Post-processed Orbit Research Articles

A method for estimating the rotation errors of BDS broadcast ephemeris using global satellite laser ranging data

Abstract The BeiDou-3 Navigation Satellite System (BDS-3) generates navigation messages from a regional ground tracking network and inter-satellite links, relying on predicted station coordinates and Earth rotation parameters (ERPs). These procedures, however, may lead to orientation errors in the broadcast ephemeris, termed constellation rotation errors. Traditionally, these errors are monitored through Helmert transformation analysis comparing broadcast and post-processed orbits, a method that highlights discrepancies between the global navigation satellite system (GNSS) terrestrial reference frame (TRF) and the International TRF (ITRF) but suffers from a two-week evaluation delay. This study proposes a near real-time approach for estimating constellation rotation errors using high-precision satellite laser ranging (SLR) data, representing the difference between GNSS TRF and ITRF through the International laser ranging service TRF. The impact of SLR data quantity and distribution on rotation estimation accuracy is investigated, and the effectiveness of this method on BDS-3 orbits with ERP-induced orientation deficiencies is validated. Results show that the root mean square of broadcast orbit errors and the orbit user ranging error reduce from 0.8/0.7/0.2 m to 0.1/0.1/0.1 m, respectively. This demonstrates the method’s capability for real-time monitoring and correcting orientation errors within BDS-3 navigation messages.

Assessment of Swarm Kinematic Orbit Determination Using Two Different Double-Difference Methods

The Swarm mission aims to study the principle and change regularities of the Earth’s magnetic field. Precise orbit determination is essential to the successful implementation of the mission and relevant scientific research. This article focuses on using two different double-difference methods to improve the accuracy of Swarm kinematic orbit determination. The accuracy of the kinematic orbit determination relies entirely on the space-borne observation data, independent of any dynamic parameters. The article analyzes the data quality of the Swarm space-borne global positioning system (GPS) receiver and presents a detailed introduction to the data pre-processing algorithms. The double-difference observation gathering and the applied orbit determination strategy using two different double-difference methods are discussed. The results of the kinematic orbits under different solar cycle conditions are presented, along with an evaluation based on analysis of GPS carrier phase residuals, subtracting from the post-processed orbits, and assessment with satellite laser ranging (SLR) measurements. The results show that the accuracy of the kinematic orbit determination is at the centimeter level for the three Swarm satellites’ orbit solutions. The daily root mean square (RMS) values of the three satellites’ phase residuals remain at around the 6 mm level. The RMS values of the position residuals between the kinematic orbits and the reduced dynamic orbits released by the European Space Agency (ESA) are at about the 2–3 cm level. The external evaluation with SLR measurements shows a good agreement with the ESA level, with the RMS values of the SLR residuals for kinematic orbits around 2 cm.

Prediction versus real-time orbit determination for GNSS satellites

To serve real-time users, the IGS (International GNSS Service) provides GPS and GLONASS Ultra-rapid (IGU) orbits with an update of every 6 h. Following similar procedures, we produce Galileo and BeiDou predicted orbits. Comparison with precise orbits from the German Research Centre for Geosciences (GFZ) and Satellite Laser Ranging (SLR) residuals show that the quality of Galileo and BeiDou 6-h predicted orbits decreases more rapidly than that for GPS satellites. Particularly, the performance of BeiDou IGSO and MEO 6-h predicted orbits is 5–6 times worse than the corresponding estimated orbits when satellites are in the eclipse seasons. An insufficient number and distribution of tracking stations, as well as an imperfect solar radiation pressure (SRP) model, limit the quality of Galileo and BeiDou orbit products. Rather than long time prediction, real-time orbit determination by means of a square root information filter (SRIF) produces precise orbits every epoch. By setting variable processing noise on SRP parameters, the filter has the capability of accommodating satellite maneuvers and attitude switches automatically. An epoch-wise ambiguity resolution procedure is introduced to estimate better real-time orbit products. Results show that the real-time estimated orbits are in general better than the 6-h predicted orbits if sufficient observations are available after real-time data preprocessing. On average, 3D RMS values of the real-time estimated orbits reduce by about 30%, 60% and 40% over the 6 h predicted orbits for GPS, BeiDou IGSO and BeiDou MEO eclipsing satellites, respectively. Galileo satellites did not enter into the eclipse season during the experimental period, the standard derivation (STD) of SLR residuals for the real-time estimated orbits are almost the same as for the post-processed orbits.

Numerical Algebra Solution: A New Algorithm for the State Transition Matrix

A new algorithm named the numerical algebra solution for the state transition matrix is proposed in this paper. The objective of the solution is to yield a comparable accuracy of the trajectory at the least computational cost. To validate it, the time consumption and accuracy performance of the numerical algebra solution are compared with those of the numerical integration and difference quotient method for both the real-time and post-processed orbit determination. Simulation results with the measurement noise only show that the time consumption of the numerical algebra solution accounts for about 60% and 40% of the numerical integration method for the real-time and post processing, respectively. Furthermore, the maximum position RMS difference of the numerical algebra solution with respect to the numerical integration method is about 1.04mm and 0.01mm for the real-time and post processing, while the position error of the numerical integration method is about 1.20m and 0.30mm, respectively. These accuracy performances demonstrate that the difference between the numerical algebra and integration solution is indistinguishable and can be accepted in the orbit determination. Advantageously, the numerical algebra solution can improve the computational efficiency greatly, which is particularly important for the real-time orbit determination.

Gravity Probe B orbit determination

The Gravity Probe B (GP-B) satellite was equipped with a pair of redundant Global Positioning System (GPS) receivers used to provide navigation solutions for real-time and post-processed orbit determination (OD), as well as to establish the relation between vehicle time and coordinated universal time. The receivers performed better than the real-time position requirement of 100 m rms per axis. Post-processed solutions indicated an rms position error of 2.5 m and an rms velocity error of 2.2 mm s−1. Satellite laser ranging measurements provided independent verification of the GPS-derived GP-B orbit. We discuss the modifications and performance of the Trimble Advance Navigation System Vector III GPS receivers. We describe the GP-B precision orbit and detail the OD methodology, including ephemeris errors and the laser ranging measurements.

Orbit improvement for Chang’E-5T lunar returning probe with GNSS technique

A global navigation satellite system (GNSS) receiver with high sensitivity is embarked by the Chang’E-5T spacecraft for a trial in the Chinese lunar exploration program. The GNSS flight experiment was activated twice on October 23 and 31, 2014. The measurement data of this experiment are analyzed here. When the distance between the Earth center and Chang’E-5T probe ranges from approximately 10,000–60,000km, the mean number of tracked GNSS satellites by the receiver onboard Chang’E-5T is 8–9, and the range of Position Dilution of Precision (PDOP) is 1–40. The noise of single-differencing C/A code pseudorange data is 5.7–8.1m (1σ). The ratio of carrier to noise spectral density (C/N0) is approximately 35dB-Hz when the distance between the spacecraft and GPS satellites was close to 60,000km. The post-processed orbit solution using terrestrial-based radiometric measurement in the 22h arc is used as the reference orbit for accuracy analysis of orbit determination and prediction. Based on this approach, the position error in the one-hour prediction from the orbit determination using GNSS single-difference pseudorange in the 1.5h arc is less than 109m, while that from the result using range and Doppler data in the 3h arc is 369m. The residual Root Mean Squares (RMS) divergence of GNSS single differential pseudorange and range in the prediction arc relative to the orbit determination arc are reduced by 65% and 90%, respectively, using GNSS data to estimate the orbit compared to using ground-based data. Furthermore, the strategy of orbit determination by combining GNSS and ground-based data is examined in the paper. The position error in the one-hour prediction using this strategy is less than 47m using the 1.5h data to determine the orbit, and the residual RMS divergences of GNSS and range measurement are reduced by 96% and 67%, respectively. Therefore, the validity of GNSS supporting orbit determination for sampling and returning from lunar explorations is verified.

The BeiDou Navigation Message

The article provides an overview of the BeiDou navigation message contents and highlights its specific communalities and differences with respect to other GNSS constellations. Making use of data collected by multi-GNSS monitoring stations of the MGEX and CONGO networks, the quality of BeiDou broadcast ephemerides is assessed through the analysis of satellite laser ranging measurements, comparison with post-processed orbit and clock products as well as positioning tests. Specific attention is given to signal-specific group delays and their proper consideration in the positioning.

DORIS: From orbit determination for altimeter missions to geodesy

In the late 1980s, the French ‘Centre national d’études spatiales' (CNES), in conjunction with the ‘Institut géographique national’ (IGN) and the ‘Groupe de recherche en géodésie spatiale’ (GRGS) developed a new geodetic tracking system called DORIS for precise orbit determination of low Earth orbiting satellites for oceanographic missions. Since then, the number of applications has increased, leading recently to the creation of an International DORIS Service (IDS), making it a part of the Global Geodetic Observation System (GGOS) currently under development within the International Association of Geodesy (IAG). The goal of this paper is to present the current applications of the DORIS system for precise orbit determination as well as for geodesy, geophysics, Earth rotation or atmospheric sciences. Current accuracies are discussed as well as already planned improvements. In particular, recent improvements in on-board real time orbit showing 5-cm radial agreement with post-processed orbits are discussed. In addition, when using a 5-satellite constellation, 1-cm precision is achievable for station position as well as sub milli-arcsecond precision for polar motion. To cite this article: P. Willis et al., C. R. Geoscience 338 (2006).