point positioning. The simulated real-time PPP service confirms that real-time positioning services of accuracy at dm-level and even cm-level is achievable with COMPASS only.     

Performance analysis of PPP ambiguity resolution with UPD products estimated from different scales of reference station networks

Integer ambiguity fixing with uncalibrated phase delay (UPD) products can significantly shorten the initialization time and improve the accuracy of precise point positioning (PPP). Since the tracking arcs of satellites and the behavior of atmospheric biases can be very different for the reference networks with different scales, the qualities of corresponding UPD products may be also various. The purpose of this paper is to comparatively investigate the influence of different scales of reference station networks on UPD estimation and user ambiguity resolution. Three reference station networks with global, wide-area and local scales are used to compute the UPD products and analyze their impact on the PPP-AR. The time-to-first-fix, the unfix rate and the incorrect fix rate of PPP-AR are analyzed. Moreover, in order to further shorten the convergence time for obtaining precise positioning, a modified partial ambiguity resolution (PAR) and corresponding validation strategy are presented. In this PAR method, the ambiguity subset is determined by removing the ambiguity one by one in the order of ascending elevations. Besides, for static positioning mode, a coordinate validation strategy is employed to enhance the reliability of the fixed coordinate. The experiment results show that UPD products computed by smaller station network are more accurate and lead to a better coordinate solution; the PAR method used in this paper can shorten the convergence time and the coordinate validation strategy can improve the availability of high precision positioning.     

Ambiguity resolution in precise point positioning with hourly data for global single receiver

Integer ambiguity resolution (IAR) can improve precise point positioning (PPP) performance significantly. IAR for PPP became a highlight topic in global positioning system (GPS) community in recent years. More and more researchers focus on this issue. Progress has been made in the latest years. In this paper, we aim at investigating and demonstrating the performance of a global zero-differenced (ZD) PPP IAR service for GPS users by providing routine ZD uncalibrated fractional offsets (UFOs) for wide-lane and narrow-lane. Data sets from all IGS stations collected on DOY 1, 100, 200 and 300 of 2010 are used to validate and demonstrate this global service. Static experiment results show that an accuracy better than 1 cm in horizontal and 1–2 cm in vertical could be achieved in ambiguity-fixed PPP solution with only hourly data. Compared with PPP float solution, an average improvement reaches 58.2% in east, 28.3% in north and 23.8% in vertical for all tested stations. Results of kinematic experiments show that the RMS of kinematic PPP solutions can be improved from 21.6, 16.6 and 37.7 mm to 12.2, 13.3 and 34.3 mm for the fixed solutions in the east, north and vertical components, respectively. Both static and kinematic experiments show that wide-lane and narrow-lane UFO products of all satellites can be generated and provided in a routine way accompanying satellite orbit and clock products for the PPP user anywhere around the world, to obtain accurate and reliable ambiguity-fixed PPP solutions.     

Precise line-of-sight vector estimation based on an inter-satellite radio frequency system

This paper proposes a precise line-of-sight (LOS) vector estimation using an inter-satellite radio frequency system. GNSS-like technology is inherited such that the ranging signals are locally generated inside the formation. However, the approach differs from the standard GNSS model usage in that the LOS vector to be of a unit length is fully explored as a priori constraint for the carrier phase integer ambiguity resolution. The constraint is lumped to the mapping process from the real-valued ambiguities to the integers by what is called validation or subset ambiguity bounding. These two approaches have the same rules of regarding the constraint as a gateway to accept or reject the ambiguity candidates, but differ by using “all-ambiguity-set” and “subset-ambiguity”. Both show remarkable improvement with up to 80% lower integer fixing failure rates than without treating the constraint. Validation provides a slightly better performance than the subset ambiguity bounding in terms of the integer fixing failure rates and the computational efficiency. The predefined tolerance regions that are critical for these two methods are analytically determined as function of the carrier noise. The paper also introduces a LOS dependent ambiguity dilution of precision (ADOP_LOS) measure that can serve as a metric to characterize the expectation of being able to successfully resolve the ambiguities. The region of ADOP_LOS lower than 0.21 is empirically summarized as the safe region where the integer fixing failure rates are less than 1%. A closed form of the ADOP_LOS is derived which is able to capture the impact of the various factors. Antenna baseline geometries and multiple frequencies in the form of an ultra-BOC signal structure are demonstrated as the most important influencing factors. With multiple properly arrayed antennas and using ultra-BOC structure, instantaneous ambiguity resolution can be achieved and the LOS accuracy can reach millimeter level.     

Improvement of PPP-inferred tropospheric estimates by integer ambiguity resolution

Integer ambiguity resolution in Precise Point Positioning (PPP) can improve positioning accuracy and reduce convergence time. The decoupled clock model proposed by Collins (2008) has been used to facilitate integer ambiguity resolution in PPP, and research has been conducted to assess the model’s potential to improve positioning accuracy and reduce positioning convergence time. In particular, the biggest benefits have been identified for the positioning solutions within short observation periods such as one hour. However, there is little work reported about the model’s potential to improve the estimation of the tropospheric parameter within short observation periods. This paper investigates the effect of PPP ambiguity resolution on the accuracy of the tropospheric estimates within one hour.     

RTK model and positioning performance analysis using Galileo four-frequency observations

This paper proposes a real-time kinematic (RTK) model that uses one common reference satellite for the Galileo system with four frequency observations. In the proposed model, the double-differenced (DD) pseudorange and carrier phase biases among the different frequencies are estimated as unknown parameters to recover the integer features of the DD ambiguities among the different frequencies for ambiguity resolution and precise positioning. Analysis results show that the E5a, E5b, and E5 frequencies have virtually the same performance in terms of the positioning accuracy, observation residuals, and ratio values of ambiguity resolution. However, the E1 frequency performs worse than the E5a, E5b, and E5 frequencies. The RTK results for the combination of multiple frequencies are much better than those for a single-frequency observation, the coordinates’ standard deviation is improved about 20–30%, and the ambiguity fix time is improved about 10%.     

Comprehensive outage compensation of real-time orbit and clock corrections with broadcast ephemeris for ambiguity-fixed precise point positioning

The main challenge in real-time precise point positioning (PPP) is that the data outages or large time lags in receiving precise orbit and clock corrections greatly degrade the continuity and real-time performance of PPP positioning. To solve this problem, instead of directly predicting orbit and clock corrections in previous researches, this paper presents an alternative approach of generating combined corrections including orbit error, satellite clock and receiver-related error with broadcast ephemeris. Using ambiguities and satellite fractional-cycle biases (FCBs) of previous epoch and the short-term predicted tropospheric delay through linear extrapolation model (LEM), combined corrections at current epoch are retrieved and weighted with multiple reference stations, and further broadcast to user for continuous enhanced positioning during outages of orbit and clock corrections. To validate the proposed method, two reference station network with different inter-station distance from National Geodetic Survey (NGS) network are used for experiments with six different time lags (i.e., 5 s, 10 s, 15 s, 30 s, 45 s and 60 s), and one set of data collected by unmanned aerial vehicle (UAV) is also used. The performance of LEM is investigated, and the troposphere prediction accuracy of low elevation (e.g., 10–20degrees) satellites has been improved by 44.1% to 79.0%. The average accuracy of combined corrections before and after LEM is used is improved by 12.5% to 77.3%. Without LEM, an accuracy of 2–3 cm can be maintained only in case of small time lags, while the accuracies with LEM are all better than 2 cm in case of different time lags. The performance of simulated kinematic PPP at user end is assessed in terms of positioning accuracy and epoch fix rate. In case of different time lags, after LEM is used, the average accuracy in horizontal direction is better than 3 cm, and the accuracy in up direction is better than 5 cm. At the same time, the epoch fix rate has also increased to varying degrees. The results of the UAV data show that in real kinematic environment, the proposed method can still maintain a positioning accuracy of several centimeters in case of 20 s time lag.     

Real-time clock comparison and monitoring with multi-GNSS precise point positioning: GPS,GLONASS and Galileo

The precise point positioning (PPP) technique is widely used in time and frequency applications. Because of the real-time service (RTS) project of the International GNSS Service, we can use the PPP technique for real-time clock comparison and monitoring. As a participant in the RTS, the Centre National d’Etudes Spatiales (CNES) implements the PPPWIZARD (Precise Point Positioning with Integer and Zero-difference Ambiguity Resolution Demonstrator) project to validate carrier phase ambiguity resolution. Unlike the Integer-PPP (IPPP) of the CNES, fixing ambiguities in the post-processing mode, the PPPWIZARD operates in the real-time mode, which is also called real-time IPPP (RT-IPPP). This paper focuses on applying the RT-IPPP for real-time clock comparison and monitoring. We review the principle of real-time clock comparison and monitoring, and introduce the methodology of the RT-IPPP technique. The observations of GPS, GLONASS and Galileo were processed for the experiments. Five processing modes were provided in the experiment to analyze the benefits of ambiguity resolution and multi-GNSS. In the clock comparison experiment, the average reduction ratios of standard deviations with respect to the G PPP mode range from 9.7% to 35.0%. In the clock monitoring experiment, G PPP mode can detect clock jumps whose magnitudes are larger than 0.9 ns. The RT-IPPP technique with GRE PPP AR (G) mode allows for the detection of any clock jumps larger than 0.6 ns. For frequency monitoring, G PPP mode allows detection of frequency changes larger than 1.1 × 10⁻¹⁴. When the RT-IPPP technique is applied, monitoring with GRE PPP AR (G) mode can detect frequency changes larger than 6.1 × 10⁻¹⁵.     

Testing a new multivariate GNSS carrier phase attitude determination method for remote sensing platforms

GNSS (Global Navigation Satellite Systems)-based attitude determination is an important field of study, since it is a valuable technique for the orientation estimation of remote sensing platforms. To achieve highly accurate angular estimates, the precise GNSS carrier phase observables must be employed. However, in order to take full advantage of the high precision, the unknown integer ambiguities of the carrier phase observables need to be resolved. This contribution presents a GNSS carrier phase-based attitude determination method that determines the integer ambiguities and attitude in an integral manner, thereby fully exploiting the known body geometry of the multi-antennae configuration. It is shown that this integral approach aids the ambiguity resolution process tremendously and strongly improves the capacity of fixing the correct set of integer ambiguities. In this contribution, the challenging scenario of single-epoch, single-frequency attitude determination is addressed. This guarantees a total independence from carrier phase slips and losses of lock, and it also does not require any a priori motion model for the platform. The method presented is a multivariate constrained version of the popular LAMBDA method and it is tested on data collected during an airborne remote sensing campaign.     

Mitigation of receiver biases in ionospheric observables from PPP with ambiguity resolution

PPP (Precise Point Positioning) is a GNSS (Global Navigation Satellite Systems) positioning method that requires SSR (State Space Representation) corrections in order to provide solutions with an accuracy of centimetric level. The so-called RT-PPP (Real-time PPP) is possible thanks to real-time precise SSR products, for orbits and clocks, provided by IGS (International GNSS Service) and its associate analysis centers such as CNES (Centre National d'Etudes Spatiales). CNES SSR products also enable RT-PPP with integer ambiguity resolution. In GNSS related literature, PPP with ambiguity resolution (PPP-AR) in real-time is often referred as PPP-RTK (PPP – Real Time Kinematic). PPP-WIZARD (PPP - With Integer and Zero-difference Ambiguity Resolution Demonstrator) is a software that is made available by CNES. This software is capable of performing PPP-RTK. It estimates slant ionospheric delays and other GNSS positioning parameters. Since ionospheric effects are spatially correlated by GNSS data from active networks, it is possible to model and provide ionospheric delays for any position in the network coverage area. The prior knowledge ionospheric delays can reduce positioning convergence for PPP-RTK users. Real-time ionospheric models could benefit from highly precise ionospheric delays estimated in PPP-AR. In this study, we demonstrate that ionospheric delays obtained throughout PPP-AR estimation are actu ally ionospheric observables. Ionospheric observables are biased by an order of few meters caused by the receiver hardware biases. These biases prohibit the use of PPP-WIZARD ionospheric delays to produce ionospheric models. Receiver biases correction is essential to provide ionospheric delays while using PPP-AR based ionospheric observables. In this contribution, a method was implemented to estimate and mitigate receiver hardware biases influence on slant ionospheric observables from PPP-AR. In order to assess the proposed approach, PPP-AR data from 12 GNSS stations were processed over a two-month period (March and April 2018). A comparison between IGS ionospheric products and PPP-AR based ionospheric observables corrected for receiver biases, resulted in a mean of differences of −39 cm and 51 cm standard deviation. The results are consistent with the accuracy of the IGS ionospheric products, 2–8 TECU, considering that 1 TECU is ~16 cm in L1. In another analysis, a comparison of ionospheric delays from 5 pairs of short baselines GNSS stations found an agreement of 0.001 m in mean differences with 22 cm standard deviation after receiver biases were corrected. Therefore, the proposed solution is promising and could produce high quality (1–2 TECU) slant ionospheric delays. This product can be used in a large variety of modeling approaches, since ionospheric delays after correction are unbiased. These results indicate that the proposed strategy is promising, and could benefit applications that require accuracy of 1–2 TECU (~16–32 cm in L1).     

Near real-time PPP-based monitoring of the ionosphere using dual-frequency GPS/BDS/Galileo data

Ionosphere delay is very important to GNSS observations, since it is one of the main error sources which have to be mitigated even eliminated in order to determine reliable and precise positions. The ionosphere is a dispersive medium to radio signal, so the value of the group delay or phase advance of GNSS radio signal depends on the signal frequency. Ground-based GNSS stations have been used for ionosphere monitoring and modeling for a long time. In this paper we will introduce a novel approach suitable for single-receiver operation based on the precise point positioning (PPP) technique. One of the main characteristic is that only carrier-phase observations are used to avoid particular effects of pseudorange observations. The technique consists of introducing ionosphere ambiguity parameters obtained from PPP filter into the geometry-free combination of observations to estimate ionospheric delays. Observational data from stations that are capable of tracking the GPS/BDS/GALILEO from the International GNSS Service (IGS) Multi-GNSS Experiments (MGEX) network are processed. For the purpose of performance validation, ionospheric delays series derived from the novel approach are compared with the global ionospheric map (GIM) from Ionospheric Associate Analysis Centers (IAACs). The results are encouraging and offer potential solutions to the near real-time ionosphere monitoring.     

基于固定模糊度PPP的低轨卫星实时精密定轨

传统动力学定轨法受制于动力学模型精度,传统几何定轨法精度受限,只能达到亚米级,而基于精密单点定位（PPP）模式的几何定轨法一般采用浮点解,定轨精度及可靠性较基于双差模式的相对定位较差。为提高PPP模式低轨定轨的定位性能,利用中国区域内外的IGS测站计算出当前所有卫星的宽巷和窄巷相位小数偏差产品,对经过中国大陆区域上空的国产低轨卫星海洋二号（HY-2）和资源三号 (ZY-3) 卫星进行固定模糊度PPP的定轨解算,与事后精密轨道结果进行比较,分析其外符合精度。结果表明：仅利用约10min弧段的HY-2和ZY-3卫星数据,切向与径向的定轨精度可达2cm左右,法向为5cm左右,较浮点解定轨精度大幅提升。基于固定模糊度PPP的定轨方法能够满足厘米级的实时精密定轨。     

基于相位偏差的实时PPP模糊度固定

采用CNES发布的实时相位偏差数据，实现包含模糊度固定的实时精密单点定位.对全球10个IGS测站10天观测数据进行RTPPP解算，分别统计模糊度首次固定时间和定位精度，结果显示利用实时相位偏差数据能在平均30min内实现模糊度首次固定，模糊度固定时水平位置误差由6cm迅速降低至2cm左右，三维位置误差由10cm迅速降低至5cm左右，同时RTPPP模糊度固定在3h观测内可保持水平3cm、三维5cm左右的定位精度.通过分析得出，基于相位偏差的RTPPP模糊度固定技术具有较高的定位精度和定位稳定性，能够快速实现cm级定位.      

基于UKF的姿态无关GPS双差整周模糊度确定

基于运动的GPS双差整周模糊度确定方法需要预先知道载体的姿态,为了消除对姿态的依赖,研究了一种新的整周模糊度确定方法。首先将多天线载波双差相位矢量观测方程转化为标量观测方程,消去了对载体姿态矩阵的依赖。经过短时离线观测,以中心估计算法和协方差白化算法估计和修正双差整周模糊度的近似解及协方差矩阵。再以该近似解和协方差矩阵为初值,由无迹卡尔曼滤波(UKF)实时估计双差整周模糊度的精确解。最后对该方法进行了仿真,仿真结果表明经过离线批处理算法的预处理UKF可准确收敛于真实解,证明了方法的正确和有效性。     

Performance assessment of real-time multi-GNSS integrated PPP with uncombined and ionospheric-free combined observables

For precise position services, the real-time precise point positioning (PPP) is a promising technology. The real-time PPP performance is expected to be improved by multi-system combination. The performance of real-time multi-system PPP needs to be periodically investigated, with the increasing number of available satellites and the continuously improved quality of real-time precise products of satellite clocks and orbits. In this study, a comprehensive performance assessment is conducted for the four-system integrated real-time PPP (FSIRT-PPP) with GPS, BDS, Galileo and GLONASS in both static and kinematic modes. The datasets from 118 stations spanning approximately a month are used for analysis, and the real-time stream CLK93 is employed. The superior performance of FSIRT-PPP is validated by comparing with the results of GPS/BDS, GPS/Galileo, GPS/GLONASS, GPS-only, BDS-only, Galileo-only and GLONASS-only cases. The FSIRT-PPP using ionospheric-free (IF) combined observables can achieve a convergence time of 10.9, 4.8 and 11.8 min and a positioning accuracy of 0.4, 0.5 and 0.7 cm in the static mode in the east, north and up directions, respectively, while the derived statistic is 15.4, 7.0 and 16.4 min, and 1.6, 1.2 and 3.4 cm in the kinematic mode in the three directions, respectively. Moreover, we also compare the position solutions of real-time PPP adopting IF combined and uncombined (UC) observables, and prove the mathematical equivalence between the two PPP models in the converged stage, provided that there are no external ionospheric corrections or constraints given to the estimated ionospheric delays in the UC model. The difference between the fully converged positioning accuracy of IF-based and UC-based real-time PPP is marginal, but the UC-based real-time PPP has longer convergence time due to the influence of the significant unmodeled time-varying errors in the real-time precise products as well as the different parameterization between them. For completeness, the real-time kinematic PPP results in harsh environments and the post-processed PPP results are also presented.     

Comparison of convergence time and positioning accuracy among BDS,GPS and BDS/GPS precise point positioning with ambiguity resolution

Precise point positioning (PPP) usually takes about 30?min to obtain centimetre-level accuracy, which greatly limits its application. To address the drawbacks of convergence speed and positioning accuracy, we develop a PPP model with integrated GPS and BDS observations. Based on the method, stations with global coverage are selected to estimate the fractional cycle bias (FCB) of GPS and BDS. The short-term and long-term time series of wide-lane (WL) FCB, and the single day change of narrow-lane (NL) FCB are analysed. It is found that the range of GPS and BDS non-GEO (IGSO and MEO) WL FCB is stable at up to a 30-day-time frame. At times frame of up to 60?days, the stability is reduced a lot. Whether for short-term or long-term, the changes in the BDS GEO WL FCB are large. Moreover, BDS FCB sometimes undergoes a sudden jump. Besides, 17 and 10 stations were used respectively to investigate the convergence speed and positioning errors with six strategies: BDS ambiguity-float PPP (Bfloat), GPS ambiguity-float PPP (Gfloat), BDS/GPS ambiguity-float PPP (BGfloat), BDS ambiguity-fixed PPP (Bfix), GPS ambiguity-fixed (Gfix), and BDS/GPS ambiguity-fixed (BGfix). The average convergence speed of the ambiguity-fixed solution is greatly improved compared with the ambiguity-float solution. In terms of the average convergence time, the Bfloat is the longest and the BGfix is the shortest among these six strategies. Whether for ambiguity-float PPP or ambiguity-fixed PPP, the convergence reduction time in three directions for the combined system is the largest compared with the single BDS. The average RMS value of the Bfix in three directions (easting (E), northing (N), and up (U)) are 2.0?cm, 1.5?cm, and 5.9?cm respectively, while those of the Gfix are 0.8?cm, 0.5?cm, and 1.7?cm. Compared with single system, the BDS/GPS combined ambiguity-fixed system (BGfix) has the fastest convergence speed and the highest accuracy, with average RMS as 0.7?cm, 0.5?cm, and 1.9?cm for the E, N, U components, respectively.     

Fast calibration of between-receiver GPS/Galileo/BDS differential phase bias with millimeter accuracy based on short baseline mode

The differential code and phase biases induced by the receiver hardware (including receiver, antenna, firmware, etc.) of the Global Navigation Satellite System (GNSS) have significant effects on precise timing and ionosphere sensing, thus deserve careful treatment. In this contribution, we propose an approach to fast fix the single-difference ambiguity to finally obtain the unbiased estimates of between-receiver differential phase bias (BR-DPB) and between-receiver differential code-phase bias (BR-DCPB) based on the short baseline mode. The key to this method is that the error sources can be significantly eliminated due to the length of the baseline is very short. At the same time, the empirical constraints and random characteristics of BR-DPB/BR-DCPB were considered, which is conducive to the resolution of single-difference ambiguity. Several sets of GNSS data (GPS L1/L2, Galileo E1/E5b, and BDS B1/B3), recorded by the short baselines in an interval of 30 s and covered a broad range of receiver/antenna types (JAVA, SEPT, LEIC, and TRIM), were used to verify the effectiveness of the proposed method. The numerical tests show that the proposed method is capable of fast fixing the single-difference ambiguity successfully within a few epochs and then providing the unbiased estimates of BR-DPB and BR-DCPB in an epoch-by-epoch manner. Experiments show that the estimated BR-DPB is in millimeter accuracy, which is of great significance for the millimeter-accuracy phase time transfer and ionospheric delay estimation. Furthermore, the calibrated BR-DPB/BR-DCPB can be treated as the known products for long-distance precise timing and ionosphere sensing based on the inter-station single-difference model.