Comparison Analysis on the Accuracy of Galileo PPP Using Different Frequency Combinations in Europe

The Galileo constellations are characterized by transmitting GNSS signals on multi-frequencies, which can benefit the robustness and accuracy of the solutions. However, the dual-frequency E1/E5a combinations are generally used for precise point positioning (PPP). In this paper, the performance of Galileo static and kinematic PPP using different dual- and multi-frequency combinations are assessed using observations from the European region. Overall, the accuracy of daily PPP achieved by the dual-frequency GPS, Galileo, and BDS is better than 5 mm in the horizontal direction and better than 10 mm in the vertical direction. Though the number of observed Galileo satellites is less than GPS, the horizontal accuracy can reach 1.6 mm/2.3 mm/5.7 mm on North/East/Up component, which is improved by 59.0% and 12.3% compared to the GPS in the north and up direction. Then, the accuracy of Galileo static PPP is analyzed using different dual- and multi-frequency combinations. Results indicate that the Galileo E1/E5b PPP can degrade the accuracy due to the inter-frequency clock biases between the E1/E5a and E1/E5b combinations. Best accuracy can be achieved for the triple- and four-frequency PPP, which is 4.8 mm in the up direction. The hourly accuracy for the static PPP can reach 5.6 mm/9.2 mm/12.6 mm in the north/east/up direction using the GPS/Galileo/GLONASS/BDS combinations. Finally, a positioning convergence ratio (PCR) indicator, which represents the accuracy of PPP over a period, is used to analyze the convergence time of kinematic PPP. Results indicated that the multi-frequency Galileo observations contribute minorly to the convergence of kinematic PPP. However, Galileo shows the best convergence performance for the single GNSS positioning, and the GPS/Galileo combined PPP achieved the best performance for the PPP using different GNSS combinations.

Performance Evaluation of Precise Point Positioning for BeiDou-3 B1c/B2a Signals in the Global Range

With the construction and development of the BeiDou navigation satellite system (BDS), the precise point positioning (PPP) performance of the BDS is worthy of research. In this study, observational data from 17 stations around the world across 20 days are used to comprehensively evaluate the PPP performance of BDS B1c/B2a signals. For greater understanding, the results are also compared with the Global Positioning System (GPS) and BDS PPP performance of different signals and system combinations. The evaluation found root mean square (RMS) values of the static PPP in the north (N), east (E), and upward (U) components, based on the B1c/B2a frequency of BDS-3, to be 6.9 mm, 4.7 mm, and 26.6 mm, respectively. Similar to the static positioning, the RMS values of kinematic PPP in the three directions of N, E, and U are 2.6 cm, 6.0 cm, and 8.5 cm, respectively. Besides this, the static PPP of BDS-3 (B1cB2a) and BDS-2 + BDS-3 (B1IB3I) have obvious system bias. Compared with static PPP, kinematic PPP is more sensitive to the number of satellites, and the coordinate accuracy in three dimensions can be increased by 27% with the combination of GPS (L1L2) and BDS. Compared with BDS-2+BDS-3 (B1IB3I), the convergence time of BDS-3 (B1CB2a) performs better in both static and kinematic modes. The antenna model does not show a significant difference in terms of the effect of the convergence speed, though the number of satellites observed has a certain influence on the convergence time.

Assessment of GPS/Galileo/BDS Precise Point Positioning with Ambiguity Resolution Using Products from Different Analysis Centers

Suffering from hardware phase biases originating from satellites and the receiver, precise point positioning (PPP) requires a long convergence time to reach centimeter coordinate accuracy, which is a major drawback of this technique and limits its application in time-critical applications. Ambiguity resolution (AR) is the key to a fast convergence time and a high-precision solution for PPP technology and PPP AR products are critical to implement PPP AR. Nowadays, various institutions provide PPP AR products in different forms with different strategies, which allow to enable PPP AR for Global Positioning System (GPS) and Galileo or BeiDou Navigation System (BDS). To give a full evaluation of PPP AR performance with various products, this work comprehensively investigates the positioning performance of GPS-only and multi-GNSS (Global Navigation Satellite System) combination PPP AR with the precise products from CNES, SGG, CODE, and PRIDE Lab using our in-house software. The positioning performance in terms of positioning accuracy, convergence time and fixing rate (FR) as well as time to first fix (TTFF), was assessed by static and kinematic PPP AR models. For GPS-only, combined GPS and Galileo PPP AR with different products, the positioning performances were all comparable with each other. Concretely, the static positioning errors can be reduced by 21.0% (to 0.46 cm), 52.5% (to 0.45 cm), 10.0% (to 1.33 cm) and 21.7% (to 0.33 cm), 47.4% (to 0.34 cm), 9.5% (to 1.16 cm) for GPS-only and GE combination in north, east, up component, respectively, while the reductions are 20.8% (to 1.13 cm), 42.9% (to 1.15 cm), 19.9% (to 3.4 cm) and 20.4% (to 0.72 cm), 44.1% (to 0.66 cm), 10.1% (to 2.44 cm) for kinematic PPP AR. Overall, the positioning performance with CODE products was superior to the others. Furthermore, multi-GNSS observations had significant improvements in PPP performance with float solutions and the TTFF as well as the FR of GPS PPP AR could be improved by adding observations from other GNSS. Additionally, we have released the source code for multi-GNSS PPP AR, anyone can freely access the code and example data from GitHub.

Ionosphere-weighted undifferenced and uncombined PPP-RTK: theoretical models and experimental results

Precise ionospheric information, as like precise satellite orbits, clocks, and code/phase biases, is a critical factor for achieving fast integer ambiguity resolution in precise point positioning (PPP-AR). This study develops an ionosphere-weighted (IW) undifferenced and uncombined PPP real-time kinematic (PPP-RTK) network model using code and phase observations. We introduce between-station single-differenced ionospheric delay pseudo-observations to take advantage of the similar characteristics of ionospheric delays between two receivers tracking the same satellite. The estimable ionospheric parameters are commonly affected by the differential code bias referring to a particular receiver assigned as pivot, which facilitates the ionospheric interpolation at the user side. Then, the kinematic positioning performance of the IW PPP-RTK user model is analyzed and compared with those of PPP-AR without ionospheric corrections, RTK, and IW-RTK models during low and high solar activity days. The results show that for the PPP-RTK model, the positioning errors converge to thresholds of 2 cm for the horizontal components and 5 cm for the vertical component within 20 epochs, and the positioning errors become stable after an initialization of 20 epochs with root-mean-squared (RMS) values of approximately 0.47, 0.58 and 1.66 cm for the east, north and up components, respectively, which are superior to those of the other three models. Owing to the high ionospheric disturbance influence, the RMS values of the east and up components increase by approximately double and the mean time-to-first-fix increases by 61.5% for the PPP-RTK case.

Initial Assessment of BDS PPP-B2b Service: Precision of Orbit and Clock Corrections, and PPP Performance

On 31 July 2020, the Beidou global navigation satellite system (BDS-3) was officially announced as being commissioned. In addition to offering global positioning, navigation, and timing (PNT) services, BDS-3 also provides precise point positioning (PPP) augmentation services. The satellite orbit correction, clock correction and code bias correction of BDS-3 and other global navigation satellite systems (GNSS) are broadcast by the BDS-3 geostationary earth orbit (GEO) satellites through the PPP-B2b signal. The PPP-B2b service is available for users in China and the surrounding area. In this study, an initial assessment of the PPP-B2b service is presented, with collected 3-day PPP-B2b messages. Based on broadcast ephemeris and PPP-B2b messages, the precise satellite orbits and clock offsets can be recovered. This precision is evaluated with the precise ephemeris from the GeoForschungsZentrum Potsdam (GFZ) analysis center as references. The results indicate that the accuracy of BDS-3 satellite orbits in the direction of radial, along-track, and cross-track is 0.138, 0.131, and 0.145 m, respectively, and for GPS a corresponding accuracy of 0.104, 0.160, and 0.134 m, respectively, could be obtained. The precision of clock offsets can reach a level of several centimeters for both GPS and BDS-3. Both the performance of static PPP and kinematic PPP are evaluated using the observations from four international GNSS monitoring assessment service (iGMAS) stations. Regarding static PPP, the average convergence time is 17.7 minutes to achieve a horizontal positioning accuracy of better than 0.3 m, and a vertical positioning accuracy of better than 0.6 m. The average positioning accuracy in the direction of east, north, and up-directions are 2.4, 1.6, and 2.3 cm. As to kinematic PPP, the average RMS values of positioning errors in the direction of east, north, and up are 8.1 cm, 3.6 cm, and 8.0 cm after full convergence.

Performance Evaluation of Triple-Frequency GPS/Galileo Techniques for Precise Static and Kinematic Applications

The objective of this research was to develop new precise point positioning (PPP) processing models using triple-frequency GPS/Galileo observations. Different triple-frequency PPP models were developed including undifferenced, between-satellite single-difference (BSSD) and semi-decoupled PPP models. Additionally, a dual-frequency ionosphere-free undifferenced PPP model was developed. The performance of our developed PPP models was evaluated for both static and kinematic applications. To validate the proposed PPP models for static applications, triple-frequency GPS/Galileo observations spanning three successive days from eight globally distributed reference stations were acquired. Then, the observations were processed using the four static PPP solutions. It is found that the 3D positioning accuracy of the triple-frequency semi-decoupled, BSSD and undifferenced PPP models is enhanced after 10 min by about 50, 41 and 29%, respectively, compared with the dual-frequency undifferenced PPP model. After 20 min of processing, improvements in the 3D positioning accuracy by 40, 31 and 21% are obtained for the triple-frequency semi-decoupled, BSSD and undifferenced PPP models, respectively, with respect to the dual-frequency PPP model. The 3D positioning accuracy is also improved after 60 min, compared with the dual-frequency solution, by 40, 40 and 35% for the triple-frequency semi-decoupled, BSSD and undifferenced PPP solutions, respectively. For kinematic application validation, a vehicle trajectory was carried out. The collected triple-frequency GPS/Galileo observations were processed using the four kinematic PPP solutions. It is shown that the triple-frequency semi-decupled, BSSD and undifferenced PPP solutions enhance the 3D positioning accuracy by 31, 23 and 10%, respectively, in comparison with the dual-frequency undifferenced PPP solutions.

Combining multi-GNSS phase bias products for improved undifferenced ambiguity resolution

<p>The rapid development of multi-GNSS constellations, e.g., Galileo and BeiDou, is catalyzing innovations in high-precision applications. Precise point positioning ambiguity resolution (PPP-AR) has been essential to achieving the highest positioning precision using multi-GNSS data in wide areas. In recent years, several International GNSS Service analysis centers (IGS ACs such as CNES, CODE, WHU) have been providing phase bias products to enable PPP-AR, but whether these AC-specific multi-GNSS (e.g., GPS/Galileo/BeiDou-2/3) products are compatible with each other and whether they can be reconciled for an IGS combination product are pending. In this study, we combined phase bias products from four organizations for GPS/Galileo/BeiDou-2/3 in 2020. All phase bias products are first converted to observable-specific representation and then reconciled with satellite clocks before the combination; their capability of recovering integer undifferenced ambiguities has been always kept after properly addressing inter-system biases and satellite attitude discrepancies. It is found that the RMS of clock alignment residuals are around 6.8, 7.1, 14.9 and 14.6 ps for GPS, Galileo BeiDou-2 and BeiDou-3, respectively. BeiDou products perform worse due largely to sparse tracking networks and deficient orbit models. In a kinematic PPP experiment with 151 global MGEX (Multi-GNSS Experiment) stations, the combined phase bias products provide better or at least equivalent positioning results as opposed to AC specific products. Compared with ambiguity-float solutions, ambiguity-fixed PPP solutions can improve the positioning precision by 29-50% in the east component. With combined phase bias products, the positioning precision of GPS/Galileo/BDS-2/3 PPP-AR solutions can achieve 0.62, 0.64 and 1.90 cm in the east, north and up components, respectively, in contrast to 0.87, 0.88 and 2.60 cm for GPS only PPP-AR solutions.</p>

An Investigation of Precise Orbit and Clock Products for BDS-3 from Different Analysis Centers

A quality evaluation of precise products for BDS-3 constellations is presented for the first time in this contribution. Then, the tropospheric delay retrieval and positioning performance of BDS-3 precise point positioning (PPP) solutions using the precise products (gbm, wum, iac, sha, cnt) with observations from 24 stations from DOY 280 to 317 in 2020 was comprehensively investigated. The orbit comparisons present consistencies of 0.09–0.22 m for the C19–C37 satellites and of 0.5–1.2 m for the C38–C46 satellites among the final products. The standard deviation (STD) values of the clock differences of iac showed the best agreement with those of gbm, followed by wum, sha. The clock differences performance of cnt was the worst. For BDS-3 PPP solutions with five Analysis centers (ACs) products, the median convergence times of static PPP mode incorporating the gbm, wum, iac, sha, and cnt products were 31.0, 33.5, 34.5, 37.8, and 72.0 min, respectively; the median convergence times of kinematic PPP model incorporating the same products were 40.5, 41.0, 50.5, 55.0, and 94.0 min, respectively. The positioning accuracies in the static and kinematic modes were approximately 1–4 cm, 2–6 cm in the horizontal and vertical components, respectively. With the final products in kinematic mode, the performance of PPP with real-time products (cnt) is poorer than all PPP with final products. The median of ZTD accuracies of the five products gbm, wum, iac, sha, and cnt were 7.84, 7.58, 7.04, 7.19, and 10.1 mm, respectively, and the accuracy differences were very small among five AC products (gbm, wum, iac, sha).