广义权阵及其在平差中的应用

本文提出了协方差阵奇异时广义权阵的概念,给出了适用于设计阵列满秩或降秩、协方差阵奇异或非奇异的所有情况下测量平差的统一准则,并利用这一准则研究了协方差阵奇异时的参数估计问题,证明了其结果和Rao最小二乘统一理论等价。本文利用矩阵的平行加性质,推导了奇异协方差传播时广义权阵的计算公式,最后介绍了广义权阵在系统误差补偿的平差中及变形参数估计中的几个实际应用。

Generalized Weight Matrices and it's Applications in Adjustment

By introducing the concept of generalized weight matrices of singular covariance matrices, the unified adjustment criterion is given for singular linear models. The result of parameters estimation is equivalent to Rao's result using unified least-square theory. In propagation of singular covariance matrices, the parallel sum of matrices is discussed for calculating the generalized weight matrices. Finally, the applications in ad ustment of additional systematic parameters and estimation of parameters of defor mation models are studied.