Undifferenced Model Research Articles

Estimation of BDS-2/3 phase observable-specific signal bias aided by double-differenced model: an exploration of fast BDS-2/3 real-time PPP

GNSS phase observable-specific signal bias (OSB) corrections are essential for widespread application of precise point positioning with ambiguity resolution (PPP-AR) or PPP-RTK. However, subject to the orbital error effects, conventional undifferenced (UD) model-derived BeiDou System (BDS) real-time (RT) OSB products are usually unsatisfactory. In this study, a novel OSB-generating method assisted by the double-differenced (DD) model is proposed. The reliable integer UD ambiguities are obtained by converting DD ambiguities with given ambiguity datums, by which the RT orbit error effects on ambiguity fixing can be reduced during the OSB extraction and PPP-AR process. Validated using data from two regional sparse GNSS reference networks in Shaanxi, China, and Europe, results show that the proposed method-derived OSB products can improve RT PPP-AR performance effectively. In the Shaanxi network, the narrow-lane ambiguity residuals for BDS-3 within ± 0.25 cycles are improved by 23.1% and 33.2% compared to those using the UD model and Centre National d’Etudes Spatiales (CNES)-derived OSB products, respectively, and the corresponding values are 15.2% and 43.1% in the European network. A centimeter- or even millimeter-level positioning accuracy can be achieved for BDS PPP using the poposed OSB products in both networks. In the kinematic PPP-AR test within the Shanxi network, the mean RMS of the BDS-2/3 fixed solutions in the east, north, and up directions is 0.9, 0.7, and 2.3 cm, with a decrease of 57.1%, 53.3%, and 46.5% compared to that using OSB derived by UD model. The median Time-To-First-Fix (TTFF) is also shortened from 23.8 to 7.5 min.

A Method to Accelerate the Convergence of Satellite Clock Offset Estimation Considering the Time-Varying Code Biases

Continuous and stable precision satellite clock offsets are an important guarantee for real-time precise point positioning (PPP). However, in real-time PPP, the estimation of a satellite clock is often interrupted for various reasons such as network fluctuations, which leads to a long time for clocks to converge again. Typically, code biases are assumed to stay constant over time in clock estimation according to the current literature. In this contribution, it is shown that this assumption reduces the convergence speed of estimation, and the satellite clocks are still unstable for several hours after convergence. For this reason, we study the influence of different code bias extraction schemes, that is, taking code biases as constants, extracting satellite code biases (SCBs), extracting receiver code biases (RCBs) and simultaneously extracting SCBs and RCBs, on satellite clock estimation. Results show that, the time-varying SCBs are the main factors leading to the instability of satellite clocks, and considering SCBs in the estimation can significantly accelerate the filter convergence and improve the stability of clocks. Then, the products generated by introducing SCBs in the clock estimation based on undifferenced observations are applied to PPP experiments. Compared with the original undifferenced model, clocks estimated using the new method can significantly accelerate the convergence speed of PPP and improve the positioning accuracy, which illustrates that our estimated clocks are effective and superior.

A model to obtain timing solution with un-differenced observations suitable for single-station/multi-station, a case study of BDS data

This study proposes a model for a BeiDou Satellite Navigation System (BDS) precise timing solution with un-differenced carrier phase observations, and it is suitable for both single-station and multi-station. With this model, not only can users employ high-precision carrier phase observations to improve the uncertainty of the timing service for single station, but they can also directly use the un-differenced model and augmentation correction which collected from the reference stations to get the timing service, which is more efficient than the traditional single-differenced model for multi-stations. The validation showed that the carrier phase observations can improve the uncertainty from 0.49 to 0.10 ns, and the mean stability improved 70 times. In addition, whether for the single-station and multi-station solution or for the single-differenced model and un-differenced model, the final uncertainty and stability were nearly the same, thus it allows for the realisation of a seamless timing solution for the single-station model and multi-station model.

The Comparison and Analysis of BDS NRTK between DD and UD Models

The BeiDou Navigation Satellite System (BDS) Network Real Time Kinematic (NRTK) position algorithm with both Double-Differenced (DD) model and Un-Differenced (UD) model is investigated in this study. This algorithm is realized and validated with experimental BDS data collected at four regional stations. For the experiment within the regional network, a short convergence time for each model is considered. The results show that the BDS NRTK is able to provide positioning service with accuracy at the cm level. Theoretically, UD-NRTK and DD-NRTK are equivalent to each other. The small differences found between the DD and UD models in this study can be clarified in that the error correction for the DD model is more precise than that for the UD model, resulting in faster solution convergence in the DD model. However, the noise of the DD model is two times of the UD model, which usually leads to larger final RMS of positioning accuracy for the DD model. Copyright © 2018 Institute of Navigation

Comparative analysis of multi-constellation GNSS single-frequency precise point positioning

We develop new single-frequency PPP models, which combine the observations of the current GNSS constellations, including GPS, GLONASS, Galileo and BeiDou. Four single-frequency GNSS PPP models are developed, namely, the undifferenced single-frequency GNSS PPP model, the undifferenced ionosphere-free (IF) code and phase model known as quasi-phase model, the between-satellite-single-difference model (BSSD) and the between-satellite-single-difference ionosphere-free (BSSDIF) model. The IGS final precise products are used to account for the orbital and clock errors. For both undifferenced and BSSD models, the IGS final global ionospheric maps (GIM) model is used to correct the ionospheric delay. The GNSS inter-system biases are treated as additional unknowns in the estimation process for the undifferenced models, while a loosely coupled technique is used for the BSSD models. Various GNSS combinations are considered in the assessment for each PPP model, including GPS/GLONASS, GPS/Galileo, GPS/BeiDou and quad-constellation GNSS observations. It is shown that the multi-GNSS observations enhance the PPP solution accuracy in comparison with the GPS-only solution. Furthermore, the use of IF-PPP technique enhances the positioning accuracy by 25, 20, 24, 20 and 19% compared with the GIM-based PPP model for the GPS-only, GPS/GLONASS, GPS/Galileo, GPS/BeiDou and quad-GNSS combinations, respectively, for 1 h of GNSS data processing. In addition, an average of 15% positioning accuracy improvement can be obtained when the BSSD techniques are used compared with the undifferenced techniques. However, for 6 h of processing, comparable positioning accuracy can be obtained from all four single-frequency models.

Multi-GNSS precise point positioning with raw single-frequency and dual-frequency measurement models

The emergence of multiple satellite navigation systems, including BDS, Galileo, modernized GPS, and GLONASS, brings great opportunities and challenges for precise point positioning (PPP). We study the contributions of various GNSS combinations to PPP performance based on undifferenced or raw observations, in which the signal delays and ionospheric delays must be considered. A priori ionospheric knowledge, such as regional or global corrections, strengthens the estimation of ionospheric delay parameters. The undifferenced models are generally more suitable for single-, dual-, or multi-frequency data processing for single or combined GNSS constellations. Another advantage over ionospheric-free PPP models is that undifferenced models avoid noise amplification by linear combinations. Extensive performance evaluations are conducted with multi-GNSS data sets collected from 105 MGEX stations in July 2014. Dual-frequency PPP results from each single constellation show that the convergence time of undifferenced PPP solution is usually shorter than that of ionospheric-free PPP solutions, while the positioning accuracy of undifferenced PPP shows more improvement for the GLONASS system. In addition, the GLONASS undifferenced PPP results demonstrate performance advantages in high latitude areas, while this impact is less obvious in the GPS/GLONASS combined configuration. The results have also indicated that the BDS GEO satellites have negative impacts on the undifferenced PPP performance given the current "poor" orbit and clock knowledge of GEO satellites. More generally, the multi-GNSS undifferenced PPP results have shown improvements in the convergence time by more than 60 % in both the single- and dual-frequency PPP results, while the positioning accuracy after convergence indicates no significant improvements for the dual-frequency PPP solutions, but an improvement of about 25 % on average for the single-frequency PPP solutions.

Performance Analysis of Several GPS/Galileo Precise Point Positioning Models

This paper examines the performance of several precise point positioning (PPP) models, which combine dual-frequency GPS/Galileo observations in the un-differenced and between-satellite single-difference (BSSD) modes. These include the traditional un-differenced model, the decoupled clock model, the semi-decoupled clock model, and the between-satellite single-difference model. We take advantage of the IGS-MGEX network products to correct for the satellite differential code biases and the orbital and satellite clock errors. Natural Resources Canada’s GPSPace PPP software is modified to handle the various GPS/Galileo PPP models. A total of six data sets of GPS and Galileo observations at six IGS stations are processed to examine the performance of the various PPP models. It is shown that the traditional un-differenced GPS/Galileo PPP model, the GPS decoupled clock model, and the semi-decoupled clock GPS/Galileo PPP model improve the convergence time by about 25% in comparison with the un-differenced GPS-only model. In addition, the semi-decoupled GPS/Galileo PPP model improves the solution precision by about 25% compared to the traditional un-differenced GPS/Galileo PPP model. Moreover, the BSSD GPS/Galileo PPP model improves the solution convergence time by about 50%, in comparison with the un-differenced GPS PPP model, regardless of the type of BSSD combination used. As well, the BSSD model improves the precision of the estimated parameters by about 50% and 25% when the loose and the tight combinations are used, respectively, in comparison with the un-differenced GPS-only model. Comparable results are obtained through the tight combination when either a GPS or a Galileo satellite is selected as a reference.

Precise Point Positioning using Multi-Constellation GNSS Observations for Kinematic Applications

AbstractTraditional precise point positioning (PPP) is commonly based on un-differenced ionosphere-free linear combination of Global Positioning System (GPS) observations. Unfortunately, for kinematic applications, GPS often experiences poor satellite visibility or weak satellite geometry in urban areas. To overcome this limitation, we developed a PPP model, which combines the observations of three global navigation satellite systems (GNSS), namely GPS, GLONASS and Galileo. Both un-differenced and between-satellite single-difference (BSSD) ionosphere-free linear combinations of pseudorange and carrier phase GNSS measurements are processed. The performance of the combined GNSS PPP solution is compared with the GPS-only PPP solution using a real test scenario in downtown Kingston, Ontario. Inter-system biases between GPS and the other two systems are also studied and obtained as a byproduct of the PPP solution. It is shown that the addition of GLONASS observations improves the kinematic PPP solution accuracy in comparison with that of GPS-only solution. However, the contribution of adding Galileo observations is not significant due to the limited number of Galileo satellites launched up to date. In addition, BSSD solution is found to be superior to that of traditional un-differenced model.