摘要
针对多种分布形式混合的观测数据,建立了p范混合模型,考虑到模型中混合数属于不完全数据,引入期望最大化(expectation-maximum,EM)算法,对该混合模型的参数进行估计,详细推导了p范混合模型参数估计的迭代公式,并给出了相应的迭代步骤。采用混合高斯分布数据、拉普拉斯分布与高斯分布混合数据及实测GPS观测值残差数据,验证了公式的正确性和适应性。算例结果表明,与单一概率分布相比,p范混合模型能够准确反映数据分布的实际情况,同时利用EM算法估计的模型参数具有较高的精度。
Objectives:Aiming at the mixed observation data of multiple distribution forms,a expectationmaximum(EM)combined p-norm distributed model(EM_p)is established.Methods:Considering that the mixed number in the mixture model belongs to incomplete data,the EM algorithm is introduced to estimate the parameters of the mixture model and the p-model mixture model parameters are derived in detail.The estimated iteration formula and the corresponding iteration steps are given.The mixture Gaussian distribu⁃tion data,Laplace distribution and Gaussian distribution mixture data,and the residual data of measured global positioning system(GPS)observations are used to verify the correctness and adaptability of the formu⁃la in this paper.Results and Conclusions:The results of the calculation examples show that,compared with the single probability distribution,the p-norm mixture model can accurately reflect the actual situation of the data distribution,and the model parameters estimated by the EM algorithm have higher accuracy.
作者
彭飞
王中
孟庆旭
潘雄
邱封钦
杨玉锋
PENG Fei;WANG Zhong;MENG Qingxu;PAN Xiong;QIU Fengqin;YANG Yufeng(College of Naval Architecture and Ocean Engineering,Naval University of Engineering,Wuhan 430033,China;School of Computer Science and Artificial Intelligence,Wuhan Textile University,Wuhan 430200,China;School of Geography and Information Engineering,China University of Geosciences(Wuhan),Wuhan 430078,China)
出处
《武汉大学学报（信息科学版）》
EI
CAS
CSCD
北大核心
2022年第9期1432-1438,共7页
Geomatics and Information Science of Wuhan University
基金
国家自然科学基金(42174010,41874009)。
关键词
混合模型
参数估计
p范分布
期望最大化算法
mixture model
parameter estimation
p-norm distribution
expectation-maximum(EM)algo⁃rithm
