Orbit Prediction Accuracy Research Articles

A method for compensating prediction errors to improve the orbit prediction accuracy of Starlink satellites

A method for compensating prediction errors to improve the orbit prediction accuracy of Starlink satellites

Optimal design of the long-term LEO almanac by considering the atmosphere drag effects

ABSTRACT Almanac is an elegant design to help Global Navigation Satellite Systems (GNSS) signal acquisition, which has been adopted by all global satellite navigation systems. For the future low Earth orbit (LEO) navigation constellation, the almanac will be more critical due to larger constellation and signal Doppler variation, while the LEO orbit prediction is more challenging due to complex perturbation forces, especially atmospheric drag. This study introduces a novel 9-parameter almanac model for LEO constellation, leveraging the Empirical Mode Decomposition (EMD) method. Our innovative approach uniquely balances almanac accuracy and simplicity by considering the atmosphere drag effects, addressing a critical gap in existing models. The proposed almanac model is validated with four in-orbit LEO satellites at various altitudes. For the LEO with a 600 km orbit or lower, our model achieves a 50% improvement in 23-day orbit prediction accuracy compared to the classical GPS almanac model. This significant enhancement extends to visibility prediction and signal acquisition performance. Our design limits the maximum elevation angle error to less than 1.5 degrees, efficiently excluding invisible satellites during LEO navigation signal acquisition. Furthermore, for visible satellite, the proposed LEO almanac reduces the signal frequency searching range by about 20 times during acquisition, with Doppler prediction errors better than 0.5 kHz/0.3 kHz for 95% of cases. These advancements represent a substantial leap in LEO navigation technology, offering improved efficiency and accuracy for future satellite systems.

Data-driven satellite orbit prediction using two-line elements

Orbit prediction is crucial for space situational awareness operations. Low earth orbit satellites are subjected to external forces such as atmospheric drag, radiation, and gravity. However, the well-known Kepler propagation model ignores these external forces. The simplified perturbation model included only the main external forces. In this study, a nonlinear programming model for orbit prediction using public two-line elements (TLE) is proposed. It has been proven that our models exhibit better performance than the standard Kepler and SPG4 models in terms of orbit prediction accuracy. Moreover, the proposed models were simple, computationally effective, and robust to disturbances. The sensitivity analysis indicates that a right ascension of the ascending node, a perigee argument, and a mean anomaly of the orbital elements are the most sensitive parameters in our models. The results also revealed that our method can be generalized to any low-earth orbit satellite with adequate data.

New Space Object Cataloguing through Very-Short-Arc Data Mining

The space surveillance network collects significant quantities of space object monitoring data on a daily basis, which varies in duration and contain observation errors. Cataloguing space objects based on these data may result in a large number of very short arcs (VSAs) being wasted due to cataloguing flaws, poor data quality, data precessing, and so on. To address this problem, an effective data mining method based on tracklet-to-object matching is proposed to improve the data utilization in new object cataloguing. The method can enhance orbital constraints based on useful track information in mined tracklets, improve the accuracy of catalogued orbits, and achieve the transformation of omitted observations into “treasures”. The performance of VSAs is evaluated in tracklet-to-object matching, which is less sensitive to tracklet duration and separation time than initial orbit determination (IOD) and track association. Further, the data mining method is applied to new space object cataloguing based on radar tracklets and achieved significant improvements. The 5-day data utilization increased by 9.5%, and the orbit determination and prediction accuracy increased by 11.1% and 23.6%, respectively, validating the effectiveness of our method in improving the accuracy of space object orbit cataloguing. The method shows promising potential for the space object cataloguing and relevant applications.

A Study of Solar Radiation Pressure Model in BDS-3 Precise Orbit Determination

For the BDS (BeiDou Navigation Satellite System) satellites, the solar radiation pressure is the major non-gravitational perturbation the satellites suffer. Due to the influence of multiple factors, accurate modeling the solar radiation pressure acting on these satellites is difficult to accomplish. The solar radiation pressure perturbation is an essential source of error in the precise orbit determination (POD) and orbit prediction processes of the BDS satellites. As the ECOMC (Empirical CODE Orbit Model 1 and 2 Combined) model adopts the advantageous features of the ECOM1 (Empirical CODE Orbit Model 1) model and the ECOM2 (Empirical CODE Orbit Model 2) model, a greater number of parameters have been introduced into the model, leading to strong correlation between the ECOMC model parameters. In response to the deficiency of the ECOMC model, the authors collected the BDS-3 satellite precise ephemeris data that were provided by Wuhan University (WHU) from January 2019 to April 2022. And by these ephemeris data, the ECOMC model’s 13 parameters were obtained through the dynamic orbit fitting method. By conducting these time sequence diagrams analysis of the ECOMC model parameters, this thesis affords the selection strategies of the solar radiation pressure parameters of the ECOMC model for BDS-3 inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellite. And the rationality of the selection strategies of the solar radiation pressure parameters for the ECOMC model was verified by orbit fitting and orbit prediction experiments. The results show that using the improved ECOMC model gains the best orbit fitting effects for BDS-3 IGSO and MEO satellite, and can also enhance the accuracy of medium and long-term orbit prediction of BDS-3 IGSO and MEO satellite.

A Case Study on the Effect of Atmospheric Density Calibration on Orbit Predictions with Sparse Angular Data

Accurately modeling the density of atmospheric mass is critical for orbit determination and prediction of space objects. Existing atmospheric mass density models (ADMs) have an accuracy of about 15%. Developing high-precision ADMs is a long-term goal that requires a better understanding of atmospheric density characteristics, more accurate modeling methods, and improved spatiotemporal data. This study proposes a method for calibrating ADMs using sparse angular data of space objects in low-Earth orbit over a certain period of time. Applying the corrected ADM not only improves the accuracy of orbit determination, but also enhances the accuracy of orbit prediction beyond the correction period. The study compares the impact of two calibration methods: atmospheric mass density model coefficient (ADMC) calibration and high precision satellite drag model (HASDM) calibration on the accuracy of orbit prediction of space objects. One month of ground-based telescope array angular data is used to validate the results. Space objects are classified as calibration objects, participating in ADM calibration, and verification objects, inside and outside the calibration orbit region, respectively. The results show that applying the calibrated ADM can significantly increase the accuracy of orbit prediction. For objects within the calibration orbit region, the calibration object’s orbit prediction error was reduced by about 55%, while that of verification objects was reduced by about 45%. The reduction in orbit prediction error outside this region was about 30%. This proposed method contributes significantly to the development of more reliable ADMs for orbit prediction of space objects with sparse angular data and can provide significant academic value in the field of space situational awareness.

Influence of Solar Activity on Precise Orbit Prediction of LEO Satellites

The perturbations of low earth orbit (LEO) satellites operating in the orbit of 300 ∼ 2000 km are complicated. In particular, the atmospheric drag force and solar radiation pressure force change rapidly over a short period of time due to solar activities. Using spaceborne global positioning system (GPS) data of the CHAMP, GRACE and SWARM satellites from 2002 to 2020, this paper studies in depth the influence of solar activity on LEO satellites’ precise orbit prediction by performing a series of orbit prediction experiments. The quality of GPS data is more susceptible to being influenced by solar activity during years when this activity is high and the changes in dynamic parameters are consistent with those of solar activity. The effects of solar activity on LEO orbit prediction accuracy are analyzed by comparing the predicted orbits with the precise ones. During years of high solar activity, the average root-mean-squares prediction errors at 10, 20, and 30 minutes are 0.15, 0.20, and 0.26 m, respectively, which are larger than the corresponding values in low-solar-activity years by 59%, 63%, and 68%, respectively. These results demonstrate that solar activity has a great influence on the orbit prediction accuracy, especially during high-solar-activity years. We should strengthen the real-time monitoring of solar activity and geomagnetic activity, and formulate corresponding orbit prediction strategies for the active solar period.

Reduction of Space Debris Collision Prediction Uncertainty Based on Q-Sat Precise Orbit

Collision probability is employed for evaluating whether there will be a dangerous encounter between 2 space objects. The fidelity of the collision probability mainly depends on the accuracies of orbit prediction and covariance prediction for the space objects. In this paper, the collision probability between the Tsinghua Gravitation and Atmosphere Science Satellite, Q-Sat, and the space debris with a North American Aerospace Defense Command ID of 49863 on 2022 January 18 was calculated. The 2 objects approached each other dangerously close and the event was reported. First, the atmospheric density model is modified by a dynamic approach-based inversion to improve the accuracy of orbit prediction for the Q-Sat. Next, predictions of position error covariance are carried out. Orbits of the next 24 hours are predicted, and the predicted orbits are compared with the actual orbits of the Q-Sat. Backpropagation neural network was trained for predicting the position error covariance. For the space debris, the 2-line element data are employed. Orbit predictions for the space debris are also conducted and compared with the actual orbit. Another backpropagation neural network for predicting the position error covariance for the space debris is trained. Using the covariances from the backpropagation neural network, the error ellipsoids of the 2 objects are established. The error ellipsoids are later projected to the encounter plane to calculate the collision probability. Different from the reports from other institutes, the closest distance between the Q-Sat and the space debris calculated by the current method was 2.71 km. The collision probability was 1.16 × 10 −11 . It was not a dangerous encounter event. The onboard precise orbit determination device enabled improved orbit determination precision and orbit prediction accuracy, which is important for space safety management.

Autonomous Tracking of ShenZhou Reentry Capsules Based on Heterogeneous UAV Swarms

The safe landing and rapid recovery of the reentry capsules are very important to manned spacecraft missions. A variety of uncertain factors, such as flight control accuracy and wind speed, lead to a low orbit prediction accuracy and a large landing range of reentry capsules. It is necessary to realize the autonomous tracking and continuous video observation of the reentry capsule during the low-altitude phase. Aiming at the Shenzhou return capsule landing mission, the paper proposes a new approach for the autonomous tracking of Shenzhou reentry capsules based on video detection and heterogeneous UAV swarms. A multi-scale video target detection algorithm based on deep learning is developed to recognize the reentry capsules and obtain positioning data. A self-organizing control method based on virtual potential field is proposed to realize the cooperative flight of UAV swarms. A hardware-in-the-loop simulation system is established to verify the method. The results show that the reentry capsule can be detected in four different states, and the detection accuracy rate of the capsule with parachute is 99.5%. The UAV swarm effectively achieved autonomous tracking for the Shenzhou reentry capsule based on the position obtained by video detection. This is of great significance in the real-time searching of reentry capsules and the guaranteeing of astronauts’ safety.

Prediction of IGS RTS Orbit Correction Using LSTM Network at the Time of IOD Change

The international GNSS service (IGS) real-time service (RTS) provides orbit and clock corrections for the global navigation satellite system (GNSS) via the internet. RTS is widely used for real-time, precise positioning and its data is transmitted via the internet. Intermittent data loss can occur and cause positioning accuracy degradation. RTS data has a discontinuity when the issue of data (IOD) changes every two hours. If the signal loss occurs immediately after the IOD change, then the performance of the RTS prediction degrades significantly. We propose an adjustment method to make the RTS data across the IOD change, which makes it possible to use long RTS data for building a prediction model. The proposed adjustment method is combined with a long-short-term memory (LSTM) network to improve long-period prediction accuracy. Experiments with GPS and RTS were performed to evaluate the RTS orbit prediction accuracy. The LSTM with the IOD adjustment outperforms other polynomial prediction methods, and the positioning accuracy with the predicted RTS orbit correction shows a significant improvement.

Impacts of Arc Length and ECOM Solar Radiation Pressure Models on BDS-3 Orbit Prediction

The BeiDou global navigation satellite system (BDS-3) has already provided worldwide navigation and positioning services for which the high-precision BDS-3-predicting orbit is the foundation. The arc length of the observed orbits and the solar radiation pressure (SRP) are two important factors for producing precise orbit predictions. The contribution studies the influences of these factors on BDS-3 orbit prediction. Three-month data from 1 July 2021 to 30 September 2021 are used to analyze optimal arc lengths and different ECOM SRP models for obtaining precise BDS-3 orbit predictions. The results show that the best-fitting arc length for the BDS-3 MEO/IGSO satellite is 42–48 h by comparing the final precise ephemeris and SLR validation. Furthermore, the ECOM9 SRP model shows improved orbit-prediction accuracy than that of the ECOM5 SRP model when the satellites move in and out of the eclipse season. As for the ECOM9 SRP model, the user range error (URE) accuracy of 6 h orbit predictions when satellites are in and outside of the eclipse season is 0.036 m and 0.030 m, respectively. In addition, the orbit prediction accuracy of the BDS-3 satellites does not decrease significantly since BDS-3 satellites apply the continuous yaw-steering (CYS) attitude mode during the eclipse season.

Orbit Propagation and Lifetime Analysis of NARSSCUBE-2 Using High Precision Numerical Approach

Due to their short mission lifetime, Cube satellites launched in the last decades have increased the number of objects in Low Earth Orbits and the number of space debris. As a result, it is important to obtain accurate measurements of CubeSats trajectories in order to determine their decay and orbital lifetime and to avoid collisions with debris. In this paper, a special perturbation technique has been used as an orbit propagator in order to model orbital motion and predict the behavior of Cube satellites subjected to perturbations. This technique is a high-precision numerical approach via Cowell's formulation with adaptive step size Runge-Kutta-Fehlberg (RKF78) for numerical integration. The technique used is named SPC (Special Perturbation using Cowell's method). Orbit propagation and orbital decay evolution of NARSSCUBE-2 have been analyzed using appropriate orbital parameters derived from historic NORAD Two Line Element sets. The results from the SPC technique have been compared with the SGP4 analytical orbit propagator and then verified with the HPOP numerical orbit propagator from FreeFlyer® astrodynamics software. The accuracy of each propagator has been verified with the observation data. The SPC orbit propagator gives a higher accuracy of orbit prediction compared to SGP4 and closely matches with HPOP.

Improvement of orbit prediction accuracy using extreme gradient boosting and principal component analysis

Abstract High-accuracy orbit prediction plays a crucial role in several aerospace applications, such as satellite navigation, orbital maneuver, space situational awareness, etc. The conventional methods of orbit prediction are usually based on dynamic models with clear mathematical expressions. However, coefficients of perturbation forces and relevant features of satellites are approximate values, which induces errors during the process of orbit prediction. In this study, a new orbit prediction model based on principal component analysis (PCA) and extreme gradient boosting (XGBoost) model is proposed to improve the accuracy of orbit prediction by learning from the historical data in a simulated environment. First, a series of experiments are conducted to determine the approximate numbers of features, which are used in the following machine learning (ML) process. Then, PCA and XGBoost models are used to find incremental corrections to orbit prediction with dynamic models. The results reveal that the designed framework based on PCA and XGBoost models can effectively improve the orbit prediction accuracy in most cases. More importantly, the proposed model has excellent generalization capability for different satellites, which means that a model learned from one satellite can be used on another new satellite without learning from the historical data of the target satellite. Overall, it has been proved that the proposed ML model can be a supplement to dynamic models for improving the orbit prediction accuracy.

Orbit Determination for All-Electric GEO Satellites Based on Space-Borne GNSS Measurements

Orbit accuracy of the transfer orbit and the mission orbit is the basis for the orbit control of all-electric-propulsion Geostationary Orbit (GEO) satellites. Global Navigation Satellite System (GNSS) simulation data are used to analyze the main factors affecting GEO satellite orbit prediction accuracy under the no-thrust condition, and an electric propulsion calibration algorithm is designed to analyze the orbit determination and prediction accuracy under the thrust condition. The calculation results show that the orbit determination accuracy of mission orbit and transfer orbit without thrust is better than 10 m using onboard GNSS technology. The calibration accuracy of electric thrust is about 10−9 m/s2 and 10−7 m/s2 with 40 h and 16 h arc length, respectively, using the satellite self-positioning data of 100 m accuracy to calibrate the electric thrust. If satellite self-positioning data accuracy is at the 10 m level, the electric thrust calibration accuracy can be improved by about one order of magnitude, and the 14-day prediction accuracy of the transfer orbit with thrust is better than 1 km.

Influence of atmospheric density and area-to-mass errors on orbit prediction accuracy

Abstract Due to the fact that the space is becoming increasingly congested, there is a high requirement for the orbit prediction accuracy of space targets to support collision warning tasks. This is especially true for space debris with high area-to-mass ratio and low orbit altitude. This paper focuses on the along-track position error caused by the atmospheric density error and area-to-mass ratio error for targets with near-circular orbit in the orbit prediction. We derive a semi-analytical expression to describe the along-track position error, and the expression’s validity is evaluated by a goodness-of-fit index compared with the simulated “true” along-track position error. The simulation is based on Encke’s special perturbation method, in which the drag error is treated as a perturbation. The drag error is modeled by the difference between the JB2008 and MISIS density model and the sinusoidal oscillation error model concerning the inexact area-to-mass ratio. Furthermore, targets with various orbit altitudes ranging from 300km to 800km are selected to investigate whether the along-track position error can meet the collision warning requirements.

Orbit determination, positioning strategy design, and accuracy evaluation of Chang’e-5

The Chang’e-5 spacecraft has some new characteristics, such as direct entry into the Earth-Moon transfer orbit, lunar surface sampling, rendezvous and docking, high-speed re-entry and return, and after completing the main mission, the orbiter being able to fly to the first Lagrangian libration point of the Sun-Earth orbit. This paper evaluates the orbit determination and prediction accuracy and lunar surface-positioning accuracy of the mission key nodes. Results showed that the position error of the orbit determination prediction 6 h before midway correction and 6 h before lunar capture is 100 m. During rendezvous and docking, the position error is ~700 m from the forecast to the handover point after the fourth remote guidance and control. This is caused by the accumulation of the ascent’s orbit and control error. Using 12-h data can effectively meet the task requirements. Besides, for the Chang’e-5 expansion mission, the overlapping arc analysis method is used, and the position error is ~500 m.

Improved orbit predictions using two-line elements through error pattern mining and transferring

As the sole orbit data source of space objects for public access, the NORAD catalog provides the basic orbital information in the form of two-line element (TLE) for various space tasks. But the accuracy of orbit prediction (OP) using TLE with the analytical Simplified General Perturbations-4 (SGP4) propagator drops quickly with time, especially for low orbits, significantly limiting the capability of TLEs for advanced space situational awareness (SSA) applications. To enhance the TLE performance over long-duration OP, this paper proposes a data-driven method for improved TLE-based orbit predictions through mining and transferring the orbit error patterns. Two state-of-the-art learning methods, the gradient boosting decision tree (GBDT) and convolutional neural networks (CNN), are applied to model the underlying error patterns, and then the learned models are used as an error corrector to modify the future orbit predictions. Experimental results demonstrate that the time-varying orbit error patterns in the past can be captured by the developed learning framework. As a result, the accuracy of orbit predictions over the future 14 days can be improved by more than 75% in the along-track direction and 90% in the cross-track and radial directions, when the model-predicted errors are used. It also shows that the error pattern learning and application process is computationally efficient, and it could be implemented for near real-time applications. This study demonstrates the promising potential of machine learning (ML)/deep learning (DL) for enhanced SSA capability with the publicly available TLEs.

Fusion of a machine learning approach and classical orbit predictions

Orbit prediction accuracy is often limited by the underlying physics-based models and estimation methods. Instead of advancing the state-of-the-art from those two aspects, we have recently developed a physics-based machine learning (ML) methodology to discover useful information from historical orbit predictions errors. This paper is posed to answer the next question: how can we fuse the ML approach with classical orbit predictions? The classical method provides valuable and reliable information and should not be abandoned. Using the extended Kalman filter (EKF) as the orbit estimation and prediction method, this paper presents an innovative fusion strategy to incorporate the ML output to the conventional framework. We define the pseudo-physical meaning of the ML output and derive an analytical model for fusion. Using a simulation-based space catalog environment, the paper demonstrates that the proposed fusion strategy can improve both the orbit prediction accuracy and precision. Discussions and insights are presented including the possible causes for some unsatisfying results. Although EKF is used in this paper, the design of the fusion strategy for the ML approach can be generalized to systems with different orbit estimation and prediction methods.

Analysis of Space Debris Orbit Prediction Using Angle and Laser Ranging Data from Two Tracking Sites under Limited Observation Environment.

The global electro-optical (EO) and laser tracking sensor network was considered to investigate improvements to orbit prediction (OP) accuracy of space debris by combining angle and laser ranging data. However, it is worth noting that weather, schedule and visibility constraints can frequently limit the operations of such sensors, which may not result in sufficient tracking data for accurate OP. In this study, several 1-day OP results for low Earth orbit (LEO) space debris targets were demonstrated under a limited observation environment to verify the OP accuracy through the combination of angle and laser ranging data from two sites. For orbit determination (OD) processes, it was considered to analyze the OP accuracy by one site providing both 2–day arc angle data and 1-day arc laser ranging data, while the other was limited to 1-day arc angle data. In addition, the initial ballistic coefficient () application method was proposed and implemented for the improvement of OD/OP accuracy, which introduces the modified correction factor depending on the drag coefficient. In the cases of combining the angle and laser ranging data, the OP results show the 3D position difference values are below 100 m root mean square (RMS) with small position uncertainty. This value satisfies the target OP accuracy for conjunction assessments and blind laser ranging (about 50–100 m at 1000 km altitude). The initial application method also shows better OP accuracy than the method without the correction factor.

Comparative evaluation of three machine learning algorithms on improving orbit prediction accuracy

In this paper, the recently developed machine learning (ML) approach to improve orbit prediction accuracy is systematically investigated using three ML algorithms, including support vector machine (SVM), artificial neural network (ANN), and Gaussian processes (GPs). In a simulation environment consisting of orbit propagation, measurement, estimation, and prediction processes, totally 12 resident space objects (RSOs) in solar-synchronous orbit (SSO), low Earth orbit (LEO), and medium Earth orbit (MEO) are simulated to compare the performance of three ML algorithms. The results in this paper show that ANN usually has the best approximation capability but is easiest to overfit data; SVM is the least likely to overfit but the performance usually cannot surpass ANN and GPs. Additionally, the ML approach with all the three algorithms is observed to be robust with respect to the measurement noise.