基于星链差分技术的捷联重力仪载体加速度提取方法研究
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摘要
基于捷联重力仪的海洋重力测量是一种以水面舰船为载体,综合应用重力仪(或加速计)、捷联惯导系统、GPS、测高和测姿等技术测定近地空间重力加速度的动态重力测量方法。基本原理是利用重力仪(或加速度计)测定包括重力加速度、载体运动加速度以及其它扰动加速度在内的总加速度,从观测值中减去利用GPS确定的载体运动加速度,再加上一些改正,从而得到重力异常信号。因此,利用GPS精确确定载体运动加速度在重力测量中至关重要。传统的载体运动加速度测量方法主要有位置微分法和载波相位直接法,这两种方法均需要在地面架设GPS参考基站,不但提高了成本,而且限制了作业范围。在测量船远离海岸而无法架设地面GPS基站的情况下,研究如何通过单GPS接收机精确地确定载体垂直加速度具有十分重要的理论和现实意义。
本文以捷联重力仪SGA-WZ的研制为背景,基于SGA-WZ在云南某水上试验场的实测数据,重点研究了基于星链差分技术精密确定垂直加速度、观测数据滤波和低阶整系数差分器的优选三个方面的理论和方法。本文的主要工作和创新点概括如下:
1.研究了利用GPS确定载体加速度的两种常用基本方法,即位置微分法和载波相位直接法,在此基础上比较和分析了上述两种方法的优缺点,给出了在不同滤波周期下利用位置微分法确定载体加速度的理论精度。分析了由差分运算引起的误差传播特性,为数字差分器的优选与低通滤波器的设计提供了理论依据;
2.比较和分析了低阶整系数差分器,研究了不同阶次差分器的幅频特性和幅频相对误差。通过仿真试验,实现了对低阶整系数差分器的优选。结合重力测量数据的噪声特性,设计了基于切比雪夫最佳一致逼近原理的FIR低通滤波器;
3.设计了检验加速度测量精度的评估方案,评估了星链差分的定位精度,通过实测数据分别在静态和动态条件下对基于星链差分的载体加速度测量精度进行了评估。试验结果表明,在静态下,经200sFIR低通滤波,加速度测量误差标准差为0.5121mGal。在动态下,经200sFIR低通滤波,加速度测量误差标准差为0.5736mGal。研究了在不同数字差分器作用下加速度测量精度,通过实测数据,验证了低阶整系数差分器优选的正确性。
The shipborne gravimetry using strapdown gravimeter has been carried out by using a system which is based on the combination of a Strapdown Inertial Navigation System(SINS) and receivers of Global Positioning System(GPS) being used in differential mode (DGPS).The basic theory of shipborne gravimetry is that gravimeter (or accelerometer) senses the total acceleration including gravity signal, inertial acceleration and other accelerations, and GPS determines the vertical acceleration of the moving-base, then the signal of gravity anomaly will be yielded if vertical acceleration can be subtracted from total acceleration with some corrections. Therefore, the accurate determination of acceleration by using GPS is one of the key problems. There are mainly two approaches estimating the acceleration of moving-base, the position differentiation method and carrier phase direct method. Both methods need to erect the reference station on the ground, not only enhanced the cost of operation, moreover, some regions are unable to erect the reference station, which limited the gravity campaign, especially when the measuring ship is far from the GPS base stations. So it is important and significant to study how using a single GPS receiver to determine the vertical acceleration precisely.
In this paper, the method of acceleration estimation based on StarFire Differential GPS System、low-pass filtering of the observed data and low-order integral coefficient differentiators were studied. The main work and innovations of this paper are summarized as follows:
1. The two main methods using GPS to determine acceleration of moving-base were studied and analyzed, and the accuracy of acceleration in theory is given in different filtering intervals. The propagation characteristics of the differential expressions are analyzed, which provide a theoretical basis to the digital differentiator preference and low-pass filter design.
2. The low-order integral coefficient differentiators were compared and analyzed. Frequency characteristics and the error of frequency in different orders were studied. Through simulation, the optimal differentiator for acceleration determination was selected. The FIR low-pass filter is designed based on the Chebyshev best uniform approximation theory by combining the noisy characteristics of gravity measurements.
3. The method of evaluating the accuracy of acceleration was created. The accuracy of positioning was evaluated. The precision of acceleration determination is evaluated by using different filtering intervals in static and kinematic respectively. The results showed that under static, the accuracy of vertical acceleration is 0.5121mGal with 200s FIR low-pass filtering. Under kinematic, the accuracy of vertical acceleration is 0.5736mGal with 200s FIR low-pass filtering. The accuracy of accelerations using different differentiators was also studied, and the optimal differentiator was given.
本文以捷联重力仪SGA-WZ的研制为背景,基于SGA-WZ在云南某水上试验场的实测数据,重点研究了基于星链差分技术精密确定垂直加速度、观测数据滤波和低阶整系数差分器的优选三个方面的理论和方法。本文的主要工作和创新点概括如下:
1.研究了利用GPS确定载体加速度的两种常用基本方法,即位置微分法和载波相位直接法,在此基础上比较和分析了上述两种方法的优缺点,给出了在不同滤波周期下利用位置微分法确定载体加速度的理论精度。分析了由差分运算引起的误差传播特性,为数字差分器的优选与低通滤波器的设计提供了理论依据;
2.比较和分析了低阶整系数差分器,研究了不同阶次差分器的幅频特性和幅频相对误差。通过仿真试验,实现了对低阶整系数差分器的优选。结合重力测量数据的噪声特性,设计了基于切比雪夫最佳一致逼近原理的FIR低通滤波器;
3.设计了检验加速度测量精度的评估方案,评估了星链差分的定位精度,通过实测数据分别在静态和动态条件下对基于星链差分的载体加速度测量精度进行了评估。试验结果表明,在静态下,经200sFIR低通滤波,加速度测量误差标准差为0.5121mGal。在动态下,经200sFIR低通滤波,加速度测量误差标准差为0.5736mGal。研究了在不同数字差分器作用下加速度测量精度,通过实测数据,验证了低阶整系数差分器优选的正确性。
The shipborne gravimetry using strapdown gravimeter has been carried out by using a system which is based on the combination of a Strapdown Inertial Navigation System(SINS) and receivers of Global Positioning System(GPS) being used in differential mode (DGPS).The basic theory of shipborne gravimetry is that gravimeter (or accelerometer) senses the total acceleration including gravity signal, inertial acceleration and other accelerations, and GPS determines the vertical acceleration of the moving-base, then the signal of gravity anomaly will be yielded if vertical acceleration can be subtracted from total acceleration with some corrections. Therefore, the accurate determination of acceleration by using GPS is one of the key problems. There are mainly two approaches estimating the acceleration of moving-base, the position differentiation method and carrier phase direct method. Both methods need to erect the reference station on the ground, not only enhanced the cost of operation, moreover, some regions are unable to erect the reference station, which limited the gravity campaign, especially when the measuring ship is far from the GPS base stations. So it is important and significant to study how using a single GPS receiver to determine the vertical acceleration precisely.
In this paper, the method of acceleration estimation based on StarFire Differential GPS System、low-pass filtering of the observed data and low-order integral coefficient differentiators were studied. The main work and innovations of this paper are summarized as follows:
1. The two main methods using GPS to determine acceleration of moving-base were studied and analyzed, and the accuracy of acceleration in theory is given in different filtering intervals. The propagation characteristics of the differential expressions are analyzed, which provide a theoretical basis to the digital differentiator preference and low-pass filter design.
2. The low-order integral coefficient differentiators were compared and analyzed. Frequency characteristics and the error of frequency in different orders were studied. Through simulation, the optimal differentiator for acceleration determination was selected. The FIR low-pass filter is designed based on the Chebyshev best uniform approximation theory by combining the noisy characteristics of gravity measurements.
3. The method of evaluating the accuracy of acceleration was created. The accuracy of positioning was evaluated. The precision of acceleration determination is evaluated by using different filtering intervals in static and kinematic respectively. The results showed that under static, the accuracy of vertical acceleration is 0.5121mGal with 200s FIR low-pass filtering. Under kinematic, the accuracy of vertical acceleration is 0.5736mGal with 200s FIR low-pass filtering. The accuracy of accelerations using different differentiators was also studied, and the optimal differentiator was given.
引文
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[3]胡明城.现代大地测量学的理论及其应用.北京:测绘出版社, 2003.
[4]王谦身.重力学.北京:地震出版社, 2003.
[5]黄谟涛,翟国君,管铮.海洋重力场测定及其应用.北京:测绘出版社, 2005.
[6] Torge, W. Gravimetry. NewYork: Walter de Gruyter, 1989.
[7] Jekeli, C. Airborne Gravimetry Using INS/GPS and Gravity Gradiometers. ION 60th Annual Meeting. Dayton, OH, 2004. 476-482.
[8]张开东.基于SINS/DGPS的航空重力测量方法研究.博士.长沙:国防科学技术大学,2007.
[9]徐卫明.卫星测高技术在海洋重力测量中的应用.地矿测绘, 2000(3): 33-35.
[10]赵建虎.现代海洋测绘上册.武汉:武汉大学出版社, 2007.
[11]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.北京:测绘出版社, 2005.
[12] Kai-dong, Z., Mei-ping, W., Ju-liang, C. The Status of Strapdown Airborne Gravimeter SGA-WZ. 2010 International Symposium on Inertial Technology and Navigation. Nanjing,China, 2010. 176-181.
[13] Brozena, J.M., Mader, G.L., Peters, M.F. Interferometric Global Positioning System: Three-Dimensional Positioning Source for Airborne Gravimetry. Journal of Geophysical Research, 1989. 94(B9): 12153-12162.
[14] Brozena, J.M. GPS and airborne gravimetry: Recent progress and future plans. Bulletin géodésiqu, 1991. 65(2): 116 -121.
[15] Kleusberg, A. Separation of inertia and gravitation in airborne gravimetry with GPS. Lecture Notes in Earth Sciences Sydney, Australia, 1989. 47-63.
[16] Kleusberg, A., Peyton, D., Wells, D. Airborne gravimetry and the Global Positioning System. IEEE Position Location and Navigation Symposium. 1990. 273-278.
[17] Hein, G.W., Hehl, K., Landau, H., Ertel, M. Experiments for an integrated precise airborne navigation and gravity recovery system. IEEE Position Location and Navigation Symposium. 1990. 279-285.
[18] Bower, D.R., Kouba, J., Beach, R.J. The spectrum of GPS measurement errors and the accuracy of airborne gravity measurements. Geophysics, 1990. 55(8): 1101-1104.
[19] Wei, M., Ferguson, S., Schwartz, K.P. Accuracy of a GPS-derived accelerationfrom moving platform tests. Proceedings of IAG Symposium No.110, From Mars to Greenland: Charting with Space and Airborne Instruments. 110, 1991. 235-249.
[20] Wei, M. Analysis of GPS-derived Acceleration from Airborne Tests. Proceedings of IAG Symposium on Airborne Gravity Field Determination, IUGG XII General Assembly. Boulder, Colorado, USA, 1995. 175-188.
[21] Klingelé, E.E., Cocard, M., Kahle, H.-G. Kinematic GPS as a source for airborne gravity reduction in the airborne gravity survey of Switzerland. Journal of Geophysical Research, 1997. 102(B4): 7705-7715.
[22] Bell, R., Childers, V., R., A., Blankenship, D., et al. Airborne gravity and precise positioning for geologic applications. Journal of Geophysical Research, 1999. 104(B7): 15281-15292.
[23] Bruton, A.M., Glennie, C.L., Schwarz, K.P. Differentiation for High-Precision GPS Velocity and Acceleration Determination. GPS Solutions, 1999. 2(4): 7-21.
[24] Bruton, A.M., Schwarz, K.P. Deriving Acceleration from DGPS: Toward Higher Resolution Applications of Airborne Gravimetry. GPS Solutions, 2002. 5(3): 1-14.
[25] Boedecker, G., V?lksen, C., Wanninger, L., Wende, W. Precise GPS-Positioning and - Acceleration for Airborne Gravimetry: A Case Study. Proceedings of Gravity and Geoid 2002. Banff, Alberta,Canada, 2002.
[26] Duquenne, F., Olesen, A.V., Cali, J. Plane Trajectory with GPS for Airborne Gravimetry. Gravity and Geoid 2002 - GG2002. Banff, Alberta,Canada, 2002.
[27]孙中苗,石磐,夏哲仁.利用GPS和数字滤波技术确定航空重力测量中的垂直加速度.测绘学报, 2004. 33(2): 111-115.
[28] Kleusberg, A., Peyton, D., Wells, D. AIRBORNE GRAVIMETRY AND THE GLOBAL POSTIONING SYSTEM. 1990.
[29]卢喜平,何荣智,王程远. StarFireTM差分GPS技术引进及水利行业应用.测绘, 2009. 32(4): 175-179.
[30]许捍卫,何江,杨艳飞.星站差分GPS在水下地形测量中的应用.水利水电科技进展, 2008. 28(2): 76-78.
[31]张彦军. StarFire全球高精度广域差分GPS系统.物探装备, 2007. 17(2): 145-151.
[32]熊刚,束焕然,廖七一,王小, et al. STAR FIRE TM-RTG星基差分实时精密单点定位原理、测试与应用.全球定位系统, 2006.
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