Quasi Accurate Detection of gross errors (QUAD)
Ou Jikun (Institute of Geodesy and Geophysics, Laboratory of Dynamical Geodesy, Chinese Academy of Sciences, Wuhan,430077)
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.