Tightly combined GPS/Galileo RTK for short and long baselines: Model and performance analysis

To ensure the compatibility and interoperability with modernized GPS, Galileo satellites are capable of broadcasting navigation signals on carrier phase frequencies that overlap with GPS, i.e., GPS/Galileo L1-E1/L5-E5a. Moreover, the GPS/Galileo L2-E5b signals have different frequencies with wavelength differences smaller than 4.2?mm. Such overlapping and narrowly spaced signals between GPS and Galileo bring the opportunity to use the tightly combined double-differenced (DD) model for precise real-time kinematic (RTK) positioning, resulting in improved performance of ambiguity resolution and positioning with respect to the classical standard or loosely combined DD model. In this paper, we focus on the model and performance assessment of tightly combined GPS/Galileo L1-E1/L2-E5b/L5-E5a RTK for short and long baselines. We first investigate the tightly combined GPS/Galileo DD observational model for both short and long baselines with simultaneously considering the GPS/Galileo overlapping and non-overlapping frequencies. Particularly, we introduce a reparameterization approach to solve the rank deficiency that caused by the correlation between the DISB parameters and the DD ionospheric parameters for both overlapping and non-overlapping frequencies. Then we present performance assessment for the tightly combined GPS/Galileo RTK model with real-time estimation of the differential inter-system bias (DISB) parameters for short and long baselines in terms of ratio value, ambiguity dilution of precision (ADOP), ambiguity conditional number, decorrelation number, search count, empirical success rate, time-to-first-fix (TTFF), and positioning accuracy. Results from both static and kinematic experiments demonstrated that compared to the loosely combined model, the tightly combined model can deliver improved performance of ambiguity resolution and precise positioning with different satellite visibility. For the car-driven short baseline experiment with 10° elevation cut-off angle, the tightly combined model can not only significantly increase the ratio value by approximately 27.5% (from 16.0 to 20.4), but also reduce the ambiguity ADOP, the conditional number, and the search count in LAMBDA by approximately 22.2% (from 0.027 to 0.021 cycles), 14.9% (from 199.2 to 169.6), and 25.4% (from 150.1 to 112.0), respectively. Comparable decorrelation number, empirical success rate, and positioning accuracy are also obtained. For the car-driven long baseline experiment, it is also observed that the ambiguity resolution performance in terms of the ratio value, the decorrelation number, the condition number, and the search count are significantly improved by approximately 18.5% (from 2.7 to 3.2), 22.0% (from 0.186 to 0.227), 55.9% (from 937.6 to 413.7), and 10.3% (from 43.8 to 39.3), respectively. Moreover, comparable ADOP, empirical success rate, and positioning accuracy are obtained as well. Additionally, the TTFF can be reduced (from 54.1 to 51.8 epochs with 10° elevation cut-off angle) as well from the results of static experiments.     

基于MLAMBDA的BDS/GPS单频RTK性能分析

GNSS RTK技术以其高精度、高效率、实时性的优点，被广泛应用于航空航天等领域.目前双频RTK技术已非常成熟并且应用较广.相比于双频，单频GNSS RTK在数据质量控制、定位误差处理等方面存在难点.因此单频RTK服务精度可能会受到限制，其定位性能有待研究.本文基于扩展卡尔曼滤波模型，通过MLAMBDA模糊度搜索方法和Ratio检验法，结合实测数据，对比分析BDS，GPS，BDS/GPS三种模式下的单频RTK定位性能.实验证明在静态场景下，三种模式的单频RTK定位精度都在厘米级，可满足高精度定位需求；动态场景下三种模式的模糊度固定率都在70%以上，可满足日常定位需求.在静态及动态应用场景下，北斗的模糊度固定率最高，模糊度解算所用时间短，能实现快速RTK定位.      

Estimating inter-system biases for tightly combined Galileo/BDS/GPS RTK

The overlapping carrier frequencies L1/E1, L5/E5a and B2/E5b from GPS/Galileo/BDS allow inter-system double-differencing of observations, which shows a clear advantage over differencing of the observations of each constellation independently. However, the inter-system biases destroy the integer nature of the inter-system double-differencing ambiguities. Two methods of direct rounding and parameter estimation are used to determine the ISB value. By analyzing data collected from Curtin University from 2015 to 2018, the phase and code inter-system bias (ISB) are related to the receiver type, firmware version and the selected overlapping frequency. Upgrade of receiver firmware version results in changes of ISB values. For example, the upgrade of Javad firmware in Dec, 15, 2017 causes the difference of 0.5 cycles ISB between BDS GEO and non-GEO satellites. By comparing the three dynamic models which include white noise process, random walk process, and random constant in the parameter estimation method, the ISB determined by the random constant model is consistent with the value obtained by the direct rounding method. After the calibration of ISBs, the performances of tightly combined positioning are assessed. The success rate of ambiguity resolution and accuracy of positioning for the tight combination (TC) are significantly improved in comparison with that for the loose combination (LC) over short baselines. For L5/E5a, on which only few satellites can be observed, the maximum increase in success rates of ambiguity resolution can reach 31.7%, i.e., from 54.9% of LC to larger than 86.6% of TC, and the positioning accuracies can even be increased by 0.13 m, i.e., from 0.208 of LC to 0.074 m of TC in East direction for the mix-receiver TRIMBLE NETR9-SEPT POLARX4 in 2018.     

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.     

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.     

单频GPS动态相对定位的模糊度逼近/搜索解法

针对目前实时动态定位(RTK)中常用搜索解法可靠度不高的缺点,利用各历元诸双差方程所形成的法方程,对其进行解耦处理以便于实时计算.在此基础上综合了逼近、搜索两种解法各自的局部优势,构成了逼近/搜索的联合解法.实际测试表明,该算法在单频全球定位系统(GPS)载波相位差分的动态相对定位过程中,用2～3min的时间即可可靠地在航解算出整周模糊度.     

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.      

Particle filter-based real-time phase line bias estimation for GNSS-based attitude determination with common-clock receivers

Global navigation satellite system (GNSS)-based attitude determination has been widely adopted in a wide variety of terrestrial, sea, air, and space applications. Recently, the emergence of commercial multi-GNSS common-clock receivers has brought new opportunities for high-precision GNSS-based attitude determination with single-differenced (SD) model. However, the key requirement of using this approach is the accurate estimation of the troublesome line bias (LB) in real-time. In this contribution, we propose a particle filter-based real-time phase LB estimation approach that apply to SD model with single-system single-frequency observations from common-clock receiver. We first analyzed the relationship between the integer ambiguity ratio value and the phase LB. It is proved that the accuracy of a given phase LB value can be qualified by the related ambiguity resolution ratio value, and the normalized ratio value can therefore be used to represent the likelihood function of observations. Then, we presented the particle filter-based real-time phase LB estimation procedure, and assessed its performance using GPS L1/BDS B1I observations from two datasets collected with different types of common-clock receivers in terms of the accuracy and convergence time of phase LB estimation, the computation load, and the positioning and attitude determination accuracy with respect to the double-differenced (DD) model. Experimental results demonstrated that the phase LB could be accurately estimated with short convergence time (generally within 15 epochs). Moreover, compared with the classical DD approach, the particle filter-based SD approach delivers comparable positioning root-mean-square (RMS) errors in the North and East components but significantly smaller RMS errors in the Up component. Accordingly, the achievable yaw accuracy is comparable whereas the pitch accuracy is remarkably improved. The improvements of positioning accuracy in the Up component and pitch accuracy are approximately 35.7 % to 63.7 %, and 33.3 % to 63.1 %, respectively. Additionally, the single-epoch computation time with our particle filter-based SD approach is generally 0.08 s, which is obviously larger than the DD approach but could still meet the requirements of real-time applications below 10 Hz sampling.     

Multivariate bootstrapped relative positioning of spacecraft using GPS L1/Galileo E1 signals

GNSS-based precise relative positioning between spacecraft normally requires dual frequency observations, whereas attitude determination of the spacecraft, mainly due to the stronger model given by the a priori knowledge of the length and geometry of the baselines, can be performed precisely using only single frequency observations. When the Galileo signals will come available, the number of observations at the L1 frequency will increase as we will have a GPS and Galileo multi-constellation. Moreover the L1 observations of the Galileo system and modernized GPS are more precise than legacy GPS and this, combined with the increased number of observations, will result in a stronger model for single frequency relative positioning. In this contribution we will develop an even stronger model by combining the attitude determination problem with relative positioning. The attitude determination problem will be solved by the recently developed Multivariate Constrained (MC-) LAMBDA method. We will do this for each spacecraft and use the outcome for an ambiguity constrained solution on the baseline between the spacecraft. In this way the solution for the unconstrained baseline is bootstrapped from the MC-LAMBDA solutions of each spacecraft in what is called: multivariate bootstrapped relative positioning. The developed approach will be compared in simulations with relative positioning using a single antenna at each spacecraft (standard LAMBDA) and a vectorial bootstrapping approach. In the simulations we will analyze single epoch, single frequency success rates as the most challenging application. The difference in performance for the approaches for single epoch solutions, is a good indication of the strength of the underlying models. As the multivariate bootstrapping approach has a stronger model by applying information on the geometry of the constrained baselines, for applications with large observation noise and limited number of observations this will result in a better performance compared to the vectorial bootstrapping approach. Compared with standard LAMBDA, it can reach a 59% higher success rate for ambiguity resolution. The higher success rate on the unconstrained baseline between the platforms comes without extra computational load as the constrained baseline(s) problem has to be solved for attitude determination and this information can be applied for relative positioning.     

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.     

Evaluation on real-time dynamic performance of BDS in PPP,RTK, and INS tightly aided modes

Since China’s BeiDou satellite navigation system (BDS) began to provide regional navigation service for Asia-Pacific region after 2012, more new generation BDS satellites have been launched to further expand BDS’s coverage to be global. In this contribution, precise positioning models based on BDS and the corresponding mathematical algorithms are presented in detail. Then, an evaluation on BDS’s real-time dynamic positioning and navigation performance is presented in Precise Point Positioning (PPP), Real-time Kinematic (RTK), Inertial Navigation System (INS) tightly aided PPP and RTK modes by processing a set of land-borne vehicle experiment data. Results indicate that BDS positioning Root Mean Square (RMS) in north, east, and vertical components are 2.0, 2.7, and 7.6?cm in RTK mode and 7.8, 14.7, and 24.8?cm in PPP mode, which are close to GPS positioning accuracy. Meanwhile, with the help of INS, about 38.8%, 67.5%, and 66.5% improvements can be obtained by using PPP/INS tight-integration mode. Such enhancements in RTK/INS tight-integration mode are 14.1%, 34.0%, and 41.9%. Moreover, the accuracy of velocimetry and attitude determination can be improved to be better than 1?cm/s and 0.1°, respectively. Besides, the continuity and reliability of BDS in both PPP and RTK modes can also be ameliorated significantly by INS during satellite signal missing periods.     

附加Doppler预报坐标约束的模糊度 动态解算新方法

利用GPS(Global Positioning System)相位观测进行动态定位的主要困难就是法方程不适定问题(秩亏或病态问题),导致模糊度浮动解及其协方差阵不准,以此构造的模糊度搜索范围比较大,使得模糊度的搜索非常困难.提出利用Doppler高精度测速预报近似坐标并对其附加约束,解决法方程求逆中的不适定问题,提高模糊度浮动解及其方差阵的准确性,缩小模糊度的搜索范围,提高模糊度搜索的成功率.结果表明,短基线情况,新方法在模糊度动态解算中取得了明显效果.      

A real-time combined quality control method for GNSS precise positioning in harsh environments

Global Navigation Satellite System (GNSS) precise positioning can be significantly affected by severe multipath effects and outliers in harsh environments, and highly relies on quality control strategies. Previous studies mainly focus on the posterior residuals to check and exclude the outliers in GNSS observations, limited work emphasizes the combined quality control method considering both the prior and posterior knowledge simultaneously. This paper proposed a real-time combined quality control method to process the multipath effects and outliers in harsh environments simultaneously. Specifically, in the prior stage, a modified multipath processing strategy is proposed for both phase and code observations, then a modified detection, identification, and adaptation (DIA) method considering the maximum times of data snooping is studied in the posterior stage. Two dedicated experiments in real harsh environments were carried out to evaluate the performance of the proposed combined quality control method. For the static experiment, the proposed method exhibits smaller positioning errors, the best positioning accuracy, and the highest availability in this study. Specifically, the proposed method exhibits an improved percentage of 55.4 %, 56.3 %, and 59.7 % for positioning accuracy compared to those without the quality control method in the E, N, and U directions, respectively. Besides, the proposed method can further improve the performance of ambiguity resolution with an improved percentage of 32.2 %. For the kinematic experiment, the three-dimensional positioning accuracy of the proposed method is 0.577 m, which exhibits a 40.0 % improvement compared to those without the quality control method. Also, the proposed method exhibits better performance under relatively strong multipath effects. In this sense, the proposed real-time combined quality control method is highly appreciated in terms of positioning availability, accuracy, and ambiguity resolution for GNSS precise positioning, especially in harsh environments.     

A novel predictive algorithm for double difference observations of obstructed BeiDou geostationary earth orbit (GEO) satellites

Transmission link disturbances and device failure cause global navigation satellite system (GNSS) receivers to miss observations, leading to poor accuracy in real-time kinematic (RTK) positioning. Previously described solutions for this problem are influenced by the length of the prediction period, or are unable to account for changes in receiver state because they use information from previous epochs to make predictions. We propose an algorithm for predicting double difference (DD) observations of obstructed BeiDou navigation system (BDS) GEO satellites. Our approach adopts the first-degree polynomial function for predicting missing observations. We introduce a Douglas-Peucker algorithm to judge the state of the rover receiver to reduce the impact of predictive biases. Static and kinematic experiments were carried out on BDS observations to evaluate the proposed algorithm. The results of our navigation experiment demonstrate that RTK positioning accuracy is improved from meter to decimeter level with fixed ambiguity (horizontal?<?2?cm, vertical?<?18?cm). Horizontal accuracy is improved by over 50%, and the vertical accuracies of the results of the static and kinematic experiments are increased by 47% and 27% respectively, compared with the results produced by the classical approach. Though as the baseline becomes longer, the accuracy is weakened, our predictive algorithm is an improvement over existing approaches to overcome the issue of missing data.     

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.     

Evaluation and analysis on positioning performance of BDS/QZSS satellite navigation systems in Asian-Pacific region

By using the observation data and products of precise obit and clock offset from Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS) and GNSS Research Centre, Curtin University in this paper, the positioning performance of BDS/QZSS satellite navigation system has been analyzed and evaluated in aspects of the quantity of visible satellites, DOP value, multipath effect, signal-to-noise ratio, static PPP and kinematic PPP. The analysis results show that compared to BDS single system when the cutoff angle are 30°and 40°, the DOP value of BDS/QZSS combined system has decreased above 20%, and the quantity of visible satellites increased about 16–30% respectively, because of the improved spatial geometric configuration. The magnitude of satellite multipath effect of BDS system shows the trend of MEO?>?IGSO?>?GEO, which is consistent with that of QZSS satellite system, as the constellation structure of the two systems is similar. The variation tendencies of signal-to-noise ratio with respect to elevation angle of the two systems are almost the same at all frequencies, showing that at the same elevation angle the signal-to-noise ratio of MEO satellites is higher than that of IGSO satellites, as the higher obit is the lower transmitting power is obtained. For having a specially designed obit, the variation of signal-to-noise ratio of BDS system is more stable. However, the magnitude of signal-to-noise ratio of QZSS system appears the trend of frequency 3?>?frequency 2?>?frequency 1. The static PPP performance of the BDS/QZSS combination system has been improved more significantly than the BDS single system in E, N and U directions. When the cutoff angle are at 7°, 15° and 30°, the PPP accuracy is increased about 25–34% in U direction, 10–13% and 23–34% in E and N directions respectively. When the elevation angle is large (40°), compared to BDS single system at lower elevation angles (7° and 15°) the PPP accuracy of the BDS/QZSS combination system is improved above 30% in U direction. In kinematic PPP performance, compared to BDS single system, the accuracy, availability and reliability of the BDS/QZSS combination system has been improved too, especially at large elevation angles (30° and 40°), the kinematic PPP accuracy in E and U directions has been improved about 10–50%, and above 50% in U direction. It can be concluded that the combination with QZSS system can improve the positioning accuracy, reliability and stability of BDS system. In the future, with the improvement of the satellite construction of Japan’s QZSS system and the global networking of China’s BDS satellites, the QZSS satellites will contribute greatly to improve the positioning accuracy, reliability, availability and stability of GNSS systems in areas such as cities, mountains, densely-packed buildings and severely covered areas in Asian-Pacific region.     

GNSS-IR双频数据融合的土壤湿度反演方法

目前全球导航卫星系统反射信号干涉测量（GNSS-IR）土壤湿度反演研究仅针对单一频点展开,提出用熵值法将2个频点数据进行融合以改进土壤湿度反演精度。首先,利用频谱分析法分别解析出各频点的信噪比（SNR）序列的振荡频率,计算出对应的等效天线高度,并利用最小二乘法求解各频点信噪比序列相位;然后,通过熵值法进行2个频点的相位观测量融合;最后,利用融合结果与实测土壤湿度建立经验模型,实现土壤湿度反演。利用地基观测实验获得的全球定位系统（GPS）L1和L2信噪比数据对该方法进行了验证,结果表明:L1和L2双频融合反演结果平均标准差为0.6%,比L1单频反演结果提高64.73%,比L2单频反演结果提高32.12%;均方根误差为0.37%,比L1频点降低72.8%,比L2频点降低73.4%。      

北斗三频相位观测值线性组合研究

以北斗三频数据为基础,给出了北斗三频组合观测值的数学模型并系统分析了组合后的波长、电离层误差以及观测噪声误差;在保持整周模糊度整数特性的前提下,以整数线性变换法为基础,通过Matlab编程实现组合系数的优化选取。通过将不同组合系数应用于伪距相位法三频数据周跳探测中,发现组合系数之和不为0的组合周跳探测值均在0.5周以上,且组合系数之和越大,波动越大;通过将不同组合系数应用于无几何CIR法三频数据模糊度解算中,发现系数之和不为0,但波长较长的组合求得的模糊度残差值大致在0.6周,通过合适的模糊度搜索方法可以得到正确的模糊度固定解,在短基线模糊度解算中可以考虑使用。     

Carrier phase prediction method for GNSS precise positioning in challenging environment

Since the signals of global navigation satellite system (GNSS) are blocked frequently in challenging environments, the discontinuous carrier phases seriously affect the application of GNSS precise positioning. To improve the carrier phase continuity, this paper proposes a carrier phase prediction method based on carrier open-loop tracking. In the open-loop tracking mode, the carrier numerically controlled oscillator (NCO) is controlled by the predicted Doppler, but not by the loop filter output. To improve the phase prediction effective time, accurate receiver clock drift estimation is studied in the prediction method. The phase prediction performance is tested on GNSS software receiver. In the phase prediction effective time tests, open-loop processes were set for the tested channel. The test results show that, when some satellite signals are blocked in 15?s, the probability of carrier phase error less than quarter cycles is more than 94%. In the real time kinematic (RTK) positioning tests, some satellite signals are blocked in 10–15?s repeatedly. The test results show that, the carrier phase continuity is basically not affected by the signal interruption, and the RTK can almost keep continuous centimeter-level positioning accuracy without re-fixing the integer ambiguity.     

Analysis of the code and phase between-receiver inter-system biases of the overlapping frequencies for GPS/Galileo/BDS

The overlapping-frequency signals from different GNSS constellations are interoperable and can be integrated as one constellation in multi-GNSS positioning when inter-system bias (ISB) is properly disposed. The look-up table method for ISB calibration can enhance the model strength, maximize the number of integer-estimable ambiguities, and thus is preferred. However, the characteristics and magnitudes of the receiver code ISB and phase fractional ISB (F-ISB) are not well known and the wrong values of the biases can seriously degrade the positioning results. In this contribution, we first estimate the between-receiver code ISB and phase F-ISB of hundreds of the baselines up to around 25km in the European Permanent GNSS Network (EPN) and the Multi-GNSS Experiment (MGEX) for the overlapping frequencies L1-E1 (L1), L5-E5a (L5) and E5b-B2b (L7). The data collected from 1st January 2016 to 1st January 2019. Second, the receiver-type and firmware-version combinations for the receivers of Trimble, Leica, Javad, Septentrio and NovAtel are carefully classified. Results show that the Septentrio receivers have consistent code and phase ISB values for the three overlapping frequencies i.e. only one value for each frequency and no receivers are different. The Leica, Trimble and Javad receivers have two or more ISB values for at least one of the three frequencies. A few receivers with biases to the groups are also found and listed. Third, the code ISB and phase F-ISB of the groups are adjusted by the least-squares method. The root mean square errors (RMSE) of the least square adjustment are 0.240 m, 0.250 m and 0.200 m for code of L1, L5 and L7 frequencies, respectively, and are 0.0009 m, 0.0015 m and 0.0031 m for phase of L1, L5 and L7 frequencies, respectively. Finally, the effects of code ISB errors on code positing are investigated with the zero-baseline MAT1_MATZ. The distance root mean square error (DRMS) of L1-E1 code positioning can be reduced by 48.2% with 5 GPS and Galileo satellites and the DRMS degrades quickly when the code ISB error is larger.