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The 3D ionosphere structure is of interest in many fields such as radio frequency communication and global navigation satellite system (GNSS) applications. However, the limited temporal and spatial coverage of measurements poses a challenge for 3D electron density modeling. To overcome this challenge, we explore the use of kriging interpolation technique. The kriging interpolation is performed to obtain 3D representation of the ionosphere over electron density measurements retrieved by GNSS radio-occultation (RO) data. RO measurements are first reduced to "shape function," the ratio of electron density to vertical total electron content (VTEC), aiming to create a background model. Then, the empirical residual semivariogram is analyzed for variation characteristics of the shape functions under different solar geomagnetic conditions. Finally, 3D kriging is adopted for shape function interpolation. Compared to the modeling results without kriging, the maximum root mean square error (RMSE) reduction reaches 3.4 × 10 - 4 km - 1 , which amounts to 3.4 × 10 11 el/m 3 of electron density when VTEC is assumed as 100 TECU. This improvement accounts for 17.8% of root mean square (RMS) of shape function. [ABSTRACT FROM AUTHOR]

The non-line-of-sight (NLOS) signal has different signal characteristics and error from multipath, and it may lead to significant errors in the Global Navigation Satellite System (GNSS) positioning at the centimeter to millimeter range. However, the current multipath error mitigation methods for carrier phase observations do not distinguish them effectively. The multipoint hemispherical grid model (MHGM) is a method to model the multipath error in the spatial domain. We detect the NLOS carrier signal at a static station by the three-dimensional environment data and evaluate the reduction effects of the MHGM on multipath and NLOS errors. In our experiments, the MHGM reduces both multipath and NLOS errors significantly for the double-differenced residuals of carrier phase observations. But after using MHGM, the accuracy of NLOS observation is still significantly lower than that of multipath. We determine the accuracy difference between multipath and NLOS observations of the station, and propose two improved strategies based on the original MHGM which is also called strategy 0: strategy 1 of eliminating NLOS signal and strategy 2 of reducing its weight in the GNSS data processing. Our kinematic positioning test indicates that with multiple satellite systems, strategies 1 and 2 improve the mean RMSE of positioning results by about 10% and 15–17%, respectively. With fewer satellite systems, strategy 1 of eliminating NLOS signals may lead to poor satellite geometry and cannot improve effectively, while strategy 2 of reducing the weight of NLOS signals is more robust and recommended. [ABSTRACT FROM AUTHOR]

The Chinese Beidou navigation satellite system (BDS) has provided regional and global navigation and positioning services for the users via the BDS-2 and BDS-3 satellites. However, BDS-2 and BDS-3 send navigation signals on different frequencies; three of those are identical to assure system compatibility and interoperability. To comparatively analyze these navigation signals, we carried out three zero-baseline experiments with five brands of receivers, including Trimble, Septentrio, NovAtel, ComNav and Unicore. BDS-2 and BDS-3 multi-frequency data were collected during these experiments. The data were processed to evaluate the code and carrier phase measurement noises and investigate the inter-system biases (ISBs) on the three identical frequencies. The effects of the ISB on ambiguity resolution (AR) and position estimation (PE) were also demonstrated using the zero-baseline data with one Trimble receiver and one Septentrio receiver. The results show some new findings: (1) the code and phase noises in BDS-3 are smaller than those in BDS-2 on the same frequencies, and the three new signals B1C, B2b and B2a have comparable noises to the present signals. Besides, millimeter-level code noises are achieved on B3I and B2a signals in NovAtel receivers; (2) the code ISBs on B1I, B2I/B2b and B3I between BDS-2 and BDS-3 were found and distinguished, while no phase ISB could be found. The code ISB seems to be receiver-related and can be as large as 1 m in heterogeneous receivers. It is stable during a whole day but may also vary due to a restart of the receiver. No code and phase ISB on all three frequencies is observed for homogeneous receivers; (3) the code ISB will hamper the reliable AR and precise PE. The HMW (Hatch–Melbourne–Wübbena) combination on B1I and B3I is severely biased by about 0.6 cycles when double differencing between BDS-2 and BDS-3. After ISB calibration, the ratio value of wide-lane (WL) AR has a slight increase, and the accuracy of DD B1I code positioning has improved more than 10%, but few improvements can be seen in the fixed solution. It should be noted that although the inter-system code bias (ISCB) between BDS-2 and BDS-3 is detected in the baseline data, this bias should be considered in the absolute positioning as well. [ABSTRACT FROM AUTHOR]

A modified multipath error mitigation method using the multi-point hemispherical grid model (MHGM) is proposed, and the influence of changes in the observation environments of IGS stations on their data quality is evaluated. The multipath error models of different satellite pairs for different observation periods can be established using the integrated multi-GNSS data in the proposed method. The test under deliberate high multipath environment reveals that this method can effectively estimate the GNSS multipath error, detect and present the orientation of the interference sources around the station. The RMS of residuals and the kinematic positioning accuracy on day 237 of 2018 are improved by 68% and 61%, respectively. Compared with the empirical site model (ESM), which can also visualize the effects of the multipath, the RMS of residuals when applying the MHGM is improved by 20%. The test with IGS historical observations shows that MHGM can effectively reflect the influence of changing multipath interference around stations on carrier phase observations, with an average improvement of 25% in the RMS of carrier phase residuals in the extrapolated 9-day validations over the past 18 years. The results of a kinematic positioning experiment in 2019 generally coincide with the RMS statistic results of carrier phase residuals as well. The MHGM demonstrates distinct potential in the influence evaluation of changes for the multipath interference around the stations on their observation quality. [ABSTRACT FROM AUTHOR]

We present an analysis of the satellite-induced pseudorange variations based on multipath combination observables from the Chinese BeiDou Navigation Satellite System. With the main focus on refinement of the current correction models, we propose a new method to model the pseudorange variations for each satellite in the inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) and develop individual models of each satellite by differencing observables between epochs. We conduct experiments to evaluate correctness and effectiveness of the developed models. The performances of different correction models are compared and analyzed using the Hatch-Melbourne-Wübbena (HMW) observable. Numerical results show that: (1) for individual IGSO and MEO satellite, the developed correction models can make an improvement of approximately 20%, compared to the current correction models. For satellite C08, a maximum improvement of 43% can be achieved at low elevation angles of less than 10°. (2) For IGSO and MEO satellites, there are remarkable improvements using our models when the elevation angle is lower than 20° or higher than 60°; the improvements are more than 30% and nearly 25%, respectively. [ABSTRACT FROM AUTHOR]

Raw observation processing method with prior knowledge of ionospheric delay could strengthen the ambiguity resolution (AR), but it does not make full use of the relatively longer wavelength of wide-lane (WL) observation. Furthermore, the accuracy of calculated atmospheric delays from the regional augmentation information has quite different in quality, while the atmospheric constraint used in the current methods is usually set to an empirical value. A proper constraint, which matches the accuracy of calculated atmospheric delays, can most effectively compensate the residual systematic biases caused by large inter-station distances. Therefore, the standard deviation of the residual atmospheric parameters should be fine-tuned. This paper presents an atmosphere-constrained AR method for undifferenced network RTK (URTK) rover, whose ambiguities are sequentially fixed according to their wavelengths. Furthermore, this research systematically analyzes the residual atmospheric error and finds that it mainly varies along the positional relationship between the rover and the chosen reference stations. More importantly, its ionospheric part of certain location will also be cyclically influenced every day. Therefore, the standard deviation of residual ionospheric error can be modeled by a daily repeated cosine or other functions with the help of data one day before, and applied by rovers as pseudo-observation. With the data collected at 29 stations from a continuously operating reference station network in Guangdong Province (GDCORS) in China, the efficiency of the proposed approach is confirmed by improving the success and error rates of AR for 10-20 % compared to that of the WL-L1-IF one, as well as making much better positioning accuracy. [ABSTRACT FROM AUTHOR]

The Chinese Beidou system, also known as Compass, has entered its trial operational stage and can already provide services for triple-frequency users. Using triple-frequency signals is expected to be of great benefit for ambiguity resolution. Based on error characteristic analysis of the Beidou frequencies, we introduce the procedure of selecting the best combinations of triple-frequency signals. The geometry-based model and geometry-free model of triple-frequency signals are presented. Three triple-frequency carrier ambiguity resolution (TCAR) methods are described, which include the cascading rounding method, the stepwise AR method and the modified stepwise AR method. In order to evaluate the performance of these methods, observations from baselines of various lengths were collected using Beidou triple-frequency receivers and were processed epoch-by-epoch using the three methods. The same observation data were also processed in a dual-frequency mode for comparison. The results show that, compared to the dual-frequency based solution, the single epoch ambiguity resolution success rate with triple frequency improved nearly 30 % for the short baselines (<20 km) and 100 % for the mid-length baselines (20-50 km) using the proposed modified stepwise AR method. [ABSTRACT FROM AUTHOR]

GNSS single-epoch real-time kinematic (RTK) positioning depends on correct ambiguity resolution. If the number of observed satellites in a single epoch is insufficient, which often happens with a standalone GNSS system, the ambiguity resolution is difficult to achieve. China's BeiDou Navigation Satellite System has been providing continuous passive positioning, navigation and timing services since December 27, 2012, covering China and the surrounding area. This new system will increase the number of satellites in view and will have a significant effect on successful ambiguity resolution. Since the BeiDou system is similar to GPS, the procedure of data processing is easier than that for the Russian GLONASS system. We briefly introduce the time and the coordinate system of BeiDou and also the BeiDou satellite visibility in China, followed by the discussion on the combined GPS/BeiDou single-epoch algorithm. Experiments were conducted and are presented here, in which the GPS/BeiDou dual-frequency static data were collected in Wuhan with the baseline distance varying from 5 to 13 km, and processed in separate and combined modes. The results indicate that, compared to a standalone GPS or BeiDou system, the combined GNSS system can increase the successful ambiguity fixing rate for single epochs and can also improve the precision of short baselines determination. [ABSTRACT FROM AUTHOR]

Network-based ambiguity resolution (AR) between reference stations is the prerequisite to realize a precise real-time kinematic positioning service. With the help of BDS triple-frequency signals, we can efficiently deal with the ionospheric delay and tropospheric delay, and achieve rapid and reliable AR. To overcome the inaccurate ionospheric delay estimated by the geometry-free three carrier ambiguity resolution (GF TCAR) technique, which leads to failure in the original ambiguity resolution, we propose an ionospheric-free (IF) TCAR method to resolve the ambiguity between the reference stations over long baselines. Taking full advantage of the known positions of the reference stations, the easily resolved extra-wide-lane (EWL) ambiguity, and the IF phase combinations, we can reliably fix the wide-lane (WL) ambiguity. A Kalman filter is applied to estimate precise IF ambiguities and the original ambiguity is resolved with the fixed WL ambiguity. A numerical analysis with triple-frequency BDS data from three long baselines of a CORS network is provided to compare the AR performance of GF TCAR with that of IF TCAR. The results show that both methods can reliably resolve the WL ambiguity with a remarkable correctly-fixed rate of higher than 99%, and the reliably-fixed rates of the IF TCAR slightly increase from 92.19, 94.67 and 94.61-98.26, 99.54 and 97.51% for the three baselines. Herein “correctly-fixed” and “reliably-fixed” mean the difference between the float ambiguity and the true one are less than ± 0.5 and ± 0.25 cycles, respectively. On the other hand, the AR performance of the original signals with the IF TCAR method is much better than that with the GF TCAR method attaining a 100% correctly-fixed rate, while the GF TCAR method can hardly fix the original ambiguity with the largest bias being as much as 4 cycles because of the amplified systematic bias. [ABSTRACT FROM AUTHOR]