Qile Zhao

Precise orbit determination of Beidou Satellites with precise positioning

Chinese Beidou satellite navigation system constellation currently consists of eight Beidou satellites and can provide preliminary service of navigation and positioning in the Asia-Pacific Region. Based on the self-developed software Position And Navigation Data Analysis(PANDA) and Beidou Experimental Tracking Stations (BETS), which are built by Wuhan University, the study of Beidou precise orbit determination, static precise point positioning (PPP), and high precision relative positioning, and differential positioning are carried out comprehensively. Results show that the radial precision of the Beidou satellite orbit determination is better than 10 centimeters. The RMS of static PPP can reach several centimeters to even millimeters for baseline relative positioning. The precision of kinematic pseudo-range differential positioning and RTK mode positioning are 2–4 m and 5–10 cm respectively, which are close to the level of GPS precise positioning. Research in this paper verifies that, with support of ground reference station network, Beidou satellite navigation system can provide precise positioning from several decimeters to meters in the wide area and several centimeters in the regional area. These promising results would be helpful for the implementation and applications of Beidou satellite navigation system.

Precise Point Positioning with the BeiDou Navigation Satellite System

By the end of 2012, China had launched 16 BeiDou-2 navigation satellites that include six GEOs, five IGSOs and five MEOs. This has provided initial navigation and precise pointing services ability in the Asia-Pacific regions. In order to assess the navigation and positioning performance of the BeiDou-2 system, Wuhan University has built up a network of BeiDou Experimental Tracking Stations (BETS) around the World. The Position and Navigation Data Analyst (PANDA) software was modified to determine the orbits of BeiDou satellites and provide precise orbit and satellite clock bias products from the BeiDou satellite system for user applications. This article uses the BeiDou/GPS observations of the BeiDou Experimental Tracking Stations to realize the BeiDou and BeiDou/GPS static and kinematic precise point positioning (PPP). The result indicates that the precision of BeiDou static and kinematic PPP reaches centimeter level. The precision of BeiDou/GPS kinematic PPP solutions is improved significantly compared to that of BeiDou-only or GPS-only kinematic PPP solutions. The PPP convergence time also decreases with the use of combined BeiDou/GPS systems.

Recent Development of PANDA Software in GNSS Data Processing

Under the financial support of several Chinese national scientific projects, PANDA (Positioning And Navigation Data Analyst) software developed originally by Wuhan University has achieved the advanced level in the world. PANDA is currently recognized as a main research tool in several famous institutes in the GNSS community. In this paper, the recent development of PANDA software is introduced, including the COSMIC orbit determination in low Earth orbits, the real-time GPS satellite orbit and clock determination and precise point positioning with ambiguity resolution. It is concluded that PANDA is of great improvement in the past five years, and more advancement will be made in its pragmatic aspect especially in engineering applications.

Real-time detection and repair of cycle slips in triple-frequency GNSS measurements

Cycle slip detection and repair are prerequisites to the use of the global navigation satellite system (GNSS) carrier phases for precise positioning. Modern GNSS techniques introduce triple- or multi-frequency signals that are beneficial for cycle slip detection and repair. We present a new real-time cycle slip detection and repair method based on the independent linear combinations of undifferenced triple-frequency GNSS observations. The proposed method forms three types of linear combinations based on the original observations. These combinations are called extra-wide lane (EWL), wide lane (WL), and narrow lane (NL). Cycle slips on the combinations are determined sequentially in three cascaded steps. The first step employs the geometry-free and ionosphere-free Hatch–Melbourne–Wübbena combination to determine and repair the EWL cycle slips. The second step subtracts the cycle-slip-repaired EWL combination from the WL combination to eliminate the geometry part of the WL combination. This subtraction results in a new function that contains the WL ambiguity and residual ionospheric delay. This function is differenced at two consecutive epochs to determine the WL cycle slips. The residual ionospheric delay difference is ignored because of its small magnitude relative to WL wavelength. The third step determines the NL cycle slips in the same manner as in the second step. The difference is that the cycle-slip-repaired EWL combination is replaced with the more accurate cycle-slip-repaired WL combination. Moreover, the residual ionospheric delay difference is compensated by the ionospheric delay rate derived from the original carrier phase observations. When the EWL, WL, and NL cycle slips are determined, cycle slips on the original carrier phase observations can be uniquely identified. The proposed approach has been tested on 30-s triple-frequency BeiDou navigation satellite system data under different levels of ionospheric variations, and on 30-s triple-frequency global positioning system and quasi-zenith satellite system data. Results indicate that the approach can effectively detect and correct cycle slips even for one cycle under low sampling rate or active ionospheric conditions on each frequency in real time.

Three-carrier ambiguity resolution using the modified TCAR method

Abstract Multi-frequency technique is expected to be widely adopted with the new generations of global navigation satellite system, which is anticipated to benefit ambiguity resolution (AR). Three-carrier AR (TCAR) is a classical AR method based on triple-frequency observations, which is efficient for AR of short baseline. However, this method ignores the residual ionospheric delay, which degrades the reliability in active ionosphere situations and reduces the success of AR for medium and long baselines. We investigate the classical TCAR method and identify the major deficiency that hampers its application, especially to medium and long baselines. To improve this algorithm, the second and third steps of the classical TCAR are modified accordingly. In step 2, the ambiguity-resolved extra-wide-lane (EWL) combination and three pseudorange observations are employed to eliminate or reduce the residual ionospheric delay, in addition to the geometry term. In step 3, besides the EWL combination and pseudoranges, the ambiguity-resolved wide-lane (WL) combination is used to completely eliminate the ionosphere and geometry terms. The combination coefficients of these pseudoranges and combinations are optimized to minimize the noise of the ambiguity estimates. In order to assess the performances, real triple-frequency observations of BeiDou navigation system of baselines with different lengths are processed by the two methods. Results show that, the classical TCAR method is very sensitive to ionospheric delay and limited to short baseline application, while the modified TCAR method is free from ionospheric delay and can be applied to AR of median and long baselines. For WL AR, the modified TCAR method shows a comparable performance with the classical TCAR method, and a better performance can be expected when the baseline becomes longer, e.g., from 100s to 1,000s kilometers. For narrow-lane AR, the modified TCAR method performs much better than the classical TCAR method for median and long baselines.

Analysis of BeiDou Satellite Measurements with Code Multipath and Geometry-Free Ionosphere-Free Combinations.

Using GNSS observable from some stations in the Asia-Pacific area, the carrier-to-noise ratio (CNR) and multipath combinations of BeiDou Navigation Satellite System (BDS), as well as their variations with time and/or elevation were investigated and compared with those of GPS and Galileo. Provided the same elevation, the CNR of B1 observables is the lowest among the three BDS frequencies, while B3 is the highest. The code multipath combinations of BDS inclined geosynchronous orbit (IGSO) and medium Earth orbit (MEO) satellites are remarkably correlated with elevation, and the systematic “V” shape trends could be eliminated through between-station-differencing or modeling correction. Daily periodicity was found in the geometry-free ionosphere-free (GFIF) combinations of both BDS geostationary Earth orbit (GEO) and IGSO satellites. The variation range of carrier phase GFIF combinations of GEO satellites is −2.0 to 2.0 cm. The periodicity of carrier phase GFIF combination could be significantly mitigated through between-station differencing. Carrier phase GFIF combinations of BDS GEO and IGSO satellites might also contain delays related to satellites. Cross-correlation suggests that the GFIF combinations’ time series of some GEO satellites might vary according to their relative geometries with the sun.

Precise orbit determination for COMPASS IGSO satellites during yaw maneuvers

Contrary to GPS and GLONASS, the COMPASS IGSO satellites use two different attitude modes depending on the Sun’s elevation angle with respect to the orbital plane, namely yaw-steering regime and yaw-fixed regime. However, transition of attitude modes will cause the significant degradation of the orbit accuracy. We present two approaches to improve the orbit accuracy based on Extended CODE Orbit Model (ECOM) and Adjustable box-wing model. The differences of overlapping orbits and SLR validation indicate that the orbit accuracy could increase to better than 30 cm from several meters level during yaw maneuvers. Furthermore, we investigate the possible reasons of orbit accuracy degradation with telemetry data, and the reasons are likely the variations of non-gravitational forces in along- and cross-track directions caused by attitude mode switches, temperature variations of −X bus and some devices on −X surface which result in non-systematic geometry of −X and +X bus.

Real‐time capture of seismic waves using high‐rate multi‐GNSS observations: Application to the 2015 Mw 7.8 Nepal earthquake

The variometric approach is investigated to measure real-time seismic waves induced by the 2015 Mw 7.8 Nepal earthquake with high-rate multi-GNSS observations, especially with the contribution of newly available BDS. The velocity estimation using GPS + BDS shows an additional improvement of around 20% with respect to GPS-only solutions. We also reconstruct displacements by integrating GNSS-derived velocities after a linear trend removal (IGV). The displacement waveforms with accuracy of better than 5 cm are derived when postprocessed GPS precise point positioning results are used as ground truth, even if those stations have strong ground motions and static offsets of up to 1–2 m. GNSS-derived velocity and displacement waveforms with the variometric approach are in good agreement with results from strong motion data. We therefore conclude that it is feasible to capture real-time seismic waves with multi-GNSS observations using the IGV-enhanced variometric approach, which has critical implications for earthquake early warning, tsunami forecasting, and rapid hazard assessment.

Enhancing Precise Orbit Determination of Compass with Inter-Satellite Observations

Abstract This paper puts forward a new concept of Inter-Satellite Observations (ISOs). ISOs can be classified into inside-layer (ILOs) and cross-layer observations (CLOs). ILOs denote inter-satellite two-way ranging observations (TWROs). CLOs denote the observations between satellites of different orbit heights, such as MEO-GEO and MEO-IGSO. GEO and IGSO observations can be obtained through MEO-borne receivers as designed in low-orbit satellites. Using integrated adjustment of satellite-ground observations (SGOs) and ISOs, satellite geometry can be strengthened and orbit accuracy is significantly improved. Upon the above thought, orbit determination simulations are performed in three scenarios (using SGOs, using SGOs and CLOs, and using SGOs and TWROs) according to the satellite constellation of the Chinese COMPASS satellite navigation system. The orbit results are assessed by position dilution of precision (PDOP), three-dimensional RMS of the estimated orbits and the simulated reference orbits. The results show that, using only one-day SGOs from 7 regional stations in China, three-dimensional RMS of GEOs, IGSOs and MEOs are respectively reduced from 6.7 m, 1.3 m and 7.9 m to 0.7 m, 0.8 m and 1.3m when CLOs with beam angle of 42 degrees are added; Orbit accuracies are better than 20cm when TWROs with beam angle of 45 degrees and 30cm amplitude period term systematic error are added.

Quality assessment of onboard GPS receiver and its combination with DORIS and SLR for Haiyang 2A precise orbit determination

The GPS, DORIS, and SLR instruments are installed on Haiyang 2A (HY2A) altimetry satellite for Precise Orbit Determination (POD). Among these instruments, the codeless GPS receiver is the state-of-art Chinese indigenous onboard receiver, and it is the first one successfully used for Low Earth Orbit (LEO) satellite. Firstly, the contribution assesses the performance of the receiver through an analysis of data integrity, numbers of all tracked and valid measurements as well as multipath errors. The receiver generally shows good performance and quality despite a few flaws. For example, L2 observations are often missing in low elevations, particularly during the ascent of GPS satellites, and the multipath errors of P1 show a slightly abnormal pattern. Secondly, the PCO (Phase Center Offset) and PCV (Phase Center Variation) of the antenna of the GPS receiver are determined in this contribution. A significant leap for Z-component of PCO up to −1.2 cm has been found on 10 October 2011. Thirdly, the obtained PCO and PCV maps are used for GPS only POD solutions. The post-fit residuals of ionosphere-free phase combinations reduce almost 50%, and the radial orbit differences with respect to CNES (Centre National d’Etudes Spatiales) Precise Orbit Ephemeris (POEs) improve about 13.9%. The orbits are validated using the SLR data, and the RMS of SLR Observed minus Computed (O-C) residuals reduces from 17.5 to 15.9 mm. These improvements are with respect to the orbits determined without PCO and PCV. Fourthly, six types of solutions are determined for HY2A satellite using different combinations of GPS, DORIS, and SLR data. Statistics of SLR O-C residuals and cross-comparison of orbits obtained in the contribution and the CNES POEs indicate that the radial accuracy of these orbits is at the 1.0 cm level for HY2A orbit solutions, which is much better than the scientific requirements of this mission. It is noticed that the GPS observations dominate the achievable accuracy of POD, and the combination of multiple types of observations can reduce orbit errors caused by data gaps and maintain more stable and continuous orbits.