卡尔曼滤波在GNSS导航系统中的应用
摘要
随着全球导航定位系统(GNSS)的不断发展,对其定位和测速以及定时的精度要求越来越高。为了提高GNSS定位测速的精度,由匈牙利数学卡尔曼研究出的卡尔曼滤波器,广泛应用于导航领域中的各种场合,包括基于kalman滤波的多普勒平滑,kalman定位测速,以及GNSS和SINS组合导航等等。
本文研究卡尔曼在GNSS导航领域中的应用,其目的是提高导航系统的定位测速精度和系统稳定性。首先,介绍卡尔曼滤波器的基本原理及其数学模型。其次,研究了几种多普勒平滑的方法,主要分为传统的基于反复求平均的多普勒平滑方法和基于kalman滤波的多普勒平滑方法,其目的是提高测速精度。接下来,本文针对最小二乘法定位解算的不足,提出了基于kalman的PVT后处理方法,这种方法是先用最小二乘法算出接收机基本的定位信息如接收机的位置和速度,然后在输入到kalman滤波的模型中,作为kalman滤波的初始值,然后通过kalman滤波计算出接收机的位置和速度,该方法显著改善接收机定位测速的精度。
最后,由于近年来捷连惯导广泛用于组合导航的领域中,组合导航根据SINS和GNSS的耦合方式不同分为松耦合、紧耦合和超紧耦合,紧耦合和超紧耦合研究难度大,开发工期长,本文用松耦合组合导航模型与SINS速度辅助相结合的方法,产生另一种新的组合导航滤波模型,以提高导航系统的稳定性。
With the development of the global navigation positioning system (GNSS), the accuracy of positioning and speed as well as the timing is more and more highly needed. In order to improve the accuracy of GNSS positioning and speed, the Hungarian mathematician Kalman research out the kalman filtering. Because of the good performance of kalman filter, it is widely used in the field of navigation on various occasions, including kalman filter based on doppler smooth, kalman filter based on positioning and speed, and GNSS/SINS integrated navigation and so on.
This paper makes a study of the kalman filer in GNSS in the field of navigation application. First of all, this paper introduces the basic principle of kalman filter and its mathematical model. Secondly, this paper introduces several kinds of doppler smoothing method, mainly divided into traditional average doppler smoothing method and kalman filtering doppler smoothing method. Next, because of the insufficiency of kalman filtering positioning calculating, this paper proposes the kalman post-processing method of PVT.This method uses least squares to calculate the receiver basic location information such as receiver position and speed, and then puts the information to the kalman filtering model as the initial value, and then through the kalman filtering calculates the receiver's position and speed.
Finally, in recent years the inertial navigation system is widely used in integrated navigation field, integrated navigation according to SINS and GNSS coupled mode different cent is divided into loosely coupled, tightly coupled and ultra tightly coupled.Tightly coupled and ultra tightly coupled research is difficult, and the development period is long. This paper will prove the combination method of the loosely coupled integrated navigation model and SINS speeding auxiliary to produce another kind of new integrated navigation filtering model.
本文研究卡尔曼在GNSS导航领域中的应用,其目的是提高导航系统的定位测速精度和系统稳定性。首先,介绍卡尔曼滤波器的基本原理及其数学模型。其次,研究了几种多普勒平滑的方法,主要分为传统的基于反复求平均的多普勒平滑方法和基于kalman滤波的多普勒平滑方法,其目的是提高测速精度。接下来,本文针对最小二乘法定位解算的不足,提出了基于kalman的PVT后处理方法,这种方法是先用最小二乘法算出接收机基本的定位信息如接收机的位置和速度,然后在输入到kalman滤波的模型中,作为kalman滤波的初始值,然后通过kalman滤波计算出接收机的位置和速度,该方法显著改善接收机定位测速的精度。
最后,由于近年来捷连惯导广泛用于组合导航的领域中,组合导航根据SINS和GNSS的耦合方式不同分为松耦合、紧耦合和超紧耦合,紧耦合和超紧耦合研究难度大,开发工期长,本文用松耦合组合导航模型与SINS速度辅助相结合的方法,产生另一种新的组合导航滤波模型,以提高导航系统的稳定性。
With the development of the global navigation positioning system (GNSS), the accuracy of positioning and speed as well as the timing is more and more highly needed. In order to improve the accuracy of GNSS positioning and speed, the Hungarian mathematician Kalman research out the kalman filtering. Because of the good performance of kalman filter, it is widely used in the field of navigation on various occasions, including kalman filter based on doppler smooth, kalman filter based on positioning and speed, and GNSS/SINS integrated navigation and so on.
This paper makes a study of the kalman filer in GNSS in the field of navigation application. First of all, this paper introduces the basic principle of kalman filter and its mathematical model. Secondly, this paper introduces several kinds of doppler smoothing method, mainly divided into traditional average doppler smoothing method and kalman filtering doppler smoothing method. Next, because of the insufficiency of kalman filtering positioning calculating, this paper proposes the kalman post-processing method of PVT.This method uses least squares to calculate the receiver basic location information such as receiver position and speed, and then puts the information to the kalman filtering model as the initial value, and then through the kalman filtering calculates the receiver's position and speed.
Finally, in recent years the inertial navigation system is widely used in integrated navigation field, integrated navigation according to SINS and GNSS coupled mode different cent is divided into loosely coupled, tightly coupled and ultra tightly coupled.Tightly coupled and ultra tightly coupled research is difficult, and the development period is long. This paper will prove the combination method of the loosely coupled integrated navigation model and SINS speeding auxiliary to produce another kind of new integrated navigation filtering model.
引文
[1]陈军,易翔,梁高波等GPS惯性导航组合(第2版)电子工业出版社2011年2月2-3页
[2]B. W. Parkinson, J. J. Spilker Jr. Global Positioning System:Theory and Applications, Volume I. Washington, DC:American Institute of Aeronautics and Astronautics, Inc,2006.
[3]张天光,王秀萍,王丽霞等捷联惯性导航技术(第2版)国防工业出版社2010年3月2-3页
[4]郑屹基于USB接口的惯导组件参数数据采集技术研究[学位论文],西安工业大学,2011年
[5]R. H. Brown, S. C. Schneider, and M. G. Mulligan, "Analysis of algorithms for velocity estimation from discrete position versus time data," IEEE Trans. Ind. Electron., vol.39, no.1, pp.11-19, Feb.1992.
[6]P. R. Belanger, "Estimation of angular velocity and acceleration from shaft encoder measurements," in Proc. IEEE Int. Conf. Robot. Automat., Nice, France,1992, pp.585-592.
[7]Liao ZO, Hu AZ, Wu XF, Chen P Application of Kalman Filter for Carrier Phase Rate Derivatio in Proc. ICCC2010, Guangxi, PRC,2010, pp.355-360. Oct.2010.
[8]廖卓一种提高多普勒精度的方法[OL]中国科技论文在线2010年12月
[9]R A Singer. Estimating Optimal Tracking Filter Performance for Manned Maneuvering Targets [J].IEEE Transactions on Aerospace and Electronic Systems (S0018-9251) 19706(4) 473-483.
[10]Kendrick J D, M aybeck P S, Reid J G. Estimation of Aircraft Target Motion UsingOrientation Measurements [J]. IEEE Transaction on Aerospace and Electronic Systems 198117(2) 154-159
[11]周宏仁机动目标跟踪国防工业出版社1991.
[12]艾伦,金玲,黄晓瑞GPS/INS组合导航技术的综述与展望北京遥测技术研究所数字通信世界2011,2(2)
[13]黄汛INS/GPS超紧耦合技术研究现状及展望飞航导弹2009
[14]唐康华,黄新生,吴美平等MIMU/GPS嵌入式组合导航中GPS信号非相干搜索算法分析国防科技大学空间科学学报2007,27(3)
[15]马骏,杨功流,紧耦合MINS/GPS组合导航系统数据融合的分析与处理天津大学传感技术学报2011年9月
[16]杨旭东,何平,胡恒章卡尔曼滤波器性能分析哈尔滨工业大学自动化技术与与应用1999年04期
[17]胡宏灿卡尔曼滤波技术在组合导航中的应用[学位论文]中国科学技术大学2005年
[18]李蔚恒基站天线伺服系统与数字引导精度的研究[学位论文]北京航空航天大学2000年
[19]朱晓娟飞行控制系统多传感器信息融合技术研究[学位论文]南京航空航天大学2008年
[20]张建军基于改进的扩展卡尔曼滤波伺服系统建模技术研究计算机应用研究2012年3月
[21]刘文博GNSS接收机定位解算的研究与实现[学位论文]北京邮电大学2010年
[22]R. G Brown, Introduction to Random Signal Analysis and Kalman Filtering. New York:John Wiley,1983
[23]R. H. Brown, S. C. Schneider, and M. G. Mulligan, "Analysis of algorithms for velocity estimation from discrete position versus time data," IEEE Trans. Ind. Electron., vol.39, no.1, pp.11-19, Feb.1992.
[24]Orfanidis, S.J., Introduction to Signal Processing, Prentice-Hall, Englewood Cliffs, NJ,1996.
[25]吴爱兵.高动态GPS滤波定位算法的仿真研究[学位论文]北京中国科学院空间科学与应用研究中心2002
[26]Y. G. Tang, Y. X. Wu, M. P. Wu, X. P. Hu, L. C. Shen, "Nonlinear tracking-differentiator for velocity determination using carrier phase measurements," IEEE J-STSP, Vol.3, no.4, pp.716-725, Aug. 2009.
[27]Kai Borre,Dennis M. Akos,Nicolaj Bertelsen A Software-Defined GPS and Galileo Receiver A Single-Frequency Approach, Birkh"auser 2000
[28]朱国良基于PC平台的单频GPS软件接收机研究与实现[学位论文]南京邮电大学2010年
[29]周宏仁机动目标跟踪国防工业出版社1991年
[30]吴爱兵 高动态GPS滤波定位算法的仿真研究[学位论文]北京中国科学院空间科学与应用研究中心2002
[31]陈新海最佳估计理论北京航空学院出版社2007年
[32]Elliott D.Kaplan, Christopher J.Hegarty,寇艳红译GPS原理与应用电子工业出版社2007年49-62页
[33]Cox, D.B., (1982) Integration of GPS with Inertial Navigation Systems.Navigation, Journal of the Institute of Navigation,1,144-153.
[34]D.T Knight,1992, Achievlng Modularity with Tightly-Coupled GPS/INS, Proceedings of IEEE PLANS, Position Locations and Navigation Symposium, pp 426-432
[35]David E.Lewis Ultra-tightly Coupled GPS/INS Tracking Performance. AAIA's 3rd Annual. Denver,Colorado:2003
[36]Savage P G Strapdown Inertial Navigation System Algorithm Design, Part 1:Attitude Algorithms 1998(01) doi:10.2514/2.4242
[37]Savage P G Strapdown Inertial Navigation System Algorithm Design, Part 2:Velocity and Position Algorithms 1998(02) doi:10.2514/2.4242
[38]Alban, S., Akos, D., Rock, S.,& Gebre-Egziobher, D., (2003) Performance Analysis and Architectures for INS-Aided GPS tracking loops. Institute of Navigation-NTM, Anaheim, CA,22-24 January,611-622.
[39]秦奋GPS接收机快速定位技术的研究与应用[学位论文]东南大学2009年
[40]Andrew N.Sloss,Dominic Symes,Chris Wright ARM嵌入式系统开发——软件设计与优化北京航空航天大学2005年
[4l]叶凯,杨文淑,包启亮基于ARM的除法运算优化策略中国科学院单片机与嵌入式系统应用2006年3月
[2]B. W. Parkinson, J. J. Spilker Jr. Global Positioning System:Theory and Applications, Volume I. Washington, DC:American Institute of Aeronautics and Astronautics, Inc,2006.
[3]张天光,王秀萍,王丽霞等捷联惯性导航技术(第2版)国防工业出版社2010年3月2-3页
[4]郑屹基于USB接口的惯导组件参数数据采集技术研究[学位论文],西安工业大学,2011年
[5]R. H. Brown, S. C. Schneider, and M. G. Mulligan, "Analysis of algorithms for velocity estimation from discrete position versus time data," IEEE Trans. Ind. Electron., vol.39, no.1, pp.11-19, Feb.1992.
[6]P. R. Belanger, "Estimation of angular velocity and acceleration from shaft encoder measurements," in Proc. IEEE Int. Conf. Robot. Automat., Nice, France,1992, pp.585-592.
[7]Liao ZO, Hu AZ, Wu XF, Chen P Application of Kalman Filter for Carrier Phase Rate Derivatio in Proc. ICCC2010, Guangxi, PRC,2010, pp.355-360. Oct.2010.
[8]廖卓一种提高多普勒精度的方法[OL]中国科技论文在线2010年12月
[9]R A Singer. Estimating Optimal Tracking Filter Performance for Manned Maneuvering Targets [J].IEEE Transactions on Aerospace and Electronic Systems (S0018-9251) 19706(4) 473-483.
[10]Kendrick J D, M aybeck P S, Reid J G. Estimation of Aircraft Target Motion UsingOrientation Measurements [J]. IEEE Transaction on Aerospace and Electronic Systems 198117(2) 154-159
[11]周宏仁机动目标跟踪国防工业出版社1991.
[12]艾伦,金玲,黄晓瑞GPS/INS组合导航技术的综述与展望北京遥测技术研究所数字通信世界2011,2(2)
[13]黄汛INS/GPS超紧耦合技术研究现状及展望飞航导弹2009
[14]唐康华,黄新生,吴美平等MIMU/GPS嵌入式组合导航中GPS信号非相干搜索算法分析国防科技大学空间科学学报2007,27(3)
[15]马骏,杨功流,紧耦合MINS/GPS组合导航系统数据融合的分析与处理天津大学传感技术学报2011年9月
[16]杨旭东,何平,胡恒章卡尔曼滤波器性能分析哈尔滨工业大学自动化技术与与应用1999年04期
[17]胡宏灿卡尔曼滤波技术在组合导航中的应用[学位论文]中国科学技术大学2005年
[18]李蔚恒基站天线伺服系统与数字引导精度的研究[学位论文]北京航空航天大学2000年
[19]朱晓娟飞行控制系统多传感器信息融合技术研究[学位论文]南京航空航天大学2008年
[20]张建军基于改进的扩展卡尔曼滤波伺服系统建模技术研究计算机应用研究2012年3月
[21]刘文博GNSS接收机定位解算的研究与实现[学位论文]北京邮电大学2010年
[22]R. G Brown, Introduction to Random Signal Analysis and Kalman Filtering. New York:John Wiley,1983
[23]R. H. Brown, S. C. Schneider, and M. G. Mulligan, "Analysis of algorithms for velocity estimation from discrete position versus time data," IEEE Trans. Ind. Electron., vol.39, no.1, pp.11-19, Feb.1992.
[24]Orfanidis, S.J., Introduction to Signal Processing, Prentice-Hall, Englewood Cliffs, NJ,1996.
[25]吴爱兵.高动态GPS滤波定位算法的仿真研究[学位论文]北京中国科学院空间科学与应用研究中心2002
[26]Y. G. Tang, Y. X. Wu, M. P. Wu, X. P. Hu, L. C. Shen, "Nonlinear tracking-differentiator for velocity determination using carrier phase measurements," IEEE J-STSP, Vol.3, no.4, pp.716-725, Aug. 2009.
[27]Kai Borre,Dennis M. Akos,Nicolaj Bertelsen A Software-Defined GPS and Galileo Receiver A Single-Frequency Approach, Birkh"auser 2000
[28]朱国良基于PC平台的单频GPS软件接收机研究与实现[学位论文]南京邮电大学2010年
[29]周宏仁机动目标跟踪国防工业出版社1991年
[30]吴爱兵 高动态GPS滤波定位算法的仿真研究[学位论文]北京中国科学院空间科学与应用研究中心2002
[31]陈新海最佳估计理论北京航空学院出版社2007年
[32]Elliott D.Kaplan, Christopher J.Hegarty,寇艳红译GPS原理与应用电子工业出版社2007年49-62页
[33]Cox, D.B., (1982) Integration of GPS with Inertial Navigation Systems.Navigation, Journal of the Institute of Navigation,1,144-153.
[34]D.T Knight,1992, Achievlng Modularity with Tightly-Coupled GPS/INS, Proceedings of IEEE PLANS, Position Locations and Navigation Symposium, pp 426-432
[35]David E.Lewis Ultra-tightly Coupled GPS/INS Tracking Performance. AAIA's 3rd Annual. Denver,Colorado:2003
[36]Savage P G Strapdown Inertial Navigation System Algorithm Design, Part 1:Attitude Algorithms 1998(01) doi:10.2514/2.4242
[37]Savage P G Strapdown Inertial Navigation System Algorithm Design, Part 2:Velocity and Position Algorithms 1998(02) doi:10.2514/2.4242
[38]Alban, S., Akos, D., Rock, S.,& Gebre-Egziobher, D., (2003) Performance Analysis and Architectures for INS-Aided GPS tracking loops. Institute of Navigation-NTM, Anaheim, CA,22-24 January,611-622.
[39]秦奋GPS接收机快速定位技术的研究与应用[学位论文]东南大学2009年
[40]Andrew N.Sloss,Dominic Symes,Chris Wright ARM嵌入式系统开发——软件设计与优化北京航空航天大学2005年
[4l]叶凯,杨文淑,包启亮基于ARM的除法运算优化策略中国科学院单片机与嵌入式系统应用2006年3月