一种高精度的GNSS伪距单点定位加权算法
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摘要
针对传统定位算法因采用单一伪距误差模型受误差分布影响较大的问题,提出一种基于伪距特征误差模型的伪距单点定位加权算法,其首先通过矩估计方法对伪距误差的标准差进行估计,再根据估计值大小选择不同伪距特征误差近似方法,最后通过径向基核函数构造权矩阵。通过多星座、多历元、多观测站的实测数据验证:新型定位算法的定位精度相较于现有算法有显著提高,特别有效提高了高程精度。对当前导航定位接收机的改进和伪距单点定位算法的研究具有较大参考价值。
To solve the problem that the traditional positioning algorithm is greatly affected by the error distribution due to the single model of pseudo-range error,this paper proposed a weighted pseudo-range single point positioning algorithm base on pseudo-range eigen-error model. The proposed algorithm estimates the standard deviation of pseudo-range error by the method of moment estimation,then chooses the different pseudo-range eigen-error approximation method by different estimated value,at last structures weight matrix by radial basis kernel function. It is proved that,by measured data from multi-constellation,multi-epoch,multi-station,the positioning precision of the proposed algorithm is much better than the existing algorithm,especially the vertical precision. This algorithm would provide a reference for improving the current navigation and positioning receivers.
To solve the problem that the traditional positioning algorithm is greatly affected by the error distribution due to the single model of pseudo-range error,this paper proposed a weighted pseudo-range single point positioning algorithm base on pseudo-range eigen-error model. The proposed algorithm estimates the standard deviation of pseudo-range error by the method of moment estimation,then chooses the different pseudo-range eigen-error approximation method by different estimated value,at last structures weight matrix by radial basis kernel function. It is proved that,by measured data from multi-constellation,multi-epoch,multi-station,the positioning precision of the proposed algorithm is much better than the existing algorithm,especially the vertical precision. This algorithm would provide a reference for improving the current navigation and positioning receivers.
引文
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[4] T Kariya,H Kurata.Generalized Least Squares[M].Chichiester,UK;John Wiley & Sons,Ltd.,2004:289-292.
[5] 许超钤,等.基于整体最小二乘的参数估计新方法及精度评定[J].测绘通报,2011,(10):1-4.
[6] 涂刚毅,等.三种GPS定位优化算法的实现及比较[J].中国惯性技术学报,2009,17(2):170-174.
[7] P F De Bakker.On User Algorithms for GNSS Precise Point Positioning[J].Research Gate,2016.
[8] 李飞,等.GNSS接收机自主完好性监测算法研究[J].测绘通报,2007,(8):14-15.
[9] P J G Teunissen,A Kleusberg.GPS for Geodesy[J].Springer Berlin,1998,60:271-318.
[10] T Qiao,H Liu.Improved Least Median of Squares Localization for Non-Line-of-Sight Mitigation[J].Communications Letters IEEE,2014,18(8):1451-1454.
[11] 李春华,等.一种高精度的北斗伪距单点定位加权算法[J].测绘科学,2015,40(9):33-38.
[12] S W Dharmadhikari,K Joag-Dev.Mean,Median,Mode III[J].Statistica Neerlandica,1983,37(4):165–168.
[13] B Abdous,R Theodorescu.Mean,median,mode IV[J].Statistica Neerlandica,2008,52(52):356-359.
[14] A R Mugdadi,I A Ahmad.A Bandwidth Selection for Kernel Density Estimation of Functions of Random Variables[J].Computation Statistics & Data Analysis,2004,47:49-62.
[15] 严士健,刘秀芳.测度与概率[M].北京:北京师范大学出版社,1994:128-230.
[16] I A Ahmad.On Multivariate Kernel Estimation for Samples from Weighted Distributions[J].Statistics and Probability Letters,1995,22(2):121-129.
[17] 陈家鼎.数理统计学讲义[M].高等教育出版社,2015:16-21.
[2] 冯浩鉴.论最小二乘平差[J].测绘通报,1985,(2):43.
[3] HE Yu-heng,M RAINER.,M B ATTILA.Approximate iterative Least Squares Algorithm for GPS Positioning[C].Signal Processing and Information Technology,2010 IEEE International Symposium,2010:231-236.
[4] T Kariya,H Kurata.Generalized Least Squares[M].Chichiester,UK;John Wiley & Sons,Ltd.,2004:289-292.
[5] 许超钤,等.基于整体最小二乘的参数估计新方法及精度评定[J].测绘通报,2011,(10):1-4.
[6] 涂刚毅,等.三种GPS定位优化算法的实现及比较[J].中国惯性技术学报,2009,17(2):170-174.
[7] P F De Bakker.On User Algorithms for GNSS Precise Point Positioning[J].Research Gate,2016.
[8] 李飞,等.GNSS接收机自主完好性监测算法研究[J].测绘通报,2007,(8):14-15.
[9] P J G Teunissen,A Kleusberg.GPS for Geodesy[J].Springer Berlin,1998,60:271-318.
[10] T Qiao,H Liu.Improved Least Median of Squares Localization for Non-Line-of-Sight Mitigation[J].Communications Letters IEEE,2014,18(8):1451-1454.
[11] 李春华,等.一种高精度的北斗伪距单点定位加权算法[J].测绘科学,2015,40(9):33-38.
[12] S W Dharmadhikari,K Joag-Dev.Mean,Median,Mode III[J].Statistica Neerlandica,1983,37(4):165–168.
[13] B Abdous,R Theodorescu.Mean,median,mode IV[J].Statistica Neerlandica,2008,52(52):356-359.
[14] A R Mugdadi,I A Ahmad.A Bandwidth Selection for Kernel Density Estimation of Functions of Random Variables[J].Computation Statistics & Data Analysis,2004,47:49-62.
[15] 严士健,刘秀芳.测度与概率[M].北京:北京师范大学出版社,1994:128-230.
[16] I A Ahmad.On Multivariate Kernel Estimation for Samples from Weighted Distributions[J].Statistics and Probability Letters,1995,22(2):121-129.
[17] 陈家鼎.数理统计学讲义[M].高等教育出版社,2015:16-21.
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