In this contribution, a novel un-differenced (UD) (PPP-RTK) concept, i.e. a synthesis of Precise Point Positioning and Network-based Real-Time Kinematic concept, is introduced. In the first step of our PPP-RTK approach, the UD GNSS observations from a regional reference network are processed based upon re-parameterised observation equations, corrections for satellite clocks, phase biases and (interpolated) atmospheric delays are calculated and provided to users. In the second step, these network-based corrections are used at the user site to restore the integer nature of his UD phase ambiguities, which makes rapid and high accuracy user positioning possible. The proposed PPP-RTK approach was tested using two GPS CORS networks with inter-station distances ranging from 60 to 100 km. The first test network is the northern China CORS network and the second is the Australian Perth CORS network. In the test of the first network, a dual-frequency PPP-RTK user receiver was used, while in the test of the second network, a low-cost, single-frequency PPP-RTK user receiver was used. The performance of fast ambiguity resolution and the high accuracy positioning of the PPP-RTK results are demonstrated.

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A novel un-differenced PPP-RTK concept

Improvement of Klobuchar model for GNSS single-frequency ionospheric delay corrections

A fusion of inertial navigation system and global positioning system (GPS) has been proposed to implement a robust navigation system for a transporter. In several cases, the GPS signals are not reliable to localize a transporter. In order to overcome this difficulty, a fault detection and isolation (FDI) algorithm has been used to detect and isolate the contaminated satellite signals. When the FDI algorithm is used alone, and the number of reliable satellite signals becomes less than four owing to GPS signal errors, the receiver cannot estimate the position precisely. In this paper, a modified FDI algorithm has been proposed and applied for the navigation of a transporter on a flat yard in order to avoid losing its positioning while it passes through a structured area. In the modified FDI algorithm, signal-to-noise ratio, measurement of quality indicator, and Doppler shift data are incorporated. In order to verify the effectiveness of the proposed algorithm, the navigation experiments have been conducted on a campus using a mobile robot to simulate the transporter on a shipbuilding yard and the results are demonstrated in this paper.

Robust Navigational System for a Transporter Using GPS/INS Fusion

The differential code bias (DCB) in global navigation satellite system (GNSS) satellites should be precisely determined using real ground GNSS data when designing certain applications, such as ionospheric remote sensing, precise positioning, and timing. Different from GPS with a full constellation, the number of BDS (BeiDou Satellite System developed by China) satellites currently in orbit is very limited, and the data from BDS are insufficient for estimating satellite DCB simultaneously with ionospheric total-electron-content modeling. In view of this, a calibration approach, namely, GPS-aided DCB determination (GPSADCB), is proposed to estimate the DCB of current BDS satellites with the aid of GPS data. The data from GPS are used to derive the ionospheric delay along the propagation path of the BDS signal. Before applying GPSADCB to estimate the DCB of current BDS satellites, the performance of this approach is first validated using two sets of GPS data in a simulated BDS case. Then, a continuous four-day data set gathered by two BDS receivers is used to determine the DCB of current BDS satellites based on GPSADCB. Validation results indicate that the difference of DCB estimates between GPSADCB and the Center for Orbit Determination in Europe is about 0.3 ns and the stability of DCB estimates in one month is about 0.2 ns. The DCB of different BDS satellites ranges from -10 ns to 13 ns, and the mean of day-to-day scatter for DCB estimates is below 0.2 ns over the period of data collection. It is demonstrated that the proposed approach can be used to estimate BDS satellite DCB at the initial stage with a few satellites in orbit.

Determination of the Differential Code Bias for Current BDS Satellites

With the development of real-time precise clock and orbit products, high-precision real-time ionospheric products have become one of the most critical resources for real-time single-frequency precise point positioning. Fortunately, there are several international GNSS service (IGS) analysis centers, e.g., UPC, WHU, and CAS, that are providing real-time global ionospheric maps (RT-GIMs). We evaluate these maps in detail over 2 years for different aspects. First, the RT-GIMs and 1-day predicted ionospheric products (C1PG GIM) differenced with the IGS final GIMs (IGSG GIM) are performed. Second, ionospheric vertical total electron content from Jason-2/3 data is set as a reference to evaluate the quality of RT-GIMs over oceanic regions. Third, 22 stations, which are not used in the generation of RT-GIMs, C1PG GIM, and IGSG GIM, are selected and the difference of slant total electron content (dSTEC) method is used to assess the accuracy and consistency of RT-GIMs over continental regions. Finally, the performance of RT-GIMs in the position domain is demonstrated based on SF-PPP solutions. The results show that the accuracy of the RT-GIMs is slightly worse than that of C1PG GIM and IGSG GIM. All RT-GIMs and the C1PG GIM have a smaller mean difference compared to the IGSG GIM by (−0.97, − 0.90, − 0.77, − 0.80) TECU for (UPC RT-GIM, CAS RT-GIM, WHU RT-GIM, C1PG GIM). Over oceanic regions, the RT-GIMs perform nearly the same as the C1PG GIM, but a slightly worse than IGSG GIM. The STDs are (3.96, 3.05, 3.25, 3.12, 2.54) TECU relative to Jason-2 and (4.94, 3.24, 3.38, 3.24, 2.65) TECU relative to Jason-3 for (UPC RT-GIM, CAS RT-GIM, WHU RT-GIM, C1PG GIM, IGSG GIM), respectively. Comparing with dSTEC values observed from the selected ground stations over continental regions, the RMS is (4.02, 2.16, 2.29, 1.86, 1.49) TECU for (UPC RT-GIM, CAS RT-GIM, WHU RT-GIM, C1PG GIM, IGSG GIM). In the position domain, the positioning accuracy of SF-PPP solution corrected by the RT-GIMs and C1PG GIM can reach decimeter level in the horizontal direction and meter level in the vertical direction, which is worse than obtained by IGSG GIM. Meanwhile, the positioning accuracy of SF-PPP corrected by RT-GIMs is almost the same as that obtained using C1PG GIM. For RT-GIMs, the accuracy of the CAS RT-GIM is slightly better than that of the other two RT-GIMs.

Performance evaluation of real-time global ionospheric maps provided by different IGS analysis centers

A method is proposed to improve the GPS broadcast ionospheric time-delay correction accuracy, using GPS observation data from the globally distributed international GNSS service (IGS) observation stations and the Crust Movement Observation Network of China (CMONOC). A new set of Klobuchar-Self coefficients can be estimated using the method. Primary results demonstrate that the refined Klobuchar-Self coefficients developed may provide better ionospheric delay corrections for single-frequency GPS receivers and improve standard single point positioning accuracies.

Refining the Klobuchar ionospheric coefficients based on GPS observations

The initial IGGtrop model proposed for Chinese BDS (BeiDou System) is not very suitable for BDS/GNSS research and application due to its large data volume while it shows a global mean accuracy of 4 cm. New versions of the global zenith tropospheric delay (ZTD) model IGGtrop are developed through further investigation on the spatial and temporal characteristics of global ZTD. From global GNSS ZTD observations and weather reanalysis data, new ZTD characteristics are found and discussed in this study including: small and inconsistent seasonal variation in ZTD between $$10^{\circ }\hbox {S}\, \mathrm{and}\, 10^{\circ }\hbox {N}$$
 and stable seasonal variation outside; weak zonal variation in ZTD at higher latitudes (north of $$60^{\circ }\hbox {N}$$
 and south of $$40^{\circ }\hbox {S}$$
 ) and at heights above 6 km, etc. Based on these analyses, new versions of IGGtrop, named $$\hbox {IGGtrop}\_{r}_{{i}}\, ({i}=1, 2, 3)$$
 , are established through employing corresponding strategies: using a simple algorithm for equatorial ZTD; generating an adaptive spatial grid with lower resolutions in regions where ZTD varies little; and creating a method for optimized storage of model parameters. Thus, the $$\hbox {IGGtrop}\_{r}_{{i}}\,({i}=1, 2, 3)$$
 models require much less parameters than the IGGtrop model, nearly 3.1–21.2 % of that for the IGGtrop model. The three new versions are validated  by five years of GNSS-derived ZTDs at 125 IGS sites, and it shows that: $$\hbox {IGGtrop}\_{r}_{1}$$
 demonstrates the highest ZTD correction performance, similar to IGGtrop; $$\hbox {IGGtrop}\_{r}_{3}$$
 requires the least model parameters; $$\hbox {IGGtrop}\_{r}_{2}$$
 is moderate in both zenith delay prediction performance and number of model parameters. For the $$\hbox {IGGtrop}\_{r}_{3}$$
 model, the biases at those IGS sites are between $$-6.4$$
 and 4.3 cm with a mean value of $$-0.8~$$
 cm and RMS errors are between 2.1 and 8.5 cm with a mean value of 4.0 cm. Different BDS and other GNSS users can choose a suitable model according to their application and research requirements.

New versions of the BDS/GNSS zenith tropospheric delay model IGGtrop

Tropospheric delays are one of the main sources of errors in the Global Navigation Satellite System (GNSS). They are usually corrected by using tropospheric delay models, which makes the accuracy of the models rather critical for accurate positioning. To provide references for suitable models to be chosen for GNSS users in China, we conduct herein a comprehensive study of the performances of the IGGtrop, EGNOS and UNB3m models in China. Firstly, we assess the models using 5 years’ Global Positioning System (GPS) derived Zenith Tropospheric Delay (ZTD) series from 25 stations of the Crustal Movement Observation Network of China (CMONOC). Then we study the effects of the models on satellite positioning by using various Precise Point Positioning (PPP) cases with different tropospheric delay resolutions, the observation data processed in PPP is from 21 base stations of CMONOC for a whole year of 2012. The results show that: (1) the Root Mean Square (RMS) of the IGGtrop model is about 4.4 cm, which improves the accuracy of ZTD estimations by about 24% for EGNOS and 19% for UNB3m; (2) The positioning error in the vertical component of the PPP solution obtained by using the IGGtrop model is about 15.0 cm, which is about 30% and 21% smaller than those of the EGNOS and UNB3m models, respectively. In summary, the IGGtrop model achieves the best performance among the three models in the Chinese region.

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Assessment of Three Tropospheric Delay Models (IGGtrop, EGNOS and UNB3m) Based on Precise Point Positioning in the Chinese Region

We focused on the researches of two models used for Jason-3 precise orbit determination (POD)—Jason-3 attitude modes and receiver phase center variation (PCV) model. A combined attitude mode for the Jason-3 satellite is designed based on experimental analysis used in some special cases, such as in the absence of quaternions or when inconvenient to use. We researched the linking of satellite attitude with antenna phase center. Specially, to verify the validity of the combined attitude, we analyzed the effects of different attitude modes on receiver phase center offset (PCO) estimation, PCO correction and POD. Meanwhile, the difference analysis of PCO correction based on attitude modes also contains the combined attitude modeling processes. The POD results showed that the orbital accuracies with the combined attitude are slightly more stable than those with attitude event file. By introducing receiver PCVs into POD, the mean residuals root-mean-square (RMS) is reduced by 1.9 mm and orbital 3D-RMS position difference is improved by 5.7 mm. The eight schemes were designed to integratedly verify the effectiveness of different attitude modes and receiver PCVs model. The results conclude that the accuracy using the combined attitude is higher than that of event file, which also prove the feasibility of the combined attitude in integrated POD and it can be as a revision of attitude event file. Using all mentioned attitude modes, the orbital accuracy by introducing PCVs can be improved by the millimeter level. The integrated effects of attitude modes and receiver PCVs on POD are almost consistent with the effects of a single variable. The optimal results of Jason-3 POD indicate that orbital mean radial RMS is close to 1 cm, and the 3D-RMS position difference is within 3 cm.

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Research on Attitude Models and Antenna Phase Center Correction for Jason-3 Satellite Orbit Determination.

Global navigation satellite system (GNSS) differential code bias (DCB) is a significant error source in ionosphere modeling that uses GNSS observation data. Given that the orbit altitudes of low earth orbit (LEO) satellites are above the F layer of ionosphere, ionized electrons come from the upper ionosphere or plasmasphere, so observations suffer from small signal delays. DCBs can be estimated using LEO data instead of that from ground stations. In most studies, LEO-based DCB estimation employs onboard data from either a single LEO or from two that are at the same orbit height. In our study, we applied four LEO satellites data from two different orbit heights to estimate GPS satellite DCBs, receiver DCBs and LEO-based vertical total electron content (VTEC) parameters simultaneously. Before DCB estimation, a data preprocessing strategy suitable for LEO onboard data was applied to obtain clear pseudorange data. We developed a processing method for the upper ionosphere using LEO onboard data from different orbit heights, by introducing LEO-based VTEC models in advance to remove its effects; two introduced VTEC models were derived from modeling results using paired data from the same orbital height, respectively. We draw some conclusions as follows. For the LEO satellites at different orbit heights, the more the number of LEO satellites involved, the more stable estimation results achieved. We also noted that the GPS satellite DCBs stability and accuracy with established LEO-based VTEC models, using multi-LEOs data from different orbit heights, were better than the achievable results using onboard data from the same orbital height or using single LEO satellite schemes. Compared with the estimation results of single LEO solutions, the monthly stabilities and accuracies for multi-LEOs solutions from different orbit heights are improved by 25–35% approximately. Among all the tested schemes, superior stability derived from simultaneous estimation using four LEO data at different orbit heights is 0.064 ns; the optimal accuracies for DCB estimation for different GPS satellites are the scheme GRACE-A and JASON-2 (two LEOs) of 0.146 ns, approximately, compared with Center of Orbit Determination of Europe products, respectively. The stability and accuracy of LEO-based DCB estimations were approximately similar to those achieved using ground solutions.

Yanju Chai

Papers

Refining the Klobuchar ionospheric coefficients based on GPS observations

New versions of the BDS/GNSS zenith tropospheric delay model IGGtrop

Assessment of Three Tropospheric Delay Models (IGGtrop, EGNOS and UNB3m) Based on Precise Point Positioning in the Chinese Region

Research on Attitude Models and Antenna Phase Center Correction for Jason-3 Satellite Orbit Determination.

Simultaneous estimation of GPS P1-P2 differential code biases using low earth orbit satellites data from two different orbit heights