Improving Gooding Initial Orbit Determination Method

Space activities over more than 60 years have resulted in nearly 1 million pieces of space debris larger than 1cm,which make the near-Earth space a strategical resource competed by many nations on one hand,and also dramatically increase the risk of space collisions on the other hand.As such,the space sustainability,national security and space asset safety are all threatened.Providing services in the space collision warning,space traffic management and space security information not only demand the development of the space surveillance technologies but also raise unprecedent challenges in the space debris orbital cataloguing.The geographical restriction on the ground-based surveillance network has necessitated the space-based surveillance for building a large-scale space catalogue.Angular data of space objects collected by space-based optical sensors is the base for cataloguing new objects,where the initial orbit determination(IOD)is the first of many key techniques.The fast relative motion between space sensors and objects makes the observed orbital arcs mostly short or very short in terms of the orbital period of a space object.The angles-only data from a short orbital arc has weak geometrical constraint on the orbit,which causes the observation equations in many IOD algorithms ill conditioned.As a result,many IOD methods are very sensitive to the angles errors that the IOD solution accuracy is low and the robustness is poor.Compared with the well-known IOD methods such as the Laplace,Gauss and Double-R method,the Gooding IOD method has a better performance in the solution accuracy and robustness.However,the Gooding method still suffers from the ill conditions originated from the short-arc geometry.Hence,this thesis is focused on improving the Gooding method.The sensitivity of the Gooding IOD method to the angles errors and orbital geometry is mathematically analyzed,and a variable to measure the degree of ill-condition is defined.Then,two strategies are proposed to ease the ill condition.The first one expands the Gooding method to k-directions from original 3-dirstions.The second strategy is to introduce the ridge estimation algorithm to ease the singularity of the solution equations,where a method to determine the ridge parameter is proposed.Three space-based surveillance simulation experiments are designed to assess the performance of the improving strategies.which are the surveillances of low Earth orbit(LEO),medium Earth orbit(MEO)and geosynchronous orbit(GEO)objects,respectively.In order to examine the effect of the arc length on the performance,the solutions from orbital arcs of 30～60 s,60 ～ 90 s and longer than 90 s are analyzed.Every short arc is processed using the range search method,Gooding method and improved method.Experiment results in all data circumstances show that,the improved method outperforms other two methods by a large margin in several major statistics.The improved method has overwhelming convergence superiority over other two methods.The accuracy of estimated orbit elements using the improved method is increased by more than 85% and 80%,comparing to that using the Gooding and range search method,respectively.Importantly,the improved method does not need eccentricity constraint required by some other methods,making it have wide applicability.The ridge-estimation assisted Gooding method is theoretically sound to ease the illcondition in the solution equations of the short/very short arc data.The methodology may be applied to improve performance of other IOD methods.The high performance in the convergence,accuracy,computation efficiency and applicability of the improved method will be engineeringly profound to the space object cataloguing capability,which is an essential part of the space situational awareness.