Research On Collision Probability Between Space Objects During Encounter

The calculation of collision probability is an important method to trajectory early warning and the safety of spacecraft. Currently, there are some problems with the algorithm of calculating collision probability, the computing efficiency is not ideal to acquire planar probability density function; the incoming error cannot be ignored when changing the integral area on the encounter plane; and the description to the equivalent model only gives one simple spherical model. Based on the short-term encounter model, a method that can compute the value of mean and variance simultaneity is proposed and a precise algorithm of collision probability at encounter plane is also put forward; the improvement of the old model is presented in detail from the attribution of density and equivalent model of space objects with corresponding algorithm. At last, the collision in the case of long-term encounter is analyzed particularly.The primary work of the paper is as follows:Firstly, the short-term encounter model is studied and the linear movement of space objects is validated in the encounter area with orbit forecast data. Experiments show that it is feasible to approximate curve with beeline in short arc. A method is put forward to obtain mean and variance of the planar probability density function simultaneously. Based on orthogonal projection and eigenvalue decomposition, it can be obtained without simultaneous equations in the process of changing the three-dimension problem to encounter plane.Secondly, one fast algorithm of collision probability is proposed based on round area. It adopts approximate integral theorem, turns the two-dimension problem to multinomial, and avoids the infection of the change of integral area to the compute precision. Experiments show that the precision of the method is close to the result of direct integral and the ratio between approximation and exact value arrives at 0.99.Thirdly, the original model is improved on probability distribution and equivalent model of space objects. A collision model is developed with corresponding algorithm when the position error submits to uniformity. Experiments show that the method can get the collision probability more efficiency and can be used as early filtration. The ellipsoid equivalent model of space objects and corresponding algorithm is developed. The experiment shows that the description of space object is more accurate to its characteristic and the model can provide an important reference to establish the actual shape model of space objects.Finally, algorithm for computing the collision probability of long-term encounter is proposed with Clohessey-Whiltshire equation and Monte Carlo integral, and the minimal variance is acquired because of the coherence of objective function and important function. At last the method of long-term encounter is compared with the algorithm of short-term encounter.