Outlier Detection On Random Model Of Multiplicative Error

It is well known that a outlier in the observed value,the result of the adjustment is not optimal.However,it is unable to identify the gross error from the data itself.So we need to take some methods or measures to identify the position of the outlier data and to weaken or even eliminate the effect in the process of adjustment.At present,the processing of outlier in measurement data can be roughly divided into two categories.The first category is outlier detection method that taking the outlier as a function model error,which is also known as the average drift model detection,such as Barrda Data detection method,t method,standard normal test method and F-T method,of which will identify the outlier data.The second category is the variance expansion model that taking outlier as the stochastic model,such as ridge estimation,Robust estimation and selection iterative method of which will reduce or eliminate the impact of outlier margin in the adjustment.What should be pointed out is that the methods above are all succeed based on the Gauss-Markov model(G-M model).However,as the data acquisition tool becoming more advanced and the observing environment more plasticity,the random error will no longer affect the observed value in the form of addition,but with the multiplicative or additive mixed disturbance.If we still use outlier detection theory and method developed from the G-M model to do the error recognition or reduced its influence in the adjustment,.Can we achieve the effect we expected?The main content of this article is to introduce the applicable condition and shortcomings of the first category methods and to derive the expression of standard normal test method,the t method and the F-T method under the random model of multiplicative error.Then,through the experiment to verify its feasibility.The findings are as follows:when the error in the a priori unit is known,no matter how many outliers exist in the sample data,the standard normal test method can detect the position of the outlier.But sometimes the existing of large a outlier or multiple outliers has a great impact on the parameters that will lead misjudgment of other points.When the error in the a priori unit is unknown,the deviation of the t method can only be used to determine the position of the outlier.When there are multiple outliers in the data,t method can only detect the location of the part of the outliers,there is a pseudo-false.Then combined with the F-T method,it will be able to detect the actual outlier match with the actual location,that will effectively avoid the mistakes happening of true and false error.Based on the experimental results,we can conclude that using the standard normal test method,t method and F-T method to carry out outlier detection of multiplicative error random model is feasible.