一种处理系统误差的新方法

测量数据处理中影响观测值的因素有2个部分：线性部分和某种干扰因素，干扰因素同观测量的关系是完全未知的，没有理由将其归入误差项，可以将其看成半参数模型中的非参数分量，即用非参数分量表达参数模型不完善的部分。本文首先利用自然样条函数法，找到符合条件的非参数自然插值样条函数；其次利用偏残差法并综合最小二乘法，导出了这种平差方法的解算公式；最后，用一个算例说明了此方法的优越性。

New method for processing systematic errors

The factors that impact observed values can be divided into two parts: the main part is a linear part, another part is certain interference factor, which has a complete unknown relationship with observed values, and there is no reason to classify it under error item. Too much information will be lost if the non-parametric model (though it has higher flexibility) is used, imitated result is bad if the linear model is adopted. Firstly, natural cubic spline method is used to find natural cubic spline function of nonparametric component. secondly, the estimators of parameters are derived by using the partial residual and least square method, and the approach of bandwidth selection in the semi-parametric surveying adjustment model is discussed.Finally, the result obtained by using new method corresponds with that by using least square method. A calculation example is used to show that the new method presented in this paper is an effective way to solve the problem, and the estimated values are closer to their theoretical values than the values obtained using adjustment method of least squares.