The Autonomous Navigation (AutoNav) mode of a Global Navigation Satellite System (GNSS) utilizes Inter- Satellite Links (ISLs) to maintain satellite operations without the service from the ground control segment. The newly launched Beidou satellites are capable of conducting ISLs for orbit determination to improve their au- tonomy, integrity, reliability, and robustness. However, the satellite orbit errors can increase over time due to various force model errors, particularly that of Solar Radiation Pressure (SRP). Accelerometers aboard satellites can measure non-conservative forces directly and have been successfully used in satellite missions for gravity recovery and atmosphere study (i.e., GRACE, CHAMP, and GOCE). This study investigates the feasibility to use accelerometers aboard Beidou satellites to improve AutoNav accuracy and service span. The results show that in a simulated 180-day AutoNav period, the orbit accuracy with the aid of accelerometers is two times better than that of using ISL data only.

Beidou satellites, especially geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites, need to be frequently maneuvered to keep them in position due to various perturbations. The satellite ephemerides are not available during such maneuver periods. Precise estimation of thrust forces acting on satellites would provide continuous ephemerides during maneuver periods and could significantly improve orbit accuracy immediately after the maneuver. This would increase satellite usability for both real-time and post-processing applications. Using 1 year of observations from the Multi-GNSS Experiment network (MGEX), we estimate the precise maneuver periods for all Beidou satellites and the thrust forces. On average, GEO and IGSO satellites in the Beidou constellation are maneuvered 12 and 2 times, respectively, each year. For GEO satellites, the maneuvers are mainly in-plane, while out-of-plane maneuvers are observed for IGSO satellites and a small number of GEO satellites. In most cases, the Beidou satellite maneuver periods last 15–25 min, but can be as much as 2 h for the few out-of-plane maneuvers of GEO satellites. The thrust forces acting on Beidou satellites are normally in the order of 0.1–0.7 mm/s2. This can cause changes in velocity of GEO/IGSO satellites in the order of several decimeters per second. In the extreme cases of GEO out-of-plane maneuvers, very large cross-track velocity changes are observed, namely 28 m/s, induced by 5.4 mm/s2 thrust forces. Also, we demonstrate that by applying the estimated thrust forces in orbit integration, the orbit errors can be estimated at decimeter level in along- and cross-track directions during normal maneuver periods, and 1–2 m in all the orbital directions for the enormous GEO out-of-plane maneuver.

Beidou geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites are frequently maneuvered to keep them in the designed orbits by thrust forces. As the thrust forces are generally unknown, precise satellite orbits are difficult to be determined during maneuver periods. At present, precise ephemerides are not available or not complete for the satellite on the day of maneuver, and sometimes even the day after. This study aims to provide continuous precise orbit for Beidou-2 satellites during the maneuver period through better modeling of the thrust forces. We firstly present a thrust model based on the thrust behavior of Beidou-2 satellites detected in our previous study. Then, for the maneuvered satellite, the precise orbit is determined by estimating the extra thrust model parameters, together with other orbit parameters of initial satellite state and solar radiation pressure (SRP). Using observations from the Multi-GNSS Experiment (MGEX) network in Sep and Oct 2017, we have detected 10 GEO in-plane, 1 GEO and 3 IGSO out-of- plane maneuvers among the 5 GEO and 6 IGSO satellites; precise orbit determination (POD) is conducted for all the GEO in-plane and IGSO maneuvered satellites. The accuracy of our recovered orbit has been evaluated by comparing to a concatenation of the dynamic orbit before/after the maneuver and kinematic orbit during the maneuver. The RMSs of orbit differences before/after maneu- vers are about 0.30, 2.34 and 0.42 m in the radial, along-track, and cross-track (RAC) directions for GEOs, and 0.33, 0.62 and 0.26 m for IGSOs. A similar level of accuracy has also been achieved during maneuvers as shown by the orbit differences and the stable POD resid- uals during the whole maneuver day. The recovered orbit accuracy is comparable to that of the normal Beidou-2 precise ephemerides from International GNSS Service (IGS) analysis centers (WHU/GFZ).

The geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites of the Beidou navigation satellite system are maneuvered frequently. The broadcast ephemeris can be interrupted for several hours after the maneuver. The orbit-only signal-in-space ranging errors (SISREs) of broadcast ephemerides available after the interruption are over two times larger than the errors during normal periods. To shorten the interruption period and improve the ephemeris accuracy, we propose a two-step orbit recovery strategy based on a piecewise linear thrust model. The turning points of the thrust model are firstly determined by comparison of the kinematic orbit with an integrated orbit free from maneuver; afterward, precise orbit determination (POD) is conducted for the maneuvered satellite by estimating satellite orbital and thrust parameters simultaneously. The observations from the IGS Multi-Global Navigation Satellite System (GNSS) Experiment (MGEX) network and ultra-rapid products of the German Research Center for Geosciences (GFZ) are used for orbit determination of maneuvered satellites from Sep to Nov 2017. The results show that for the rapidly recovered ephemerides, the average orbit-only SISREs are 1.15 and 1.0 m 1 h after maneuvering for GEO and IGSO respectively, which is comparable to the accuracy of Beidou broadcast ephemerides in normal cases.

Precise orbit products are essential and a prerequisite for global navigation satellite system (GNSS) applications, which, however, are unavailable or unusable when satellites are undertaking maneuvers. We propose a clock-constrained reverse precise point positioning (RPPP) method to generate the rather precise orbits for GNSS maneuvering satellites. In this method, the precise clock estimates generated by the dynamic precise orbit determination (POD) processing before maneuvering are modeled and predicted to the maneuvering periods and they constrain the RPPP POD during maneuvering. The prediction model is developed according to different clock types, of which the 2-h prediction error is 0.31 ns and 1.07 ns for global positioning system (GPS) Rubidium (Rb) and Cesium (Cs) clocks, and 0.45 ns and 0.60 ns for the Beidou navigation satellite system (BDS) geostationary orbit (GEO) and inclined geosynchronous orbit (IGSO)/Median Earth orbit (MEO) satellite clocks, respectively. The performance of this proposed method is first evaluated using the normal observations without maneuvers. Experiment results show that, without clock-constraint, the average root mean square (RMS) of RPPP orbit solutions in the radial, cross-track and along-track directions is 69.3 cm, 5.4 cm and 5.7 cm for GPS satellites and 153.9 cm, 12.8 cm and 10.0 cm for BDS satellites. When the constraint of predicted satellite clocks is introduced, the average RMS is dramatically reduced in the radial direction by a factor of 7–11, with the value of 9.7 cm and 13.4 cm for GPS and BDS satellites. At last, the proposed method is further tested on the actual GPS and BDS maneuver events. The clock-constrained RPPP POD solution is compared to the forward and backward integration orbits of the dynamic POD solution. The resulting orbit differences are less than 20 cm in all three directions for GPS satellite, and less than 30 cm in the radial and cross-track directions and up to 100 cm in the along-track direction for BDS satellites. From the orbit differences, the maneuver start and end time is detected, which reveals that the maneuver duration of GPS satellites is less than 2 min, and the maneuver events last from 22.5 min to 107 min for different BDS satellites.

Satellites Autonomous Navigation (AutoNav) mode utilizes inter-satellite crosslink measurements to maintain satellites operation, without relying on ground control facilities. The newly launched BeiDou (BD) satellites are capable of conducting satellite to satellite tracking (SST). However, as there is no absolute reference frame control with SST data only, satellite constellation will experience rotation related to the earth fixed reference frame, due to various force perturbations. The main problem for orbit determination is how to precisely model the non-conservative forces (i.e. Solar Radiation Pressure (SRP)). Space-borne accelerometers have been successfully used for gravity recovery and atmosphere study in GRACE, CHAMP, and GOCE missions to measure the non-conservative forces directly. This study investigates the feasibility to use accelerometers onboard BD satellites to improve BD AutoNav accuracy and service span. Using simulated BD orbits and SST data, AutoNav has been performed using SST data only or SST data with accelerometers. Using the simulated inter-satellite range observations of decimeter level accuracy (σ=0.75 m), AutoNav with accelerometer data can achieve 15 m and 8 m horizontal orbit accuracies for GEO/IGSO and MEO satellites within a 180-day AutoNav period, which is significantly better than the results from SST data only.

Autonomous navigation (AutoNav) is a crucial technique for enhancing the navigation satellite system, such as GPS, autonomy and decreasing systemic vulnerability. However, AutoNav using only inter-satellite link (ISL) observations can lead to constellation rotation problem over time, mainly due to the complex perturbations. The conservative perturbations, such as the Earth non-spherical perturbations, tidal perturbation, the solar, lunar attractions, etc. can be precisely modeled with latest force models. The non-conservative ones, mainly the Solar Radiation Pressure (SRP), on the other hand, are difficult to be modeled precisely and have become the main factors affecting AutoNav accuracy. Accelerometers onboard satellites are capable of measuring non-conservation forces and have been successfully used in the scientific missions, e.g., CHAMP, GRACE, and GOCE. This study investigates the feasibility of using accelerometers for GPS. Based on the IGS precise ephemerides, inter-satellite range measurements of decimeter accuracy (σ=0.31m) are simulated. AutoNav using only ISL measurements and ISL together with accelerometers have been carried out, respectively. The results show that AutoNav with accelerometer data can achieve 0.3 to 0.5 m orbit accuracy in radial direction, less than 8 m in the horizontal direction during the 180-day AutoNav period, several times better than that without accelerometer data. Also, the AutoNav performances of GPS and Beidou are compared.

Aiming at the singularity problem in satellite orbit theory, the singularity-free Lagrangian/Gaussian equations of motion is analyzed.Considering the original and physical meaning of the Lagrangian and Gaussian equations of motion, a new Lagrangian/Gaussian singularity-free disturbed equations of motion is proposed and then discussed in three cases:the circular orbit, equatorial orbit, circular and equatorial orbit.Besides, the continuity of these equations is explored.The proposed equations eliminate the zero factor and in this way the singularity problem in the orbital mechanics is solved.

Autonomous orbit determination is a crucial step for GNSS development to improve GNSS vulnerability, integrity, reliability and robustness. The newly launched BeiDou (BD) satellites are capable of conducting satellite to satellite tracking (SST), which can be used for autonomous orbit determination. However, using SST data only, the BD satellite system (BDS) will have whole constellation rotation in the absence of absolute constraints from ground or other celestial body over time, due to various force perturbations. The perturbations can be categorized into conservative forces and non-conservative forces. The conservative forces, such as the Earth non-spherical perturbations, tidal perturbation, the solar, lunar and other third-body perturbations, can be precisely modeled with latest force models. The non-conservative forces (i.e. Solar Radiation Pressure (SRP)), on the other hand, are difficult to be modeled precisely, which are the main factors affecting satellite orbit determination accuracy. In recent years, accelerometers onboard satellites have been used to directly measure the non-conservative forces for gravity recovery and atmosphere study, such as GRACE, CHAMP, and GOCE missions. This study investigates the feasibility to use accelerometers onboard BD satellites to improve BD autonomous orbit determination accuracy and service span. Using simulated BD orbit and SST data, together with the error models of existing space-borne accelerometers, the orbit determination accuracy for BD constellation is evaluated using either SST data only or SST data with accelerometers. An empirical SRP model is used to extract non-conservative forces. The simulation results show that the orbit determination accuracy using SST with accelerometers is significantly better than that with SST data only. Assuming 0.33 m random noises and decimeter level signal transponder system biases in SST data, IGSO and MEO satellites decimeter level orbit accuracy can be achieved over a service life of two months using SST data and accelerometers. If only SST data are used, the orbit accuracy is 3~6 m with the same time period, which is an order worse.

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