状态转移矩阵的差分算法及其应用

指出用数值积分方法计算状态转移矩阵在程序实现时存在的困难。根据精密定轨和参数解算的实际需要，提出用差分算法，即通过两条接近的轨道的差来计算状态转移矩阵差分算法的优点是程序具有良好的结构且编程简单，其不足之处是差分时可能损失精度。将差分算法与数值积分方法的结果进行比较，提出克服其不足处的方法。

THE DIFFERENCE ALGORITHM FOR STATE TRANSITION MATRIX AND ITS APPLICATIONS

The difficulties to code the numerical integration for the computation of state transition matrix are analyzed. First of all, the partials of the acceleration vector with respect to the state vector are needed. But the partials may be very complicated and time consuming for some dynamical models, such as the earth gravitation field and radiation model. For some dynamical models like the CIRA96 atmospheric density, it would be even impossible to obtain the partials with analytic method. Secondly, the matrix product imposes serious problems on both the programming and computer memory when the state vector has large dimensions. In view of the practice of precise orbit determination and parameter solution, the difference algorithm to compute state transition matrix is proposed. The basic idea is to difference two nearby orbits rather than to differentiate them. As a good approximation to the numerical integration, the difference algorithm is easy to program as illustrated in this paper. It is also pointed out that the accuracy might be lost near the initial epoch. The results of both methods are compared and the ways to assure the accuracy of the difference algorithm are discussed. It may be concluded that the difference algorithm will play an important role in the future data analysis practice because not only it is accurate enough, but also it simplifies the structure of the program.