利用零相位Kaiser窗滤波器改善MEX多普勒数据定轨精度
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摘要
精密轨道确定在深空探测中至关重要,而定轨数据中的白噪声会影响定轨性能。基于零相位分析,比较了FRR(forward-filter reverse-filter reverse-output)、RRF(reverse-filter reverse-filter forward-output)和Matlab中的filtfilt这3种滤波器的优劣,设计了一种零相位Kaiser窗低通滤波器。利用火星快车号(Mars Express,MEX)的仿真数据和实测数据验证了零相位Kaiser窗低通滤波器的性能,结果发现滤除白噪声后MEX数据的定轨精度有了显著改善。双程测速数据残差均方根(root mean square,RMS)减小为原来的1/3左右,达到了0.031 mm/s;轨道位置和速度与欧空局(European Space Agency,ESA)精密轨道的差异明显变小。该滤波算法作为定轨前的数据预处理可以提高定轨精度,从而为中国火星探测器的轨道数据处理提供一定的参考。
Precise orbit determination is crucial in deep space exploration,and white noise in orbital tracking data can affect orbit determination performance. Based on the analysis of zero phase,we compared three kinds of filters,FRR,RRF and filtfilt in Matlab,and designed a zero-phase low pass filter using Kaiser window. The performance of the filter was verified by simulated and measured tracking data of MEX. After filtering white noise in the MEX measurement,the accuracy of MEX orbit determination could be significantly improved. For the two-way Doppler tracking data,the RMS of the velocity residuals was reduced to about one third of the original,that is,in the level of 0.031 mm/s; the difference of orbital position and velocity with the ESA reconstructed orbit was significantly reduced. The filtering process can be used as data preprocessing to improve orbit determination accuracy,and can also provide some reference for Chinese Mars exploration mission.
Precise orbit determination is crucial in deep space exploration,and white noise in orbital tracking data can affect orbit determination performance. Based on the analysis of zero phase,we compared three kinds of filters,FRR,RRF and filtfilt in Matlab,and designed a zero-phase low pass filter using Kaiser window. The performance of the filter was verified by simulated and measured tracking data of MEX. After filtering white noise in the MEX measurement,the accuracy of MEX orbit determination could be significantly improved. For the two-way Doppler tracking data,the RMS of the velocity residuals was reduced to about one third of the original,that is,in the level of 0.031 mm/s; the difference of orbital position and velocity with the ESA reconstructed orbit was significantly reduced. The filtering process can be used as data preprocessing to improve orbit determination accuracy,and can also provide some reference for Chinese Mars exploration mission.
引文
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[3]Patzold M,Hausler B,Tyler G L,et al.Mars Express10 Years at Mars:Observations by the Mars Express Radio Science Experiment(MaRS)[J].Planetary and Space Science,2016,127:44-90
[4]Huang Yong,Hu Xiaogong,Cao Jianfeng,et al.The Mars Satellite Orbit Determination Software at Shanghai Astronomical Observatory[J].Journal of Spacecraft TT&C Technology,2009,28(6):83-89(黄勇,胡小工,曹建峰,等.上海天文台火星卫星定轨软件系统[J].飞行器测控学报,2009,28(6):83-89)
[5]Hu Songjie,Tang Geshi.BACC Orbit Determination and Analysis Software for Deep-Space Explo-rers[J].Journal of Spacecraft TT&C Technology,2010,29(5):69-74(胡松杰,唐歌实.北京中心深空探测器精密定轨与分析软件系统[J].飞行器测控学报,2010,29(5):69-74)
[6]Rosenblatt P,Lainey V,Le Maistre S,et al.Accurate Mars Express Orbits to Improve the Determination of the Mass and Ephemeris of the Martian Moons[J].Planetary and Space Science,2008,56(7):1 043-1053
[7]Yan J G,Yang X,Ye M,et al.Independent Mars Spacecraft Precise Orbit Determination Software Development and Its Applications[J].Astrophysics&Space Science,2017,362:123-1-123-15
[8]Ye Mao,Li Fei,Yan Jianguo,et al.Wuhan University Deep-Space Orbit Determination and Gravity Recovery System(WUDOGS)and Its Application Analysis[J].Acta Geodaetica et Cartographica Sinica,2017,46(3):288-296(叶茂,李斐,鄢建国,等.深空探测器精密定轨与重力场解算系统(WUDOGS)及其应用分析[J].测绘学报,2017,46(3):288-296)
[9]Huang Zhiwei.Design of Radio Transmitting and Receiving Circuits[M].Beijing:Beihang University Press,2004(黄智伟.无线电发射与接收电路设计[M].北京:北京航空航天大学出版社,2004)
[10]Xie Chao.The Analysis of Thermal Noise Characteristics of the RF Front-End in Receivers[D].Changsha:National University of Defense Techno-logy,2008(谢超.接收机射频通道的热噪声特性分析[D].长沙:国防科学技术大学,2008)
[11]Andert T P.Masses of Small Bodies:Mass Estimation of Small Solar System Bodies Using Radio Science Data from Close Flybys[D].Cologne:Universitt zu K9ln,2010
[12]Liu Q,Matsumoto K,Iwata T,et al.Effect of Phase Pattern of Antennas Onboard Flying Spin Satellites on Doppler Measurements[J].IEEE Transactions on Aerospace&Electronic Systems,2011,47(1):405-419
[13]Liu Yicheng.Digital Signal Processing[M].Beijing:Publishing House of Electronics Industry,2004(刘益成.数字信号处理[M].北京:电子工业出版社,2004)
[14]Ji Yuebo,Qin Shuren,Tang Baoping.Zero-Phase Digital Filter[J].Journal of Chongqing University(Natural Science Edition),2000,23(6):4-7(纪跃波,秦树人,汤宝平.零相位数字滤波器[J].重庆大学学报(自然科学版),2000,23(6):4-7)
[15]Gustafsson F.Determining the Initial States in Forward-Backward Filtering[J].IEEE Transactions on Signal Processing,2010,44(4):988-992
[16]Karlsson G,Vetterli M.Extension of Finite Length Signals for Sub-band Coding[J].Signal Processing,1989,17(2):161-168
[17]Datar A,Jain A,Sharma P C.Design of Kaiser Window Based Optimized Prototype Filter for Cosine Modulated Filter Banks[J].Signal Processing,2010,90(5):1 742-1 749
[18]Lin Y P,Vaidyanathan P P.A Kaiser Window Approach for the Design of Prototype Filters of Cosine Modulated Filterbanks[J].Signal Processing Letters IEEE,1998,5(6):132-134
[19]Creusere C D,Mitra S K.A Simple Method for Designing High-Quality Prototype Filters for M-band Pseudo QMF Banks[J].IEEE Transactions on Signal Processing,1995,43(4):1 005-1 007