Improvement of Orbit Prediction Algorithm for Spacecraft Through Simplified Precession-Nutation Model Using Cubic Spline Interpolation Method

For the on-orbit flight missions,the model of orbit prediction is critical for the tasks with high accuracy requirement and limited computing resources of spacecraft.The precession-nutation model,as the main part of extended orbit prediction,affects the efficiency and accuracy of on-board operation.In this paper,the previous research about the conversion between the Geocentric Celestial Reference System and International Terrestrial Reference System is briefly summarized,and a practical concise precession-nutation model is proposed for coordinate transformation computation based on Celestial Intermediate Pole(CIP).The idea that simplifying the CIP-based model with interpolation method is driven by characteristics of precession-nutation parameters changing with time.A cubic spline interpolation algorithm is applied to obtain the required CIP coordinates and Celestial Intermediate Origin locator.The complete precession nutation model containing more than 4000 parameters is simplified to the calculation of a cubic polynomial,which greatly reduces the computational load.In addition,for evaluating the actual performance,an orbit propagator is built with the proposed simplified precession-nutationmodel.Compared with the orbit prediction results obtained by the truncated series of IAU2000/2006 precession-nutation model,the simplified precession-nutation model with cubic spline interpolation can significantly improve the accuracy of orbit prediction,which implicates great practical application value in further on-orbit missions of spacecraft.

Effect of lunar gravity models on Chang'E-2 orbit determination using VLBI tracking data

The precise orbit determination of ChanE-2 is the most important issue for successful mission and scientific applications, while the lunar gravity field model with big un- certainties has large effect on Chang＇E-2 orbit determination. Recently, several new gravity models have been produced using the latest lunar satellites tracking data, such as LP16SP, SGM1SOJ, GL0900D and GRGM900C. In this paper, the four gravity models mentioned above were evaluated through the power spectra analysis, admittance and coherence analysis. Effect of four lunar gravity models on Chang＇E-2 orbit determination performance is investigated and assessed using Very Long Baseline Interferometry （VLBI） tracking data. The overlap orbit analysis, the posteriori data residual, and the orbit prediction are used to evaluate the orbit precision between successive arcs. The LPI65P model has better orbit overlap performance than the SGM150J model for Chang＇E-2100 km x 100 km orbit and the SGM150J model performs better for Chang＇E-2100 km x 15 km orbit, while GL0900D and GRGM900C have the best orbit overlap results for the two types of Chang＇E-2 orbit. For the orbit prediction, GRGM900C has the best orbit prediction performance in the four models.

Evaluation of strategies for the ultra-rapid orbit prediction of BDS GEO satellites

The quality of BeiDou Navigation Satellite System(BDS)Geostationary Earth Orbit(GEO)ultrarapid products is unsatisfactory because GEO satellites are nearly stationary relative to ground stations.To optimize the quality of these ultra-rapid orbit products,we investigated the effects of the fitting arc length,an a priori Solar-Radiation Pressure(SRP)model,and the along-track empirical acceleration on the prediction of BDS GEO satellite orbits.The predicted orbit arcs of 24-h were evaluated through comparisons with the corresponding observed orbit arc and Satellite Laser Ranging(SLR)observations.In both eclipse and non-eclipse seasons,accuracy of the orbit predictions obtained using a 48-h fitting arc length were better than those obtained using 24-h and 72-h fitting arc lengths.Although the overlapping precision of predicted orbits exhibited no obvious improvement when an a priori SRP model was employed,the systematic bias in the SLR residuals was significantly reduced.Specifically,the mean value of SLR residuals decreased from−0.248 m to−0.024 m during non-eclipse seasons and from−0.333 m to−0.041 m during eclipse seasons,respectively.In addition,when an empirical acceleration in the along-track direction was introduced,the three-Dimensional Root-Mean-Square(3D RMS)of overlapping orbits during eclipse seasons decreased from 2.964 to 1.080 m,which is comparable to that during non-eclipse seasons.Furthermore,the Standard Deviation(STD)of SLR residuals decreased from 0.419 to 0.221 m during eclipse seasons.The analysis of SRP estimates shows that the stability of SRP parameters was significantly enhanced after the introduction of along-track empirical acceleration in eclipse seasons.The optimal BDS GEO ultra-rapid orbit prediction products were yielded by using a 48-h fitting arc length,an a priori SRP model and an along-track empirical acceleration.

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.

Reconstructing the cruise-phase trajectory of deep-space probes in a general relativistic framework:An application to the Cassini gravitational wave experiment

Einstein’s theory of general relativity is playing an increasingly important role in fields such as interplanetary navigation,astrometry,and metrology.Modern spacecraft and interplanetary probe prediction and estimation platforms employ a perturbed Newtonian framework,supplemented with the Einstein-Infeld-Hoffmann n-body equations of motion.While time in Newtonian mechanics is formally universal,the accuracy of modern radiometric tracking systems necessitate linear corrections via increasingly complex and error-prone post-Newtonian techniques—to account for light deflection due to the solar system bodies.With flagship projects such as the ESA/JAXA BepiColombo mission now operating at unprecedented levels of accuracy,we believe the standard corrected Newtonian paradigm is approaching its limits in terms of complexity.In this paper,we employ a novel prototype software,General Relativistic Accelerometer-based Propagation Environment,to reconstruct the Cassini cruise-phase trajectory during its first gravitational wave experiment in a fully relativistic framework.The results presented herein agree with post-processed trajectory information obtained from NASA’s SPICE kernels at the order of centimetres.

An optimal design of the broadcast ephemeris for LEO navigation augmentation systems

As the deployment of large Low Earth Orbiters(LEO)communication constellations,navigation from the LEO satellites becomes an emerging opportunity to enhance the existing satellite navigation systems.The LEO navigation augmentation(LEO-NA)systems require a centimeter to decimeter accuracy broadcast ephemeris to support high accuracy positioning applications.Thus,how to design the broadcast ephemeris becomes the key issue for the LEO-NA systems.In this paper,the temporal variation characteristics of the LEO orbit elements were analyzed via a spectrum analysis.A non-singular element set for orbit fitting was introduced to overcome the potential singularity problem of the LEO orbits.Based on the orbit characteristics,a few new parameters were introduced into the classical 16 parameter ephemeris set to improve the LEO orbit fitting accuracy.In order to identify the optimal parameter set,different parameter sets were tested and compared and the 21 parameters data set was recommended to make an optimal balance between the orbit accuracy and the bandwidth requirements.Considering the real-time broadcast ephemeris generation procedure,the performance of the LEO ephemeris based on the predicted orbit is also investigated.The performance of the proposed ephemeris set was evaluated with four in-orbit LEO satellites and the results indicate the proposed 21 parameter schemes improve the fitting accuracy by 87.4%subject to the 16 parameters scheme.The accuracy for the predicted LEO ephemeris is strongly dependent on the orbit altitude.For these LEO satellites operating higher than 500 km,10 cm signal-in-space ranging error(SISRE)is achievable for over 20 min prediction.