The core performance elements of global navigation satellite system include availability, continuity, integrity and accuracy, all of which are particularly important for the developing BeiDou global navigation satellite system (BDS-3). This paper describes the basic performance of BDS-3 and suggests some methods to improve the positioning, navigation and timing (PNT) service. The precision of the BDS-3 post-processing orbit can reach centimeter level, the average satellite clock offset uncertainty of 18 medium circular orbit satellites is 1.55 ns and the average signal-in-space ranging error is approximately 0.474 m. The future possible improvements for the BeiDou navigation system are also discussed. It is suggested to increase the orbital inclination of the inclined geostationary orbit (IGSO) satellites to improve the PNT service in the Arctic region. The IGSO satellite can perform part of the geostationary orbit (GEO) satellite’s functions to solve the southern occlusion problem of the GEO satellite service in the northern hemisphere (namely the “south wall effect”). The space-borne inertial navigation system could be used to realize continuous orbit determination during satellite maneuver. In addition, high-accuracy space-borne hydrogen clock or cesium clock can be used to maintain the time system in the autonomous navigation mode, and stability of spatial datum. Furthermore, the ionospheric delay correction model of BDS-3 for all signals should be unified to avoid user confusion and improve positioning accuracy. Finally, to overcome the vulnerability of satellite navigation system, the comprehensive and resilient PNT infrastructures are proposed for the future seamless PNT services.

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Basic performance and future developments of BeiDou global navigation satellite system

In order to better understand the differential code biases (DCBs) of global navigation satellite system, the IGGDCB method is extended to estimate the intra- and inter-frequency biases of the global positioning system (GPS), GLONASS, BeiDou navigation satellite system (BDS), and Galileo based on observations collected by the multi-GNSS experiment (MGEX) of the international GNSS service (IGS). In the approach of IGGDCB, the local ionospheric total electronic content is modeled with generalized triangular series (GTS) function rather than using a global ionosphere model or a priori ionospheric information. The DCB estimated by the IGGDCB method is compared with the DCB products from the Center for Orbit Determination in Europe (CODE) and German Aerospace Center (DLR), as well as the broadcast timing group delay (TGD) parameters over a 2-year span (2013 and 2014). The results indicate that GPS and GLONASS intra-frequency biases obtained in this work show the same precision levels as those estimated by DLR (about 0.1 and 0.2–0.4 ns for the two constellations, respectively, with respect to the products of CODE). The precision levels of IGGDCB-based inter-frequency biases estimated over the 24-month period are about 0.29 ns for GPS, 0.56 ns for GLONASS, 0.36 ns for BDS, and 0.24 ns for Galileo, respectively. Here, the accuracies of GPS and GLONASS biases are assessed relative to the products of CODE, while those of BDS and Galileo are compared with the estimates of DLR. In addition, the monthly stability indices of IGGDCB-based DCBs are 0.11 (GPS), 0.18 (GLONASS), 0.17 (BDS), and 0.14 (Galileo) ns for the individual constellation.

Determination of differential code biases with multi-GNSS observations

Measurements of Global Navigation Satellite System
(GNSS) receivers are affected
by systematic offsets re-
lated to group and phase delays of the signal generation
and processing chain. The resulting code and phase biases
depend on the transmission frequency and the employed
signal modulation. Within this study differential code
biases (DCBs) of legacy an
d modernized GNSS signals
are derived from pseudodrange observations of a global
multi-GNSS receiver network.
Global ionosphere maps
(GIMs) are employed for th
e correction of ionospheric
path delays. Satellite and receiver-specific contributions
are separated based on the a
ssumption of additive biases
and a zero-mean condition for the satellite biases within a
constellation. Based on 6 months of data collected within
the Multi-GNSS Experiment (M
GEX) of the International
GNSS Service (IGS), DCBs for the publicly available
signals of GPS, Galileo and BeiDou have been deter-
mined. The quality of the resulting DCB estimates is as-
sessed and compared against group delay parameters
transmitted by the GNSS providers as part of the broad-
cast ephemeris data.

Differential Code Bias Estimation using Multi-GNSS Observations and Global Ionosphere Maps

This contribution summarizes the strategy used by Wuhan University (WHU) to determine precise orbit and clock products for Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS). In particular, the satellite attitude, phase center corrections, solar radiation pressure model developed and used for BDS satellites are addressed. In addition, this contribution analyzes the orbit and clock quality of the quad-constellation products from MGEX Analysis Centers (ACs) for a common time period of 1 year (2014). With IGS final GPS and GLONASS products as the reference, Multi-GNSS products of WHU (indicated by WUM) show the best agreement among these products from all MGEX ACs in both accuracy and stability. 3D Day Boundary Discontinuities (DBDs) range from 8 to 27 cm for Galileo-IOV satellites among all ACs’ products, whereas WUM ones are the largest (about 26.2 cm). Among three types of BDS satellites, MEOs show the smallest DBDs from 10 to 27 cm, whereas the DBDs for all ACs products are at decimeter to meter level for GEOs and one to three decimeter for IGSOs, respectively. As to the satellite laser ranging (SLR) validation for Galileo-IOV satellites, the accuracy evaluated by SLR residuals is at the one decimeter level with the well-known systematic bias of about $$-5$$
  cm for all ACs. For BDS satellites, the accuracy could reach decimeter level, one decimeter level, and centimeter level for GEOs, IGSOs, and MEOs, respectively. However, there is a noticeable bias in GEO SLR residuals. In addition, systematic errors dependent on orbit angle related to mismodeled solar radiation pressure (SRP) are present for BDS GEOs and IGSOs. The results of Multi-GNSS combined kinematic PPP demonstrate that the best accuracy of position and fastest convergence speed have been achieved using WUM products, particularly in the Up direction. Furthermore, the accuracy of static BDS only PPP degrades when the BDS IGSO and MEO satellites switches to orbit-normal orientation, particularly for COM products, whereas the WUM show the slightest degradation.

Precise orbit determination for quad-constellation satellites at Wuhan University: strategy, result validation, and comparison

The dual frequency radio signals of the Global Positioning System (GPS) allow measurements of the total number of electrons, called total electron content (TEC), along a ray path from GPS satellite to receiver. We have developed a new technique to construct two-dimensional maps of absolute TEC over Japan by using GPS data from more than 1000 GPS receivers. A least squares fitting procedure is used to remove instrumental biases inherent in the GPS satellite and receiver. Two-dimensional maps of absolute vertical TEC are derived with time resolution of 30 seconds and spatial resolution of 0.15° × 0.15° in latitude and longitude. Our method is validated in two ways. First, TECs along ray paths from the GPS satellites are simulated using a model for electron contents based on the IRI-95 model. It is found that TEC from our method is underestimated by less than 3 TECU. Then, estimated vertical GPS TEC is compared with ionospheric TEC that is calculated from simultaneous electron density profile obtained with the MU radar. Diurnal and day-to-day variation of the GPS TEC follows the TEC behavior derived from MU radar observation but the GPS TEC is 2 TECU larger than the MU radar TEC on average. This difference can be attributed to the plasmaspheric electron content along the GPS ray path. This method is also applied to GPS data during a magnetic storm of September 25, 1998. An intense TEC enhancement, probably caused by a northward expansion of the equatorial anomaly, was observed in the southern part of Japan in the evening during the main phase of the storm.

A new technique for mapping of total electron content using GPS network in Japan

The differential code bias (DCB) in satellites of the Global Navigation Satellite Systems (GNSS) should be precisely corrected when designing certain applications, such as ionospheric remote sensing, precise point positioning, and time transfer. In the case of COMPASS system, the data used for estimating DCB are currently only available from a very limited number of global monitoring stations. However, the current GPS/GLONASS satellite DCB estimation methods generally require a large amount of geographically well-dis- tributed data for modeling the global ionospheric vertical total electron content (TEC) and are not particularly suitable for current COMPASS use. Moreover, some satellites with unstable DCB (i.e., relatively large scatter) may affect other satellite DCB estimates through the zero-mean reference that is currently imposed on all satellites. In order to overcome the inadequacy of data sources and to reduce the impact of unsta- ble DCB, a new approach, designated IGGDCB, is developed for COMPASS satellite DCB determination. IGG stands for the Institute of Geodesy and Geophysics, which is located in Wuhan, China. In IGGDCB, the ionospheric vertical TEC of each individual station is independently modeled by a gener- alized triangular series function, and the satellite DCB refer- ence is selected using an iterative DCB elimination process. By comparing GPS satellite DCB estimates calculated by the IGGDCB approach based on only a handful (e.g., seven) of tracking stations against that calculated by the currently existing methods based on hundreds of tracking stations, we are able to demonstrate that the accuracies of the IGGDCB- based DCB estimates perform at the level of about 0.13 and 0.10 ns during periods of high (2001) and low (2009) solar activity, respectively. The iterative method for DCB reference selection is verified by statistical tests that take into account the day-to-day scatter and the duration that the satellites have spent in orbit. The results show that the impact of satellites with unstable DCB can be considerably reduced using the IGGDCB method. It is also confirmed that IGGDCB is not only specifically valid for COMPASS but also for all other GNSS.

http://973.spaceweather.ac.cn/document/4/paper/8.pdf

Two-step method for the determination of the differential code biases of COMPASS satellites

To take maximum advantage of the increasing Global Navigation Satellite Systems (GNSS) data to improve the accuracy and resolution of global ionospheric TEC map (GIM), an approach, named Spherical Harmonic plus generalized Trigonometric Series functions (SHPTS), is proposed by integrating the spherical harmonic and the generalized trigonometric series functions on global and local scales, respectively. The SHPTS-based GIM from January 1st, 2001 to December 31st, 2011 (about one solar cycle) is validated by the ionospheric TEC from raw global GPS data, the GIM released by the current Ionospheric Associate Analysis Center (IAAC), the TOPEX/Poseidon satellite and the DORIS. The present results show that the SHPTS-based GIM over the area where no real data are available has the same accuracy level (approximately 2–6 TECu) to that released by the current IAAC. However, the ionospheric TEC in the SHPTS-based GIM over the area covered by real data is more accurate (approximately 1.5 TECu) than that of the GIM (approximately 3.0 TECu) released by the current IAAC. The external accuracy of the SHPTS-based GIM validated by the TOPEX/Poseidon and DORIS is approximately 2.5–5.5 and 1.5–4.5 TECu, respectively. In particular, the SHPTS-based GIM is the best or almost the best ranked, along with those of JPL and UPC, when they are compared with TOPEX/Poseidon measurements, and the best (in addition to UPC) when they are validated with DORIS data. With the increase in the number of GNSS satellites and contributing stations, the performance of the SHPTS-based GIM can be further improved. The SHPTS-based GIM routinely calculated using global GPS, GLONASS and BDS data will be found at the website http://www.gipp.org.cn.

SHPTS: towards a new method for generating precise global ionospheric TEC map based on spherical harmonic and generalized trigonometric series functions

A global ionospheric delay correction model (BeiDou global broadcast ionospheric delay correction model [BDGIM]) is proposed for the single-frequency ionospheric delay correction of the third phase of the BeiDou navigation satellite system (BDS-3). An initial performance assessment of BDGIM was conducted with data collected in China and worldwide. For regional analysis, the broadcast coefficients of BDGIM were provided by the operational control system of BDS, while for global analysis, the coefficients of BDGIM were estimated using global positioning system (GPS)-derived total electron contents (TECs) obtained from 19 globally distributed monitoring sites. In China, the performance of BDGIM was evaluated by GPS-TEC derived from 40 test sites during day of year (DOY) 060 to 181, 2015. The ionospheric errors can be mitigated by 80.9% for BDGIM. On the global scale, the ionospheric TECs derived from 50 sites of the International Global Navigation Satellite System (GNSS) Services (IGS) were used as references during DOY 220 to 365, 2014, and BDGIM can correct for 77.6% of the ionospheric delay.

The BeiDou global broadcast ionospheric delay correction model (BDGIM) and its preliminary performance evaluation results

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

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.

Xingliang Huo

Papers

Two-step method for the determination of the differential code biases of COMPASS satellites

SHPTS: towards a new method for generating precise global ionospheric TEC map based on spherical harmonic and generalized trigonometric series functions

The BeiDou global broadcast ionospheric delay correction model (BDGIM) and its preliminary performance evaluation results

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

Refining the Klobuchar ionospheric coefficients based on GPS observations