Study On Optimum Selection And Solution Of Rational Function Model Parameters

With the increasing number of high-resolution satellites,the demand for orthophoto images in production is expanding.The original satellite images are mainly produced by using rigorous imaging geometry model or rational function model.However,due to commercial confidentiality,satellite merchants often do not provide users with parameters such as satellite orbit parameters and sensor attitude.Users have no condition to build their rigorous imaging geometry model.Generally,satellite image data are attached with rational function model parameters file to hide strict imaging model parameters,which not only achieve the purpose of commercial confidentiality,but also meet the needs of users or researchers.The unknown parameters of the rational function model can be solved independently of or depending on the terrain scheme.Satellite quotient constructs a three-dimensional virtual control grid through strict imaging model parameters and fits the parameters of rational function model.This method does not need real control points on the surface,and is called terrain-independent scheme.Depending on the topographic scheme,the control points are collected on the spot by means of GPS-RTK and so on.Under special circumstances,a certain number of uniformly distributed control points can also be obtained on large-scale topographic maps.Then,according to the least square rule,the unknown parameters of the rational function model are fitted and solved.Generally,the unknown coefficients of rational polynomials are solved by adjustment based on least square theory.Because of the non-uniform distribution of control points or the over-parameterization of the model,the normal equation is easily ill-conditioned when solving the parameters of the higher-order rational function model,and the least square method can not get the correct solution at this time.Aiming at the ill-conditioned situation of solving equation by rational function model,two methods are given in this paper.According to whether the number of parameters of the standard rational function model changes,it can be divided into direct solution method and optimum parameter method.Optimized parameter method removes some parameters with strong correlation through complex collinearity diagnosis,so as to weaken the morbidity of normal equation and improve the fitting accuracy of rational function model.The direct solution method solves the ill-conditioned normal equation without changing the rational function model and the number of parameters.There are truncated singular value method,Tikhonov regularization method,iterative solution method and genetic algorithm,etc.This paper mainly introduces the regularization method.This paper mainly adopts L-curve method and GCV curve method to determine regularization parameters,and then solves the regularization solution of the normal equation of rational function model,and compares the stability,feasibility and accuracy of the two methods.Based on L-curve-Tikhonov regularization method and mean square error theory,an improved optimal regularization method is proposed.This method determines the optimal regularization parameters and then the optimal regularization solution of the normal equation.In this method,the regularization parameters determined by L-curve are taken as initial values,and the optimal regularization parameters are determined when the mean square error is the smallest.Essentially,it is a fine-tuning method for L-curve regularization parameters.In the aspect of parameter optimization,correlation coefficient method and conditional index-variance decomposition ratio method are mainly introduced.The optimal threshold value corresponding to specific data is selected by adjusting the threshold value,so that the normal equation constructed by the optimal parameter model is not ill-conditioned and the fitting accuracy is high enough,within 0.01-0.1 pixels.In addition,the influence of the distribution,number and RPC type of control points on the fitting accuracy of rational function model is studied for terrain-dependent schemes.For the independent topographic scheme,the relationship between the size of control point grid,the number of elevation layers and the fitting accuracy of rational function model is studied.