Ballistic Coefficient Estimation Research Articles

Space Event and Outlier Detection Based on Expectation Maximization Algorithm

The United States provide Element Sets (ELSET) database in Two-Line Element (TLE) format for public use, which plays an important role in the inversion of atmospheric density in the thermosphere, ballistic coefficient estimation, early-warning and so on. Due to large uncertainties existing in the TLE generation process, space environment changes, and space events, ELSET database contains a large number of abnormal TLE data to be filtered, such as corrected TLE, orbital element outlier, and Bstar outlier. The existing methods to filter out the outliers lack general applicability and are very complicated, which are only applicable to a few space targets in certain orbit regions. To overcome the shortcomings of the existing methods, a filtering method is proposed based on Expectation Maximization (EM) algorithm employing a sliding window and polynomial fitting method, which can detect outliers for different orbital elements and space events. The research shows that the algorithm can effectively single out the outliers in TLE sequences and is suitable for all orbital debris.

Machine learning-based approach for ballistic coefficient estimation of resident space objects in LEO

The increasing number of Resident Space Objects poses a serious threat to the safe operation of satellites. Alongside with mitigation policies, it is fundamental to predict the trajectories of such objects which requires the accurate estimation of the physical characteristics that influence their orbits. An important role is played by the area-to-mass ratio, i.e., the ratio between the area exposed to the atmosphere/the Sun and the mass of the space object for the LEO/MEO and GEO region. Current literature proposes several approaches for the estimation of the area-to-mass ratio, ranging from semi-analytical to numerical methods. As regards the latter category, recent studies have focused on classification or regression algorithms for specific types of orbits (e.g., sun-synchronous, geostationary).In this context, this paper proposes a machine learning-based regression approach for the estimation of the ballistic coefficient (i.e., the product between the drag coefficient and the area-to-mass ratio) in Low Earth Orbit, covering a wide set of orbital parameters. Using a synthetic space catalogue, the performance of different types of machine learning techniques is evaluated and compared. A sensitivity analysis is carried out to analyse the effect on performance of the number of trainings, the propagation time, the number of objects of the training data set, and the frequency of the measurements. The applicability of the presented approach is tested and discussed using both real (i.e., based on publicly available catalogues of Two-Line Elements) and synthetic datasets.

Ballistic Coefficient Estimation Based on ODTK

Accurate ballistic coefficients play an important role in orbit determination and target recognition of space targets. In order to quickly and effectively calculate the target’s ballistic coefficient, AGI's ODTK (Orbit Determination Tool Kit) software is introduced, detailed operation steps and parameter settings are designed, and simulation is build to verify the effectiveness of executing the task of ballistic coefficient estimation by the ODTK software. The results of this paper have reference value for researchers engaged in space target surveillance.

창정 5B호 발사체의 재진입 시점 예측 분석

This paper represents a reentry time prediction analysis of CZ-5B rocket-body in China, subject to analysis of the Inter-Agency Space Debris Coordination Committee Reentry (IADC) reentry test campaign conducted in May 2021. Predicting the reentry of space objects is difficult to accurately predict due to the lack of accurate physical information about target, and uncertainty in atmospheric density. Therefore, IADC conducts annual re-entry campaigns to verify analysis techniques by each agency, and the Korea Aerospace Research Institute has also participated in them since 2015. Ballistic coefficient estimation method proposed to predict target reentry time and the result confirmed the difference of 73 seconds, which confirms the accuracy of the proposed method.

Ballistic Coefficient Estimation for Reentry Prediction of Rocket Bodies in Eccentric Orbits Based on TLE Data

Spent rocket bodies in geostationary transfer orbit (GTO) pose impact risks to the Earth’s surface when they reenter the Earth’s atmosphere. To mitigate these risks, reentry prediction of GTO rocket bodies is required. In this paper, the reentry prediction of rocket bodies in eccentric orbits based on only Two-Line Element (TLE) data and using only ballistic coefficient (BC) estimation is assessed. The TLEs are preprocessed to filter out outliers and the BC is estimated using only semimajor axis data. The BC estimation and reentry prediction accuracy are analyzed by performing predictions for 101 rocket bodies initially in GTO and comparing with the actual reentry epoch at different times before reentry. Predictions using a single and multiple BC estimates and using state estimation by orbit determination are quantitatively compared with each other for the 101 upper stages.

An analysis of very short-arc orbit determination for low-Earth objects using sparse optical and laser tracking data

The requirement to regularly track an increasing number of objects will result in straining existing tracking networks. This paper investigates the orbit prediction capability of an orbit determination process using very short-arc optical and laser debris tracking data for objects in low-Earth orbits. An analysis is carried out to determine the reduction in orbit prediction accuracy when tracking data over 5s from each pass is only available for an orbit determination.The results show that the reduction in accuracy is not extensive and good orbit predictions are still possible when using only 5s of data from the beginning of each pass. The results are achievable due to an accurate ballistic coefficient estimation and accurate tracking data. The dependence of the results on the perigee altitude of the objects is obvious, indicating modelling error of the atmospheric mass density in lower orbits remains the dominant source of error.

Ballistic coefficient estimation of satellite in low Earth orbit and atmosphere model error analysis

利用低轨（LEO）航天器在轨期间两行轨道根数（TLEs）数据，结合经验大气密度模型NRLMSISE00，反演计算得到其在轨期间的弹道系数<em>B</em>’，以31年<em>B</em>’的平均值代替弹道系数真值，分别通过标准球形目标卫星对比以及物理参数基本相同的非球形目标卫星对比，对弹道系数真值进行了检验；利用不同外形目标卫星弹道系数在不同太阳活动周内的变化规律，结合太阳和地磁活动变化，估计经验大气密度模型的误差分布. 结果表明，利用反演弹道系数31年的平均值来代替真值，其在理论值的正常误差范围内；大气密度模型误差在210～526km高度范围内存在相同的变化趋势，且模型误差随高度增加而增大；在短周期内<em>B</em>’变化与太阳活动指数<em>F</em>_10.7存在反相关性；密度模型不能有效模拟2008年出现的大气密度异常低. 以上结果表明，经验大气密度模型结果需要修正，尤其是在太阳活动峰年和谷年，此外，磁暴期间模型误差的修正对卫星定轨和轨道预报等也具有重要意义.

Variable-structured interacting multiple model algorithm for the ballistic coefficient estimation of a re-entry ballistic target

This paper presents the ballistic coefficient β-model based Variable-Structured Interacting Multiple Model (β-VSIMM) algorithm for real-time tracking of an unknown reentry ballistic target (RBT). Recently, RBT tracking has been a quite challenging subject due to the increase of air attacks in the modern battlefield environments. The RBT dynamics show highly nonlinear characteristics due to a sudden change of the ballistic coefficient of the RBT. Thus the ballistic coefficient should be estimated accurately in order to achieve a reliable tracking performance. Various algorithms for RBT tracking have been proposed over several decades, however, the existing algorithms to estimate target states have performance limitations. A comparative assessment of several RBT tracking algorithms is carried out for verifying the tracking performance of the proposed algorithm.

Comparison of Ballistic-Coefficient-Based Estimation Algorithms for Precise Tracking of a Re-Entry Vehicle and its Impact Point Prediction

This paper studies the problem of tracking a re-entry vehicle (RV) in order to predict its impact point on the ground. Re-entry target dynamics combined with super-high speed has a complex non-linearity due to ballistic coefficient variations. However, it is difficult to construct a database for the ballistic coefficient of a unknown vehicle for a wide range of variations, thus the reliability of target tracking performance cannot be guaranteed if accurate ballistic coefficient estimation is not achieved. Various techniques for ballistic coefficient estimation have been previously proposed, but limitations exist for the estimation of non-linear parts accurately without obtaining prior information. In this paper we propose the ballistic coefficient <TEX>${\beta}$</TEX> model-based interacting multiple model-extended Kalman filter (<TEX>${\beta}$</TEX>-IMM-EKF) for precise tracking of an RV. To evaluate the performance, other ballistic coefficient model based filters, which are gamma augmented filter, gamma bootstrapped filter were compared and assessed with the proposed <TEX>${\beta}$</TEX>-IMM-EKF for precise tracking of an RV.

Further evidence of long-term thermospheric density change using a new method of satellite ballistic coefficient estimation

[1] Building on work from previous studies a strong case is presented for the existence of a long-term density decline in the thermosphere. Using a specially developed orbital propagator to predict satellite orbit evolution, combined with a new and accurate method of determining satellite ballistic coefficients, a long-term thermospheric density change has been detected using a different method compared to previous studies. Over a 40-year period between the years 1970 and 2010, thermospheric density has appeared to reduce by a few percent per decade. However, the results do not show the thermospheric density reduction to vary linearly with time. Therefore, by analyzing the derived density data over varying solar activity levels, as well as performing a Fourier spectral analysis to highlight any periodicities, connections with physical phenomena, where possible, are proposed.

IRS Orbit Determination Accuracy Improvement

Orbit determination results are obtained for all IRS satellites by ISRO operational orbit determination software developed at ISRO Satellite Centre, Bangalore, using a batch least-squares estimator to process S-band rangeand range rate measurements. The orbit solutions are obtained through estimation of ballistic coefficient in addition to orbital parameters. A noteworthy improvement in orbit determination accuracy is noticed through this method. The position and velocity errors are in the range of 50 m to 80 m and 5 cm/s to 8 cm/s respectively.