Due to the nonlinear characteristics of satellite navigation positioning equations, the traditional positioning methods need to linearize the equations before solving, which would reduce the accuracy of positioning. Cubature Kalman filter (CKF) algorithm based on Bayesian estimation and cubature transformation could effectively improve the accuracy of nonlinear filtering estimation. In this paper, cubature Kalman filter algorithm is applied to satellite positioning solution. The transfer and measurement models of the positioning solution system are established. The three-dimensional position coordinates of the receiver are recursively solved by time update and measurement update. The positioning solution algorithm based on cubature Kalman filter is verified by IGS observation data tests, and compared with the least square method and extended Kalman filter algorithm. The results show that the application of CKF algorithm in satellite positioning is of higher precision and faster convergence speed.
ZHANG Jie
,
LI Jinghua
,
HU Chao
. Solution method of satellite navigation positioning based on cubature Kalman filter[J]. Journal of University of Chinese Academy of Sciences, 2021
, 38(4)
: 532
-537
.
DOI: 10.7523/j.issn.2095-6134.2021.04.013
[1] Kaplan E D, Hegarty C. Understanding GPS:principles and applications[M]. 2nd edition. Norwood:Artech House, 2006:322-332.
[2] 谢钢. GPS原理与接收机设计[M]. 北京:电子工业出版社, 2009:96-106.
[3] 秦永元, 张洪钺, 汪叔华. 卡尔曼滤波与组合导航原理[M]. 2版. 西安:西北工业大学出版社, 2012:1-3.
[4] Arasaratnam I, Haykin S. Cubature Kalman filters[J]. IEEE Transactions on Automatic Control, 2009, 54(6):1254-1269.
[5] 唐李军. Cubature卡尔曼滤波及其在导航中的应用研究[D]. 哈尔滨:哈尔滨工程大学, 2012.
[6] 杨峻巍. 水下航行器导航及数据融合技术研究[D]. 哈尔滨:哈尔滨工程大学, 2012.
[7] Havlicek M, Jan J, Brazdil M, et al. Nonlinear estimation of BOLD signal based on cubature particle filter[C]//The 20th Int EURASIP Conf on BIOSIGNAL 2010. Brno, 2010:328-332.
[8] Roy A, Mitra D. Multi-target trackers using cubature Kalman filter for Doppler radar tracking in clutter[J]. IET Signal Processing, 2016, 10(8):888-901.
[9] 葛磊. 容积卡尔曼滤波算法研究及其在导航中的应用[D]. 哈尔滨:哈尔滨工程大学, 2013.
[10] 王宏健, 李村, 么洪飞, 等. 基于高斯混合容积卡尔曼滤波的UUV自主导航定位算法[J]. 仪器仪表学报, 2015, 36(2):254-261.
[11] Pesonen H, Piché R. Cubature-based Kalman filters for positioning[C]//20107th Workshop on Positioning, Navigation and Communication (WPNC). Dresden, Germany:IEEE Press, 2010:45-49.
[12] Cui B B, Chen X Y, Tang X H. Improved cubature Kalman filter for GNSS/INS based on transformation of posterior sigma-points error[J]. IEEE Transactions on Signal Processing, 2017, 65(11):2975-2987.
[13] Ito K, Xiong K. Gaussian filters for nonlinear filtering problems[J]. IEEE Transactions on Automatic Control, 2000, 45(5):910-927.
[14] 陈杨毅. GPS与BD双模GNSS接收机定位解算技术研究[D]. 厦门:厦门大学, 2014.
[15] Gao C F, Wu F, Chen W R, et al. An improved weight stochastic model in GPS Precise Point Positioning[C]//International Conference on Proceedings Transportation, Mechanical, and Electrical Engineering(TMEE). 2011 Changchun, China:IEEE Press, 2011:629-632.
[16] 王慧, 王伟. 一种改进的卡尔曼滤波定位算法研究[J]. 船舶工程, 2006, 28(4):34-38.
