Researches On Orbit Error Propagation For Space Objects

A key Space Situational Awareness(SSA)task is to provide orbital information of space objects.With this,other services are possible,such as the space collision warning and orbit anomaly detection which are critical to space safety.Full orbital information should contain both the equally important orbit state and its error.Although it is clear that the orbital error information is important,its use in SSA is well below expectation,and SAA service capability in the more complex space environment is affected,because of difficulties in accurately determining and propagating orbital errors.All these have made the determination and propagation of orbital errors of space objects a priority research topic.The orbital dynamics system is a highly nonlinear system,in which the orbit motion of a space object is subject to many perturbation forces.Existence of perturbation model errors and orbit measurement errors,and imperfect orbit determination techniques make the errors in the orbit determination inevitable,and the probability distribution of errors of determined orbit state may be not exactly known.The high nonlinearity of the orbit dynamics system,on the other hand,makes the propagated orbital error severely distorted.A well known example is the bananoid of propagated orbit state covariance,which occurs when using a linear propagation method in a Earth-centered Cartesian coordinate system over just a day or even a few hours.The state error in the SSA is commonly termed state uncertainty,and the state error covariance is the most used description of the uncertainty.To improve the expression accuracy of the covariance and uncertainty,or the covariance and uncertainty realism,extensive researches on the theory,methods and techniques about the orbit errors have been undertaken,and the efforts are well paid off.Many of these researches are on covariance calibrations,uncertainty propagation methods and coordinate systems for appropriate uncertainty description.Acknowledging the rapidly increasing need for accurate and timely orbital state error information,and that the state uncertainty propagation of space objects is an enduring and extremely challenging research,this thesis is focused only on a few important issues.It is hoped that advancements are made in the efficient use of data,effective reuse of models,sound selection of coordinate systems,and appropriate description of errors,which all help improve the realism of the orbit state covariance and uncertainty,and achieve a better preparation for the SSA servicing challenges.1.At present,the material on the orbit state uncertainty is scattered,and lacks of systematicness.For this,this thesis defines the category the errors and uncertainty in the space object surveillance and orbit determination belong to,and makes analyses on sources of the error and uncertainty.From the perspective of whether precise ephemeris of space objects can be obtained,space objects can be divided into cooperative and non-cooperative.Based on this division,related work about the propagation of orbit state uncertainty has been summarized and generalized.2.There are obvious differences in methods for state and error transformation between coordinate systems,and for interpolation.There is also a problem that the covariance matrix determined from an orbit determination process in the data sparseness environment is nonpositive definitive.Following the fundaments of orbit theory,this thesis proposes the concept of integrated propagation of orbit state and uncertainty.Summary on the methods of covariance transformation and interpolation,and those for correcting the nonpositive definitiveness is presented,and comprehensive analyses on the methods are made,which lead to suggestions on method use.3.When the realism of the orbit state covariance is poor,calibration techniques are usually taken,but there is no unified standard and procedure to assess the calibration effectiveness.Applying basic theory and methods of statistical hypothesis test,this thesis proposes a standard and procedure to assess the effectiveness of covariance calibration.Experiments on the using the scaling technique to calibrate the state covariance of Swarm B satellite,with the initial covariance determined from the use of sparse SLR tracking data,are performed.It is shown that,following the proposed standard and procedure,the scaling technique achieves 42.85% improved covariance realism.4.The covariance calibration techniques,with the scaling one as a represent,perform poorly in terms of the generalization capability and computation efficiency.As such,a covariance calibration approach based on the machine learning is developed.The algorithm is computationally efficient and performs well in the covariance calibration.Models learnt for an object possess good generalization capability,and can be used to other objects having similar spatial-temporal characteristics with the learnt object.The Jaccard similarity is applied to measure the spatial-temporal closeness between two objects.It is shown that,applying machine learning models to objects of high similarity in the same constellation can improve the covariance realism by more than 50%.5.Propagation filter,coordinate system for uncertainty description and probability density function for presenting uncertainty are the three main factors affecting the propagation of orbit state uncertainty of space object.The initial uncertainty is normally described by a Gaussian,but choices on the filter and coordinate are less certain.To investigate the effects of used filter and coordinate system on the uncertainty propagation,experiments on 6 combinations,with one of UKF(Unscented Karman Filter)and CUTF(Conjugate Unscented Filter)as filter and one of ECI,EqOE(Equinoctial Orbital Elements)and GEqOE(Generalized Equinoctial Orbital Elements)as coordinate system,are carried out.Results demonstrate that,for LEO,HEO and GEO objects,the combination of CUTF and GEqOE achieves the longest time in keeping the fidelity of propagated covariance.