对F-J方法中采样算法的改进  

Improvement on the Sampling Algorithm of F-J Method

作　　者：张彦栋 陈建忠 赵中飞[2] ZHANG Yandong;CHEN Jianzhong;ZHAO Zhongfei(School of Geodesy and Geomatics,Wuhan University,Wuhan 430079,China;Shandong Surveying and Mapping Institute of Land and Resources,Jinan 250102,China)

机构地区：[1]武汉大学测绘学院,湖北武汉430079 [2]山东省国土测绘院,山东济南250102

出　　处：《测绘地理信息》2019年第6期83-88,共6页Journal of Geomatics

基　　金：国家自然科学基金(41431069)

摘　　要：介绍了基于贝叶斯理论的线性-非线性模型的反演方法(F-J方法),在理论上可以求出模型参数的概率分布,可以通过马尔可夫链蒙特卡洛(Markov chain Monte Carlo, MCMC)采样估计参数值及其精度。为了评估F-J方法反演效果,给出了线性-非线性模型的最小二乘方法以及假设检验步骤。针对MCMC采样算法中参数的随机游走步长会影响最佳采样数量的问题,对采样算法作了改进,模拟数据算例表明,改进的采样算法基本消除了部分参数游走步长选取不合适对确定采样次数的影响,解决了随机游走采样难以确定最佳采样点数量的问题。This paper introduces Fukuda and Johnson’s method(F-J method) for linear-non-linear problems, which can obtain the probabilistic distribution of model parameters and then estimate the model parameters and their accuracy by sampling the probability density function with Markov chain Monte Carlo. To evaluate the results of F-J method,this paper formulates how to apply least squares method and hypothesis testing to the linear-non-linear model. In dealing with the problem that the times of sampling necessary is dependent on the random-walk step size, improvement on the sampling algorithm is made. Inversion results on synthetic data set show that the improved algorithm cancels the influence that random-walk step size has on the times of sampling necessary, thus overcoming the difficulty of determining the optimal times of sampling.

关 键 词：线性-非线性模型 贝叶斯理论 马尔可夫链蒙特卡洛 迭代最小二乘 假设检验 改进采样算法 

分 类 号：P207[天文地球—测绘科学与技术]