Spacecraft Orbit Determination Research Articles

Orbit Determination of High Orbit Spacecraft based on BDS-3 using Extended Kalman Filter

The positioning of highly elliptical orbit (HEO) spacecraft is very important in deep space exploration and other missions. The Beidou Navigation Satellite System (BDS-3), which was completed in 2020, has put forward new ideas for using GNSS technology to make up for the lack of earth-based TT&C systems. At the same time, the selection of the gravity field order and the perturbation forces must be considered when using dynamical methods for HEO spacecraft positioning. In this paper, simulation experiments are carried out based on the Two-Line Orbital Element (TLE) data of BDS. Two HEO satellites with different semimajor-axis (67509.6 km, 212857.3 km) are selected as the target spacecraft orbits. The single point positioning (SPP) method and Extended Kalman Filter (EKF) method are used for HEO spacecrafts positioning respectively. The experiments show that a 20×20 order gravity field model can be chosen for the orbital integral of HEO spacecraft orbits, and the integration error caused by solar gravity and lunar gravity should be taken into account with the change of orbital altitude. Adding Geostationary Orbit (GEO) and Inclined GeoSynchronous Orbit (IGSO) navigation satellites improved the visibility of these two orbits by 19.45% and 16.64%, respectively, and improved the GDOP value by 14.1% and 3.8%, respectively, compared to observing MEO satellites only. The use of the EKF method can effectively improve the positioning accuracy of the HEO spacecraft compared to the SPP method. For the spacecraft in HEO-1, the RMS value of the positioning errors of the EKF method was 67.82 m, and the accuracy of each direction was improved by 44.28%, 38.85%, and 38.62%, respectively. For the spacecraft in HEO-2, the positioning errors in the x direction of EKF method was within 12 km and within 2 km in the y and z directions. The accuracy of these three directions was improved by 84.91%, 79.24%, and 58.64%, respectively.

Precise Orbit Determination of the MESSENGER Spacecraft

The NASA MESSENGER mission explored Mercury for more than four years to investigate the properties of the planet. To safely operate in the harsh conditions around Mercury, the spacecraft was in a highly eccentric orbit with a low periapsis altitude. The radiation environment had a strong impact on the spacecraft orbit evolution because of the proximity of Mercury to the Sun. A detailed modeling of the nonconservative forces is then a key factor to enhance the precise orbit determination of the spacecraft. We present here refined models of the nonconservative forces, including thermal reradiation effects, that enabled significant improvements in the trajectory reconstruction. A crossover analysis based on the Mercury Laser Altimeter (MLA) data was carried out to cross-check the accuracy of the orbit determination results. The trajectories retrieved by using the refined spacecraft dynamical model provide reduced height misfit at crossover points, indicating a high-quality reconstruction. Our new solutions of the spacecraft orbits are then archived to be used as auxiliary information for the data analysis of other MESSENGER instruments.

Performance evaluation of real-time orbit determination for LUTAN-01B satellite using broadcast earth orientation parameters and multi-GNSS combination

Real-time orbit determination (RTOD) for spacecraft using the space-borne GNSS technique needs earth orientation parameters (EOPs) for the required coordinate transformation between earth-fixed and inertial reference frames. GPS and BDS transmit EOPs in modernized navigation messages, which enables GNSS-equipped spacecraft to update EOPs onboard and improves the RTOD automaticity. However, the impact of broadcast EOP errors on RTOD has not yet been evaluated. With the GPS and BDS-3 observations collected from a Chinese low-earth orbit (LEO) mission, the LUTAN-01B satellite, we analyze the LEO RTOD performance with broadcast EOPs and GPS/BDS-3 combination for the first time. In RTOD, we parameterize the ephemeris signal-in-space range error (SISRE) to account for its slow-varying signature and to compensate for the EOP errors. Without estimating SISRE, the RTOD precision using broadcast EOPs is 70.1 cm with only GPS observations and 42.4 cm with only BDS-3, revealing degradations of 5.1 cm (7.8%) and 3.3 cm (8.4%) compared to those using the precise C04 EOPs, respectively. With SISRE estimated, the impact of broadcast EOP error is compensated and the RTOD precisions with broadcast EOPs show identical results to those with C04, reaching 36.3 cm with GPS and 25.8 cm with BDS-3. Combining GPS and BDS-3 further improves the RTOD precision to 23.9 cm. Furthermore, we show that the RTOD precision can be further improved by using GPS and BDS broadcast EOPs’ differences to correct ephemeris rotation errors. With this correction, the precision improvement of BDS-3 independent and GPS/BDS-3 combined RTOD increases significantly when BDS-3 broadcast EOPs suffer large errors due to long update intervals. During the experiment period, their maximum orbital improvements reach 10.2 and 7.7 cm, respectively, while the average improvements are both around 1.5 cm.

Initial Identification of Thrust and Orbit Elements for Continuous Thrust Spacecraft in Circular Orbit

Continuous thrust spacecraft in circular orbits have had a great influence on the identification and cataloging of space targets. Gaussian-type orbital element variational equations are simplified and approximated. Ground-based radar observation datasets are transformed into orbit elements datasets. The initial thrust and orbit elements are obtained by optimally solving the spatial parameter error sum of squares minimization problem with the Levenberg–Marquardt method. The simulation analysis is carried out under the high-precision orbit model, and the solution error of tangential acceleration is around 5 × 10−7 m/s2, and that of normal acceleration is around 3 × 10−6 m/s2; the accuracy of the semi-major axis is 350 m, and the accuracy of inclination is 0.095°. The method is applicable to the preliminary identification of thrust and orbit elements for circular orbit continuous thrust spacecraft and can provide reliable initial values for the subsequent precision orbit determination of such spacecraft.

An on‐orbit calibration method for time delay of inter‐satellite link transponder in tracking and data relay satellite

AbstractThe tracking and data relay satellite (TDRS) in geosynchronous orbit (GEO) can provide ranging and communication services for user spacecraft in low Earth orbit (LEO) through the inter‐satellite link (ISL). The time delay of TDRS ISL transponder in orbit differs from its pre‐launch state and changes due to the complex space environment, adding significant errors to the user spacecraft's orbit determination based on four‐way ranging data. The authors have developed a calibration system and proposed an efficient on‐orbit calibration method for the ISL transponder's time delay in TDRS. Experimental results demonstrate the effectiveness of the authors’ method, and the RMS of calibration residuals is less than 0.5 m.

Fully Autonomous Orbit Determination and Synchronization for Satellite Navigation and Communication Systems in Halo Orbits

This paper presents a solution for autonomous orbit determination and time synchronization of spacecraft in Halo orbits around Lagrange points using inter-satellite links. Lagrange points are stable positions in the gravitational field of two large bodies that allow for a sustained presence of a spacecraft in a specific region. However, a challenge in operating at these points is the lack of fixed landmarks for orbit determination. The proposed solution involves using inter-satellite links to perform range and range-rate measurements, allowing for accurate computation of the spacecraft’s orbit parameters without the need for any facilities on Earth. Simulations using a fleet of three satellites in Near Rectilinear Halo Orbits around the Earth–Moon Lagrange point, proposed for the Lunar Gateway stations, were conducted to demonstrate the feasibility of the approach. The results show that inter-satellite links can provide reliable and accurate solutions for orbit determination with a DRMS error lower than one meter (90th percentile) and synchronization errors of around one nanosecond. This solution paves the way for a fully autonomous fleet of spacecraft that can be used for observation, telecommunication, and navigation missions.

Lunar Orbit VLBI Experiment Ground Validation System

China is planning to launch a relay satellite in the coming years with a payload for the Earth-Moon Very-Long-Baseline Interferometer (VLBI) observation research and scientific applications, known as the Lunar Orbit VLBI Experiment (LOVEX) system. This system will perform the lunar orbit VLBI experiments for in the world, and will improve the accuracy of planetary spacecraft orbit determination and the scientific observation capabilities of astrophysics and astrometry. Prior to launch, key technologies of the system must be verified, so we have established a LOVEX ground validation system with similar performance to the LOVEX system. The LOVEX ground validation system consists of a 4.5-meter ring-focus antenna, X-band receiver, frequency converter and digital backend, hydrogen maser, and monitoring and control software. Using this system, we have successfully conducted VLBI differential observation experiments with the Shanghai 65m radio telescope and Beijing 50m radio telescope. The experimental results show that, after calibration with NRAO150, the standard deviations of delay error of Tianwen-1 is within 0.5 ns, consistent with the theoretical timing accuracy, verifying the feasibility of the LOVEX time delay calibration.

Prediction of Orbit Decay for Large-Scale Spacecraft considering Rarefied Aerodynamic Perturbation Effects

The growing risk of falling debris from outer space as well as the atmospheric interaction effect makes the orbit decay prediction of large spacecraft in very low earth orbit (VLEO) increasingly significant. Focusing on the aerodynamic perturbation effects under multiscale and nonequilibrium states on the orbit decay of the large spacecraft in VLEO at the end of its lifetime, we developed a novel perturbation prediction model covering the entire altitude range before reentry to perform long-term and short-term predictions of the large-scale spacecraft. A unified local rapid engineering algorithm for aerodynamic force and moment coefficients covering all flow regimes is proposed. The orbit perturbation models, combining the components of aerodynamics solved by the engineering algorithm, are built for the large-scale spacecraft. For altitudes ranging from 350 km to 250 km, which we defined as the slow descending stage (SDS), the two-line orbital elements (TLEs) and simplified general perturbation 4 (SGP4) model were used for long-term prediction, whereas for altitudes from 250 km to 120 km, which we defined as the rapid falling stage (RFS), Kepler two-body motion dynamics with acceleration perturbations were applied. All the relevant orbital elements were analytically solved and numerically simulated by the Runge–Kutta integration method. Thus, the decay orbit for large spacecraft from 350 km to 120 km altitudes can be evaluated by the platform we built. All the predicted results were broadly consistent with the measurement data. The findings in this paper can be further applied into the orbit determination of noncooperative spacecraft.

Analysis on navigation accuracy of high orbit spacecraft based on BDS GEO and IGSO satellites

To make up for the insufficiency of earth-based TT&C systems, the use of GNSS technology for high-orbit spacecraft navigation and orbit determination has become a new technology. It is of great value to applying Geosynchronous Earth Orbit (GEO) and Inclined GeoStationary Orbit (IGSO) navigation satellites for supporting the navigation of high-orbit spacecraft since there are three different types of navigation satellites in BeiDou Navigation Satellite System (BDS): Medium Earth Orbit (MEO), GEO and IGSO. This paper conducts simulation experiments based on Two-Line Orbital Element (TLE) data to analyze and demonstrate the role of these satellites in the navigation of high-orbit spacecraft. Firstly, the spacecraft in GEO was used as the target satellite to conduct navigation experiments. Experiments show that for the spacecraft on the GEO orbit, after adding GEO and IGSO respectively on the basis of receiving MEO navigation satellite signals, the accuracies were improved by 7.22 % and 6.06 % respectively. When adding both GEO and IGSO navigation satellites at the same time, the accuracy can reach 16 m. In the second place, navigation and positioning experiments were carried out on three high elliptical orbit (HEO) satellites with different semimajor axis (32037.2 km, 42385.9 km, 67509.6 km). The experiments show that the number of visible satellites has been improved significantly after adding GEO and IGSO navigation satellites at the same time. The visible satellites in these three orbits were improved by 32.84 %, 41.12 % and 37.68 %, respectively compared with only observing MEO satellites.The RMS values of the navigation positioning errors of these three orbits are 25.59 m, 87.58 m and 712.48 m, respectively.

A LSTM assisted orbit determination algorithm for spacecraft executing continuous maneuver

Orbit determination (OD) for spacecraft with unknown maneuver is always a challenging task. This paper proposes a novel framework for efficiently solving continuously maneuvering spacecraft OD problems by merging the Long Short-Term Memory (LSTM) neural network and the filter algorithms. A polynomial-representation fitted the unknown continuous maneuver is first proposed. Rather than directly output the estimated maneuver, the LSTM is trained to detect the unknown maneuver and then estimate the coefficients of the polynomial-representation. Then a fusion is designed to combine the prediction of the LSTM and the estimation of the filter for a more accurate estimation. The proposed LSTM-based framework is successfully applied to solve a Low-Earth-orbit OD problem and a Middle-Earth-orbit OD problem. The continuously maneuvering target is well tracked and the unknown maneuver is accurately estimated. Numerical simulations show that the LSTM trained based on one training dataset can also be applied to other scenarios that share some common features with the training dataset.

Decoupled and coupled moons’ ephemerides estimation strategies application to the JUICE mission

When reconstructing natural satellites' ephemerides from space missions' tracking data, the dynamics of the spacecraft and natural bodies are often solved for separately, in a decoupled manner. Alternatively, the ephemeris generation and spacecraft orbit determination can be performed concurrently. This method directly maps the available data set to the estimated parameters' covariances while fully accounting for all dynamical couplings. It thus provides a statistically consistent solution to the estimation problem, whereas this is not directly ensured with the decoupled strategy. For the Galilean moons in particular, the JUICE mission provides a unique, although challenging, opportunity for ephemerides improvement. For such a dynamically coupled problem, choosing between the two state estimation strategies will be influential. This paper quantifies the Galilean moons' state uncertainties attainable when applying a coupled estimation strategy to simulated JUICE data, and discusses the challenges that remain to be addressed to achieve such a coupled solution from real observations. We first provide a detailed, explicit formulation for the coupled approach, which was still missing in the literature although already used in past studies. We then assessed the relative performances of the two ephemerides generation techniques for the JUICE test case. To this end, we used both decoupled and coupled models on simulated JUICE radiometric data. We compared the resulting covariances for the Galilean moons' states, and showed that the decoupled approach yields slightly lower formal errors for the moons' tangential positions. However, the coupled model can reduce the state uncertainties by more than one order of magnitude in the radial direction ( i.e. towards the central body). It also proved more sensitive to the dynamical coupling between Io, Europa and Ganymede, allowing the state solutions for the first two moons to fully benefit from JUICE orbital phase around Ganymede. On the other hand, we showed that the choice of state estimation methods does not strongly affect the moons' gravity field determination. Many issues still remain to be solved before a concurrent estimation strategy can be successfully applied, especially to reconstruct the moons’ dynamics over long timescales. Nonetheless, our analysis highlights promising ephemerides improvements and thus motivates future efforts to reach a coupled state solution for the Galilean moons.

Autonomous orbit determination for satellite formations using relative sensing: Observability analysis and optimization

Orbit determination of spacecraft in orbit has been mostly dependent on either GNSS satellite signals or ground station telemetry. Both methods present their limitations, however: GNSS signals can only be used effectively in earth orbit, and ground-based orbit determination presents an inherent latency that increases with the Earth–spacecraft distance. For spacecraft flying formations, an alternative method of orbit determination, independent of external signals, consists in the observation of the spacecraft’s position with respect to the central body through the relative positioning history of the spacecraft within the formation. In this paper, the potential of the relative positioning method is demonstrated in the context of the SunRISE mission, and compared with the mission’s previously proposed orbit determination methods. An optimization study is then made to find the optimal placement of a new spacecraft in the formation so as to maximize the positioning accuracy of the system. Finally, the possibility of removing part of the system’s relative bearing measurements while maintaining its observability is also studied. The resulting system is found to be observable, but ill-conditioned.

Maneuvering Spacecraft Orbit Determination Using Polynomial Representation

This paper proposed a polynomial representation-based method for orbit determination (OD) of spacecraft with the unknown maneuver. Different from the conventional maneuvering OD approaches that rely on specific orbit dynamic equation, the proposed method needs no priori information of the unknown maneuvering model. The polynomials are used to represent the unknown maneuver. A transformation is made for the polynomials to improve the convergence and robustness. The Extended Kalman Filter (EKF) is used to process incoming observation data by compensating the unknown maneuver using the polynomials. The proposed method is successfully applicated into the OD problem of spacecraft with trigonometric maneuver. Numerical simulations show that the eighth-order polynomials are accurate enough to represent a trigonometric maneuver. Moreover, Monte Carlo simulations show that the position errors are smaller than 1 km, and the maneuver estimated errors are no more than 0.1 mm/s2 using the eighth-order polynomials. The proposed method is accurate and efficient, and has potential applications for tracking maneuvering space target.

Autonomous Spacecraft Orbit Determination from Incident Light Intensity via Eclipse Transient Timing

Autonomous orbit determination methods requiring minimal hardware, computational power, and external reference are desirable for small, low-cost spacecraft, or as a backup on larger craft. This paper presents a set of methods for orbit identification and estimation using only scalar measurements of the incident sunlight intensity, which should be available to most spacecraft without the need for additional dedicated hardware. By using these data to time the duration and transients of eclipse, a spacecraft may maintain a provided orbital estimate or develop a new orbital estimate from scratch. The presented methods use a novel sun-referenced orbit parameter conversion to identify candidate orbits, and an unscented Kalman filter based on the simplified general perturbations model and an atmosphere-corrected eclipse transient model to refine estimates and identify the correct candidate. These navigation methods are tested against public two-line element set data and are shown to provide continuous position estimates with an orbit-averaged error typically on the order of several kilometers in a variety of low-Earth-orbit geometries. So long as the spacecraft is in an eclipsing orbit about a known body, the algorithms described herein can provide orbital state estimates even to satellites without dedicated navigation hardware or external tracking.

An Empirical Atmospheric Density Calibration Model Based on Long Short-Term Memory Neural Network

The accuracy of the atmospheric mass density is one of the most important factors affecting the orbital precision of spacecraft at low Earth orbits (LEO). Although there are a number of empirical density models available to use in the orbit determination and prediction of LEO spacecraft, all of them suffer from errors of various degrees. A practical way to reduce the error of a particular model is to calibrate the model using precise density data or tracking data. In this paper, a long short-term memory (LSTM) neural network is proposed to calibrate the NRLMSISE-00 density model, in which the densities derived from spaceborne accelerometer data are the main input. The resulted LSTM-NRL model, calibrated using the accelerometer data from Challenging Minisatellite Payload (CHAMP) satellite, is extensively experimented to evaluate the calibration performance. With data in one month to train the LSTM-NRL model, the model is shown to effectively reduce the root mean square error of the model densities outside the training window by more than 40% in various time spans and space weather environment. The LSTM-NRL model is also shown to have remarkable transferring performance when it is applied along the GRACE satellite orbits.

Precise Orbit Determination of MEX Flyby Phobos Using Simulated Radiometric and Image Data.

A navigation camera or topography camera is a standard payload for deep space missions and the image data are normally used for auto-navigation. In this work, we study the potential contribution of image data in precise orbit determination for deep space spacecraft. The Mars Express (MEX) spacecraft has generated extensive Phobos image data during flybys of Phobos, but these data have not been used in precise orbit determination because of the difficulty in employing these image data. Therefore, we did an experiment using simulated image data as the first step for exploring how to use real image data in precise orbit determination of spacecraft. Our results demonstrate that image data can provide stronger constraints on orbit in the tangential and normal directions than Doppler data. When the image data were used in the MEX orbit determination during the MEX Phobos flyby, the orbit determination accuracies in the tangential and normal directions were significantly improved. This work will provide a reference for real image data processing during MEX Phobos flyby to improve MEX orbit accuracy as well as Phobos ephemeris accuracy.

Evaluation of Time Difference of Arrival (TDOA) Networks Performance for Launcher Vehicles and Spacecraft Tracking

Time Difference of Arrival (TDOA) networks could support spacecraft orbit determination or near-space (launcher and suborbital) vehicle tracking for an increased number of satellite launches and space missions in the near future. The evaluation of the geometry of TDOA networks could involve the dilution of precision (DOP), but this parameter is related to a single position of the target, while the positioning accuracy of the network with targets in the whole celestial vault should be evaluated. The paper presents the derivation of the MDOP (minimum dilution of precision), a parameter that can be used for evaluating the performance of TDOA networks for spacecraft tracking and orbit determination. The MDOP trend with respect to distance, number of stations and target altitude is reported in the paper, as well as examples of applications for network performance evaluation or time precision requirement definitions. The results show how an increase in the baseline enables the inclusion of more impactive improvements on the MDOP and the mean error than an increase in the number of stations. The target altitude is demonstrated as noninfluential for the MDOP trend, making the networks uniformly applicable to lower altitude (launchers and suborbital vehicles) and higher altitude (Low and Medium Earth Orbits satellites) spacecraft.

On the Feasibility of Orbit Determination From Gravity Gradient Invariants

The capability of full-tensor gravity gradients for spacecraft orbit determination has been demonstrated in recent studies. The advantages lie in its independence from ground-based systems and its immunity against spoofing attacks. A common practice is to use Earth rotation parameters and star sensor measurements to isolate the orientation contributions to gravity gradients, which implies that the orbit determination accuracy is affected by the quality of attitude data. This article investigates the feasibility of orbit determination using gravity gradient invariants instead of full-tensor gravity gradients in order to eliminate the necessity of attitude information for frame transformation. The orbit observability is first partially explained by formulating the geometric relationship between orbital elements and geocentric distance and latitude, the latter of which can be obtained from gravity gradient invariants. Then a covariance analysis technique based on the computation of a posterior Cramér–Rao lower bound is developed to assess the orbit determination accuracy. It is assumed that the gravity gradient biases due to bandwidth limitation have been calibrated. Simulations are carried out to analyze the effects of sampling rate, orbital inclination, orbital height, and gradiometer noise level. Results show that orbit determination from gravity gradient invariants has better position accuracy in the radial direction but has degraded accuracies in the along-track and cross-track directions compared to orbit determination using full-tensor gravity gradients. The covariance analysis technique is applied to real flight data from gravity field and steady-state ocean circulation explorer. Radial, along-track, and cross-track position accuracies of 1.8, 78, and 255 m have been achieved. Future study will deal with biases in actual measurements to fulfill real orbit determination.

Mars’ atmospheric calibration of radio tracking data for precise orbit determination

The accurate navigation of Mars' orbiters requires the precise modeling the radio tracking measurements. The Martian atmosphere perturbs the optical path of the radio links leading to significant Doppler shifts (i.e., up to 5–10 Hz) that affect the spacecraft orbit determination solutions. To process the data occulted by the Martian atmosphere, we present a method that fully calibrates the path delays induced by the neutral atmosphere and ionosphere. Mars’ atmospheric models are used to predict the refractive index of these media, and the estimation of scale factors enables a complete compensation of these perturbative effects. This technique allowed us to reanalyze MRO radio tracking data that were previously discarded to avoid aliasing in the results of our gravity investigation. This precise calibration of the Martian atmosphere will also impact the navigation of future missions during aerobraking phases and science operations at low altitudes.

Delta-DOR Observations Using VLBI Antennas

Delta-DOR (differential one-way ranging) is a technique which addresses the problem of orbit determination of a target deep-space spacecraft, in particular by determining its angular position in the sky. This can be achieved by means of analyzing both quasar signals, using this radio source as a calibrator, and a proper signal transmitted by the target spacecraft. These signals should be received by two or more stations, possibly set at a large distance from each other. Nowadays, European Space Agency (ESA) can count only on a few stations, more precisely the largest ones, since large signal-to-noise ratios are required to acquire the faint transmissions involved. This study has the aim to exploit a different set of stations, the ones belonging to the very long baseline interferometry (VLBI) network, to perform Delta-DOR measurements. VLBI antennas have in general the right hardware requirements but lack a proper recording output; therefore, a software translation of the recorded signal is required. As a proof-of-concept of the proposed technique, a shadow pass, involving an Italian VLBI station, of a standard ESA Delta-DOR session has been scheduled. The recorded data were successfully translated and analyzed by means of the ESA’s software correlator, showing the feasibility of this innovative procedure.