| With the rapid development of global positioning technology in recent years,the demand for high-resolution,high-precision geoid models are increasing.As a necessary means to directly convert the geodetic height to normal height,it has very important socio-economic value and scientific significance for related interdisciplinary subjects.This article used the KTH method to refine the regional geoid model,and combined three types of Earth gravity field models:EGM2008,XGM2016 and XGM2019,to refine the similar geoid model in Jilin Province using high-precision GPS/leveling points.The main contents were:（1）Introduced the research status and application of Earth gravity field model,methods of modifying Stokes kernel function,geoid refinement,Remove-Compute-Restore technology and KTH method.（2）The basic principles of the KTH method for refining the geoid were introduced,including the least-squares modification Stokes method,the approximate geoid undulation,the combined topographic correction,the combined atmospheric correction,the downward continuation correction,the ellipsoid correction and the calculation methods of three least-squares modification methods:biased,unbiased,optimum and their global RMSE,etc.In addition,the formulas for other necessary parameters were provided before the calculation,such as:the truncation error,the gravity field model coefficient error,the terrestrial gravity data error,Molodenskii’s truncation coefficients and the coefficient0)96))（0）.（3）Introduced the key of the KTH method—the calculation method of least-squares parameters,including singular value decomposition,truncated singular value decomposition,truncated total least squares method,Tikhonov regularization and L-curve method,the principle of solving the optimal inflection point.（4）Introduced the method of quasi-geoid-to-geoid conversion,including the calculation method of gravity field model and the calculation method of applied terrestrial gravity data based on the quadratic term of elevation.And this paper also introduced the principle of Four-parameter and Seven-parameter model fitting to remove system errors.（5）Applied the influence of the modification parameters in the KTH method on the global RMSE,used fixed parameters（the gravity anomaly degree variances,the geopotential harmonic error degree variances）,optional parameters（modification limits,the integral radius）and external parameters（the terrestrial gravity error variance）to evaluate the theoretical differences and global aspects of the EGM2008,XGM2016 and XGM2019 models when applying the KTH method refinement from the global mean square error and modified Stokes kernel value.The results showed that the global RMSE calculated based on the EGM2008 model was larger than that based on the XGM2016 and XGM2019 models under the same conditions,and the ability to correct the decline of the Stokes kernel value and approach the 0 value was also weak;The numerical differences between the results of the XGM2016 and XGM2019 models in each experiment were at the millimeter or sub-millimeter level;the error of the terrestrial gravity data was the main influence of the global mean square error,the model coefficient error was the second,and the truncation error was no longer significant.（6）The quasi-geoid model of Jilin Province was composed of the geoid calculated by the KTH method and the separation between geoid and quasi-geoid,and the accuracy evaluation of the model by using 76 B-level first-class GPS-leveling points in and around Jilin Province.One-parameter fitting results showed that the refined geoid-like level based on the XGM2019 Earth gravity field model had the highest accuracy in the entire research area compared to the other two models,with a standard deviations and error intervals of±3.0cm and 12.3cm,respectively.Based on the XGM2016model,the standard deviation and the error interval reached±3.1cm and 15.1cm,respectively.The EGM2008 model was more sensitive to the terrestrial gravity data error,so the accuracy of the quasi-geoid based on the EGM2008 model in mountain areas was lower than the original model.In the plain area of Jilin Province,based on the refined results of the EGM2008 model,the standard deviations and error intervals were±3.6cm and 15.9cm,respectively.The standard deviations and error intervals based on the XGM2016 model were±2.8cm and 13.1cm,respectively.The XGM2019model was relatively best,with a standard deviation and error intervals of±2.6cm and10.8cm,respectively.In this paper,Four-Parameter and Seven-Parameter models were used in the plain area to fit the quasi-geoid model to remove system errors.The accuracy was improved in millimeters compared to one parameter.The seven-parameter fitting results based on the XGM2019 model were the best,with a standard deviation reached±2.3cm,and the error interval reached 9.4cm. |
