An Analytical Method for Calculating Short-Term Space Interception Probability

Algorithm 1: The complete process of analytical calculation of short-term space interception probability.

1. Input:

 Orbital information and orbital error distribution of target and interceptor at the initial moment , ; Target and interceptor diameter , ; The number of items of power series N.

2. Error propagation calculation

 1) Get the TCA and MD from the orbit extrapolation according to the initial orbit information of the target and interceptor;

 2) Calculate the true anomaly of the target orbit and the true anomaly of the interceptor orbit corresponding to the TCA;

 3) Calculate and according to formula (25);

 4) Calculate the eccentric anomaly of the target orbit and the eccentric anomaly of the interceptor orbit corresponding to the TCA;

 5) Calculate , according to the appendix, formula (6), formula (30), and formula (35);

 6) According to equation (36), the state error covariance matrix and of the target and the interceptor at the TCA are obtained from and .

3. Error projection and coordinate system rotation

 1) According to equations (41), (43), and (44), calculate the joint error covariance matrix of the target and the interceptor at the TCA in the encounter plane;

 2) Calculate the rotation angle according to equation (46), and obtain the joint error distribution parameters , , , and in the calculation coordinate system according to equation (48).

4. Space interception probability calculation

 1) Calculate , , , and according to equation (58), and calculate ~ according to equation (66) and the term number N of power series;

 2) Calculate space interception probability and maximum truncation error according to equations (65) and (75).

5. Output:

 Space interception probability and maximum truncation error .

Algorithm 1: The complete process of analytical calculation of short-term space interception probability.