Research On Orbital Prediction Error And Collision Probability Of Space Objects

The amount of on-orbit space objects has been growing continuously because ofthe increasing and frequent aerospace activities, which has been strongly affecting thespace environment and the sustainable development of aerospace industry. Thishighlights the practical necessity of conjunction assessment and collision avoidance.Taking the process of conjunction assessment as research object, this dissertation mainlystudies the orbital prediction error and collision probability problems involved inconjunction assessment. The main achievements are summarized as follows:The propagation characteristics of initial orbital error and negativecorrelation characteristics of position and velocity error are studied based on therelative motion theory. Considering that the orbital prediction error is much smallerthan the radius of object, the true state and predicted state of space object can be seen astwo objects: a real one and a virtual one, and the prediction error can be seen as therelative motion between them. The propagation characteristics of initial error of circularand eccentric orbit are respectively analyzed based on C-W Equations and T-HEquations, which belong to the algebraic model. The negative correlation characteristicsof position and velocity error in the case of near-circular orbit are studied based on thegeometrical model of relative motion. The application of negative correlationcharacteristics in the determination of initial error covariance is discussed. Thecorrelation characteristics are validated by historical orbital data.A methodology for periodicity characterization and Poisson series fitting fororbital prediction error based on historical orbital data is presented. The predictedstates in an orbital period centered at its epoch are taken as reference states. Thecomparison is conducted in a whole period so that the residuals can reflect theperiodicity. The Poisson coefficient matrices of each error components are fitted usingleast squares method. Effects of polynomial, trigonometric, and mixed terms of Poissonseries are discussed. As error-fitting function, the Poisson series can describe variationof error with respect to propagation duration and on-orbit position of objects. ThePoisson coefficient matrices can be obtained before close approach analysis.The explicit expressions of collision probability (Pc) in the cases of circularorbit and general orbit are derived based on analysis of conjunction geometry. Inthe case of circular orbit, Pcis expressed as explicit functions of the RSW componentsof relative position or the conjunction geometries (crossing altitude difference and timedifference of the line of intersection of two orbital planes, the angle between orbitalplanes, etc.). In the case of general orbit, Pcis expressed as explicit functions of theconjunction geometries (crossing altitude difference and time difference of the commonperpendicular line to two velocities, the angle between two velocities, etc.) or the NTW components of relative position. The explicit expression relates Pcwith components ofrelative position. The eccentricity’s bound of explicit expression in the case of circularis determined. The precision of explicit expression is sufficient for conjunction riskassessment and decision-making for most LEO objects.The sensitivity of Pcand maximum collision probability (Pcmax) is analyzedbased on the explicit expression of Pc, the integrated procedure for estimating Pcmaxis provided. The sensitivities of Pcto RSW components of relative position, orbitalerror standard deviations, conjunction angle and object’s size are analyzed based on theexplicit expression of Pc. Analytical expressions of Pcmaxin terms of conjunctiongeometries or components of relative position are deduced in both cases of fixed andarbitrary error ellipsoid shape. Special cases when one of the coordinates in conjunctionplane tends to zero are discussed. The integrated procedure for estimating Pcmaxandcorresponding error standard deviations is provided.The probabilities of missing alarm and false alarm are studied based on theexplicit expressions of Pc, the comprehensive assessment of collision riskconsidering multi-factors is researched. The conjunction assessment is substantially adiscriminant analysis problem. The safety-region and danger-region of conjunctionassessment are defined by using explicit expression of Pc. The definition, formulae, andbasic property of probabilities of missing alarm and false alarm are provided. Thecomprehensive assessment of collision risk considering both risk assessment and qualityassessment parameters is introduced and implemented.The conjunction assessment software system is introduced and demonstratedby Two Line Element (TLE) data of space catalogued objects. The constituentmodules and parallel computing environment of conjunction assessment softwaresystem are introduced, in which the methods of orbital error analysis and collisionprobability analysis achieved in this dissertation have been applied. The softwaresystem is demonstrated by TLE data of space catalogued objects.Motivated by practical requirement of conjunction assessment, this dissertationfocuses on the involved orbit error and collision probability problem. This dissertationhas developed the conjunction assessment methodology. The achievements will providetechnical support for the establishment and improvement of conjunction assessmentengineering system.