Research On Collision Probability In Space Objects Collision Detection

The collision probability problems in space objects collision detection and avoidance were mainly researched in this thesis, including calculational methods, the explicit expression, influencing factors and the confidence level of the collision probability, and propagation characteristics of the error covariance of the orbital prediction, which laid the foundation of the collision detection and avoidance of space objects.The brief situation of the orbital environment was introduced, and then, key techniques of the collision detection and avoidance of space objects were discussed, and the basic frame of the collision detection and avoidance based on the collision probability was advanced.Calculational methods of the collision probability were deeply studied. The encounter coordinates and the integral-calculation coordinates were defined, with the help of coordinate transformation and the projection of the position error covariance, the 3-dimensional collision probability problem was degraded into the integral of a 2-dimensional probability density function (PDF) over the region of a circle. Through the space compression, the integral of anisotropic PDF over the region of the circle was transformed to the integral of isotropic PDF over the region of an ellipse. And two calculational methods of the probability integral were advanced. The expressions of the maximal collision probability and the corresponding position error covariance were deeply analyzed based on the approximate results. The calculation of the collision probability in the case of the lower relative velocity was also discussed.The explicit expression of the collision probability was deduced under the assumption that the orbit was a circle, the collision probability was expressed as an explicit function of the encounter geometry (crossing altitude difference and time difference of the line of the intersection of the two orbital planes, orbital planes included angle) and position error variance in RSW coordinates. With the help of the explicit expression, the influencing factors of the collision probability were analyzed, some significant conclusions were obtained.The confidence level of the collision probability and its estimation technique were discussed. For describing the creditability of the calculated collision probability, concepts of the confidence interval of the collision probability and confidence level were introduced. Considering that the collision probability was a function of the encounter geometry and the position error variance, the confidence level of the collision probability was determined by the confidence level of the position error variance. Based on the confidence level and the confidence interval of the position error variance, the confidence level and the confidence interval of the collision probability were analyzed with the explicit expression of collision probability.Characteristics of the propagation of the error covariance matrix which was essential in the probability calculation were analyzed; an assumption was advanced to explain the characteristics. Based on Hill equation and the CADET technique, the propagation of the initial error covariance of TLE was discussed. By using the Hill equation which took no account of the perturbation deviation and the Hill equation which took account of atmospheric drag deviation respectively, the initial error covariance of TLE was separated.In the end, a space collision avoidance maneuver example and a weekly probability-maximum encounter event published by SCORATES were analyzed by the means of the collision probability presented previously. The results indicated that the collision probability method advanced in this thesis was accurate and efficient, and could be used in engineering practice.