航空重力测量测线网平差的理论与方法
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摘要
航空重力测量是一种新型的重力测量技术，它以飞机为载体，综合应用重力传感器、GPS、高度传感器、姿态传感器等设备测定近地空间重力加速度。航空重力测量是重力测量的一次历史性变革。它可以快速获取精度良好、分布均匀、大面积的地球重力场信息，而且能够在一些难以实施地面重力测量的特殊地区如沙漠、冰川、沼泽、原始森林等进行作业，从而能够满足大地测量学、地球物理学、海洋学及资源勘探等学科和领域对地球重力场信息的需求，并能为空间科学提供强有力的地球重力场保障。
依据测量值的类型不同，它可以分为航空标量重力测量和航空矢量重力测量两类，前者用以测定重力加速度的大小，后者不仅测定重力的大小，而且同时测定重力的方向。本文中所指航空重力测量特指航空标量重力测量。
为了尽可能构成重复观测，正确评价测量精度，航空重力测量的测线往往布设成网状，显然，必然形成交叉。由于受到各种误差源的干扰和影响，造成了交叉点上重力观测值不相同，即存在交叉点重力观测值不符值。这些干扰和影响或表现为系统性，或表现为随机性。航空重力测量测线网平差就是在分析、总结航空重力测量的主要误差源基础上，研究建立反映航空重力观测系统误差变化规律的误差模型，根据交叉点不符值条件，平差求解各测线上重力观测值系统误差改正数，然后对各测线上所有重力观测值进行改正(补偿)。航空重力测量测线网平差是航空重力测量的关键技术之一，这也是本文的主要内容。为此，本文从以下几个方面对航空重力测量测线网平差的理论与方法及相关内容进行研究，并得出若干初步结论：
1、结合航空重力测量的实际情况，提出了两种实用的交叉点搜索方法，即跳跃搜索法和图形辅助搜索法。利用模拟数据对这两种方法进行了比较，结果表明，两种方法都能快速、准确地搜索到交叉点的位置，与逐一比对搜索方法相比，搜索效率分别提高了91倍和176倍。当测量时间较长、采样率较高、相交测线较多时，两种搜索方法搜索速度快的优点就更加明显。
2、根据概率论和数理统计的理论与方法及误差理论，结合航空重力测量的特点，建立了有关检验统计量，并将其应用于航空重力测量测线系统误差的显著性检验。计算结果表明几种检验方法均可有效地对测线上的系统误差进行显著性检验。
3、根据附加系统参数平差的理论，在分析、总结航空重力测量的主要误差源基础上，研究建立了反映航空重力测量系统误差变化规律的误差模型，并根据三种不同的情况建立了相应的测线网平差模型。平差结果表明三种平差模型均对测线系统误差进行了有效的补偿，补偿后的精度提高了2.74～7.11毫伽，而且，对补偿后的测线网进行测线系统误差显著性检验，检验结果显示测线系统误差的影响已不再显著。
4、基于抗差估计理论，讨论了航空重力测量系统误差模型参数的抗差M估计方法与实现。通过比较，对于各测线上所有采样点的系统误差补偿来说，系统误差模型的抗差估计比最小二乘估计的可靠性更高。
Airborne gravimetry is a new kind of technique for surveying the gravity acceleration over the earth's surface and is advanced in gravimetry history, which basing on aircraft, including gravimeter, GPS, altimeter and attitude sensor etc.. Airborne gravimetry is applied to rapidly get extensively and precisely well-distributed information of the earth gravity field in order to meet the needs of Geodesy, Geophysics, Oceanography, Exploration, Space-Science and the other fields.
Airborne gravimetry includes scalar airborne gravimetry and vector airborne gravimetry. Scalar airborne gravimetry is used to get the value of the gravity acceleration, and vector airborne gravimetry can get not only the value but also the direction of the gravity acceleration. Airborne gravimetry which is discussed in this paper denote scalar airborne gravimetry only.
In order to estimate the accuracy of airborne gravity measurements, the tracks of an airborne gravity survery are generally planed to join each other. Discrepancies between measurements on different tracks may exist at the intersection because airborne gravity data are unavoidably affected by different kinds of error source. Furthermore, the performances of these errors may appear systematic or random. Based on an analysis of the sources of errors in airborne gravity measurements, an error model is studied to constructed mathematically which can characterize the change of systematic errors, with which the network adjustment is carried out and the model parameters are determined simultaneously. And finally, the compensation of systematic errors is realized. The network adjustment is one of key techniques for airborne gravimetry, it is also an important component in this paper. Consequently, the paper investigates the following aspects about the network adjustment theory and practice for airborne gravimetry, m
oreover, some questions correlated with solving the adjustment problem are discussed in detail.
1. Based on actualities of airborne gravimetry, two practical methods of searching crossovers are proposed, i. e. the skip-searching method and the graphic aid-searching method. A simulate network is used to test the efficiency and the reliability of these methods.Result demonstrates cross- points can be searched out rapidly and exactly by using these two methods.Compared with searching crossovers one by one, the skip-searching method increases the efficiency 91 times, and the graphic aid-searching method increases the efficiency 176 times.
2. According to the characteristic of airborne gravity survey, several statistic variables are derived from theory of probability and mathematical statistics combined with knowledge of errors principles. These statistic variables are applie to the significance test of systematic errors in every surveying line. Two practical applications prove their efficiency.
3. Using knowledge of adjustment with additional systematic parameters, based on an analysis of the sources of errors in airborne gravity measurements, an error model is studied to constructed mathematically which can characterize the change of systematic errors and with which three kinds of new crossover adjustment models are presented. Two practical survey data sets are used as a case study to verify the efficiency and reliability of the compensation method. The results show that the precision of the compensated network has been increased from 2.74mgal to 7.11magal.
4. Based on an M-estimation principle, a robust estimator of parameters of systematic errors model is introduced in every surveying line. Comparison of the estimator from the least-squares method with the robust method shows that the estimator from the robust estimator is more reliable.
依据测量值的类型不同，它可以分为航空标量重力测量和航空矢量重力测量两类，前者用以测定重力加速度的大小，后者不仅测定重力的大小，而且同时测定重力的方向。本文中所指航空重力测量特指航空标量重力测量。
为了尽可能构成重复观测，正确评价测量精度，航空重力测量的测线往往布设成网状，显然，必然形成交叉。由于受到各种误差源的干扰和影响，造成了交叉点上重力观测值不相同，即存在交叉点重力观测值不符值。这些干扰和影响或表现为系统性，或表现为随机性。航空重力测量测线网平差就是在分析、总结航空重力测量的主要误差源基础上，研究建立反映航空重力观测系统误差变化规律的误差模型，根据交叉点不符值条件，平差求解各测线上重力观测值系统误差改正数，然后对各测线上所有重力观测值进行改正(补偿)。航空重力测量测线网平差是航空重力测量的关键技术之一，这也是本文的主要内容。为此，本文从以下几个方面对航空重力测量测线网平差的理论与方法及相关内容进行研究，并得出若干初步结论：
1、结合航空重力测量的实际情况，提出了两种实用的交叉点搜索方法，即跳跃搜索法和图形辅助搜索法。利用模拟数据对这两种方法进行了比较，结果表明，两种方法都能快速、准确地搜索到交叉点的位置，与逐一比对搜索方法相比，搜索效率分别提高了91倍和176倍。当测量时间较长、采样率较高、相交测线较多时，两种搜索方法搜索速度快的优点就更加明显。
2、根据概率论和数理统计的理论与方法及误差理论，结合航空重力测量的特点，建立了有关检验统计量，并将其应用于航空重力测量测线系统误差的显著性检验。计算结果表明几种检验方法均可有效地对测线上的系统误差进行显著性检验。
3、根据附加系统参数平差的理论，在分析、总结航空重力测量的主要误差源基础上，研究建立了反映航空重力测量系统误差变化规律的误差模型，并根据三种不同的情况建立了相应的测线网平差模型。平差结果表明三种平差模型均对测线系统误差进行了有效的补偿，补偿后的精度提高了2.74～7.11毫伽，而且，对补偿后的测线网进行测线系统误差显著性检验，检验结果显示测线系统误差的影响已不再显著。
4、基于抗差估计理论，讨论了航空重力测量系统误差模型参数的抗差M估计方法与实现。通过比较，对于各测线上所有采样点的系统误差补偿来说，系统误差模型的抗差估计比最小二乘估计的可靠性更高。
Airborne gravimetry is a new kind of technique for surveying the gravity acceleration over the earth's surface and is advanced in gravimetry history, which basing on aircraft, including gravimeter, GPS, altimeter and attitude sensor etc.. Airborne gravimetry is applied to rapidly get extensively and precisely well-distributed information of the earth gravity field in order to meet the needs of Geodesy, Geophysics, Oceanography, Exploration, Space-Science and the other fields.
Airborne gravimetry includes scalar airborne gravimetry and vector airborne gravimetry. Scalar airborne gravimetry is used to get the value of the gravity acceleration, and vector airborne gravimetry can get not only the value but also the direction of the gravity acceleration. Airborne gravimetry which is discussed in this paper denote scalar airborne gravimetry only.
In order to estimate the accuracy of airborne gravity measurements, the tracks of an airborne gravity survery are generally planed to join each other. Discrepancies between measurements on different tracks may exist at the intersection because airborne gravity data are unavoidably affected by different kinds of error source. Furthermore, the performances of these errors may appear systematic or random. Based on an analysis of the sources of errors in airborne gravity measurements, an error model is studied to constructed mathematically which can characterize the change of systematic errors, with which the network adjustment is carried out and the model parameters are determined simultaneously. And finally, the compensation of systematic errors is realized. The network adjustment is one of key techniques for airborne gravimetry, it is also an important component in this paper. Consequently, the paper investigates the following aspects about the network adjustment theory and practice for airborne gravimetry, m
oreover, some questions correlated with solving the adjustment problem are discussed in detail.
1. Based on actualities of airborne gravimetry, two practical methods of searching crossovers are proposed, i. e. the skip-searching method and the graphic aid-searching method. A simulate network is used to test the efficiency and the reliability of these methods.Result demonstrates cross- points can be searched out rapidly and exactly by using these two methods.Compared with searching crossovers one by one, the skip-searching method increases the efficiency 91 times, and the graphic aid-searching method increases the efficiency 176 times.
2. According to the characteristic of airborne gravity survey, several statistic variables are derived from theory of probability and mathematical statistics combined with knowledge of errors principles. These statistic variables are applie to the significance test of systematic errors in every surveying line. Two practical applications prove their efficiency.
3. Using knowledge of adjustment with additional systematic parameters, based on an analysis of the sources of errors in airborne gravity measurements, an error model is studied to constructed mathematically which can characterize the change of systematic errors and with which three kinds of new crossover adjustment models are presented. Two practical survey data sets are used as a case study to verify the efficiency and reliability of the compensation method. The results show that the precision of the compensated network has been increased from 2.74mgal to 7.11magal.
4. Based on an M-estimation principle, a robust estimator of parameters of systematic errors model is introduced in every surveying line. Comparison of the estimator from the least-squares method with the robust method shows that the estimator from the robust estimator is more reliable.
引文
(按字母先后顺序排列)
[1] 程广义．航空重力测量中GPS动态定位的理论与方法．解放军测绘学院硕士论文，1999
[2] 黄谟涛．试论海洋重力测量中的半系统差．海洋测绘，1985
[3] 黄谟涛，管铮，翟国君，欧阳永忠．海洋重力测量中系统误差的补偿研究．海洋测绘，1997
[4] 黄维彬．近代平差理论及应用．北京：解放军出版社，1992
[5] 李德仁．误差处理和可靠性理论．北京：测绘出版社，1988
[6] 李明叁，刘雁春，翟国君．海洋测线网误差分析的LL图直视判定法．第十三届海洋测绘综合性学术研讨会论文集，2001
[7] 李庆海，陶本藻．概率统计原理和在测量中的应用．北京：测绘出版社，1982
[8] 孙中苗．航空重力测量中数字滤波技术的设计及应用．解放军测绘学院硕士论文，1997
[9] 夏哲仁，石磐等．航空重力测量系统．第三届两岸测绘发展研讨会测绘与可持续发展论文集，香港，2000
[10] 夏哲仁．空间重力测量技术．军事测绘，1997
[11] 肖云．利用GPS确定航空重力测量载体运动状态的理论与方法．武汉测绘科技大学硕士论文，2000
[12] 许厚泽，陆仲连等．中国地球重力场与大地水准面．北京：解放军出版社，1997
[13] 杨元喜．抗差估计理论及其应用．北京：八一出版社，1993
[14] 杨元喜，宋力杰，徐天河．大地测量相关观测抗差估计理论．
[15] 翟国君，黄谟涛，谢锡君，欧阳永忠．卫星测高数据处理的理论与方法．北京：测绘出版社，2000
[16] 周江文．经典误差理论与抗差估计．测绘学报，Vol．18，NO．2，1989．
[17] Bastos,L.P.Tome,T.Cunha, S.Cunha(2000),Gravity Anomalies from Airborne Measurements-Experiments Using a Low Cost IMU,In Proceedings of IAG International Symposium on Gravity, Geoid and Geodynamics 2000,July 31-August 4 2000,Banff, Canada.
[18] Brozena,J.M.,Peters M.F.(1988).Constraint criteria for adjustment of potential field surveys. Journal of Geophysics,Vol.53,No.12(DECEMBER 1988):pp.1601-1604.
[19] Brozena,J.,V.A.Childers(2000).The NRL Airborne Geophysics Program,In Intema-tional Association of Geodesy Symposia, Vol. 121, Schwarz(ed):Geodesy Beyond 2000-The Challenges of the First Decade,Springer,Berlin,Heidelburg,pp.126-130.
[20] Brutton,A.M.(1997).Reduction of GPS Receiver Noise Using Adaptive Filters,In Proceedings of the 101th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS 97),pp.645-653.
[21] Brutton,A.M.,K.P. Schwarz (1997).Airborne Gravity Estimation using Adaptive Filter, In Proceedings of International Symposium on Kinematic Systems in Geodesy,Geomatics and Navigation(KIS97), Banff,Canada,June 3-6,pp.605-612.
[22] Bruton,A.M.,K.P.Schwarz,S.Ferguson,M.Kem,M.Wei(2000).Deriving Acceleration from DGPS:Toward Higher Resolution Applications of Airborne Crravimetry,Submitted to GPS Solutions,December,2000.
[23] Childers,V.A.,R.E.Bell,J.M.Bmzena(1999).Airborne Gravimetry:An Investigation of Filtering,Geophysics,Vol.64,No.1,pp.61-69.
[24] Cunha,S.R.(1998) .On the INS and GPS Data Processing For Airborne Gravimetry Applications,Presented at International Workshop on Airborne Gravity and the Polar Gravity Field,Kangerlussuaq, Greenland, June2-4,1998．
[25] Czompo,J.(1991) .Acceleration Determination using Kinematic GPS Measurements,In Proceedings of the 4th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS 91) .
[26] Czompo,J.(1994) .Airborne Scalar Gravimetry Systems in the Spectral Domain,Ph.D.Thesis, UCGE Report No,20067,Department of Geomatics Engineering at the University of Calgary,Calgary,Canada.
[27] Fernandes,M.J.,L.Bastos,R.Forsberg,A.Oleson,F.Leite(2000) .Geoid Modeling in Coastal Region Using Airborne and Satellite Data: Case Study in the Azoresjn International Association of Geodesy Symposia,Vol.121, Schwarz(ed):Geodesy Beyond 2000-The Challenges of the First Decade,Springer,Berlin,Heidelburg,pp. 112-117．
[28] Ferguson,S.,Y.Hammada(2000) .Experiences with AIRGrav:Results from a New Airborne Gravimeter, In Proceedings of IAG International Symposium on Gravity,Geoid and Geodynamics 2000, My 31-August 4 2000,Banff,Canada.
[29] Forsberg,R.,A.V.Oleson,K.Keller( 1999) .Airborne Gravity Survey of the North Greenland Shelf 1998,Technical Report 10,Danish National Survey and Cadastre.Denmark.
[30] Glennie,C.(1999) .An Analysis of Airborne Gravity by Strapdown INS/DGPS,Ph.D. Thesis, Department of Geomatics Engineering,The University of Calgary,UCGE Report No.20125．
[31] Glennie.C., K.P.Schwarz(1999) .A Comparison and Analysis of Airborne Gravimetry Results from Two Strapdown Intertial/DGPS Systems, Journal of Geodesy,73,6,pp.311-321
[32] Hammada,Y.(1996) .A Comparison of Filtering Techniques for Airborne Gravimetry, M.Sc.Thesis,Department of Geomatics Engineering,The University of Calgary,UCGE Report No.20089．
[33] Hammada,Y(1996) .Optimal Versus Non-Optimal Low-pass Filtering in Airborne Gravimetry,In Proceedings of International Symposium on Kinematic Systems in Geodesy,Geomatics and Navigation(KIS97) , Banff,Canada, June 3-6,pp.633-640．
[34] Han,S.,C.Jekeli,J.H.Kwon(2000) .Precision Absolute GPS Positioning and its Use to Obtain Kinematic Acceleration,In Proceedings of LAG International Symposium on Gravity,Geoid and Geodynamics 2000,July 31-August 4 2000,Banff,Canada.
[35] Harrison,J.C.,J.D.MacQueen,A.C.Rauhut,J.Y.Cruz(1995) .The LCT Airborne Gravity System,In Proceedings IAG Symposium G4 Airborne Gravity Field Determination,XXI General Assembly of the IUGG, Boulder Colorado,July 2-14,1995,pp.l63-168．
[36] Huber PJ(1964) .Robust estimation of a location parametenAnn Math Statist 35:73-101
[37] Jekeli,C.,R.Garcia(1997) .GPS Phase Acceleration for Moving-Base Vector Gravimetry,Joumal of Geodesy,71 ,pp.630-639．
[38] Jekeli,C.,J.H.Kwon(1999) .Results of Airborne Vetor (3-D) Gravimetry,Geophysical Research Letters,Vol.26,No.23, pp. 3533-3536, December 1．
[39] Kubik K(1982) .An error theory for Danish method.International Symposium on Numercial Methods for Photogrammetric Mapping, Helsinki, 1982,Helsinki
[40] Li,Y.(2000) .Airborne Gravimetry and Geoid Determination, Ph.D.Thesis,Department of Geomatics Engineering,The University of Calgary,UCGE Report No.20141．
[41] Mary F. Peters and John M. Brozena(1988) :Constraint criteria for adjustment of potential
field surveys. GEOPHYSICS. VOL.53． NO.12: P1601-1604．
[42] Novak,P.,M.Kern,K.P.Schwarz(2000) .Continuation of Airborne Gravity,Unpublished internal report.Department of Geomatics Engineering.University of Calgary, Calgary, Canada.
[43] Schwarz,K.P.,Z.Li(1996) .An Introduction to Airborne Gravimetry and its Boundary Value Problems.Lecture Notes,IAG International Summer School,Como Italy,May 26-June 7．
[44] Tscherning,C.C.,F.Rubek,R.Forsberg( 1997) .Combining Airborne and Ground Gravity Using Collocation,In IAG Symposia Vol 119,Forsberg et al.(Eds):Geodesy on the move,Springer Verlag,pp. 18-23．
[45] Van Dierendonck,J.K.,M.E.Cannon,M.Wei,K.P.Schwarz(1994) .Error Sources in GPS-Determined Acceleration for Airborne Gravimetry,In Proceedings of the ION National Technical Meeting,San Diego, CAJanuary 24-26．
[46] Wei,M., K.P.Schwarz(1998) .Flight Test Results from a Strapdown Airborne Gravity System, Journal of Geodesy,72,pp.323-332．
[47] Yang Yuan-xi(1994) .Robust Estimation for Dependent Observation. Manuscripta Geodaetica, 1994,19(1) :10-17
[1] 程广义．航空重力测量中GPS动态定位的理论与方法．解放军测绘学院硕士论文，1999
[2] 黄谟涛．试论海洋重力测量中的半系统差．海洋测绘，1985
[3] 黄谟涛，管铮，翟国君，欧阳永忠．海洋重力测量中系统误差的补偿研究．海洋测绘，1997
[4] 黄维彬．近代平差理论及应用．北京：解放军出版社，1992
[5] 李德仁．误差处理和可靠性理论．北京：测绘出版社，1988
[6] 李明叁，刘雁春，翟国君．海洋测线网误差分析的LL图直视判定法．第十三届海洋测绘综合性学术研讨会论文集，2001
[7] 李庆海，陶本藻．概率统计原理和在测量中的应用．北京：测绘出版社，1982
[8] 孙中苗．航空重力测量中数字滤波技术的设计及应用．解放军测绘学院硕士论文，1997
[9] 夏哲仁，石磐等．航空重力测量系统．第三届两岸测绘发展研讨会测绘与可持续发展论文集，香港，2000
[10] 夏哲仁．空间重力测量技术．军事测绘，1997
[11] 肖云．利用GPS确定航空重力测量载体运动状态的理论与方法．武汉测绘科技大学硕士论文，2000
[12] 许厚泽，陆仲连等．中国地球重力场与大地水准面．北京：解放军出版社，1997
[13] 杨元喜．抗差估计理论及其应用．北京：八一出版社，1993
[14] 杨元喜，宋力杰，徐天河．大地测量相关观测抗差估计理论．
[15] 翟国君，黄谟涛，谢锡君，欧阳永忠．卫星测高数据处理的理论与方法．北京：测绘出版社，2000
[16] 周江文．经典误差理论与抗差估计．测绘学报，Vol．18，NO．2，1989．
[17] Bastos,L.P.Tome,T.Cunha, S.Cunha(2000),Gravity Anomalies from Airborne Measurements-Experiments Using a Low Cost IMU,In Proceedings of IAG International Symposium on Gravity, Geoid and Geodynamics 2000,July 31-August 4 2000,Banff, Canada.
[18] Brozena,J.M.,Peters M.F.(1988).Constraint criteria for adjustment of potential field surveys. Journal of Geophysics,Vol.53,No.12(DECEMBER 1988):pp.1601-1604.
[19] Brozena,J.,V.A.Childers(2000).The NRL Airborne Geophysics Program,In Intema-tional Association of Geodesy Symposia, Vol. 121, Schwarz(ed):Geodesy Beyond 2000-The Challenges of the First Decade,Springer,Berlin,Heidelburg,pp.126-130.
[20] Brutton,A.M.(1997).Reduction of GPS Receiver Noise Using Adaptive Filters,In Proceedings of the 101th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS 97),pp.645-653.
[21] Brutton,A.M.,K.P. Schwarz (1997).Airborne Gravity Estimation using Adaptive Filter, In Proceedings of International Symposium on Kinematic Systems in Geodesy,Geomatics and Navigation(KIS97), Banff,Canada,June 3-6,pp.605-612.
[22] Bruton,A.M.,K.P.Schwarz,S.Ferguson,M.Kem,M.Wei(2000).Deriving Acceleration from DGPS:Toward Higher Resolution Applications of Airborne Crravimetry,Submitted to GPS Solutions,December,2000.
[23] Childers,V.A.,R.E.Bell,J.M.Bmzena(1999).Airborne Gravimetry:An Investigation of Filtering,Geophysics,Vol.64,No.1,pp.61-69.
[24] Cunha,S.R.(1998) .On the INS and GPS Data Processing For Airborne Gravimetry Applications,Presented at International Workshop on Airborne Gravity and the Polar Gravity Field,Kangerlussuaq, Greenland, June2-4,1998．
[25] Czompo,J.(1991) .Acceleration Determination using Kinematic GPS Measurements,In Proceedings of the 4th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS 91) .
[26] Czompo,J.(1994) .Airborne Scalar Gravimetry Systems in the Spectral Domain,Ph.D.Thesis, UCGE Report No,20067,Department of Geomatics Engineering at the University of Calgary,Calgary,Canada.
[27] Fernandes,M.J.,L.Bastos,R.Forsberg,A.Oleson,F.Leite(2000) .Geoid Modeling in Coastal Region Using Airborne and Satellite Data: Case Study in the Azoresjn International Association of Geodesy Symposia,Vol.121, Schwarz(ed):Geodesy Beyond 2000-The Challenges of the First Decade,Springer,Berlin,Heidelburg,pp. 112-117．
[28] Ferguson,S.,Y.Hammada(2000) .Experiences with AIRGrav:Results from a New Airborne Gravimeter, In Proceedings of IAG International Symposium on Gravity,Geoid and Geodynamics 2000, My 31-August 4 2000,Banff,Canada.
[29] Forsberg,R.,A.V.Oleson,K.Keller( 1999) .Airborne Gravity Survey of the North Greenland Shelf 1998,Technical Report 10,Danish National Survey and Cadastre.Denmark.
[30] Glennie,C.(1999) .An Analysis of Airborne Gravity by Strapdown INS/DGPS,Ph.D. Thesis, Department of Geomatics Engineering,The University of Calgary,UCGE Report No.20125．
[31] Glennie.C., K.P.Schwarz(1999) .A Comparison and Analysis of Airborne Gravimetry Results from Two Strapdown Intertial/DGPS Systems, Journal of Geodesy,73,6,pp.311-321
[32] Hammada,Y.(1996) .A Comparison of Filtering Techniques for Airborne Gravimetry, M.Sc.Thesis,Department of Geomatics Engineering,The University of Calgary,UCGE Report No.20089．
[33] Hammada,Y(1996) .Optimal Versus Non-Optimal Low-pass Filtering in Airborne Gravimetry,In Proceedings of International Symposium on Kinematic Systems in Geodesy,Geomatics and Navigation(KIS97) , Banff,Canada, June 3-6,pp.633-640．
[34] Han,S.,C.Jekeli,J.H.Kwon(2000) .Precision Absolute GPS Positioning and its Use to Obtain Kinematic Acceleration,In Proceedings of LAG International Symposium on Gravity,Geoid and Geodynamics 2000,July 31-August 4 2000,Banff,Canada.
[35] Harrison,J.C.,J.D.MacQueen,A.C.Rauhut,J.Y.Cruz(1995) .The LCT Airborne Gravity System,In Proceedings IAG Symposium G4 Airborne Gravity Field Determination,XXI General Assembly of the IUGG, Boulder Colorado,July 2-14,1995,pp.l63-168．
[36] Huber PJ(1964) .Robust estimation of a location parametenAnn Math Statist 35:73-101
[37] Jekeli,C.,R.Garcia(1997) .GPS Phase Acceleration for Moving-Base Vector Gravimetry,Joumal of Geodesy,71 ,pp.630-639．
[38] Jekeli,C.,J.H.Kwon(1999) .Results of Airborne Vetor (3-D) Gravimetry,Geophysical Research Letters,Vol.26,No.23, pp. 3533-3536, December 1．
[39] Kubik K(1982) .An error theory for Danish method.International Symposium on Numercial Methods for Photogrammetric Mapping, Helsinki, 1982,Helsinki
[40] Li,Y.(2000) .Airborne Gravimetry and Geoid Determination, Ph.D.Thesis,Department of Geomatics Engineering,The University of Calgary,UCGE Report No.20141．
[41] Mary F. Peters and John M. Brozena(1988) :Constraint criteria for adjustment of potential
field surveys. GEOPHYSICS. VOL.53． NO.12: P1601-1604．
[42] Novak,P.,M.Kern,K.P.Schwarz(2000) .Continuation of Airborne Gravity,Unpublished internal report.Department of Geomatics Engineering.University of Calgary, Calgary, Canada.
[43] Schwarz,K.P.,Z.Li(1996) .An Introduction to Airborne Gravimetry and its Boundary Value Problems.Lecture Notes,IAG International Summer School,Como Italy,May 26-June 7．
[44] Tscherning,C.C.,F.Rubek,R.Forsberg( 1997) .Combining Airborne and Ground Gravity Using Collocation,In IAG Symposia Vol 119,Forsberg et al.(Eds):Geodesy on the move,Springer Verlag,pp. 18-23．
[45] Van Dierendonck,J.K.,M.E.Cannon,M.Wei,K.P.Schwarz(1994) .Error Sources in GPS-Determined Acceleration for Airborne Gravimetry,In Proceedings of the ION National Technical Meeting,San Diego, CAJanuary 24-26．
[46] Wei,M., K.P.Schwarz(1998) .Flight Test Results from a Strapdown Airborne Gravity System, Journal of Geodesy,72,pp.323-332．
[47] Yang Yuan-xi(1994) .Robust Estimation for Dependent Observation. Manuscripta Geodaetica, 1994,19(1) :10-17