病态不确定性平差模型的岭估计算法  

Ridge estimation algorithm to ill-posed uncertainty adjustment model

作　　者：鲁铁定[1,2,3] 吴光明 周世健[4] LU Tieding;WU Guangming;ZHOU Shijian(Faculty of Geomatics, East China University of Technology, Nanchang330013, China;Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASMG, Nanchang 330013, China;Jiangxi Province KeyLab for Digital Land, Nanchang 330013, China;Nanchang Hangkong University, Nanchang 330063, China)

机构地区：[1]东华理工大学测绘工程学院,江西南昌330013 [2]流域生态与地理环境监测国家测绘地理信息局重点实验室,江西南昌330013 [3]江西省数字国土重点实验室,江西南昌330013 [4]南昌航空大学,江西南昌330063

出　　处：《测绘学报》2019年第4期403-411,共9页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金(41464001);测绘地理信息公益性行业科技专项(201512026);江西省教育厅科技项目(KJLD12077);国家重点研发计划(2016YFB0501405; 2016YFB0502601-04);江西省自然科学基金(2017BAB203032)~~

摘　　要：测量数据在获取的过程中,常存在不确定性,它们会影响参数估计结果,不确定性平差模型的解算方法可以有效提高参数估计的有效性和可靠性。当观测方程的系数矩阵存在接近零的奇异值,采用岭估计可有效抑制观测方程病态性对参数估值结果的影响。当不确定性平差模型出现病态,其受系数矩阵误差和观测值误差的影响更为严重,本文将岭估计法应用于病态不确定性平差模型,推导了迭代算法,以提高解的稳定性,并用算例验证,结果表明了新方法的有效性和可行性。Uncertainties usually exist in the process of acquisition of measurement data, which affects the parameter estimation results.The solution method of uncertainty adjustment model can effectively improve the validity and reliability of parameter estimation.When the coefficient matrix of the observation equation has a singular value close to zero, the ridge estimation can effectively suppress the influence of the ill-posed state of the observation equation on the parameter estimation results.When the uncertainty adjustment model is ill- posed, it is more seriously affected by the error of the coefficient matrix and the observation,this paper applies ridge estimation method to ill-posed uncertainty adjustment model, derives an iterative algorithm to improve the stability and reliability of the result, and verifies it with two examples.The results show that the new method is effective and feasible.

关 键 词：病态 不确定性 平差模型 岭估计 

分 类 号：P227[天文地球—大地测量学与测量工程]