GPS双差观测值的方差-协方差分量估计

Variance-Covariance Component Estimation and Analysis of GPS Double-differenced Observables

随机模型是测量平差的重要组成部分,不合理的随机模型可能导致平差结果失真。因此,方差-协方差分量估计长期以来是数据处理界研究的热点。本文假定各历元的GPS双差观测值具有相同的方差-协方差矩阵,在历元之间相互独立,采用极大似然法、最小二乘法和MINQUE估计法三种方差-协方差估计方法计算方差-协方差阵的所有元素。根据实测GPS数据,三种方法估计的方差-协方差阵非常接近,但与GPS基线解算时常用的先验协方差阵有明显区别,说明GPS基线解算有必要进行方差-协方差分量估计。

The stochastic model plays the same important role in adjustment as the function model. Study of the observables is an essential prerequisite in order to estimate correctly the unknown parameters. Improper stochastic model will cause systematic deviations and disaccord with the real results. This Paper defines the covariance matrix in double-differenced GPS observables which meets the conditions as follows： the observables are independent between the different epochs, the different variance and covariance components between any two observables within epoch and the same dual-differenced satellites have the same variance in the different epochs. The variance matrix is estimated based on the Maximum Likelihood, Least-square and MINQUE algorithm respectively. The results estimated by the three methods are coincided with each other, but significantly different from the normally used （co） variance matrix in GPS processing.