PEIV模型参数估计新算法

A New Algorithm of Parameter Estimation for PEIV Model

PEIV(Partial Errors-In-Variables)模型是EIV模型的扩展,它能解决系数矩阵含有非随机元素或存在结构特性的问题。针对常规PEIV模型算法的复杂性,提出了一种PEIV模型参数估计的新算法。该算法将系数矩阵含误差的元素看成是一类观测值,与平差模型原观测值构成两类观测值,将PEIV平差模型表示为类似于传统的最小二乘间接平差模型,再通过非线性最小二乘平差理论,推导出了算法的迭代公式和精度评定公式。算法迭代格式与间接平差类似,通过算例验证了算法的可行性和正确性。

EIV（ Errors-In-Variables） model is expanded to PEIV（ Partial Errors-In-Variables） model, in which not all the elements of the design matrix are random. A new iteration algorithm of totla least squares and accuracy evaluation formulas for PEIV model are deuced by the nonlinear least squares adjustment theory and the method. The elements which contain errors in the coefficient matrix is taken as one class of observations. The examples illustrate that the new algorithm proposed in this paper is efficient and simple, which can be used in a general case in practice.