Improved Grey Prediction Model And Its Application In Surveying And Mapping Data Processing

A Scientific prediction is a formation of a more objective response to the future development trends on the basis of the past information.Scientific prediction is the fundamental purpose and main task of a forecast.Among the existing forecasting methods,grey prediction model is widely used in various fields due to its features of less sample and calculation.Although the grey prediction modeling has already made some gratifying research results after 30 years of development,as a subject,the theoretical system needs to be enriched and improved.In this paper,the model is improved and optimized by deeply analyzing the factors that affect the accuracy of grey prediction model.The main results include the following aspects:(1)For the problem of the optimization of model GM(1,1)initial condition,A new optimal initial condition solving algorithm is derived.That is,transformed the optimal initial condition selection problem into finding the optimal C value.The least squares method is used twice to obtain the smallest values that satisfy the sum of squares of errors.It is shown by numerical examples,the algorithm in this paper is not only of high precision and high efficiency,simple and intuitive,but also more conducive to the realization of the program.(2)As the robustness of the least squares method used in the grey GM(1,1)model parameter estimation is not strong,and the raw data with a small amount of gross errors affect the cumulative generation of data that may lead to greater deviation of the parameter estimation,the least absolute deviations with a strong robustness is used directly to the original data to estimate the parameters.Linearize the nonlinear reduction function and use the idea of linear programming to estimate the parameters.The experimental results show that the algorithm proposed in this paper has strong robustness and is more suitable for parameter estimation when the sequence of exponential changes is mixed with the gross errors.(3)By analyzing the defects of background values constructed by GM(1,1)and PGM(1,1)models in the process of parameter solving,different weight background parameters are introduced for different moments,at the same time,combined greynonlinear model with particle weight algorithm to further improve the prediction accuracy of the model,then the PSO-GM model based on particle swarm optimization and weighted grey combination is established.The reliability and practicability of the new model are verified by theoretical analysis and examples.(4)The GM(1,1)model based on double variable weight buffer operator is constructed.the traditional GM(1,1)model is optimized by combining the variable weight weakening buffer operator and the weighted background value,and it is applied to the Beidou satellite clock short-term forecast,which effectively improves the prediction accuracy of the traditional GM(1,1)model and expands the application scope of the model.(5)For the traditional multivariable MGM(1,n)model,the nearest neighbor mean value of the cumulative value is taken as the background value in the parameter solving.By assigning different weights to each associated point to construct the background value,And the genetic algorithm is used to find a set of weights that satisfy the minimum square sum of errors.The results show that the accuracy of the optimized model is much improved on the basis of the traditional model.