Novel gross error detection approaches of small samples based on GM(1,1) model

摘要

Aiming at the gross error detection problem of small samples whose distribution is unknown, two novel detection approaches based on GM(1,1) model, direct modeling detection approach and extrapolated precision detection approach were proposed. Firstly, the mechanism of GM(1,1) and the correlative modeling parameters were introduced. Secondly, the detection principles and steps of two approaches were put forward. The direct modeling detection approach was based on the changing rate of the residual error square sum. The extrapolated precision detection approach was based on the modeling precision and extrapolated value precision synthetically. Then the gross error detection example of a practical test sequence was given. The simulation example results show that the proposed approaches are feasible and effective. And they have no demands for the distribution of small samples. In the end, the questions of sample quantities, the rationality of the approaches and so on, are discussed.