线性化通用EIV平差模型的岭估计解法

Ridge estimation method for linearized general EIV adjustment model

通用EIV(errors-in-variables)平差模型作为经典平差模型的一般化形式,具有同时顾及多种随机误差的优势.在通用EIV平差模型加权总体最小二乘(WTLS)的线性化估计基础上,引入正则化准则.正则化矩阵为单位矩阵时为岭估计,添加目标函数,通过建立拉格朗日目标函数的最小化求解,导出加权通用EIV平差模型对应的岭估计解式,给出了确定岭参数的U曲线法和L曲线法.计算了通用EIV平差模型的线性化估计、两种岭估计及其对应的方差分量值;验证岭估计对通用EIV模型的线性化估计具有促进性,可减少迭代次数,使得参数方差分量更快趋于平稳,降低参数估计的计算量.

As a general form of classical adjustment model,general errors-in-variables(EIV)adjustment model has the advantage of taking into account multiple random errors.Based on the linear estimation of the weighted total least squares of the general EIV adjustment model,the regularization criterion is introduced.When the regularization matrix is the unit matrix,it is called the ridge estimation.The objective function is then added.By establishing the minimization solution of the Lagrange objective function,the ridge estimation solution corresponding to the weighted general EIV adjustment model is derived.The U curve method and L curve method for determining ridge parameters are given.The linear estimation,two ridge estimations and their corresponding variance components of the general EIV adjustment model are calculated.It is validated that ridge estimation can promote the linearization estimation of general EIV model,reduce the times of iterations,make the parameter variance component more stable and reduce the calculation of parameter estimation.