The Algorithm of the Dual Adaptive Factors Filtering

doi:10.11947/j.AGCS.2015.20130286

Abstract

Abstract: The robust adaptive algorithm solves the status robust solution first, and calculates the adaptive factor by previous solution to adjust the dynamic model error. This article brings the ideas of dual adaptive factors, which the influence of different errors on the state estimations is adjusted by a respective adaptive factor in the case of both model information imprecise and observation gross. It derives the filter formula of the algorithm of the dual adaptive factors filtering, and provides the method of computing dual factors by referring single factors. Finally, it is compared between dual adaptive factors algorithm and robust adaptive algorithm by simulation, the results show that the dual adaptive factors algorithm can basically reach the normal state estimates obtained by normal observation in case of the observation gross errors; and it is to some extent waken the impact of the model inaccurate in the condition of the kinetic model for small-scale short time exception error occurring.

Key words: the dynamical adaptive factor, the observation adaptive factor, root-mean-square error

CLC Number:

P228

SU Tianxiang, WEN Yuanlan, ZHU Jun. The Algorithm of the Dual Adaptive Factors Filtering[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(1): 26-31.

References

[1] ZHOU Jiangwen. Classical Theory of Errors and Robust Estimation[J].Acta Geodaetica et Cartographica Sinica, 1989, 18(2): 115-120.(周江文. 经典误差理论和抗差估计[J]. 测绘学报,1989,18(2):115-120.)
[2] YANG Yuanxi. Adaptively Robust Least Squares Estimation[J]. Acta Geodaetica et Cartographica Sinica, 1996, 25(3): 205-211.(杨元喜.自适应抗差最小二乘估计[J]. 测绘学报,1996,25(3):205-211.)
[3] YANG Yuanxi. Robust Estimation for Dependent Observations[J].Manuscripta Geodaetica,1994, 19: 10-17.
[4] YANG Yuanxi, HE Haibo, XU Tianhe. Adaptive Robust Filtering for Kinematic GPS Positioning[J]. Acta Geodaetica et Cartographica Sinica, 2001, 30(4): 293-298.(杨元喜, 何海波, 徐天河. 论动态自适应滤波[J]. 测绘学报,2001,30(4): 293-298.)
[5] YANG Yuanxi, REN Xia, XU Yan. Major Progress in Adaptive Robust Filtering Theory and Application[J]. Navigation and Positioning, 2013,1:9-15.(杨元喜, 任夏, 许艳. 自适应抗差滤波理论及应用的主要进展[J]. 导航定位学报,2013,1:9-15.)
[6] YANG Yuanxi. Adaptive Navigation and Kinematic Positioning [M]. Beijing: Surveying and Mapping Press,2006.(杨元喜. 自适应动态导航定位[M]. 北京: 测绘出版社, 2006.)
[7] CUI Xianqiang, YANG Yuanxi. Adaptively Robust Filtering with Classified Adaptive Factors[J]. Progress in Nature Science, 2006, 16(8): 846-851.
[8] HUANG Guanwen, YANG Yuanxi, ZHANG Qin. Estimate and Predict Satellite Clock Error Using Adaptively Robust Sequential Adjustment with Classified Adaptive Factors Based on Opening Windows[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(1):15-21.(黄观文, 杨元喜, 张勤. 开窗分类因子抗差自适应序贯平差用于卫星钟差参数估计与预报[J]. 测绘学报,2011, 40(1): 15-21.)
[9] ZHANG Liping, ZENG Anmin. Determination of Coordinate Transformation Parameters by Adaptively Adjustment Method with Classified Adaptive Factors [J]. Geodesy and Geodynamics, 2008,28(2):110-114.(张丽萍, 曾安敏. 用分类因子自适应序贯平差法确定坐标转换参数[J]. 大地测量与地球动力学,2008,28 (2): 110-114.)
[10] YANG Yuanxi, CUI Xianqiang. Adaptively Robust Filter with Multi Adaptive Factors[J]. Survey Review, 2008, 40(309): 260-270.
[11] SU Tianxiang. The Rresearch of Autonomous Orbit Determination of Navigation Constellation with Distribution Algorithm Based on Ground-based Anchor [D]. Changsha: National University of Defense Technology,2012.(苏天祥. 基于锚固站的导航星座自主定轨技术研究[D]. 长沙: 国防科技大学, 2012.)
[12] LIU Jun, XIA Zhixun. Dynamics System Identification and Modeling[M].Changsha: Press of National University of Defense Technology,2007.(刘君, 夏智勋. 动力学系统辨识与建模[M]. 长沙: 国防科技大学出版社, 2007.)
[13] HUBER. Robust Statistics[M]. New York: John Wiley, 1981.
[14] WU Fumei, YANG Yuanxi. An Extended Adaptive Kalman Filtering in Tight Coupled GPS/INS Integration[J].Survey Review,2010,40(316):146-154.
[15] YANG Yuanxi, GAO Weiguang, Zhang Shuangcheng. Robust Kalman Filtering with Constraints: a Case Study for Integrated Navigation[J].Journal of Geodesy, 2010,84:373-381.
[16] YANG Yuanxi. Properties of Adaptive Robust Filtering for Kinematic GPS Positioning[J]. Acta Geodaetica et Cartographica Sinica, 2003, 32(3): 189-192.(杨元喜. 动态定位自适应滤波解的性质[J]. 测绘学报,2003,32(3): 189-192.)
[17] LI Chong, HUANG Guanwen, TAN Li, et al. Adaptive Robust Kalman Filtering Applied in GPS Precise Point Positioning[J]. Science of Surveying and Mapping, 2011, 36(4): 22-24.(李冲, 黄观文, 谭理等. 抗差自适应卡尔曼滤波在GPS精密单点定位中的应用[J] 测绘科学,2011, 36(4): 22-24.)
[18] WU Fumei, YANG Yuanxi. A New Two Step Adaptive Robust Kalman Filtering in GPS/INS Integrated Navigation System[J]. Acta Geodaetica et Cartographica Sinica, 2010, 39(5):522-527.(吴富梅, 杨元喜. 一种两步自适应抗差Kalman滤波在GPS/INS组合导航中的应用[J]. 测绘学报, 2010,39 (5): 522-527.)
[19] GAO Weiguang, YANG Yuanxi, ZHANG Shuangcheng. Adaptive Robust Kalman Flitering Based on the Current Statistical Model[J]. Acta Geodaetica et Cartographica Sinica, 2006, 35(1):15-19.(高为广, 杨元喜, 张双成. 基于当前加速度模型的抗差自适应KALMAN滤波[J]. 测绘学报,2006, 35(1):15-19.)
[20] YANG Yuanxi, GAO Weiguang. Comparison of Two Fading Filtering and Adaptively Robust Filter[J]. Geometrics and Information Science of Wuhan University,2006, 31(11): 980-982.(杨元喜, 高为广. 两种渐消滤波与自适应抗差滤波的综合比较分析[J].武汉大学学报:信息科学版,2006, 31(11): 980-982.)
[21] GAO Weiguang, ZHANG Shuangcheng, WANG Fei, et al. Adaptive Robust Kalman Filtering Algorithm in GPS Navigation[J]. Science of Surveying and Mapping,2005,30(2):98-100.(高为广, 张双成, 王飞,等. GPS导航中的抗差自适应Kalman滤波算法[J]. 测绘科学,2005,30(2):98-100.)