长航时高精度惯性导航系统重力补偿研究
|
摘要
惯导系统的独立性决定了它们可以有效避免信号的干扰,在一些干扰信号强烈的区域,惯性导航有很大的应用前景。惯导精度不仅与陀螺仪和加速度计器件精度有关,更与重力补偿的精度相关。真实重力与模型重力之间存在偏差,此偏差就是重力扰动,重力补偿就是指对重力扰动的补偿。短航时中低精度的惯导系统中,通常都是由重力模型提供的重力代替真实重力。长航时高精度惯导系统中,由于器件精度量级高于重力扰动量级,因此,重力扰动不应该被忽略,需要进行重力补偿。我国对重力补偿的研究起步较晚,现有成果还不能满足高精度惯性导航的要求。本文对惯性导航系统的重力补偿问题开展了研究,重点对比分析了“直接线性插值法”和“最小二乘配置法”两种重力补偿方法。主要研究内容包括:
1、介绍了常用的重力模型及重力扰的概念。本文介绍了仿真用到的WGS84模型“重力模型”,以及最小二乘法所使用的统计学倒数距离“重力扰动模型”(RDM);为获得扰动所需的先验数据,以及检验两种重力补偿方法的效果,需首先获取一定区域的重力扰动数据,因此,本文还介绍了一些常用的重力扰动测量方法,并着重对比了“基于模型法”和“直接求差法”两种方法的优劣性。
2、针对重力扰动对导航精度的影响进行了研究。根据导航误差模型提取出北向单通道位置误差模型,并以此为基础推导出北向重力扰动与北向位置误差之间的解析关系式,并通过垂线偏差、仿真以及实测数据分析的方法验证了解析式的正确性。
3、通过仿真将各向重力扰动对水平方向位置误差的影响做了定量分析。仿真结果表明,北向和东向位置误差随各向重力扰动增长而成比例的增长,但位置误差不会随时间发散,而是在做周期性振荡。垂向重力扰动对水平方向的位置误差较小,可以忽略,但与器件误差造成的影响相比水平方向的重力扰动分量造成的定位误差在高精度惯性导航系统中较大,因此水平方向的重力扰动分量不能忽略。
4、针对“最小二乘配置法”和“直接线性插值法”两种补偿方法进行了对比分析。介绍了两种方法的原理,并通过仿真分析对两者的抗噪性能及受重力数据密度的影响程度两个方面进行对比,仿真结果表明:重力扰动数据密度对两种补偿方法有很大影响,数据越密集,补偿效果越好;在噪声量级低于重力扰动量级的情况下,两种补偿效果的抗噪性能均表现优良;在仿真条件下,对比“最小二乘配置法”与“直接线性插值法”,前者对重力扰动的估测更准确。最后通过实测数据的分析验证了仿真结果的正确性。
The self-contained nature of inertial-navigation systems and their immunity to enemy jamming make them extremely attractive. Long-term high accuracy inertial navigation depends on not only the quality of the inertial sensors (accelerometers and gyros),but also the ability to compensate for the gravity disturbances. Gravity disturbances are the errors between true gravity and the gravity calculated by gravity model,and gravity compensation is the compensation for gravity disturbances. During short-term low accuracy INS, substituting model gravity obtained from certain gravity model approximately for true gravity is adequate enough. However, during long-term high accuracy INS, the east position error caused by the neglect of the vertical channel gravity disturbance will grow unboundedly with time; With the development of high accuracy INS,the precision of accelerometers and gyroscopes are highly enhanced, the error of gravity becomes the main error of INS. This paper talks about two ways of gravity compensation:“Linear direct interpolation”(DLI) and“Least square collocation”(LSC). And the main contributions include the following aspects:
1. Analyze the position error affected by gravity disturbances on INS. According to navigation error model, we can extract error model of single channel, base on the model, we can deduce the formula between the north position error and north gravity disturbance. Formula is validated through the theory of“deflections of vertical”, the analysis of simulation and experiment data.
2. Introduce several kinds of gravity models and several ways to measure gravity disturbances. The gravity model used for simulation in this paper is WGS84, and“Least square collocation”compensation method use reciprocal distance model(RDM) as the gravity disturbance model. For the sake of obtaining gravity data to validate the effect of LSC and DLI, this paper talks about how to measure gravity disturbances in several ways, and focus on the comparison among them.
3. Research the relationship between horizontal position error and gravity disturbance of different channels. The result concludes that: the horizontal position errors grow in proportion with gravity disturbances,but the error won’t grow unboundedly with time; however the horizontal position error caused by gravity disturbances of horizontal channel is too large to be neglected so that we need to compensate them .
4. Deep research is carried out aiming at the comparison of two compensation method. After introduce the principle of LSC and DLI, we analyze their resistance to noise and research the effect of density of the gravity data. The result shows that: both of them are good at resisting noise, and the larger the density of the data, the better compensation will be. And for most of time LSC is better than DLI. At last we use experiment to validate the result concluded by simulation.
1、介绍了常用的重力模型及重力扰的概念。本文介绍了仿真用到的WGS84模型“重力模型”,以及最小二乘法所使用的统计学倒数距离“重力扰动模型”(RDM);为获得扰动所需的先验数据,以及检验两种重力补偿方法的效果,需首先获取一定区域的重力扰动数据,因此,本文还介绍了一些常用的重力扰动测量方法,并着重对比了“基于模型法”和“直接求差法”两种方法的优劣性。
2、针对重力扰动对导航精度的影响进行了研究。根据导航误差模型提取出北向单通道位置误差模型,并以此为基础推导出北向重力扰动与北向位置误差之间的解析关系式,并通过垂线偏差、仿真以及实测数据分析的方法验证了解析式的正确性。
3、通过仿真将各向重力扰动对水平方向位置误差的影响做了定量分析。仿真结果表明,北向和东向位置误差随各向重力扰动增长而成比例的增长,但位置误差不会随时间发散,而是在做周期性振荡。垂向重力扰动对水平方向的位置误差较小,可以忽略,但与器件误差造成的影响相比水平方向的重力扰动分量造成的定位误差在高精度惯性导航系统中较大,因此水平方向的重力扰动分量不能忽略。
4、针对“最小二乘配置法”和“直接线性插值法”两种补偿方法进行了对比分析。介绍了两种方法的原理,并通过仿真分析对两者的抗噪性能及受重力数据密度的影响程度两个方面进行对比,仿真结果表明:重力扰动数据密度对两种补偿方法有很大影响,数据越密集,补偿效果越好;在噪声量级低于重力扰动量级的情况下,两种补偿效果的抗噪性能均表现优良;在仿真条件下,对比“最小二乘配置法”与“直接线性插值法”,前者对重力扰动的估测更准确。最后通过实测数据的分析验证了仿真结果的正确性。
The self-contained nature of inertial-navigation systems and their immunity to enemy jamming make them extremely attractive. Long-term high accuracy inertial navigation depends on not only the quality of the inertial sensors (accelerometers and gyros),but also the ability to compensate for the gravity disturbances. Gravity disturbances are the errors between true gravity and the gravity calculated by gravity model,and gravity compensation is the compensation for gravity disturbances. During short-term low accuracy INS, substituting model gravity obtained from certain gravity model approximately for true gravity is adequate enough. However, during long-term high accuracy INS, the east position error caused by the neglect of the vertical channel gravity disturbance will grow unboundedly with time; With the development of high accuracy INS,the precision of accelerometers and gyroscopes are highly enhanced, the error of gravity becomes the main error of INS. This paper talks about two ways of gravity compensation:“Linear direct interpolation”(DLI) and“Least square collocation”(LSC). And the main contributions include the following aspects:
1. Analyze the position error affected by gravity disturbances on INS. According to navigation error model, we can extract error model of single channel, base on the model, we can deduce the formula between the north position error and north gravity disturbance. Formula is validated through the theory of“deflections of vertical”, the analysis of simulation and experiment data.
2. Introduce several kinds of gravity models and several ways to measure gravity disturbances. The gravity model used for simulation in this paper is WGS84, and“Least square collocation”compensation method use reciprocal distance model(RDM) as the gravity disturbance model. For the sake of obtaining gravity data to validate the effect of LSC and DLI, this paper talks about how to measure gravity disturbances in several ways, and focus on the comparison among them.
3. Research the relationship between horizontal position error and gravity disturbance of different channels. The result concludes that: the horizontal position errors grow in proportion with gravity disturbances,but the error won’t grow unboundedly with time; however the horizontal position error caused by gravity disturbances of horizontal channel is too large to be neglected so that we need to compensate them .
4. Deep research is carried out aiming at the comparison of two compensation method. After introduce the principle of LSC and DLI, we analyze their resistance to noise and research the effect of density of the gravity data. The result shows that: both of them are good at resisting noise, and the larger the density of the data, the better compensation will be. And for most of time LSC is better than DLI. At last we use experiment to validate the result concluded by simulation.
引文
[1] Akeila, E., Salcic, Z., Swain, A. Direct Gravity Estimation and Compensation in Strapdown INS Applications[C]. Department of Electrical and Computer Engineering .International Conference on Sensing Technology Auckland, New Zealand, 2008. 6.
[2] Kopcha, P.D. NGA Gravity Support for Inertial Navigation[C]. 2004.
[3] Kriegsman*, B.A., Mahar, K.B. Gravity-Model Errors in Mobile Inertial-Navigation Systems[J]. Journal of Guidance and Control, 1985: 10.
[4] Kwon, J.H. Gravity Compensation Methods for Precision INS[C]. 2004.
[5] Kopcha, P.D. NGA Gravity Support for Inertial Navigation[C]. National Geospatial-Intelligence Agency. 2004.6. 8.
[6] Harriman, D.W., Harrison, J.C. Gravity-Induced Errors in Airborne Inertial Navigation[J]. Journal of Guidance and Control, 1986: 8.
[7] Kwon, J.H. Gravity Compensation Methods for Precision INS[C]. Department of Civil and Environmental Engineering and Geodetic Science. Columbus, Ohio, 2004.6. 8.
[8]程力,张雅杰,蔡体菁.重力辅助导航匹配区域选择准则[J].中国惯性技术学报, 2007(10).
[9]张开东.基于SINS/DGPS的航空重力测量方法研究[D].博士.长沙:中国人民解放军国防科学技术大学,2007.
[10]黄谟涛,翟国君,管铮,欧阳永忠, et al.,海洋重力场测定及其应用. 2005,测绘出版社:北京.
[11] Heiskanen, Moritz. Physical Geodesy[J]. 1996.
[12] Jekeli, C. Inertial Navigation Systems with Geodetic Applications[J]. Walter de Gruyter, 2001.
[13] Grejner-Brzezinska, D.A., Wang, J. Gravity Modeling for High-Accuracy GPS/INS Integration[J]. Journal of The Institute of Navigation, 1998.
[14] Grejner-Brzezinska, D.A., Yi, Y., Tothb, C., Andersonc, R., et al. On Improved Gravity Modeling Supporting Direct Georeferencing of Multisensor Systems改.PDF[D].
[15] Humphrey, I., Inertial System Requirements for Deflection of the Vertical Compensations. 1999. p. 82.
[16] R.C.ANDERSON, J.A.DAVENPORT. Determination of Gravity Data Spacing Required For Inertial Navigation[J]. Journal of The Institude of Navigation, 1999: 6.
[17] B. A. Kriegsman* , Mahar, K.B. Gravity-Model Errors in Mobile Inertial-Navigation Systems[J]. Journal of Guidance and Control, 2004.
[18] Grejner-Brzezinska, D.A., Yi, Y., Toth, C. Enhanced Gravity Compensation for Improved Inertial Navigation Accuracy[C]. Department of Civil and Environmental Engineering and Geodetic Science. Ohio, 2003,9. 13.
[19]宁津生.卫星重力与地球重力场[J].地理空间信息, 2008(01).
[20]宁津生.基于能量守恒的星间距离变率与地球重力场频谱关系的建立与分析[J].武汉大学学报, 2008(03).
[21]宁津生.基于多尺度边缘约束的重力场信号的向下延拓[J].测绘文摘,2004(02).
[22]李卓,闫海蛟.中国海及领域重力异常的惯性系统误差分析[J].青岛大学学报, 2004. 17(03).
[23]袁书明,孙枫.重力图形匹配技术在水下导航中的应用[J].中国惯性技术学报, 2004(2).
[24] Edwards, R.M. Gravity Model Performance in Inertial Navigation[J]. Journal of Guidance and Control, 1982.
[25] Eissfeller, B., Spietz, P. Shaping filter design for the anomalous gravity field by means of spectral factorization[J]. Manuscripta Geodaetica, 1989.
[26] Estes, Peter. Deflection of the Vertical (DOV) Aiding to INS on F-117A[C]. NGA Advanced Navigation Systems Support Conference. 2004.
[27] Forsberg, R. A New Covariance Model for Inertial Gravimetry and Gradiometry[J]. Journal of Geophsical Research, 1987.
[28] Titterton, D.H., Weston, J.L. Strapdown Inertial Navigation Technology. Second Edition.[M]. Second ed, ed. Zarchan, P.: MIT LincolnLaboratory, Lexington, Massachusetts., 2004.
[29] Chatfield, A.B.高精度惯性导航基础[M].北京:国防工业出版社(内部出版), 2002.
[30] Department of Defense World Geodetic System 1984. Edition 3, 1997. , NIMA Technical Report TR8350.2,.
[31]郭恩志,房建成,俞文伯.一种重力异常对弹道导弹惯性导航精度影响的补偿方法[J].中国惯性技术学报, 2005.
[32]艾贵斌,李勇,耿忠.惯性定位测量重力空间参数的逼近计算与工程实践[J].中国惯性技术学报, 2002.02. 10(1).
[33]练军想,高精度惯性导航中的重力场问题. 2010.8.
[34] Jekeli, C. Gravity on Precise, Short-Term, 3-D Free-Inertial Navigation[J]. Journal of The Institute of Navigation, 1997.
[35] Moritz, H. physical geodesy[M]: Springer Wien NewYork, 2005.
[36]吴太旗,边少锋,勃,蒋.,勇,陈.重力场对惯性导航定位误差影响研究与仿真[J].测绘科学技术学报, 2006.
[37] Rogers, R.M. Application mathematics in integrated navigation system[M].
[38] Grejner-Brzezinska, D.A., Yi, Y., Toth, C. Enhanced Gravity Compensation for Improved Inertial Navigation Accuracy[J]. 2003.
[39]张开东.基于SINS/DGPS的航空重力测量方法研究[D]. 2007.
[40] Titterton, D.H. Strapdown Inertial Navigation Technology(2nd edition)[M], ed. American Institute of Aeronautics and Astronautics, I., 2004.
[41] Salychev, O.S. Applied Inertial Navigation: Problems and Solutions[M]. Moscow: BMSTU Press, 2004.
[42] Jekeli, C. Inertial Navigation Systems with Geodetic Applications[M]: Walter de Gruyter,Berlin, 2001.
[43] Jordan, S.K. Self-consistent Statistical Models for the Gravity Anomaly, Vertical Deflections and Undulations of the Geoid[J]. Journal of Geophsical Research, 1972. 77: 3660-3670.
[44] Jordan, S.K., Mooman, P.J. State-Space Models of Gravity Disturbance Gradients[J]. IEEE Transaction on Aerospace and Electronic Systems, 1981. AES-17(5): 610-618.
[45] Forsberg, R. A New Covariance Model for Inertial Gravimetry and Gradiometry[J]. Journal of Geophsical Research, 1987. 92(B2): 1305-1310.
[46] Gleason, D.M. Extracting gravity vectors from the integration of Global Positioning System and Inertial Navigation System data[J]. Journal of Geophsical Research, 1992. 97(B6): 8853-8864.
[47]陈永冰,边少锋,刘勇.重力异常对平台式惯性导航系统误差的影响分析[J].中国惯性技术学报, 2005.12. 13(6).
[48] David.H.Titterton, L.westor, J. Strapdown Inertial Navigation Technology[M]: The institution of Electrical Engineers, 2004.
[49] Anderson, R.C., Davenport, J.A., Jekeli, C. Determination of Gravity Data Spacing Required For Inertial Navigation[J]. Journal of The Institute of Navigation, 2000.
[50] Y.Hsu, D., J.Brockstein, A. GRAVITY VECTOR COMPENSATION SYSTEM[J]. 2001.6.19.
[51] Rogers, R.M. Application mathematics in integrated navigation system[M].
[2] Kopcha, P.D. NGA Gravity Support for Inertial Navigation[C]. 2004.
[3] Kriegsman*, B.A., Mahar, K.B. Gravity-Model Errors in Mobile Inertial-Navigation Systems[J]. Journal of Guidance and Control, 1985: 10.
[4] Kwon, J.H. Gravity Compensation Methods for Precision INS[C]. 2004.
[5] Kopcha, P.D. NGA Gravity Support for Inertial Navigation[C]. National Geospatial-Intelligence Agency. 2004.6. 8.
[6] Harriman, D.W., Harrison, J.C. Gravity-Induced Errors in Airborne Inertial Navigation[J]. Journal of Guidance and Control, 1986: 8.
[7] Kwon, J.H. Gravity Compensation Methods for Precision INS[C]. Department of Civil and Environmental Engineering and Geodetic Science. Columbus, Ohio, 2004.6. 8.
[8]程力,张雅杰,蔡体菁.重力辅助导航匹配区域选择准则[J].中国惯性技术学报, 2007(10).
[9]张开东.基于SINS/DGPS的航空重力测量方法研究[D].博士.长沙:中国人民解放军国防科学技术大学,2007.
[10]黄谟涛,翟国君,管铮,欧阳永忠, et al.,海洋重力场测定及其应用. 2005,测绘出版社:北京.
[11] Heiskanen, Moritz. Physical Geodesy[J]. 1996.
[12] Jekeli, C. Inertial Navigation Systems with Geodetic Applications[J]. Walter de Gruyter, 2001.
[13] Grejner-Brzezinska, D.A., Wang, J. Gravity Modeling for High-Accuracy GPS/INS Integration[J]. Journal of The Institute of Navigation, 1998.
[14] Grejner-Brzezinska, D.A., Yi, Y., Tothb, C., Andersonc, R., et al. On Improved Gravity Modeling Supporting Direct Georeferencing of Multisensor Systems改.PDF[D].
[15] Humphrey, I., Inertial System Requirements for Deflection of the Vertical Compensations. 1999. p. 82.
[16] R.C.ANDERSON, J.A.DAVENPORT. Determination of Gravity Data Spacing Required For Inertial Navigation[J]. Journal of The Institude of Navigation, 1999: 6.
[17] B. A. Kriegsman* , Mahar, K.B. Gravity-Model Errors in Mobile Inertial-Navigation Systems[J]. Journal of Guidance and Control, 2004.
[18] Grejner-Brzezinska, D.A., Yi, Y., Toth, C. Enhanced Gravity Compensation for Improved Inertial Navigation Accuracy[C]. Department of Civil and Environmental Engineering and Geodetic Science. Ohio, 2003,9. 13.
[19]宁津生.卫星重力与地球重力场[J].地理空间信息, 2008(01).
[20]宁津生.基于能量守恒的星间距离变率与地球重力场频谱关系的建立与分析[J].武汉大学学报, 2008(03).
[21]宁津生.基于多尺度边缘约束的重力场信号的向下延拓[J].测绘文摘,2004(02).
[22]李卓,闫海蛟.中国海及领域重力异常的惯性系统误差分析[J].青岛大学学报, 2004. 17(03).
[23]袁书明,孙枫.重力图形匹配技术在水下导航中的应用[J].中国惯性技术学报, 2004(2).
[24] Edwards, R.M. Gravity Model Performance in Inertial Navigation[J]. Journal of Guidance and Control, 1982.
[25] Eissfeller, B., Spietz, P. Shaping filter design for the anomalous gravity field by means of spectral factorization[J]. Manuscripta Geodaetica, 1989.
[26] Estes, Peter. Deflection of the Vertical (DOV) Aiding to INS on F-117A[C]. NGA Advanced Navigation Systems Support Conference. 2004.
[27] Forsberg, R. A New Covariance Model for Inertial Gravimetry and Gradiometry[J]. Journal of Geophsical Research, 1987.
[28] Titterton, D.H., Weston, J.L. Strapdown Inertial Navigation Technology. Second Edition.[M]. Second ed, ed. Zarchan, P.: MIT LincolnLaboratory, Lexington, Massachusetts., 2004.
[29] Chatfield, A.B.高精度惯性导航基础[M].北京:国防工业出版社(内部出版), 2002.
[30] Department of Defense World Geodetic System 1984. Edition 3, 1997. , NIMA Technical Report TR8350.2,.
[31]郭恩志,房建成,俞文伯.一种重力异常对弹道导弹惯性导航精度影响的补偿方法[J].中国惯性技术学报, 2005.
[32]艾贵斌,李勇,耿忠.惯性定位测量重力空间参数的逼近计算与工程实践[J].中国惯性技术学报, 2002.02. 10(1).
[33]练军想,高精度惯性导航中的重力场问题. 2010.8.
[34] Jekeli, C. Gravity on Precise, Short-Term, 3-D Free-Inertial Navigation[J]. Journal of The Institute of Navigation, 1997.
[35] Moritz, H. physical geodesy[M]: Springer Wien NewYork, 2005.
[36]吴太旗,边少锋,勃,蒋.,勇,陈.重力场对惯性导航定位误差影响研究与仿真[J].测绘科学技术学报, 2006.
[37] Rogers, R.M. Application mathematics in integrated navigation system[M].
[38] Grejner-Brzezinska, D.A., Yi, Y., Toth, C. Enhanced Gravity Compensation for Improved Inertial Navigation Accuracy[J]. 2003.
[39]张开东.基于SINS/DGPS的航空重力测量方法研究[D]. 2007.
[40] Titterton, D.H. Strapdown Inertial Navigation Technology(2nd edition)[M], ed. American Institute of Aeronautics and Astronautics, I., 2004.
[41] Salychev, O.S. Applied Inertial Navigation: Problems and Solutions[M]. Moscow: BMSTU Press, 2004.
[42] Jekeli, C. Inertial Navigation Systems with Geodetic Applications[M]: Walter de Gruyter,Berlin, 2001.
[43] Jordan, S.K. Self-consistent Statistical Models for the Gravity Anomaly, Vertical Deflections and Undulations of the Geoid[J]. Journal of Geophsical Research, 1972. 77: 3660-3670.
[44] Jordan, S.K., Mooman, P.J. State-Space Models of Gravity Disturbance Gradients[J]. IEEE Transaction on Aerospace and Electronic Systems, 1981. AES-17(5): 610-618.
[45] Forsberg, R. A New Covariance Model for Inertial Gravimetry and Gradiometry[J]. Journal of Geophsical Research, 1987. 92(B2): 1305-1310.
[46] Gleason, D.M. Extracting gravity vectors from the integration of Global Positioning System and Inertial Navigation System data[J]. Journal of Geophsical Research, 1992. 97(B6): 8853-8864.
[47]陈永冰,边少锋,刘勇.重力异常对平台式惯性导航系统误差的影响分析[J].中国惯性技术学报, 2005.12. 13(6).
[48] David.H.Titterton, L.westor, J. Strapdown Inertial Navigation Technology[M]: The institution of Electrical Engineers, 2004.
[49] Anderson, R.C., Davenport, J.A., Jekeli, C. Determination of Gravity Data Spacing Required For Inertial Navigation[J]. Journal of The Institute of Navigation, 2000.
[50] Y.Hsu, D., J.Brockstein, A. GRAVITY VECTOR COMPENSATION SYSTEM[J]. 2001.6.19.
[51] Rogers, R.M. Application mathematics in integrated navigation system[M].