Yize Zhang

Performance of Real-Time Precise Point Positioning

The IGS Real-time Pilot Project (IGS-RTPP) provides real-time precise orbits and clocks, which support real-time positioning for single stations over large areas using the Precise Point Positioning (PPP) technique. This paper investigates the impact of real-time orbits, network configuration, and analysis strategies on real-time PPP implementation and demonstrates the real-time PPP performance. One month of data from the IGS network is analyzed in a real-time simulation mode. Results reveal the following: (1) In clock estimation, differential approaches are much more efficient than the zero-differenced approach. (2) The precision of IGS Ultra rapid (IGU) orbits could meet the IGS-RTPP requirement for precise clock estimation and PPP positioning. (3) Considering efficiency and precision, a network with 50 stations is recommended for the IGS-RTPP. It is demonstrated that the real-time satellite clock precision is 0.1 ns supporting hourly static PPP with a mean precision of 2–3 cm in the North component and 3–4 cm in the other components. Kinematic PPP assessed with onboard GPS data collected from a buoy provided mean coordinate precision of 2.2, 4.2, 6.1 cm in the North, East and Up directions, compared to the RTK solutions.

Application of Inter-system Hardware Delay Bias in GPS/GLONASS PPP

GPS applies Code Division Multiple Access technique in signal coding, while GLONASS’s signal is produced with Frequency Division Multiple Access technique. The differences in signal frequency results in inter-system hardware delay bias for GPS/GLONASS receivers. Subjecting to these hardware delays, strategies and models of GPS/GLONASS PPP based positioning needs to be modified. We derived a GPS/GLONASS combined PPP positioning models by introducing inter-system hardware delay biases. Several scenarios were simulated to test the introduced models using the observation of IGS stations. The results show that: ① Adding a couple of GLONASS satellites can improve the positioning accuracy in the environment without enough GPS satellites being tracked; ② The inter-system hardware delay bias is stable on daily base, and it could be predicted and be fixed in the GPS/GLONASS combined PPP.

Modeling and Assessment of GPS/BDS Combined Precise Point Positioning

Precise Point Positioning (PPP) technique enables stand-alone receivers to obtain cm-level positioning accuracy. Observations from multi-GNSS systems can augment users with improved positioning accuracy, reliability and availability. In this paper, we present and evaluate the GPS/BDS combined PPP models, including the traditional model and a simplified model, where the inter-system bias (ISB) is treated in different way. To evaluate the performance of combined GPS/BDS PPP, kinematic and static PPP positions are compared to the IGS daily estimates, where 1 month GPS/BDS data of 11 IGS Multi-GNSS Experiment (MGEX) stations are used. The results indicate apparent improvement of GPS/BDS combined PPP solutions in both static and kinematic cases, where much smaller standard deviations are presented in the magnitude distribution of coordinates RMS statistics. Comparisons between the traditional and simplified combined PPP models show no difference in coordinate estimations, and the inter system biases between the GPS/BDS system are assimilated into receiver clock, ambiguities and pseudo-range residuals accordingly.

Improving Efficiency of Data Analysis for Huge GNSS Network

The development of GNSS system and its applications is accompanied by the fast development of the ground tracking networks. The expansion of tracking network could contribute to the improvement of precision of satellite orbits, clocks, ERPs and so on. However, the increase of number of tracking stations causes non-linear gain of computing time, especially in the case of data processing based on the Zero-difference (ZD) strategy. Parameter elimination is one of the most used methods to fasten ZD data processing, nevertheless it involves matrix transformation and inversion at each epoch and the computing time is still very long in case of huge network and Multi-GNSS combined solutions. The first part of the paper presents the current status of ZD data processing in case of huge networks and Multi-GNSS data processing. Using 110 GPS/GLONASS stations from the IGS network, we perform classical IGR-like data processing with different data sampling ranging from 5, 6, 7….. till 15 min. Estimated parameters including orbits, clocks, ZTDs, coordinates, ERPs etc. Comparison of the products using different sampling data shows: precision of orbit and clock somehow linearly increases with sampling rate changing from 5 to 15 min, and ERP precision is not influenced by the change of sampling rate. To analyze the impacts of products based on different data sampling on positioning applications, we perform PPP for 22 globally distributed IGS stations using 4 weeks’ data and kinematic precise orbit determination for GRACE satellites. Results show that the coordinates/orbits precision is at the same level: precision of PPP coordinate is of 2.3, 3.8, 8.8 mm in NEU directions using products based on 5 min sampling data, and of 2.5, 4.3, 8.6 mm in case of using 15 min sampling data.

Assessment of the Contribution of QZSS Combined GPS/BeiDou Positioning in Asia-Pacific Areas

Three QZSS satellites are launched in 2017, which implies that a four satellites regional system is to be established in 2018. There is no doubt that QZSS will play a more important role in the future global GNSS constellations. So it is quite necessary to investigate the importance of current QZSS constellation in positioning. In this paper, the number of visible satellite and PDOP (Position Dilution of Precision) value improvement by combining QZSS with the existing GPS and BeiDou system is analyzed among Asia-Pacific areas. 9 IGS stations are selected to evaluate the performance of SPP (Single Point Positioning) and PPP (Precise Point Positioning) using GPS, BeiDou and GPS + QZSS, BeiDou + QZSS system. Analysis results show that QZSS improves SPP performance for both GPS and BeiDou at different level. Especially when the satellite number is reduced, such as in urban areas or when the elevation cutoff is high, the positioning error will reduce after adding QZSS satellite and the availability of other GNSS systems will also improves. For kinematic PPP users, QZSS could also reduce the convergence period. Meanwhile, the dual frequency and single frequency RTK (Real Time Kinematic) positioning performance is compared after adding QZSS satellite into GPS and BeiDou. Kinematic car test in urban environment shows that when combining QZSS satellite with GPS and BeiDou, the rate of instantaneous ambiguity resolution will increase for both single and dual-frequency users.

Analysis of BDS Satellite Clock Prediction Contribution to Rapid Orbit Recovery

The BDS-2 system is designed as a GEO/IGSO/MEO mixed constellation. Generally, there exists satellite maintaining operation for GEO or IGSO satellite every 7–10 days. During this period the maneuver satellite is out of service. It will be about 5–6 h starting from the beginning of satellite maneuver to the release of the first group of recovery orbit. Strategy of satellite clock assisted precise orbit determination (POD) is normally implement, where the most critical factor that contributes to the availability of maneuver satellites is the length of accumulation of data. However, the last hour of real-time observed pseudo-range data of tracking station could not be included in POD, due to the reason that the satellite clock could not be observed in real-time. In this paper, we propose to use the polynomial fitting method to forecast the satellite clocks and use it in POD. We analyze the accuracy of satellite clocks prediction and its contribution to the rapid orbit recovery. Results show that the satellite unavailability time could be shortened by at least 1 h, which effectively improves satellite availability. And it improves the accuracy of orbit determination and prediction by more than 15 and 70%.

Real-Time Detection and Repair of Cycle-Slip Based on Pseudo-range Phase Combinations for Un-differenced GNSS Triple-Frequency Observations

For the detection and repair of cycle-slip for un-differenced GNSS triple-frequency observations, current algorithms have difficulties in efficiency, stability and even some special cycle-slip combinations cannot be detected. This paper investigates the strategies in real-time detection and repair of cycle-slip. Geometry free ionospheric free code-phase combinations together with phase combinations are used, where the selection criteria of combination coefficients is based on the principle of the minimal condition number. Advantage of the method is that each cycle-slip value can be calculated without searching, thus the efficiency is improved and success rate is still high. Experiment results show that even under the severe ionospheric conditions, cycle-slips of triple-frequency un-differenced observations can be detected and repaired.

Initial Assessment of BDS Zone Correction

Zone correction is a new type of differential corrections for BeiDou wide area augmentation system. As broadcasted together with the equivalent satellite clock and orbit corrections by BDS satellites, they enable user decimeter-level real-time positioning capability using the carrier-phase observations. In this paper, we give a brief introduction of zone corrections, and the function model of precise point positioning (PPP) for dual- and single-frequency users using the zone corrections. Tracking data of 30 stations in mainland China are used to evaluate the zone-divided PPP performance, and the handling of troposphere delay and ionosphere delay are discussed. Results show that the zone-divided PPP performance improves when fixing the troposphere delay. Model of UofC is much suitable for single frequency user. The dual-frequency PPP can convergences to 0.5 m in 25 min and the positioning accuracy are 0.15 m in horizontal and 0.2 m in vertical, respectively. As for single frequency PPP, the positioning accuracy convergences to 0.8 m in 20 min, while the positioning accuracy is 0.3 m in horizontal and 0.5 m in vertical.

BDS Code Bias and Its Effect on Wide Area Differential Service Performance

The integrated wide-area differential system of BDS broadcasts differential corrections to compensate broadcast ephemeris errors and enhance user positioning accuracy. It uses real-time pseudo-range observations from ground monitoring stations and calculates differential corrections, which are then broadcasted to users through the GEO satellites. Previous studies show that apparent code biases exist for BDS tracking stations, which in turn will affect the accuracy of differential corrections. This paper analyses the long-term pseudo-range biases based on the residuals in the Precise Orbit Determination (POD), the characteristics of the mean and standard deviation of the pseudo-range bias are studied. A code bias correction model is proposed and applied to BDS wide-area differential calculation. Performance of the code bias model is analysed in real-time pseudo-range based positioning. Results show that: UDRE and user positioning accuracy are improved, where the satellite UDRE is reduced from 0.43 to 0.35 m, and the user positioning accuracy is increased by 10.6% and 14.6% in horizontal and height directions, respectively.

Mitigation of Orbit Integration Errors for Eclipsing Satellites

Numerical integration assumes that accelerations at each node are continuous and smooth. However, when satellite enters into shadow, perturbation caused by solar radiation pressure will jump. Therefore, mathematical theory of numerical integrator cannot match the real motion of satellite, which will bring about integration errors. In order to deal with the problem, some experiments are done for different constellations. The result shows that 99 % of error occurs in along-track direction and will accumulate when crossing more shadow boundaries. For different integrators, errors are different. Runge-Kutta4 integrator is sensitive to step size, especially for eclipsing satellites, and is not competent for long arc integration. Adams integrator relies on former steps, needs a fixed step size, and will induce more integration errors when crossing shadow boundaries. Runge-Kutta9 integrator brings less error during eclipsing season than Runge-Kutta4 and Adams integrators, and can change step size flexibly. To mitigate integration errors during eclipses, this contribution introduces an improved method based on Runge-Kutta9 integrator. We use dichotomy to detect the exact epoch of penumbra boundary, change the step size, and restart the integration. Result shows that after boundary detection, accuracy for 1-day arc improves 65.8 %, 2-day arc improves 55.5 %, 3-day arc improves 33.2 %. This method is suitable for both extended filter and least square method.