多定位源数据分析的特征向量空间滤波模型及仿真实验
|
摘要
目前,在室内定位中,鲜有研究者将多个定位源的空间布局这一重要因素考虑到定位结果的估计中来。室内定位中,众多定位源可以看作多个随机变量的一次实现,每个定位源结果并非严格独立,通常存在一定空间布局,可以模拟为确定性空间结构函数或统计空间自相关模型。定位源空间自相关会导致不同定位源影响系数(回归系数)方差膨胀效应和定位结果偏移效应。方差膨胀将导致参数估值的不确定性被低估,最终导致定位结果存在较大偏差。本文特征向量空间滤波模型(Eigenvector Spatial Filtering Model,ESF)将多定位源空间布局归结为一个代理变量,加入一般多元线性回归模型,构造最终的多定位源融合算法。定位源空间自相关效应通过特征向量空间滤波模型的空间代理变量来表征和分离,从而特征向量空间滤波模型满足独立(定位源结果彼此独立)同分布的一般线性回归模型条件。仿真分析表明运用特征向量空间滤波模型使用户定位结果和回归系数估值的精度均有明显提高。
In indoor positioning,so far few researchers take the spatial layout of multiple positioning sources into consideration for estimation of positioning results.In indoor positioning,many positioning sources(or sensors) can be regarded as the realization of multiple random variables.The results of each positioning source are not strictly independent,and there somewhat exists spatial autocorrelation.Spatial autocorrelation of location-based source results will lead to variance inflation of regression coefficient of different location-based sources,and furthermore variance inflation will lead to underestimated uncertainty of parameter values,which will lead to large deviation of ultimate positioning result.In the Eigenvector Spatial Filtering Model(ESF),the multi-location source space layout can be reduced to a proxy variable,which is one item of the general multi-location linear regression model for the purpose of multiple positioning sources.The eigenvector spatial filtering model satisfies the condition of independent and identical distribution of general linear regression models.It is assumed that the positioning source results are independent of each other.Simulation analysis shows that the accuracies of ultimate location result and regression coefficient estimation are improved obviously by using eigenvector spatial filtering model.
In indoor positioning,so far few researchers take the spatial layout of multiple positioning sources into consideration for estimation of positioning results.In indoor positioning,many positioning sources(or sensors) can be regarded as the realization of multiple random variables.The results of each positioning source are not strictly independent,and there somewhat exists spatial autocorrelation.Spatial autocorrelation of location-based source results will lead to variance inflation of regression coefficient of different location-based sources,and furthermore variance inflation will lead to underestimated uncertainty of parameter values,which will lead to large deviation of ultimate positioning result.In the Eigenvector Spatial Filtering Model(ESF),the multi-location source space layout can be reduced to a proxy variable,which is one item of the general multi-location linear regression model for the purpose of multiple positioning sources.The eigenvector spatial filtering model satisfies the condition of independent and identical distribution of general linear regression models.It is assumed that the positioning source results are independent of each other.Simulation analysis shows that the accuracies of ultimate location result and regression coefficient estimation are improved obviously by using eigenvector spatial filtering model.
引文
[1]Deng Zhongliang,Yu Yan Pei,Yuan Xie,et al.Situation and Development Tendency of Indoor Positioning[J].China Communications,2013,10(3):42~55.
[2]Weiser M.The Computer for the 21st Century[J].IEEEPervasive Computing,1999,3(3):3~11.
[3]刘鹏,卢潭城,高翔.基于射频识别的室内定位技术综述[J].太赫兹科学与电子信息学报,2014,12(2):195~201.
[4]彭逸凡,李广云,王力等.UWB室内定位测站布设PDOP值分析[J].导航定位学报,2017,5(2):103~106.
[5]LER W.A Computer Movie Simulating Urban Growth in the Detroit region[J].Economic Geography,1970,46(2):234~240.
[6]Tiefelsdorf M,Griffith D A.Semiparametric Filtering of Spatial Autocorrelation:The Eigenvector Approach[J].Environment&Planning A,2007,39(5):1193~1221.
[7]Griffith D A.A Linear Regression Solution to the Spatial Autocorrelation Problem[J].Journal of Geographical Systems,2000,2(2):141~156.
[8]严莹莹.空间计量模型及其在我国的应用研究[D].武汉:华中科技大学,2012,65.
[9]Moonan W J.Linear Transformation to a Set of Stochastically Dependent Normal Variables[J].Publications of the American Statistical Association,1957,52(278):247~252.
[10]Box G E P,Muller M E.A Note on the Generation of Random Normal Deviates[J].Annals of Mathematical Statistics,1958,29(2):610~611.
[11]Beaumont C.A Guide to Simulation[J].Journal of the Operational Research Society,1984,35(4):365~366.
[12]徐钟济.蒙特卡罗方法[M].上海:上海科学技术出版社,1985.
[13]朱本仁.蒙特卡罗方法引论[M].济南:山东大学出版社,1987.
[14]文德智,卓仁鸿,丁大杰等.蒙特卡罗模拟中相关变量随机数序列的产生方法[J].物理学报,2012,61(22):20~27.
[2]Weiser M.The Computer for the 21st Century[J].IEEEPervasive Computing,1999,3(3):3~11.
[3]刘鹏,卢潭城,高翔.基于射频识别的室内定位技术综述[J].太赫兹科学与电子信息学报,2014,12(2):195~201.
[4]彭逸凡,李广云,王力等.UWB室内定位测站布设PDOP值分析[J].导航定位学报,2017,5(2):103~106.
[5]LER W.A Computer Movie Simulating Urban Growth in the Detroit region[J].Economic Geography,1970,46(2):234~240.
[6]Tiefelsdorf M,Griffith D A.Semiparametric Filtering of Spatial Autocorrelation:The Eigenvector Approach[J].Environment&Planning A,2007,39(5):1193~1221.
[7]Griffith D A.A Linear Regression Solution to the Spatial Autocorrelation Problem[J].Journal of Geographical Systems,2000,2(2):141~156.
[8]严莹莹.空间计量模型及其在我国的应用研究[D].武汉:华中科技大学,2012,65.
[9]Moonan W J.Linear Transformation to a Set of Stochastically Dependent Normal Variables[J].Publications of the American Statistical Association,1957,52(278):247~252.
[10]Box G E P,Muller M E.A Note on the Generation of Random Normal Deviates[J].Annals of Mathematical Statistics,1958,29(2):610~611.
[11]Beaumont C.A Guide to Simulation[J].Journal of the Operational Research Society,1984,35(4):365~366.
[12]徐钟济.蒙特卡罗方法[M].上海:上海科学技术出版社,1985.
[13]朱本仁.蒙特卡罗方法引论[M].济南:山东大学出版社,1987.
[14]文德智,卓仁鸿,丁大杰等.蒙特卡罗模拟中相关变量随机数序列的产生方法[J].物理学报,2012,61(22):20~27.