利用随机先验信息克服秩亏问题的方差分量估计

Variance Components Estimation for the Uncertain Priori Information to Overcome the Rank-Deficiency

利用研究方差分量模型解决随机先验信息在线性模型秩亏平差问题中不确定性的问题,利用最优不变二次无偏估计进行先验信息与观测信息两部分的方差分量估计,得到合理的随机模型,最终达到使先验信息成为可靠基准的目的。从一个典型的大地水准测量案例出发,观测数据为高差观测值,没有绝对高程基准的加入,先验信息便是先前估计得到的高程基准。推导先验信息和观测信息两部分的方差分量,以便引入的基准在平差过程中更加合理可靠。

In this paper,we use variance components estimation to solve the uncertainty problem of the random priori information in the linear rank-deficiency adjustment.The variance component of the two parts is estimated by the best invariant quadratic unbiased estimation,then a reasonable stochastic model is obtained to make sure the priori information as a reliable benchmark.Starting from a typical geodetic leveling network,the observation data is the elevation difference vector,without the addition of absolute elevation datum.The priori information is the elevation datum obtained by previous estimation.The variance components of these two parts are derived to make the introduced datum more reasonable and reliable in the adjustment process.