基于SMSS-UKF的机载单站无源定位算法
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摘要
基于机载单站无源定位中常用的扩展卡尔曼滤波具有近似线性方程的雅可比矩阵计算困难、不敏卡尔曼滤波(UKF)具有计算量较大的问题,提出了基于改进的变尺度最小斜度不敏卡尔曼滤波(SMSS-UKF)的机载单站无源定位算法,该方法采用最小斜度采样策略进行Sigma点采样,减少Sigma点提高计算效率,利用变尺度不敏变换克服了采样点非局部效应问题。同时,针对大部分定位跟踪模型中状态方程为线性方程的特点,依据在线性状态方程情况下的贝叶斯理论,运用卡尔曼滤波状态预测的方法进行UKF的最优状态预测,使状态预测避免了不敏变换的数值近似误差和Sigma采样点计算的复杂性,提高了算法的运行效率和滤波精度。仿真实验的结果证明了SMSS-UKF滤波算法的有效性。
In order to solve the problems of difficulty for acquiring approximate linear equation of Jacobian matrix in extended Kalman filter and difficulty of complex calculation for unscented Kalman filter( UKF),a passive location algorithm for single airborne observer based on scaled minimal skew simplex unscented Kalman filter( SMSS-UKF) is presented. To decrease Sigma point and to improve the computational efficiency,minimal skew simplex sampling strategy is used in the algorithm to carry out Sigma point sampling. And scaled unscented transformation is used to overcome the problem of non-local effects of sampling. For state equation is linear equation in a majority of location & tracking model,according to Bayesian and linear equation,this paper derives that state prediction in UKF can use the state prediction of the Kalman filter to predict accurately. The numerical value approximate error in unscented transformation and the complexity of the Sigma point computing is avoided. Therefore the efficiency and filtering accuracy of the algorithm is also improved. Validity of the SMSS-UKF algorithm is verified by the simulation examples.
In order to solve the problems of difficulty for acquiring approximate linear equation of Jacobian matrix in extended Kalman filter and difficulty of complex calculation for unscented Kalman filter( UKF),a passive location algorithm for single airborne observer based on scaled minimal skew simplex unscented Kalman filter( SMSS-UKF) is presented. To decrease Sigma point and to improve the computational efficiency,minimal skew simplex sampling strategy is used in the algorithm to carry out Sigma point sampling. And scaled unscented transformation is used to overcome the problem of non-local effects of sampling. For state equation is linear equation in a majority of location & tracking model,according to Bayesian and linear equation,this paper derives that state prediction in UKF can use the state prediction of the Kalman filter to predict accurately. The numerical value approximate error in unscented transformation and the complexity of the Sigma point computing is avoided. Therefore the efficiency and filtering accuracy of the algorithm is also improved. Validity of the SMSS-UKF algorithm is verified by the simulation examples.
引文
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[9]郭福成,贾兴江,皇甫堪.仅用相位差变化率的机载单站无源定位方法及其误差分析[J].航空学报,2009,30(6):1090-1095.GUO Fucheng,JIA Xingjiang,HUANG Fu kan.A single observer passive localization method using phase difference changing rate only and its error analysis[J].Acta Aeronautica Et Astronautica Sinica,2009,30(6):1090-1095.
[10]秦明峰,郝青儒,范广伟.运动单站无源定位性能分析[J].无线电工程,2014,44(4):50-53.QIN Mingfeng,HAO Qingru,FAN Guangwei.Analysis on passive Localization performance of moving single observer[J].Radio Engineering of China,2014,44(4):50-53.
[11]JULIER S J.The scaled unscented transformation[C]//Proceedings of the American Control Conference.Jefferson City:Anchorage,2002:4555-4559.
[12]HUANG Wenlong,WANG Xiaodan,WANG Yi,et al.Immune adaptive gaussian mixture particle filter for state estimation[J].Journal of Systems Engineering and Electronics,2015,26(4):877-885.
[13]ZHAN R H,LIU S Q,HU J M,et al.Maneuvering target track-before-dectect via multiple-model bernoulli particle filter[J].Journal of Central South University,2015,22(10):3935-3945.
[14]LI T C,VILLARRUBIA G,SUN S D,et al.Resampling methods for particle filtering:identical distribution,a new method,and comparable study[J].Frontiers of Information Technology&Electronic Engineering,2015,16(11):969-984.
[15]SUBHASH C,MARK R M,ROBIN J E,et al.Fundamentals of object tracking[M].Cambridge:Cambridge University,2011:1-41.
[16]HO Y C,LEE R C K.A bayesian approach to problems in stochastic estimation and control[J].IEEE Transactions on Automatic Control,1964,9(4):333-339.
[17]ANDERSON B D O,MOORE J B.Optimal filtering[C]//Prentice-Hall.New Jersey:Englewood Cliffs,1979:511-519.
[18]张文,孙瑞胜.EKF与UKF的性能比较与应用[J].南京理工大学学报,2015,39(5):614-618.ZHANG Wen,SUN Ruisheng.Research on performance comparison of EKF and UKF and their application[J].Journal of Nanjing University of Science and Technology,2015,39(5):614-618.
[2]吴昊,陈树新,张衡阳.基于递推总体最小二乘的机载单站无源定位算法[J].空军工程大学学报:自然科学版,2013,14(1):62-65.WU Hao,CHEN Shuxin,ZHANG Hengyang.Recursive total least squares-based airborne single-observer passive location algorithm[J].Journal of Air Force Engineering University:Natural Acience Edition,2013,14(1):62-65.
[3]吴卫华,江晶,范雄华,等.WGS-84坐标下机载单站PDR/DFR无源定位滤波算法[J].系统工程与电子技术,2014,36(1):31-37.WU Weihua,JIANG Jing,FAN Xionghua,et al.Filtering algorithms of passive location based on PDR/DFR by single airborne platform in WGS-84[J].Systems Engineering and Electronics,2014,36(1):31-37.
[4]李望西,黄长强,王勇,等.利用相位差变化率的机载无源定位跟踪改进算法[J].电子与信息学报,2013,35(1):68-73.LI Wangxi,HUANG Changqiang WANG Yong,et al.An improved airborne passive location&tracking algorithm using the rate of change of phase difference[J].Journal of Electronics&Information Technology,2013,35(1):68-73.
[5]ZHANG M,GUO F C,ZHOU Y Y.A closed-form solution for moving source localization using LBI changing rate of phase difference only[J].Chinese Journal of Aeronautics,2014,27(2):365-374.
[6]张艺航,陈树新,吴昊,等.基于抗差EKF的机载单站无源定位算法[J].空军工程大学学报:自然科学版,2014,15(4):75-78.ZHANG Yihang,CHEN Shuxin,WU Hao,et al.Airborne single-observer passive location algorithm based on robust EKF[J].Journal of Air Force Engineering University:Natural Science Edition,2014,15(4):75-78.
[7]黄强,俞建国.基于ATUKF的地面动目标跟踪算法[J].现代雷达,2014,36(6):45-48.HUANG Qiang,YU Jianguo.Algorithm of ground moving target tracking based on adaptive turn unscented Kalman filter[J].Modern Radar,2014,36(6):45-48.
[8]黄耀光,李建新,高博.基于UKF的单站无源定位改进算法[J].现代雷达,2012,34(11):45-48.HUANG Yaoguang,LI Jianxin,GAO Bo.An improved single-observer passive location algorithm based on UKF[J].Modern Radar,2012,34(11):45-48.
[9]郭福成,贾兴江,皇甫堪.仅用相位差变化率的机载单站无源定位方法及其误差分析[J].航空学报,2009,30(6):1090-1095.GUO Fucheng,JIA Xingjiang,HUANG Fu kan.A single observer passive localization method using phase difference changing rate only and its error analysis[J].Acta Aeronautica Et Astronautica Sinica,2009,30(6):1090-1095.
[10]秦明峰,郝青儒,范广伟.运动单站无源定位性能分析[J].无线电工程,2014,44(4):50-53.QIN Mingfeng,HAO Qingru,FAN Guangwei.Analysis on passive Localization performance of moving single observer[J].Radio Engineering of China,2014,44(4):50-53.
[11]JULIER S J.The scaled unscented transformation[C]//Proceedings of the American Control Conference.Jefferson City:Anchorage,2002:4555-4559.
[12]HUANG Wenlong,WANG Xiaodan,WANG Yi,et al.Immune adaptive gaussian mixture particle filter for state estimation[J].Journal of Systems Engineering and Electronics,2015,26(4):877-885.
[13]ZHAN R H,LIU S Q,HU J M,et al.Maneuvering target track-before-dectect via multiple-model bernoulli particle filter[J].Journal of Central South University,2015,22(10):3935-3945.
[14]LI T C,VILLARRUBIA G,SUN S D,et al.Resampling methods for particle filtering:identical distribution,a new method,and comparable study[J].Frontiers of Information Technology&Electronic Engineering,2015,16(11):969-984.
[15]SUBHASH C,MARK R M,ROBIN J E,et al.Fundamentals of object tracking[M].Cambridge:Cambridge University,2011:1-41.
[16]HO Y C,LEE R C K.A bayesian approach to problems in stochastic estimation and control[J].IEEE Transactions on Automatic Control,1964,9(4):333-339.
[17]ANDERSON B D O,MOORE J B.Optimal filtering[C]//Prentice-Hall.New Jersey:Englewood Cliffs,1979:511-519.
[18]张文,孙瑞胜.EKF与UKF的性能比较与应用[J].南京理工大学学报,2015,39(5):614-618.ZHANG Wen,SUN Ruisheng.Research on performance comparison of EKF and UKF and their application[J].Journal of Nanjing University of Science and Technology,2015,39(5):614-618.