Prediction Of Atmospheric Reentry Of Space Objects Based On TLE Data

One of the main tasks of space situational awareness is the space surveillance and object cataloging,which aims to provide full chain orbit data services,including reentry and decay prediction of space objects.With the increasing human space activities and the rapid development of space technology and its applications,the number of spacecrafts,rocket bodies and orbital debris in the near-Earth space will increase substantially,and this will lead to consequential large increase in the atmospheric reentry and decay events of space objects.As such,high-precision reentry and decay prediction is highly desirable and demanding.Due to the atmospheric drag,large spacecraft and rocket bodies that are less decomposable and ablating will very likely decay to the ground.At present,at least one spacecraft of integrated structure or a rocket body with an average mass of about 2000 kg,re-enters the atmosphere every week,posing a threat to people and assets on the ground.There are two types of reentry,controlled and uncontrolled,with 70% of them being uncontrolled reentry.Controlled reentry is usually designed to land in a remote area to avoid possible harm to human beings.The time and position of uncontrolled reentry are totally following the orbit and atmospheric dynamics.In the process of reentry and decay,the geometric structure of a space object may disintegrate,resulting in large or even an order of magnitude changes in many key parameters in the equations of motion,such as the drag coefficient and surface to mass ratio.These critical parameters are unlikely estimated during the reentry and decay because of the extreme difficulty to make observations of the object.In addition,the atmospheric density models are not accurate enough.All these make the high-precision uncontrolled reentry and decay prediction a big challenge.On the other hand,the Space Track website allows public access to the two line element(TLE)catalogue,which is the largest in terms of the number of cataloged space objects and is an important data source for the research of orbital mechanics of the Earth orbiting objects.Considering the shortage of observation data,it is vital to use the TLE catalogue to realize the accurate prediction of the reentry time and location,and decay area of uncontrolled objects for space debris management and ground safety assessment.With concerns on the TLE data quality and inaccurate knowledge of space objects,the uncontrolled reentry prediction is usually made in several steps,which include the TLE outlier cleaning,ballistic coefficient estimation,orbit determination before the reentry prediction.The main contributions of this thesis are as follows.1.TLE outlier cleaning.There are possible outliers existing in all six orbit elements of a TLE set,which will lead to inaccurate and unreliable orbit determination that affects subsequent reentry prediction.Generally,a sliding window strategy is applied for all the elements,but specific measures may be used for different elements,and outlier thresholds are set based on experience,which are greatly affected by human factors and the cleaning is likely not well done.In this thesis,it is proposed to clean outliers in the TLE based on the maximum expectation(ME)algorithm.First,a series of an orbit element in a sliding window is fitted with polynomial regression where the EM algorithm is applied,and thus the prediction can be made outside the window,and the prediction error can be computed.The threshold setting is then determined considering the property of Gaussian errors.The theory for the proposed TLE outlier cleaning algorithm is more rigorous,and the algorithm can be applied to any orbit element of TLE and a wider range of orbits.The results are significantly better than those by existing techniques.For example,using the clean TLEs to estimate the ballistic coefficients can more or less improve their estimation accuracy,and some are better off by 2.5 times.2.Orbit determination.Generally,the least squares approach is used to determine a TLE set,but it could have numerical issues in the matrix operation,which could cause the solution unstable the inferred error information unreliable.In this thesis,it is proposed to use the simplex method,a local optimization algorithm,to determine the TLE orbit elements,in which matrix operations are avoided.In order to ease the problem of the local optimality of the simplex method,a process frequently using the Monte Carlo(MC)sampling technique is implemented.First,an initial simplex is constructed in the feasible region of the solution by the MC sampling.The optimal solution with respect to the initial simplex is obtained when the minimum value of an objective function is reached by search.Second,a distribution of the “optimal” solutions is generated by repeating this process.At last,the final optimal solution and error information are obtained by computing the expectation and variance of the distribution.This method is not affected by the initial state error,and is suitable for any orbit type.An example to demonstrate the effectiveness of the proposed method is with GOCE satellite whose precise ephemeris is known.The use of the simplexbased method to determine an optimal TLE set from 15-20 TLEs results in higher orbit determination accuracy and stable orbit prediction error,while the least squares solution makes the orbit prediction errors grow exponentially after five days.3.Reentry prediction.In this thesis,the reentry prediction is studied for some Chinese rocket bodies already decayed.In the research of one-month reentry prediction,the results using a high precision numerical orbit propagator(HPOP)and the Wuhan University semi-analytical orbital propagator(WHU-SST)are compared.It shows that the prediction errors from the WHU-SST are less than those of HPOP,but the prediction errors as a whole are still large.A likely cause is the inaccuracy of the used drag model.Thus,the drag coefficient model based on the Reynolds number is used.As a result,the reentry prediction accuracy is significantly improved,and the prediction error can be reduced by up to 13%.With the problem of short-term 24-hour reentry prediction,the initial state and drag coefficient are sampled by using the MC technique,and the uncertainty of atmospheric density is also considered.These measures result in a statistical distribution of the prediction.The error of reentry prediction time is within 2.5 orbital periods if it is taken as the expectation of the distribution.4.Decay prediction.The minimum requirement is that the actual decay location should be within the predicted decay area.In case there are only TLEs available to estimate the key parameters in the equations of decay,it is important how to appropriately consider their errors to achieve this objective.Therefore,first,the proposed simplex approach is applied to determine an optimal estimate of the last set of TLE before the reentry and its errors as the reference for their MC sampling;and then,the drag coefficient is also MC sampled;again,the uncertainty of the atmospheric density is considered.For Tiangong-1,the atmospheric drag models based on the Reynolds number and the equivalent sphere are used,respectively.The results show that the reentry time prediction using the former is more accurate.For the spherical and cylinder objects whose decay sites are known,when the atmospheric drag model based on the equivalent sphere is used to predict the decay site,it is found that its distribution is mainly affected by the uncertainties of the orbital eccentricity and inclination.The expectation of the decay time can be calculated from its statistical distribution,and then,an uncertain time window of 1-3 hours is applied,which can greatly reduce the distribution range of the predicted decay location and ensure that the actual decay location is within the prediction area.