Method of Multi-dimensional Gross Errors Snooping of GPS Velocity Estimation in Airborne Gravimetry

doi:10.11947/j.AGCS.2016.20150481

Abstract

Abstract: Precision velocity plays an important role in airborne gravimetry. Since the aircraft in a state of stable flight, we could establish a strict state equation with constant acceleration model for it, then obtained predicted velocity which was used for constructing a priori residual Q to detect the gross errors. Theoretical research showed that Q was influenced by the accuracy of predicted velocity and the measurement errors. According to the statistical features of Q combined with IGG Ⅲ principle, we could lower the contribution of the observation that contained the gross errors. Static testing was used for analyzing the characteristic of measurement errors as well as the accuracy of predicted velocity under the simulated ideal flight environment where the acceleration was approximate to a constant, the results also showed the relationship between the sampling rate and the ability of detecting gross errors. Both the static and kinematic tests demonstrate that new method can well detect the gross error smaller than 1 cycle.

Key words: airborne gravimetry, constant acceleration model, GPS velocity estimation, IGG Ⅲ scheme, detection for multi-dimensional gross error

CLC Number:

P228

ZHENG Kai, LIU Zhanke, XIAO Xuenian, ZHANG Xiaohong. Method of Multi-dimensional Gross Errors Snooping of GPS Velocity Estimation in Airborne Gravimetry[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(6): 663-669.

References

[1] 孙中苗. 航空重力测量理论、方法及应用研究[D]. 郑州:信息工程大学, 2004. SUN Zhongmiao. Theory, Methods and Applications of Airborne Gravimetry[D]. Zhengzhou:Information Engineering University, 2004.
[2] BRUTON A M. Improving the Accuracy and Resolution of SINS/DGPS Airborne Gravimetry[D]. Calgary, Alberta:University of Calgary, 2000.
[3] JEKELI C, GARCIA R. GPS Phase Accelerations for Moving-base Vector Gravimetry[J]. Journal of Geodesy, 1997, 71(10):630-639.
[4] 肖云, 孙中苗, 程广义. 利用多普勒观测值精确确定运动载体的速度[J]. 武汉测绘科技大学学报, 2000, 25(2):113-118. XIAO Yun, SUN Zhongmiao, CHENG Guangyi. Precise Determination of Velocity for Airborne Gravimetry Using the GPS Doppler Observations[J]. Journal of Wuhan Technical University of Surveying and Mapping, 2000, 25(2):113-118.
[5] 张开东. 基于SINS/DGPS的航空重力测量方法研究[D]. 长沙:国防科学技术大学, 2007. ZHANG Kaidong.Research on the Methods of Airborne Gravimetry Based on SINS/DGPS[D].Changsha:National University of Defense Technology, 2007.
[6] HEBERT C J, KEITH J, RYAN S, et al. DGPS Kinematic Carrier Phase Signal Simulation Analysis for Precise Aircraft Velocity Determination[C]//Proceedings of the ION GPS-97.Albuquerque:[s.n.], 1997.
[7] BRUTON A M, GLENNIE C L, SCHWARZ K P. Differentiation for High-precision GPS Velocity and Acceleration Determination[J]. GPS Solutions, 1999, 2(4):7-21.
[8] ZHANG J J.Precise Velocity and Acceleration Determination Using a Standalone GPS Receiver in Real Time[D]. Melbourne:RMIT University, 2007.
[9] 范龙, 翟国君, 白鸽. 基于抗差最小二乘估计的载体速度计算方法[J]. 测绘学报, 2011, 40(S1):95-99. FAN Long, ZHAI Guojun, BAI Ge. Calculating the Carrier Velocity Based on Robust Least Square Estimation[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(S1):95-99.
[10] 杨元喜. 等价权原理——参数平差模型的抗差最小二乘解[J]. 测绘通报, 1994(6):33-35, 29. YANG Yuanxi.Theory of Equivalent Weight:The Least Squares Solution of Parameter Adjustment Model[J]. Bulletin of Surveying and Mapping, 1994(6):33-35, 29.
[11] 彭军还. 非线性M估计研究及其应用[D]. 武汉:武汉大学, 2003. PENG Junhuan.Research on Non-linear M-estimates and Its Application[D]. Wuhan:Wuhan University, 2003.
[12] 於宗俦, 李明峰. 多维粗差的同时定位与定值[J]. 武汉测绘科技大学学报, 1996, 21(4):323-329. YU Zongchou, LI Mingfeng. Simultaneous Location and Evaluation of Multi-dimensional Gross Errors[J]. Journal of Wuhan Technical University of Surveying and Mapping, 1996, 21(4):323-329.
[13] 杨玲, 沈云中, 楼立志. 基于中位参数初值的等价权抗差估计方法[J]. 测绘学报, 2011, 40(1):28-32. YANG Ling, SHEN Yunzhong, LOU Lizhi. Equivalent Weight Robust Estimation Method Based on Median Parameter Estimates[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(1):28-32.
[14] 林旭, 罗志才, 姚朝龙. 常加速度模型的简化自协方差最小二乘法[J]. 测绘学报, 2014, 43(11):1144-1150. DOI:10.13485/j.cnki.11-2089.2014.0143. LIN Xu, LUO Zhicai, YAO Chaolong. Simplified Autocovariance Least-squares Method for Constant Acceleration Model[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(11):1144-1150. DOI:10.13485/j.cnki.11-2089.2014.0143.
[15] SINGER R A. Estimating Optimal Tracking Filter Performance for Manned Maneuvering Targets[J]. IEEE Transactions on Aerospace and Electronic Systems, 1970, AES-6(4):473-483.
[16] SALAZAR D,HERNANDEZ-PAJARES M, JUAN-ZORNOZA J M, et al. EVA:GPS-based Extended Velocity and Acceleration Determination[J]. Journal of Geodesy, 2011, 85(6):329-340.
[17] ZHANG Xiaohong, GUO Bofeng, GUO Fei, et al. Influence of Clock Jump on the Velocity and Acceleration Estimation with a Single GPS Receiver Based on Carrier-phase-derived Doppler[J]. GPS Solutions, 2013, 17(4):549-559.
[18] SERRANO L, KIM D, LANGLEY R B, et al. A GPS Velocity Sensor:How Accurate Can It Be?-A First Look[C]//Proceedings of the ION NTM. San Diego:Institute of Navigation, 2004:875-885.
[19] JIN Shuanggen, WANG J, PARK P H. An Improvement of GPS Height Estimations:Stochastic Modeling[J]. Earth, Planets and Space, 2005, 57(4):253-259.
[20] SHUMWAY R H, STOFFER D S. Time Series Analysis and Its Applications:With R Examples[M]. New York:Springer-Verlag, 2011.
[21] 杨元喜. 自适应抗差最小二乘估计[J]. 测绘学报, 1996, 25(3):206-211. YANG Yuanxi.Adaptively Robust Least Squares Estimation[J]. Acta Geodaetica et Cartographica Sinica, 1996, 25(3):206-211.