利用正交变换方法计算协方差分析的统计量

COMPUTATION OF THE STATISTICAL QUANTITIES FOR COVARIANCE ANALYSIS USING THE ORTHOGONAL TRANSFORMATION METHOD

证明用Givens—Gentleman正交变换给出的加仅最小二乘解与统计定轨理论求得的解一致．采用正交变换方法计算其它的一些重要的统计量，如考察协方差矩阵、摄动矩阵等，并计算这些量随时间的传播．这种算法的优点是通过降低法方程的条件数提高计算的稳定性，同时可以方便地对不同的参数组合情况求解而不需多次解算法方程．

The solution of weighted least-square problems obtained with the CivensGentleman orthogonal transformation method is shown to be equivalent to that in the statistical orbit determination theory. By using this method, the covariance analysis quantities of statistical significance, such as the considered covariance matrix and sensitivity matrix, are derived along with their propagation from initial epoch. It turns out that the covariance analysis with this method has the merits of more flexibility in parameters' combination for the achievement of optimal solution as well as a better numerical stability.