杨承午, 刘志平, 徐永明.L-M算法优化的灰色模型在GPS卫星钟差预报中的应用[J].河南理工大学学报（自然科学版）,2020,39(2):47-52.

YANG C W, LIU Z P, XU Y M.Application of L-M algorithm optimized gray model in GPSsatellite clock error predication[J].Journal of Henan Polytechnic University(Natural Science) ,2020,39(2):47-52.

L-M算法优化的灰色模型在GPS卫星钟差预报中的应用

杨承午1,2, 刘志平1,2, 徐永明1,2

1.中国矿业大学自然资源部国土环境与灾害监测重点实验室，江苏徐州 221116；2.中国矿业大学环境与测绘学院，江苏 徐州  221116

摘要:针对灰色模型在模型参数估计方面存在的不足，提出一种基于L-M算法对模型参数全局迭代优化估计方法。该方法通过对发展系数、灰色作用量和时间响应函数初始值3个方面改进优化，解决了常规差分灰色模型背景值生成因子不确定性、时间响应函数初始值固有偏差和模型参数解估计局部最优问题。实验算例表明，相较二次多项式模型和灰色模型，改进模型在不同类型的原子钟钟差预报精度方面均得到提升，6 h和24 h预报精度平均提高了48.5% 和46. 3%，验证了改进方法的有效性和优越性。

关键词:灰色模型;L-M算法;全局迭代优化;钟差预报

doi:10.16186/j.cnki.1673-9787.2020.2.7

基金项目:国家自然科学基金重点资助项目（41730109）；国家自然科学基金面上项目（41771416 ）；自然资源部精密工程与工业测量 重点实验室开放基金资助项目（PF2017-12）

收稿日期:2019/06/09

修回日期:2019/07/22

出版日期:2020/03/15

Application of L-M algorithm optimized gray model in GPSsatellite clock error predication

YANG Chengwu1,2, LIU Zhiping1,2, XU Yongming1,2

1.Key Lab of Land， Environment and Disaster Monitoring， Ministry of Natural Resources， China University of Mining and Technology， Xuzhou  221116 ， Jiangsu， China；2.School of Environment Science and Spatial Informatics， China University of Mining and Technology， Xuzhou 221116 ， Jiangsu， China

Abstract:A global iterative optimization estimation method for the deficiencies of the grey model in the parameters estimation based on L-M algorithm was proposed to solves the local optimal problems of background value of conventional difference of the grey model，which included uncertainty of the generation factor，inherent deviation of the initial value of time response function and the model parameter solution estimation through the improvement and optimization of development coefficient， gray action and initial value of time response function. The experimental results showed that the new method improved the prediction accuracy of different types of atomic clock difference in comparison with the quadratic polynomial model and the gray model.The accuracy of 6 hours and 24 hours prediction increased by an average of 48.5% and 46.3%.The effectiveness and superiority of the improved method were verified.

Key words:grey model;Levenberg-Marquardt algorithm;global iterative optimization;clock error prediction

L_M算法优化的灰色模型在GPS卫星钟差预报中的应用_杨承午.pdf