两种新的GNSS-R镜面反射点位置估计算法
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摘要
基于全球导航卫星系统反射信号(GNSS-R)的几何关系,提出了基于地球椭球面法线的椭球面算法和基于站心坐标系的平面算法.前者将实际地球形状近似为椭球,以法线为基准线;后者以站心坐标系为参考,对于地基GNSS接收机情形,将GNSS卫星在镜面反射点和GNSS接收机处的高度角近似相等,且两种算法都满足Snell反射定律.理论和实验证明:椭球面算法只要给定镜面反射点的高程,就能确定其在实际反射面上的空间位置,能适用于GNSS接收机位于任何位置情形,且迭代次数少,仅需6次迭代,就能获得正确结果,即使镜面反射点的高程不准确,其对平面位置的影响也较小;平面算法适用于GNSS接收机靠近反射面情形,计算过程比椭球面算法更加简单,且无需迭代计算,效率更高.当GNSS接收机处于静态地基情形时,不同轨道上GNSS卫星得到的镜面反射点的平面位置轨迹形状相似,且卫星高度角越大镜面反射点越靠近,反之亦然.
This paper puts forward two algorithms in accordance with the geometrical relationship of GNSS-R:ellipsoid algorithm based on normal ellipsoid of the earth and plane algorithm based on the topocentric coordinate system.The former considers the earth shape as an ellipsoid and adopts the normal line as baseline while the latter takes the topocentric coordinate system as the reference.With regard to conditions of ground-based GNSS receiver,elevation angles of GNSS satellite on specular reflection points are considered to be equal to that of the location of receiver,and the two algorithms conform to Snell law of reflection.Theories and experiments show that for ellipsoid algorithm,if elevation of the specular reflection point is given,its spatial location on actual reflection surface can be determined,and it can be applied to GNSS receiver located in any location.Furthermore,less iteration is required,and the correct result can be obtained with iteration of only 6times.Even if the height of a specular reflection point is inaccurate,it has less impact on the plane location of the specular reflection point.Theplane algorithm is applicable when GNSS receiver is close to the reflection surface.The counting process is simpler compared to that of ellipsoid algorithm.No iterative computations are required,and the efficiency is even higher.When the GNSS receiver is under static ground-based condition,the track shapes of plane position consisted of specular reflection points calculated from GNSS satellites in different orbits are similar,and as the satellites elevation angles increase,the specular reflection points locate closer,and vice versa.
This paper puts forward two algorithms in accordance with the geometrical relationship of GNSS-R:ellipsoid algorithm based on normal ellipsoid of the earth and plane algorithm based on the topocentric coordinate system.The former considers the earth shape as an ellipsoid and adopts the normal line as baseline while the latter takes the topocentric coordinate system as the reference.With regard to conditions of ground-based GNSS receiver,elevation angles of GNSS satellite on specular reflection points are considered to be equal to that of the location of receiver,and the two algorithms conform to Snell law of reflection.Theories and experiments show that for ellipsoid algorithm,if elevation of the specular reflection point is given,its spatial location on actual reflection surface can be determined,and it can be applied to GNSS receiver located in any location.Furthermore,less iteration is required,and the correct result can be obtained with iteration of only 6times.Even if the height of a specular reflection point is inaccurate,it has less impact on the plane location of the specular reflection point.Theplane algorithm is applicable when GNSS receiver is close to the reflection surface.The counting process is simpler compared to that of ellipsoid algorithm.No iterative computations are required,and the efficiency is even higher.When the GNSS receiver is under static ground-based condition,the track shapes of plane position consisted of specular reflection points calculated from GNSS satellites in different orbits are similar,and as the satellites elevation angles increase,the specular reflection points locate closer,and vice versa.
引文
[1]杨东凯,张其善.GNSS反射信号处理基础与实践[M].北京:电子工业出版社,2012:31-42.
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[5]严颂华,龚健雅,张训械,等.GNSS-R测量地表土壤湿度的地基实验[J].地球物理学报,2011,54(11):2735-2744.YAN Songhua,GONG Jianya,ZHANG Xunxie,et al.Ground based GNSS-R observations for soil moisture[J].Chinese Journal of Geophysics,2011,54(11):2735-2744.
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[9]张波,王峰,杨东凯.基于线段二分法的镜面反射点估计算法[J].全球定位系统,2013,38(5):11-16.ZHANG Bo,WANG Feng,YANG Dongkai.The algorithm for the determination of the GNSS-R specular point based on the dichotomy of the line segment[J].GNSS World of China,2013,38(5):11-16.
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[11]孔祥元,郭际明,刘宗泉.大地测量学基础[M].武汉:武汉大学出版社,2010:63-77.
[12]张华海,王宝山,赵长胜,等.应用大地测量学[M].徐州:中国矿业大学出版社,2011:31-48.
[13]李征航,黄劲松.GPS测量与数据处理[M].武汉:武汉大学出版社,2010:81-94.
[14]HELM A.Ground-based GPS altimetry with the L1Open GPS receiver using carrier phase-delay observations of reflected GPS signals[R].08/10,Deutsches GeoForschungsZentrum,2008.
[15]胡伍生,潘庆林.土木工程测量[M].南京:东南大学出版社,2012:66-73.
[16]孙小荣,李明峰,刘支亮,等.常用坐标系间GNSS基线向量误差转换方法研究[J].大地测量与地球动力学,2014,34(5):114-119.SUN Xiaorong,LI Mingfeng,LIU Zhiliang,et al.On conversion of GNSS baseline vector error between common coordinate systems[J].Journal of Geodesy and Geodynamics,2014,34(5):114-119.
[17]卞和方,张书毕,张秋昭,等.在常用坐标系下GNSS点位误差转换方法研究[J].大地测量与地球动力学,2012,32(4):83-86.BIAN Hefang,ZHANG Shubi,ZHANG Qiuzhao,et al.On GNSS positional error transformation between common coordinate systems[J].Journal of Geodesy and Geodynamics,2012,32(4):83-86.
[18]郑南山,张秋昭,张书毕,等.IMU/GPS组合导航交互式多模型鲁棒滤波研究[J].中国矿业大学学报,2014,43(5):920-926.ZHENG Nanshan,ZHANG Qiuzhao,ZHANG Shubi,et al.Improved algorithm based on interacting multiple model and H∞filtering for IMU/GPS navigation[J].Journal of China University of Mining&Technology,2014,43(5):920-926.
[19]张秋昭,张书毕,郑南山,等.GPS/INS组合系统的多重渐消鲁棒容积卡尔曼滤波[J].中国矿业大学学报,2014,43(1):162-168.ZHANG Qiuzhao,ZHANG Shubi,ZHENG Nanshan,et al.Multiplefading robust Cubature Kalman filter for GPS/INS integrated navigation[J].Journal of China University of Mining&Technology,2014,43(1):162-168.
[2]GLEASON S,GEBRE-EGZIABHER D.GNSS applications and methods[M].Artech House,2009:53-71.
[3]万玮,陈秀万,李国平,等.GNSS-R遥感国内外研究进展[J].遥感信息,2012,27(3):112-119.WAN Wei,CHEN Xiuwan,LI Guoping,et al.GNSS reflectometry:A review of theories and empirical applications in ocean and land surfaces[J].Remote Sensing Information,2012,27(3):112-119.
[4]李黄,夏青,尹聪,等.我国GNSS-R遥感技术的研究现状与未来发展趋势[J].雷达学报,2013,2(4):389-399.LI Huang,XIA Qing,YIN Cong,et al.The current status of research on GNSS-R remote sensing technology in china and future development[J].Journal of Radars,2013,2(4):389-399.
[5]严颂华,龚健雅,张训械,等.GNSS-R测量地表土壤湿度的地基实验[J].地球物理学报,2011,54(11):2735-2744.YAN Songhua,GONG Jianya,ZHANG Xunxie,et al.Ground based GNSS-R observations for soil moisture[J].Chinese Journal of Geophysics,2011,54(11):2735-2744.
[6]WU S C,MEEHAN T,YOUNG L.The potential use of GPS signals as ocean altimetry observable[C]//The Institute of Navigation 1997 National Technical Meeting.
[7]WAGNER C,KLOKOCNIK J.The value of ocean reflections of GPS signals to enhance satellite altimetry:Data distribution and error analysis[J].Journal of Geodesy,2003(77):128-138.
[8]KOSTELECKY J,KLOKOCNIK J,WAGNERC.Geometry and accuracy of reflecting points in bistatic satellite altimetry[J].Journal of Geodesy,2005(79):421-430.
[9]张波,王峰,杨东凯.基于线段二分法的镜面反射点估计算法[J].全球定位系统,2013,38(5):11-16.ZHANG Bo,WANG Feng,YANG Dongkai.The algorithm for the determination of the GNSS-R specular point based on the dichotomy of the line segment[J].GNSS World of China,2013,38(5):11-16.
[10]TORGE W.Geodesy[M].New York:Water de Gruyter Berlin,2001:45-60.
[11]孔祥元,郭际明,刘宗泉.大地测量学基础[M].武汉:武汉大学出版社,2010:63-77.
[12]张华海,王宝山,赵长胜,等.应用大地测量学[M].徐州:中国矿业大学出版社,2011:31-48.
[13]李征航,黄劲松.GPS测量与数据处理[M].武汉:武汉大学出版社,2010:81-94.
[14]HELM A.Ground-based GPS altimetry with the L1Open GPS receiver using carrier phase-delay observations of reflected GPS signals[R].08/10,Deutsches GeoForschungsZentrum,2008.
[15]胡伍生,潘庆林.土木工程测量[M].南京:东南大学出版社,2012:66-73.
[16]孙小荣,李明峰,刘支亮,等.常用坐标系间GNSS基线向量误差转换方法研究[J].大地测量与地球动力学,2014,34(5):114-119.SUN Xiaorong,LI Mingfeng,LIU Zhiliang,et al.On conversion of GNSS baseline vector error between common coordinate systems[J].Journal of Geodesy and Geodynamics,2014,34(5):114-119.
[17]卞和方,张书毕,张秋昭,等.在常用坐标系下GNSS点位误差转换方法研究[J].大地测量与地球动力学,2012,32(4):83-86.BIAN Hefang,ZHANG Shubi,ZHANG Qiuzhao,et al.On GNSS positional error transformation between common coordinate systems[J].Journal of Geodesy and Geodynamics,2012,32(4):83-86.
[18]郑南山,张秋昭,张书毕,等.IMU/GPS组合导航交互式多模型鲁棒滤波研究[J].中国矿业大学学报,2014,43(5):920-926.ZHENG Nanshan,ZHANG Qiuzhao,ZHANG Shubi,et al.Improved algorithm based on interacting multiple model and H∞filtering for IMU/GPS navigation[J].Journal of China University of Mining&Technology,2014,43(5):920-926.
[19]张秋昭,张书毕,郑南山,等.GPS/INS组合系统的多重渐消鲁棒容积卡尔曼滤波[J].中国矿业大学学报,2014,43(1):162-168.ZHANG Qiuzhao,ZHANG Shubi,ZHENG Nanshan,et al.Multiplefading robust Cubature Kalman filter for GPS/INS integrated navigation[J].Journal of China University of Mining&Technology,2014,43(1):162-168.