不完全量测下长基线系统的水下目标跟踪算法
|
摘要
针对不完全量测情况下长基线系统对水下目标跟踪精度会下降的问题,提出了最小二乘-容积卡尔曼滤波(Least Squares-Cubature Kalman Filter,LS-CKF)算法。选取容积卡尔曼滤波(Cubature Kalman Filter,CKF)为基本跟踪算法并将其改进为两步滤波模式.增加的第1步滤波使用最小二乘估计优化时间更新阶段的容积点,提高了第2步滤波中量测更新的精度。进一步推导了量测信息为距离时新算法的简化形式,降低了运算复杂度,使其能更好地应用于水下跟踪系统.仿真实验和湖试数据的处理结果表明,在丢失量测数据较多且初始状态误差很大的恶劣情况下,LS-CKF收敛速度比标准CKF算法提升了1倍,且跟踪误差降低10%以上。
A Least Squares-Cubature Kalman Filter(LS-CKF)algorithm is proposed,aiming at increasing the tracking accuracy of underwater maneuvering target with incomplete measurements of the long baseline system.Firstly,a practical two-dimensional mathematical model of underwater target tracking with incomplete measurements is established.Secondly,a two-layer CKF is introduced where the expression of the cubature point under the latest measurement constraint is derived via least square estimation in the first layer to improve the accuracy of the measurement updating process.Finally,considering the underwater tracking system is power-limited,a simplified form of the new algorithm with ranges-only measurements is derived.The accuracy of the proposed algorithm is improved because the latest measurement is effectively integrated into each cubature point with the Least-Squares method,which allows the cubature points to move from the a prior area to the high likelihood region.The results of the simulation and the lake trial both show that the new algorithm significantly improves the tracking accuracy on condition that severe incomplete measurements and large initial error.Compared with the standard CKF algorithm,the convergence speed of LS-CKF is double while the tracking error is reduced by more than 10%.
A Least Squares-Cubature Kalman Filter(LS-CKF)algorithm is proposed,aiming at increasing the tracking accuracy of underwater maneuvering target with incomplete measurements of the long baseline system.Firstly,a practical two-dimensional mathematical model of underwater target tracking with incomplete measurements is established.Secondly,a two-layer CKF is introduced where the expression of the cubature point under the latest measurement constraint is derived via least square estimation in the first layer to improve the accuracy of the measurement updating process.Finally,considering the underwater tracking system is power-limited,a simplified form of the new algorithm with ranges-only measurements is derived.The accuracy of the proposed algorithm is improved because the latest measurement is effectively integrated into each cubature point with the Least-Squares method,which allows the cubature points to move from the a prior area to the high likelihood region.The results of the simulation and the lake trial both show that the new algorithm significantly improves the tracking accuracy on condition that severe incomplete measurements and large initial error.Compared with the standard CKF algorithm,the convergence speed of LS-CKF is double while the tracking error is reduced by more than 10%.
引文
1 Erol-Kantarci M,Mouftah H T,Oktug S.Localization techniques for underwater acoustic sensor networks.IEEE Commun.Surv.Tutorials,2011; 13(3):487—502
2 Tan H P,Diamant R,Seah W K G et al. A survey of techniques and challenges in underwater localization.Ocean Eng.,2011; 38(14):1663-1676
3 Qu F,Wang S,Wu Z et al. A survey of ranging algorithms and localization schemes in underwater acoustic sensor network.China Commun.,2016; 13(3):66-81
4封金星,丁士圻.水下运动目标长基线定位解算研究.声学学报,1996; 21(5):832-837
5 Wu Y,Yan S,Li S et al.An acoustic positioning of underwater vehicles using synthetic long baseline navigation.Oceans'16,IEEE,Shanghai,China,2016:1-5
6李敏,孙贵青,李启虎.分布式浮标阵水下高速运动声源三维被动定位.声学学报,2009; 34(4):289—295
7韩云峰,郑翠娥,孙大军.长基线声学定位系统跟踪解算优化方法.声学学报,2017; 42(1):14—20
8李想.水下高速运动目标轨迹测量技术研究.博士学位论文,哈尔滨:哈尔滨工程大学,2011
9田坦.水下定位与导航技术.北京:国防工业出版社,2007:16-24
10姬长琳.卡尔曼滤波在长基线水下定位系统中的应用研究与实现.硕士学位论文,哈尔滨:哈尔滨工程大学,2014
11 Wang X,Fu M,Zhang H.Target tracking in wireless sensor networks based on the combination of KF and MLE using distance measurements.IEEE Trans.Mob.Comput.,2012; 11(4):567-576
12 Li T,Ekpenyong A,Huang Y F.Source localization and tracking using distributed asynchronous sensors.IEEE Trans.Signal Process.,2006; 54(10):3991—4003
13徐鹏,郭良浩,闫超.方位和径向速度联合的浅海目标运动分析方法.声学学报,2018;43(3):323-333
14 Julier S J,Uhlmann J K.Corrections to"Unscented Filtering and Nonlinear Estimation".P-roc.IEEE,2005;92(12):1958-1958
15石勇,韩崇昭.自适应UKF算法在目标跟踪中的应用.自动化学报,2011;37(6):755-759
16 Arasaratnam I,Haykin S.Cubature Kalman filters.IEEE Trans.Autom.Control,2009;54(6):1254—1269
17 Leong P H,Arulampalam S,Lamahewa T A et al. A Gaussian-sum based cubature Kalman filter for bearingsonly tracking.IEEE Trans.Aerosp.Electron.Syst.,2013;49(2):1161—1176
18李天成,范红旗,孙树栋.粒子滤波理论、方法及其在多目标跟踪中的应用.自动化学报,2015;41(12):1981-2002
19 Wu Y,Wang J,Zhang P C.Least-squares particle filter.Electron.Lett.,2014; 50(24):1881-1882
20许志刚,陈黎,穆育强等.不完全量测下Cramer-Rao下界与数据丢失位置的关系.自动化学报,2009;35(8):1080—1086
21 Sinopoli B,Schenato L,Franceschetti M et al.Kalman iltering with intermittent observations.IEEE Trans.Autom.Control,2004;49(9):1453-14642
22 Epstein M,Shi L,Tiwari A et al.Probabilistic performance f state estimation across a lossy network.Automatica,2008;44(12):30466-3053
23 Kluge S,Reif K,Brokate M.Stochastic stability of the exended Kalman filter with intermittent observations.IEEE Trans.Autom.Control,2010;55(2):514-518
24李松,胡振涛,李晶等.基于多传感器不完全量测下的机动目标踪算法.计算机科学,2013;40(8):277-281
25陈黎,许志刚,盛安冬.不完全量测下一类非线性光电跟踪系统滤波器设计计航空学报,2009;30(9):1745-1753
26LI Zhuang,QIAO Gang,Muhammad Asim Ismail.Integration of time-reversal mirror technique in short baseline positioning.Chinese Jo-urnal of Acoustics,2013; 32(3):222-232
27 Li X R,Jilkov V P.Survey of maneuvering target tracking.Part I.Dynamic models.IEEE Trans.Aerosp.Electron.Syst.,2004; 39(4):1333-1364
28 HAN Yunfeng,ZHENG Cuie,SUN Dajun.A high precision calibration method for long baseline acoustic positioning systems.Chinese Journal of Acoustics,2017; 36(4):899-500
29 Zhu Z,Hu S L J.Model and algorithm improvement on ingle beacon underwater tracking.IEEE J.Oceanic Eng.,018;43(4):1143-1160
2 Tan H P,Diamant R,Seah W K G et al. A survey of techniques and challenges in underwater localization.Ocean Eng.,2011; 38(14):1663-1676
3 Qu F,Wang S,Wu Z et al. A survey of ranging algorithms and localization schemes in underwater acoustic sensor network.China Commun.,2016; 13(3):66-81
4封金星,丁士圻.水下运动目标长基线定位解算研究.声学学报,1996; 21(5):832-837
5 Wu Y,Yan S,Li S et al.An acoustic positioning of underwater vehicles using synthetic long baseline navigation.Oceans'16,IEEE,Shanghai,China,2016:1-5
6李敏,孙贵青,李启虎.分布式浮标阵水下高速运动声源三维被动定位.声学学报,2009; 34(4):289—295
7韩云峰,郑翠娥,孙大军.长基线声学定位系统跟踪解算优化方法.声学学报,2017; 42(1):14—20
8李想.水下高速运动目标轨迹测量技术研究.博士学位论文,哈尔滨:哈尔滨工程大学,2011
9田坦.水下定位与导航技术.北京:国防工业出版社,2007:16-24
10姬长琳.卡尔曼滤波在长基线水下定位系统中的应用研究与实现.硕士学位论文,哈尔滨:哈尔滨工程大学,2014
11 Wang X,Fu M,Zhang H.Target tracking in wireless sensor networks based on the combination of KF and MLE using distance measurements.IEEE Trans.Mob.Comput.,2012; 11(4):567-576
12 Li T,Ekpenyong A,Huang Y F.Source localization and tracking using distributed asynchronous sensors.IEEE Trans.Signal Process.,2006; 54(10):3991—4003
13徐鹏,郭良浩,闫超.方位和径向速度联合的浅海目标运动分析方法.声学学报,2018;43(3):323-333
14 Julier S J,Uhlmann J K.Corrections to"Unscented Filtering and Nonlinear Estimation".P-roc.IEEE,2005;92(12):1958-1958
15石勇,韩崇昭.自适应UKF算法在目标跟踪中的应用.自动化学报,2011;37(6):755-759
16 Arasaratnam I,Haykin S.Cubature Kalman filters.IEEE Trans.Autom.Control,2009;54(6):1254—1269
17 Leong P H,Arulampalam S,Lamahewa T A et al. A Gaussian-sum based cubature Kalman filter for bearingsonly tracking.IEEE Trans.Aerosp.Electron.Syst.,2013;49(2):1161—1176
18李天成,范红旗,孙树栋.粒子滤波理论、方法及其在多目标跟踪中的应用.自动化学报,2015;41(12):1981-2002
19 Wu Y,Wang J,Zhang P C.Least-squares particle filter.Electron.Lett.,2014; 50(24):1881-1882
20许志刚,陈黎,穆育强等.不完全量测下Cramer-Rao下界与数据丢失位置的关系.自动化学报,2009;35(8):1080—1086
21 Sinopoli B,Schenato L,Franceschetti M et al.Kalman iltering with intermittent observations.IEEE Trans.Autom.Control,2004;49(9):1453-14642
22 Epstein M,Shi L,Tiwari A et al.Probabilistic performance f state estimation across a lossy network.Automatica,2008;44(12):30466-3053
23 Kluge S,Reif K,Brokate M.Stochastic stability of the exended Kalman filter with intermittent observations.IEEE Trans.Autom.Control,2010;55(2):514-518
24李松,胡振涛,李晶等.基于多传感器不完全量测下的机动目标踪算法.计算机科学,2013;40(8):277-281
25陈黎,许志刚,盛安冬.不完全量测下一类非线性光电跟踪系统滤波器设计计航空学报,2009;30(9):1745-1753
26LI Zhuang,QIAO Gang,Muhammad Asim Ismail.Integration of time-reversal mirror technique in short baseline positioning.Chinese Jo-urnal of Acoustics,2013; 32(3):222-232
27 Li X R,Jilkov V P.Survey of maneuvering target tracking.Part I.Dynamic models.IEEE Trans.Aerosp.Electron.Syst.,2004; 39(4):1333-1364
28 HAN Yunfeng,ZHENG Cuie,SUN Dajun.A high precision calibration method for long baseline acoustic positioning systems.Chinese Journal of Acoustics,2017; 36(4):899-500
29 Zhu Z,Hu S L J.Model and algorithm improvement on ingle beacon underwater tracking.IEEE J.Oceanic Eng.,018;43(4):1143-1160