顾及映射函数误差的对流层延迟两步估计法
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摘要
利用VLBI、GNSS等空间大地测量数据估计对流层延迟时,通常不考虑映射函数的误差,但这种处理策略最终会对估计结果造成不可忽略的影响。首先,根据多年的气象资料,分析了映射函数误差随高度角的变化特性,然后构建了映射函数误差模型,进而提出了一种顾及映射函数误差的对流层延迟两步估计法。试验表明,本文提出的方法可有效削弱斜路径延迟残差,并在一定程度上改善对流层湿延迟的估计精度。
Mapping function errors are usually not taken into consideration, when space geodetic data observed by VLBI, GNSS and some other techniques are utilized to estimate troposphere delay, which could, however, probably bring non-ignorable errors to solutions. After analyzing the variation of mapping function errors with elevation angles based on several-year meteorological data, this paper constructed a model of this error and then proposed a two-step estimation method of troposphere delay with consideration of mapping function errors. The experimental results indicate that the method puted forward by this paper could reduce the slant path delay residuals efficiently and improve the estimation accuracy of wet tropospheric delay to some extent.
Mapping function errors are usually not taken into consideration, when space geodetic data observed by VLBI, GNSS and some other techniques are utilized to estimate troposphere delay, which could, however, probably bring non-ignorable errors to solutions. After analyzing the variation of mapping function errors with elevation angles based on several-year meteorological data, this paper constructed a model of this error and then proposed a two-step estimation method of troposphere delay with consideration of mapping function errors. The experimental results indicate that the method puted forward by this paper could reduce the slant path delay residuals efficiently and improve the estimation accuracy of wet tropospheric delay to some extent.
引文
[1] DAVIS J L, ELGERED G, NIELL A E, et al. Ground-based measurement of gradients in the “wet” radio refractivity of air[J]. Radio Science, 1993, 28(6): 1003-1018.
[2] TEKE K, NILSSON T, B?HM J, et al. Troposphere delays from space geodetic techniques, water vapor radiometers, and numerical weather models over a series of continuous VLBI Campaigns[J]. Journal of Geodesy, 2013, 87(10-12): 981-1001.
[3] 谢劭峰, 张朋飞, 王新桥, 等. 对流层延迟模型映射函数研究[J]. 大地测量与地球动力学, 2016, 36(11): 941-945, 950. XIE Shaofeng, ZHANG Pengfei, WANG Xinqiao, et al. Research on mapping functions of troposphere delay model[J]. Journal of Geodesy and Geodynamics, 2016, 36(11): 941-945, 950.
[4] 郭际明, 章迪, 史俊波, 等. 利用射线追踪法分析三种典型对流层映射函数在中国区域的精度[J]. 武汉大学学报(信息科学版), 2015, 40(2): 182-187. GUO Jiming, ZHANG Di, SHI Junbo, et al. Using ray-tracing to analyse the precision of three classical tropospheric mapping functions in China[J]. Geomatics and Information Science of Wuhan University, 2015, 40(2): 182-187.
[5] BOEHM J, WERL B, SCHUH H. Troposphere mapping functions for GPS and very long baseline interferometry from European Centre for Medium-Range Weather Forecasts operational analysis data[J]. Journal of Geophysical Research: Solid Earth, 2006, 111(B2): B02406, DOI: 10.1029/2005JB003629.
[6] ZUS F, DICK G, DOUSA J, et al. Systematic errors of mapping functions which are based on the VMF1 concept[J]. GPS Solutions, 2015, 19(2): 277-286.
[7] LANDSKRON D, B?HM J. VM/GPT3: Refined discrete and empirical troposphere mapping functions[J]. Journal of Geodesy, 2018, 92(4): 349-360.
[8] HASE H, BEHREND D, MA C, et al. The emerging VGOS network of the IVS[C]//Proceedings of the 7th General Meeting. Madrid, Spain:[s.n.], 2012: 8-12.
[9] CHEN G, HERRING T A. Effects of atmospheric azimuthal asymmetry on the analysis of space geodetic data[J]. Journal of Geophysical Research, 1997, 102(B9): 20489-20502.
[10] SAASTAMOINEN J. Contributions to the theory of atmospheric refraction[J]. Bulletin Géodésique, 1972, 105(1): 279-298.
[11] NIELL A E. Global mapping functions for the atmosphere delay at radio wavelengths[J]. Journal of Geophysical Research, 1996, 101(B2): 3227-3246.
[12] HERRING T A, DAVIS J L, SHAPIRO I I. Geodesy by radio interferometry: the application of Kalman filtering to the analysis of very long baseline interferometry data[J]. Journal of Geophysical Research, 1990, 95(B8): 12561-12581.
[13] HOFMEISTER A. Determination of path delays in the atmosphere for geodetic VLBI by means of ray-tracing[D]. Vienna, Austria: Vienna University of Technology, 2016: 41-59.
[14] GARCIA-ESPADA S, HAAS R, COLOMER F. Application of ray-tracing through the high resolution numerical weather model HIRLAM for the analysis of European VLBI[C]//Proceedings of the 10th European VLBI Network Symposium and EVN Users Meeting. Hobart, Australia, 2010: 232-236.
[15] 隋立芬, 陶大欣. 有偏估计、参数加权平差及秩亏自由网平差的关系与比较[J]. 解放军测绘学院学报, 1999, 16(4): 257-259. SUI Lifen, TAO Daxin. The relation and comparison of biased estimation, adjustment of parameter with prior weight and adjustment of free network[J]. Journal of the PLA Institute of Surveying and Mapping, 1999, 16(4): 257-259.
[16] 李全海. 坐标参数加权平差法在线路补测中的应用[J]. 测绘学报, 2002, 31(S1): 77-80. DOI: 10.3321/j.issn:1001-1595.2002.z1.017.LI Quanhai. Application of parameter adjustment with weighted coordinates in additional control survey of route[J]. Acta Geodaetica et Cartographica Sinica, 2002, 31(S1): 77-80. DOI: 10.3321/j.issn:1001-1595.2002.z1.017.
[17] SCHUH H. Geodetic and astrometric very long baseline interferometry (VLBI) the IVS and its future perspectives[R]. Espoo, Finland: EGU and IVS Training School on VLBI for Geodesy and Astrometry, 2013.
[18] PANY A, B?HM J, MACMILLAN D, et al. Monte Carlo simulations of the impact of troposphere, clock and measurement errors on the repeatability of VLBI positions[J]. Journal of Geodesy, 2011, 85(1): 39-50.
[19] NILSSON T, HAAS R. An assessment of atmospheric turbulence for CONT05 and CONT08[C]//Proceedings of the 19th European VLBI for Geodesy and Astrometry Working Meeting. Bordeaux, France:[s.n.], 2009: 39-43.
[20] PETRACHENKO B, NIELL A, BEHREND D, et al. Design aspects of the VLBI2010 system[R]. America: NASA Technical Memorandum, 2009.
[21] 孙中苗, 范昊鹏. VLBI全球观测系统(VGOS)研究进展[J]. 测绘学报, 2017, 46(10): 1346-1353. DOI: 10.11947/j.AGCS.2017.20170326.SUN Zhongmiao, FAN Haopeng. Research progress of VLBI global observing system (VGOS)[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(10): 1346-1353. DOI: 10.11947/j.AGCS.2017.20170326.
[22] SUN Jing, B?HM J, NILSSON T, et al. New VLBI2010 scheduling strategies and implications on the terrestrial reference frames[J]. Journal of Geodesy, 2014, 88(5): 449-461.
[2] TEKE K, NILSSON T, B?HM J, et al. Troposphere delays from space geodetic techniques, water vapor radiometers, and numerical weather models over a series of continuous VLBI Campaigns[J]. Journal of Geodesy, 2013, 87(10-12): 981-1001.
[3] 谢劭峰, 张朋飞, 王新桥, 等. 对流层延迟模型映射函数研究[J]. 大地测量与地球动力学, 2016, 36(11): 941-945, 950. XIE Shaofeng, ZHANG Pengfei, WANG Xinqiao, et al. Research on mapping functions of troposphere delay model[J]. Journal of Geodesy and Geodynamics, 2016, 36(11): 941-945, 950.
[4] 郭际明, 章迪, 史俊波, 等. 利用射线追踪法分析三种典型对流层映射函数在中国区域的精度[J]. 武汉大学学报(信息科学版), 2015, 40(2): 182-187. GUO Jiming, ZHANG Di, SHI Junbo, et al. Using ray-tracing to analyse the precision of three classical tropospheric mapping functions in China[J]. Geomatics and Information Science of Wuhan University, 2015, 40(2): 182-187.
[5] BOEHM J, WERL B, SCHUH H. Troposphere mapping functions for GPS and very long baseline interferometry from European Centre for Medium-Range Weather Forecasts operational analysis data[J]. Journal of Geophysical Research: Solid Earth, 2006, 111(B2): B02406, DOI: 10.1029/2005JB003629.
[6] ZUS F, DICK G, DOUSA J, et al. Systematic errors of mapping functions which are based on the VMF1 concept[J]. GPS Solutions, 2015, 19(2): 277-286.
[7] LANDSKRON D, B?HM J. VM/GPT3: Refined discrete and empirical troposphere mapping functions[J]. Journal of Geodesy, 2018, 92(4): 349-360.
[8] HASE H, BEHREND D, MA C, et al. The emerging VGOS network of the IVS[C]//Proceedings of the 7th General Meeting. Madrid, Spain:[s.n.], 2012: 8-12.
[9] CHEN G, HERRING T A. Effects of atmospheric azimuthal asymmetry on the analysis of space geodetic data[J]. Journal of Geophysical Research, 1997, 102(B9): 20489-20502.
[10] SAASTAMOINEN J. Contributions to the theory of atmospheric refraction[J]. Bulletin Géodésique, 1972, 105(1): 279-298.
[11] NIELL A E. Global mapping functions for the atmosphere delay at radio wavelengths[J]. Journal of Geophysical Research, 1996, 101(B2): 3227-3246.
[12] HERRING T A, DAVIS J L, SHAPIRO I I. Geodesy by radio interferometry: the application of Kalman filtering to the analysis of very long baseline interferometry data[J]. Journal of Geophysical Research, 1990, 95(B8): 12561-12581.
[13] HOFMEISTER A. Determination of path delays in the atmosphere for geodetic VLBI by means of ray-tracing[D]. Vienna, Austria: Vienna University of Technology, 2016: 41-59.
[14] GARCIA-ESPADA S, HAAS R, COLOMER F. Application of ray-tracing through the high resolution numerical weather model HIRLAM for the analysis of European VLBI[C]//Proceedings of the 10th European VLBI Network Symposium and EVN Users Meeting. Hobart, Australia, 2010: 232-236.
[15] 隋立芬, 陶大欣. 有偏估计、参数加权平差及秩亏自由网平差的关系与比较[J]. 解放军测绘学院学报, 1999, 16(4): 257-259. SUI Lifen, TAO Daxin. The relation and comparison of biased estimation, adjustment of parameter with prior weight and adjustment of free network[J]. Journal of the PLA Institute of Surveying and Mapping, 1999, 16(4): 257-259.
[16] 李全海. 坐标参数加权平差法在线路补测中的应用[J]. 测绘学报, 2002, 31(S1): 77-80. DOI: 10.3321/j.issn:1001-1595.2002.z1.017.LI Quanhai. Application of parameter adjustment with weighted coordinates in additional control survey of route[J]. Acta Geodaetica et Cartographica Sinica, 2002, 31(S1): 77-80. DOI: 10.3321/j.issn:1001-1595.2002.z1.017.
[17] SCHUH H. Geodetic and astrometric very long baseline interferometry (VLBI) the IVS and its future perspectives[R]. Espoo, Finland: EGU and IVS Training School on VLBI for Geodesy and Astrometry, 2013.
[18] PANY A, B?HM J, MACMILLAN D, et al. Monte Carlo simulations of the impact of troposphere, clock and measurement errors on the repeatability of VLBI positions[J]. Journal of Geodesy, 2011, 85(1): 39-50.
[19] NILSSON T, HAAS R. An assessment of atmospheric turbulence for CONT05 and CONT08[C]//Proceedings of the 19th European VLBI for Geodesy and Astrometry Working Meeting. Bordeaux, France:[s.n.], 2009: 39-43.
[20] PETRACHENKO B, NIELL A, BEHREND D, et al. Design aspects of the VLBI2010 system[R]. America: NASA Technical Memorandum, 2009.
[21] 孙中苗, 范昊鹏. VLBI全球观测系统(VGOS)研究进展[J]. 测绘学报, 2017, 46(10): 1346-1353. DOI: 10.11947/j.AGCS.2017.20170326.SUN Zhongmiao, FAN Haopeng. Research progress of VLBI global observing system (VGOS)[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(10): 1346-1353. DOI: 10.11947/j.AGCS.2017.20170326.
[22] SUN Jing, B?HM J, NILSSON T, et al. New VLBI2010 scheduling strategies and implications on the terrestrial reference frames[J]. Journal of Geodesy, 2014, 88(5): 449-461.