综合半参数变系数和GRNN神经网络的对流层延迟模型  

Tropospheric delay model based on semiparametric varying coefficient and GRNN neural network

作　　者：潘雄 张思莹 李涛[1] 黄伟凯 金丽宏 张红星 PAN Xiong;ZHANG SiYing;LI Tao;HUANG WeiKai;JIN LiHong;ZHANG HongXing(School of Computer Science and Artificial Intelligence,Wuhan Textile University,Wuhan 430200,China;School of Mathematical and Physical Sciences,Wuhan Textile University,Wuhan 430200,China;Innovation Academy for Precision Measurement Sciences and Technology,CAS,Wuhan 430071,China)

机构地区：[1]武汉纺织大学计算机与人工智能学院,武汉430200 [2]武汉纺织大学数理科学学院,武汉430200 [3]中国科学院精密测量科学与技术创新研究院,武汉430071

出　　处：《地球物理学报》2025年第1期54-65,共12页Chinese Journal of Geophysics

基　　金：国家自然科学基金面上项目(42174010,41874009)资助。

摘　　要：对流层延迟是卫星导航定位的主要误差源之一,精准地预测对流层延迟对于提高全球导航卫星系统的定位精度至关重要.本文将半参数变系数模型(Semiparametric Varying Coefficient,Semi-VC)引入到对流层延迟建模中,构建一种综合半参数变系数与神经网络的新型经验对流层模型.首先,将频谱分析提取的主周期信号作为参数分量,将剩余周期信号和其他误差归入到非参数分量,建立半参数对流层天顶延迟模型(Semiparametric tropospheric zenith delay model,Semi);其次,为了减弱核函数和窗宽参数选择对估计值精度的影响,利用泰勒展式将参数分量展开到一次项,将窗宽参数与参数解算综合考虑,扩充为半参数变系数模型,综合核估计和最小二乘法,利用三步估计方法得到了参数分量和非参数分量的估计值及观测值的拟合残差;然后,引入广义回归神经网络模型(Generalized Regression Neural Network,GRNN)对拟合残差进行补偿建模,利用贝叶斯优化算法(Bayesian Optimization Algorithm,BOA)进行超参数选择,进一步提升混合模型对ZTD(Zenith Tropospheric Delay)的估计精度.最后,利用陆态网络2020至2022年的210个GNSS(Global Navigation Satellite System)测站的实测数据,对本文提出的半参数变系数与广义回归神经网络组合模型(Semiparametric Varying Coefficient-GRNN,Semi-VC-GRNN)与常用模型从系统误差分离和时空分布特性方面进行了对比分析.结果表明,Semi-VC-GRNN模型在2022年210个测站的测试中平均RMSE(Root Mean Square Error)和平均Bias分别为16.8 mm和0.4 mm,平均RMSE相较于5°分辨率和1°分辨率下的GPT3模型分别提升51.25%和50.07%.Tropospheric delay stands as a primary error source in satellite navigation positioning,and predicting it is crucial for enhancing the precision of global navigation satellite systems.This study introduces a Semiparametric Varying Coefficient model(Semi-VC)into atmospheric delay modeling,devising a novel empirical model integrating semi-parametric coefficients with neural network techniques.Initially,spectral analysis extracts dominant periodic signals as parametric components,while residual periodic signals and other errors are categorized into non-parametric components,establishing a semiparametric tropospheric zenith delay model(Semi).Subsequently,to mitigate the influence of kernel function and window width parameter selection on estimation accuracy,Taylor series expansion is employed to linearize parametric components to first order,integrating window width parameters with periodic terms,thus expanding into a semi-parametric coefficient model.Combining kernel estimation methods with least squares,a three-step estimation approach is utilized to obtain estimates of periodic and non-parametric components along with fitting residuals of observed values.Next,a Generalized Regression Neural Network(GRNN)is introduced to compensate for fitting residuals,employing Bayesian optimization algorithm(BOA)for hyperparameter selection,further enhancing the estimation accuracy of the hybrid model for Zenith Tropospheric Delay(ZTD).Finally,utilizing observed data from 210 Global Navigation Satellite System(GNSS)stations from 2020 to 2022,a comparative analysis is conducted between the proposed Semiparametric Varying Coefficient-GRNN(Semi-VC-GRNN)model and common models,focusing on aspects such as separation of systematic errors and spatiotemporal distribution characteristics.Results indicate that the Semi-VC-GRNN model exhibits an average RMSE and Bias of 16.8 mm and 0.4 mm,respectively,across the 210 stations in 2022.The average RMSE is improved by 51.25%and 50.07%compared to the GPT3 model with 5°resolution and 1°resolut

关 键 词：天顶对流层延迟 半参数变系数模型 广义回归神经网络模型 陆态网络 

分 类 号：P223[天文地球—大地测量学与测量工程]