粗差的拟准检定法(QUAD法)

Quasi Accurate Detection of gross errors (QUAD)

以往对付粗差的各种方法都是以余差（残差）为研究对象的。本文提出一种全新的研究思路和方法，从真误差入手。真误差与观测值有确定的解析关系。但关系式的系数阵是秩亏的。本文借鉴周江文的“拟稳平差”思想，提出“拟准观测”的概念，附加“拟准观测的真误差范数极小”的条件，解决了关于真误差的秩亏方程组求确定解的问题，推导了粗差的拟准检定法算式。该方法依据真误差估值的分布特征，检测粗差准确可靠。不仅能有效地同时定位多个粗差，估计其大小，而且能严密评定估值精度。它适合于过去用到最小二乘法（ＬＳ）的各种学科领域处理粗差。文章最后简要介绍两个算例，说明拟准检定法实施过程和效果。

The residuals in the Least Squares have been taken as the studied objects in the vary methods on dealing with gross errors in the past. A new idea and a distinctive method are proposed in this paper, which relate to real errors and their estimators. There exists a determinate and analytic representation relationship between real errors and observation values written as R Δ=- RL . However, the coefficiency matrix R is rank deficient. The unique solution on real errors in this equation can not be got directly. By using the idea of “Quasi Stable Adjustment” created by prof. Zhou Jiangwen for reference, the new concept on “Quasi Accurate Observation” is presented. Then the rank deficiency equation on real errors are resolved by adding the conditions in which the minimum of the norm of the real errors related to quasi accurate observations is restrained. The new method called as “Quasi Accurate Detection of gross errors (QUAD)” is derived in detail. The reliability and accuracy of the new method in detection of gross errors are much higher since the gross errors can be easily distinguished from the estimators of real errors according to their distributed characteristics. By using of this method, not only multiple gross errors can be exactly located and their estimators calculated accurately, but also the co variance matrices of the estimators can be evaluated strictly. The more the gross errors existed in the observations, the more evident the effectiveness of this method is. This method may be suitable to deal with the gross errors existed in different fields of science and engineering. Finally, the method of QUAD is illustrated by the two numerical examples.