快速交互式多模型算法的导航定位解算
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摘要
针对卫星导航定位中单模型在急速转弯条件下出现较大偏差和交互式多模型系统运算量大的问题,该文提出了一种快速的交互式多模型算法。该算法先对CS模型进行改进,然后利用CV模型和改进的CS模型构成多模型系统,结合修正的滤波发散判据与次优的极大后验估计,根据载体实际的运动状态自行调整扩展卡尔曼滤波采用的运动模型,从而弥补了单模型描述复杂运动的不足。实验结果表明:与单模型相比,该方法有效解决了急速转弯误差大的问题;与标准交互式多模型相比,该方法对位置的估计精度提高了39.4%,而运算时间却缩短了47.4%。
Aiming at the problem which single model appeared large deviation under the condition of rapid turn and the large computation of interactive multiple model system in satellite navigation and positioning,a fast IMM algorithm was proposed.First,the current statistics(CS)model was improved;then the constant velocity(CV)model and the improved CS model were used to form a multiple model system.Based on the modified filter divergence criterion and the subprime maximum a posteriori estimation,the motion model of extended kalman filter was changed automatically according to the actual movement of carrier.In this way,the shortcoming of single model in describing the complex movement was improved.The experimental results showed that compared with the single model,the method effectively solved the problem of the great error in the sharp turn;compared with standard IMM,the location estimation precision of the method was improved by 39.4%,and the operation time was shortened by 47.4%.
Aiming at the problem which single model appeared large deviation under the condition of rapid turn and the large computation of interactive multiple model system in satellite navigation and positioning,a fast IMM algorithm was proposed.First,the current statistics(CS)model was improved;then the constant velocity(CV)model and the improved CS model were used to form a multiple model system.Based on the modified filter divergence criterion and the subprime maximum a posteriori estimation,the motion model of extended kalman filter was changed automatically according to the actual movement of carrier.In this way,the shortcoming of single model in describing the complex movement was improved.The experimental results showed that compared with the single model,the method effectively solved the problem of the great error in the sharp turn;compared with standard IMM,the location estimation precision of the method was improved by 39.4%,and the operation time was shortened by 47.4%.
引文
[1]宁津生,姚宜斌,张小红.全球导航卫星系统发展综述[J].导航定位学报,2013,1(1):3-8.(NING Jinsheng,YAO Yibin,ZHANG Xiaohong.Review of the development of global satellite navigation system[J].Journal of Navigation and Positioning,2013,1(1):3-8.)
[2]刘宇玺,吴鹏,刘文祥,等.引入强跟踪滤波的IMM算法在导航定位解算中的应用[J].全球定位系统,2014,39(5):46-50.(LIU Yuxi,WU Peng,LIU Wenxiang,et al.The application of IMM algorithm combined with strong tracking filter on navigation positioning[J].GNSS World of China,2014,39(5):46-50.)
[3]兰义华,任浩征,张勇,等.一种基于“当前”模型的改进卡尔曼滤波算法[J].山东大学学报(工学报),2012,42(5):12-17.(LAN Yihua,REN Haozheng,ZHANG Yong,et al.An improved Kalman filter algorithm based on the“current”model[J].Journal of Shandong University(Engineering Science),2012,42(5):12-17.)
[4]李朋,徐博,刘文祥,等.基于载波相位平滑伪距的卡尔曼滤波定位方法[J].全球定位系统,2013,38(4):16-19.(LI Peng,XU Bo,LIU Wenxiang,et al.An algorithm of positioning with Kalman filter based on carrier phase smoothed pseudo range[J].GNSS World of China,2013,38(4):16-19.)
[5]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):22-23.(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):22-23.)
[6]LI R X,JILKOV V P.Survey of maneuvering target tracking.Part V.Multiple-model methods[J].IEEE Transactions on Aerospace and Electronic Systems,2005,41(4):1254-1280.
[7]赵奇.卡尔曼滤波在GPS定位中的研究与实现[D].成都:电子科技大学,2013.(ZHAO Qi.The research and implementation of Kalman filter in GPS positioning system[D].Chengdu:University of Electronic Science and Technology of China,2013.)
[8]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,2012:41-52.(QIN Yongyuan,ZHANG Hongyue,WANG Shuhua.Kalman filter and the principle of integrated navigation[M].2nd ed.Xi′an:Northwestern Polytechnical University Press,2012:41-52.)
[9]杨宏,李亚安,李国辉.一种改进扩展卡尔曼滤波新方法[J].计算机工程与应用,2010,46(19):18-20.(YANG Hong,LI Yaan,LI Guohui.New method of improved extended Kalman filter[J].Computer Engineering and Applications,2010,46(19):18-20.)
[10]CHUI C K,CHEN Guanrong.卡尔曼滤波及其实时应用[M].4版.北京:清华大学出版社,2013:17-22.(CHUI C K,CHEN Guanrong.Kalman filter and its application in real time[M].4th ed.Beijing:Tsinghua University Press,2013:17-22.)
[11]邓胡滨,张磊,吴颖,等.基于卡尔曼滤波算法的轨迹估计研究[J].传感器与微系统,2012,31(5):4-7.(DENG Hubin,ZHANG Lei,WU Ying,et al.Research on track estimation based on Kalman filtering algotirhm[J].Transducer and Microsystem Technologies,2012,31(5):4-7.)
[12]RYCROFT M J.GPS原理与应用[M].2版.北京:电子工业出版社,2012:153-172.(RYCROFT M J.Understanding GPS principles and applications[M].2nd ed.Beijing:Publishing House of Electronics Industry,2012:153-172.)
[13]罗笑冰,王宏强,黎厢.模型转换概率自适应的交互式多模型跟踪算法[J].电子信息学报,2005,27(10):1593-1595.(LUO Xiaobing,WANG Hongqiang,LI Xiang.Interacting multiple model algorithm with adaptive markov transition probabilities[J].Journal of Electronics&Information Technology,2005,27(10):1593-1595.)
[2]刘宇玺,吴鹏,刘文祥,等.引入强跟踪滤波的IMM算法在导航定位解算中的应用[J].全球定位系统,2014,39(5):46-50.(LIU Yuxi,WU Peng,LIU Wenxiang,et al.The application of IMM algorithm combined with strong tracking filter on navigation positioning[J].GNSS World of China,2014,39(5):46-50.)
[3]兰义华,任浩征,张勇,等.一种基于“当前”模型的改进卡尔曼滤波算法[J].山东大学学报(工学报),2012,42(5):12-17.(LAN Yihua,REN Haozheng,ZHANG Yong,et al.An improved Kalman filter algorithm based on the“current”model[J].Journal of Shandong University(Engineering Science),2012,42(5):12-17.)
[4]李朋,徐博,刘文祥,等.基于载波相位平滑伪距的卡尔曼滤波定位方法[J].全球定位系统,2013,38(4):16-19.(LI Peng,XU Bo,LIU Wenxiang,et al.An algorithm of positioning with Kalman filter based on carrier phase smoothed pseudo range[J].GNSS World of China,2013,38(4):16-19.)
[5]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):22-23.(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):22-23.)
[6]LI R X,JILKOV V P.Survey of maneuvering target tracking.Part V.Multiple-model methods[J].IEEE Transactions on Aerospace and Electronic Systems,2005,41(4):1254-1280.
[7]赵奇.卡尔曼滤波在GPS定位中的研究与实现[D].成都:电子科技大学,2013.(ZHAO Qi.The research and implementation of Kalman filter in GPS positioning system[D].Chengdu:University of Electronic Science and Technology of China,2013.)
[8]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,2012:41-52.(QIN Yongyuan,ZHANG Hongyue,WANG Shuhua.Kalman filter and the principle of integrated navigation[M].2nd ed.Xi′an:Northwestern Polytechnical University Press,2012:41-52.)
[9]杨宏,李亚安,李国辉.一种改进扩展卡尔曼滤波新方法[J].计算机工程与应用,2010,46(19):18-20.(YANG Hong,LI Yaan,LI Guohui.New method of improved extended Kalman filter[J].Computer Engineering and Applications,2010,46(19):18-20.)
[10]CHUI C K,CHEN Guanrong.卡尔曼滤波及其实时应用[M].4版.北京:清华大学出版社,2013:17-22.(CHUI C K,CHEN Guanrong.Kalman filter and its application in real time[M].4th ed.Beijing:Tsinghua University Press,2013:17-22.)
[11]邓胡滨,张磊,吴颖,等.基于卡尔曼滤波算法的轨迹估计研究[J].传感器与微系统,2012,31(5):4-7.(DENG Hubin,ZHANG Lei,WU Ying,et al.Research on track estimation based on Kalman filtering algotirhm[J].Transducer and Microsystem Technologies,2012,31(5):4-7.)
[12]RYCROFT M J.GPS原理与应用[M].2版.北京:电子工业出版社,2012:153-172.(RYCROFT M J.Understanding GPS principles and applications[M].2nd ed.Beijing:Publishing House of Electronics Industry,2012:153-172.)
[13]罗笑冰,王宏强,黎厢.模型转换概率自适应的交互式多模型跟踪算法[J].电子信息学报,2005,27(10):1593-1595.(LUO Xiaobing,WANG Hongqiang,LI Xiang.Interacting multiple model algorithm with adaptive markov transition probabilities[J].Journal of Electronics&Information Technology,2005,27(10):1593-1595.)