Research On Associating Un-Correlated Tracks Based-on Only Very Short Arc Angle Observations Of Space Debris

With the development of space technologies in various countries,the number of space debris continues to increase.The population of cent-meter sized space debris is over 500,000 and they pose a serious threat to the normal operation of human spacecraft or satellites.The increasing risk of collisions between space objects seriously threatens the sustainable use of space.The astonishing collision event between the defunct Cosmos 2251 and the operating Iridium 33 satellite in 2009 shocked the world,and the danger of space debris has attracted increasing attention.One of the main reasons for the occurrence of this kind of space collision events is that numerous space debris are uncatalogued,and it is impossible to carry out collision warning and avoidance operations for uncatalogued debris.To avoid collisions,building a large-scale catalogue of space debris,improving cataloging accuracy and expanding the cataloging ability from the current 10 cm objects to 1 cm in LEO have become an important and urgent task for the space powers in the field of Space Situational Awareness(SSA).In fact,space debris cataloging is the basis for conducting space collision warning,debris avoidance by spacecraft,Space Traffic Management(STM),etc.It is of great theoretical and practical significance to study the space debris-cataloging problem.The observations are the basis for cataloguing the space debris.One of the main means is the optical detection and tracking by telescope,and it has the advantages of low cost and convenience.When a telescope is operated in the sky survey mode,since the relative motion between the telescope and the space debris is usually very fast(7-10 km/s)and small field of view,the duration of the observation data(arc length)is usually very short,mostly less than 1 minute for the LEO objects,or even only a dozen of seconds.It is called a Very Short Arc(VSA).There are two key issues in cataloging new space debris using VSA angles,namely the Initial Orbit Determination(IOD)and correlation of multiple VSAs.IOD is to determine a set of initial orbit elements.There are various IOD algorithms with the VSA angles.However,the errors of the IOD elements from the VSA angles are usually very large(e.g.,the semi-major axis error usually reaches tens of kilometers).However,since the errors of IOD elements from a single VSA are too large,the elements cannot be used to be directly catalog a debris.The element accuracy can be significantly improved by process two or more VSAs,and thus it is necessary to correlate the observations of multiple VSAs or IOD elements from the same object to allow for the Precise Orbit Determination(POD)from the correlated multiple arcs.Without any prior information,the process to determine whether the two sets of IODs are from the same object is called UCT(un-correlated track)association.A great amount of data would be wasted without correct UCT association.In particular,spacebased optical surveillance devices can collect thousands of VSA observations per satellite per day.Without effective UCT correlation technology,it will not be able to realize the huge potential of the space-based optical surveillance in cataloguing small debris.In the past decade,scientists all over the world have been engaged in a lot of research on the UCT or observation correlation of space objects,and proposed or improved a number of methods.Most of these algorithms are theoretical sound,but difficult to implement.For example,the CBTA(covariance-based track association)method requires accurate propagation of the IOD elements errors.However,accurately propagating orbit elements errors in the highly non-linear orbital dynamics system is another challenging problem in the field of SSA.Since it is still difficult to obtain the precise analytical solution,only the numerical solutions with different degrees of approximation are available now,which would require comprehensive computing capacity.The demand for a theoretically sound and algorithmically effective method to deal with the association of vast VSA data collected by the near-future space-based optical space surveillance system is the main driving force for this Ph D research.Set by the space-based VSA angles,large IOD element errors,and the practical difficulties in applying existing methods,this thesis approaches the UCT association problem based on a profound analysis on the relationship between the orbital parameter errors and the position error,and develops a pure geometrical UCT association method without any need to use error information of IOD elements.The new UCT association method is experimented and its performance is evaluated with comprehensive simulated and real VSA angles data.The contributions of this thesis are summarized as following:1)The current research status of the observation data correlation of space objects or UCT association is presented and analyzed.The algorithms proposed by domestic scholars mainly aim at radar data and the algorithm for UCT association of VSA angle data is rarely founded.The methods for the UCT or observation correlation are grouped into five,namely the AR(Admissible Region)method,the IVP(Initial Value Problem)and BVP(Boundary Value Problem)method,the CBTA(Covariance-based Track Association)method,the JPDA(Joint Probabilistic Data Association)method,and the MTT(Multi-Target Tracking)method.These methods are introduced and their advantages and disadvantages are analyzed.It is pointed that these methods need the propagation of covariance matrix of IOD elements or the propagation of angular data errors,or the algorithms are extremely complex to implement,or the computation burden is very heavy,all of which make their practical applications problematic.2)The relationship between the orbital element errors and the 3D position errors is analyzed,followed by the detailed derivation of the proposed geometrical method of the UCT correlation.Theoretically,the along track error is almost linearly related to the SMA(semi-major axis).Based on this property,the along-track positional difference at the middle epoch between two independent sets of IOD elements,after the proper propagation,from the same object,is close to zero,if the error of the SMA of one IOD has the same magnitude but opposite sign as the other,since the effects of other element errors on the along-track difference are almost constant.Use of this prominent error behavior,the geometrical UCT association is developed,in that one SMA can be adjusted to make the along-track positional difference at the middle epoch approach zero,if two IODs are from the same object;if two IODs are from two different objects,the SMA adjustment would not result in zero along-track difference at the middle epoch.3)The performance of the geometrical method is examined by using simulated VSA angles of LEO,MEO and GEO objects collected by LEO telescopes.Considering the scarcity of the space-based observations,the different space-based sensors are designed and the observations are generated.The mean duration of the VSAs of LEO,MEO and GEO objects observed by space-based LEO sensors are 23 s,115 s,and 99 s,respectively.Then the IOD elements determined by the Range-Search(RS)based IOD method are associated with both the CBTA method and the geometrical method.The results show that when the time interval between two IODs is less than three days,the TP(true positive)rate are 84.0% and 78.6% for LEO,95.8% and 49.4% for MEO,and 75.8% and 53.4% for GEO objects,with the geometrical method and the CBTA method,respectively.This suggests that the TP rate by the geometrical method is significantly higher than that by the CBTA method.In terms of the computation efficiency,the geometrical method is several hundred even one thousand times faster than the CBTA method.4)The geometrical method is validated with the VSAs observed by a ground-based EO array at Changchun Observatory.The application of the geometrical method to the VSA association results in the TP rate of 90% while the TP rate is only 48% with the CBAT method,which clearly illustrates the superiority of the geometrical method over the well-recognized CBTA method.415 “new” objects are tentatively catalogued with the VSAs from the EO obtained from Aug 2017 to Sep,2017.5)The software for cataloguing space objects with VSAs is developed with particular objective to effectively use Space-based VSA angles.To this end,a space debris orbit cataloging software system with wholly owned intellectual property is designed,programmed,and tested.The software contains the following functions: the identification of new debris,IOD with VSAs,IOD correlation,and POD from multiple VSA angles,etc.The software system,on one hand,is now able to serve the expansion and maintenance of the space debris catalogue,and on the other hand,can be used a platform for further research on the UCT association and debris catalogue buildup.