改进的Helmert方差分量估计方法在精密定轨中的应用

Application of the Improved Helmert Method for Variance Component Estimation in Precise Orbit Determination

分析了 Helmert方差分量估计方法用于人造卫星精密定轨时出现负方差的原因 ,认为主要是由于观测资料信息不足而使法矩阵秩亏引起的 ,在此基础上 ,提出了利用待估参数先验信息来避免负方差的“改进的 Helmert方差分量估计方法”。试算表明 ,利用本文中的方法可以有效地消除负方差的产生。为了与现用的精密定轨软件相兼容 ,便于程序实现 ,将 Givens-Gentleman正交变换方法用于方差分量估计 ,给出了详细的计算公式。分析了先验约束的强弱对定轨计算和方差分量估计结果的影响 ,认为在一般情况下 ,先验约束应在保证定轨计算收敛并消除负方差的基础上尽可能地弱 ,以最大限度地利用实际观测值中所包含的信息。最后 ,从方差分量估计的角度讨论了先验约束对观测值自由度的影响。

The Helmert method for Variance Component Estimation (VCE) can be successfully applied to Precise Orbit Determination (POD). But sometimes, negative unit variance may be obtained. In this paper, the authors analyze this unreasonable phenomenon, and come to the conclusion that the insufficient information in observations is the main reason, which might cause rank deficiency. Based on this analysis, the authors develop an improved Helmert method for variance component estimation by using the a priori information of the estimated parameters to avoid the occurrence of negative variance. Experimental computation indicates that this method is effectual. Furthermore, considering the compatibility with the present POD software developed by Shanghai Astronomical Observatory, the authors apply the Givens Gentleman orthogonal transformation to VCE process in order to facilitate the program realization. Detailed formulae are deduced in this paper. Moreover, the effect of the strength of a priori constraints on the results of VCE is analyzed. The authors hold that in general, the a priori constraints should be as weak as possible while the POD can converge and the negative variance can be avoided. At last, the effect of a priori constraints on the degree of freedom for observations is discussed from the viewpoint of VCE.