Research On Spatial Data Interpolation Modeling Based On Linear Maximum Entropy Principle

With the development of geographic information system,remote sensing and global positioning system,the accuracy of spatial data model is becoming higher and higher.However,the existing interpolation methods have their own disadvantages and applicability.For example,the traditional spatial data interpolation method relies too much on the number of sample data,and the maximum entropy model interpolation method is not unique.These factors will make the accuracy of the established spatial data model is not high,and even distortion will occur,which brings great inconvenience to the generation of subsequent surveying and mapping products.In order to improve the disadvantages mentioned above and further improve the accuracy and efficiency of spatial interpolation,this paper proposes an interpolation method based on the principle of linear maximum entropy,in order to quickly generate a high-precision spatial data model,so as to have a positive impact on people’s subsequent production and life.This paper proposes an interpolation method based on the principle of linear maximum entropy,which takes the production probability value p representing the spatial domain variable in the maximum entropy model as the expansion point to carry out Taylor expansion of the entropy function.The linear formula obtained after expansion is taken as the objective function,and the mathematical expectation and variance of the elevation value of the sample points are used to establish the equality constraint conditions.The maximum and minimum weight inequality constraints were set up,and the height of the fixed point was determined by solving the weight coefficient of the fixed point through the maximum entropy value.Linprog function in MATLAB software platform was used to solve the linear maximum entropy model.In order to verify the effectiveness of this method,the experiment of this paper is based on topographic data and non-topographic data,and discusses the application of linear maximum entropy principle in spatial data interpolation modeling through two application directions of DEM interpolation and point cloud data hole repair.In this paper,the inverse distance weight method is selected as the representative of the traditional spatial interpolation method to build a model,and the maximum entropy model and linear maximum entropy model interpolation methods are respectively used for interpolation modeling,and then the inverse distance weight method and the measured data are compared and analyzed.In this paper,root-mean-square error is selected as the evaluation standard of model accuracy,and then this method is demonstrated and analyzed from three aspects of mapping effect,result stability and operation efficiency,so as to judge the interpolation method which can establish the optimal spatial data model.The results show that the linear maximum entropy model interpolation method can not only solve the disadvantages of the traditional method which relies too much on the number of sample data,but also solve the problem that the results of the maximum entropy model interpolation method are not unique and the calculation speed is slow.The linear maximum entropy model interpolation method has the best model effect and the fastest operation speed,and its stability is obviously better than that of the maximum entropy model interpolation method.Therefore,no matter DEM interpolation or point cloud data hole repair,interpolation method based on linear maximum entropy principle has the best interpolation accuracy,result stability and operation rate,indicating that this method can better meet the needs of spatial data models under the current situation,and provide certain reference basis for the generation of DEM,three-dimensional model and other surveying and mapping products.