A Decoupled Interacting Multiple Model Algorithm with Unbiased 3D Converted Measurements Based on Modified Weighted Matrix
LI Wei1,2, LI Yiping1,2, FENG Xisheng1
1. State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China;
2. University of Chinese Academy of Sciences, Beijing 100049, China
李为, 李一平, 封锡盛. 基于修正加权矩阵的3 维解耦无偏量测转换交互式多模型算法[J]. 机器人, 2015, 37(2): 237-245,253.DOI: 10.13973/j.cnki.robot.2015.0237.
LI Wei, LI Yiping, FENG Xisheng. A Decoupled Interacting Multiple Model Algorithm with Unbiased 3D Converted Measurements Based on Modified Weighted Matrix. ROBOT, 2015, 37(2): 237-245,253. DOI: 10.13973/j.cnki.robot.2015.0237.
In order to solve the problem of mutual influence among the estimations of each coordinate caused by the canonical transform used for decoupling high-dimensional coupled kinematic state models in maneuvering targets tracking applications, an improved decoupling method is presented. At first, explicit expressions for unbiased compensation coefficients and unbiased covariance statistics based on Kalman filter predictions related to the 3D measurements are given. And then, based on the canonical transform, an improved decoupling method using the modified weighted matrix is presented in detail. At last, simulation experiments are conducted combining with the IMM (interacting multiple model) algorithm. Results indicate that the proposed algorithm can reduce computational burden and eliminate influences among three Cartesian coordinates, which is good for analysis and application of IMM algorithm.
[1] Blackman S. Multiple target tracking with radar applications[M]. Dedham, USA: Artech House, 1986.[2] Lerro D, Bar-shalom Y. Tracking with debiased consistent converted measurements versus EKF[J]. IEEE Transactions on Aerospace and Electronic Systems, 1993, 29(3): 1015-1022. [3] Mo L B, Song X Q, Zhou Y Y, et al. Unbiased converted measurements for tracking[J]. IEEE Transactions on Aerospace and Electronic Systems, 1998, 34(3): 1023-1027. [4] Duan Z S, Han C Z. Comments on “unbiased converted measurements for tracking”[J]. IEEE Transactions on Aerospace and Electronic Systems, 2004, 40(4): 1374-1377. [5] Spitzmiller J N, Adhami R R. Tracking with estimateconditioned debiased 3-D converted measurements[C]//IEEE Aerospace Conference. Piscataway, USA: IEEE, 2010: 1-16.[6] Mei W, Bar-Shalom Y. Unbiased Kalman filter using converted measurements: Revisit[C]//Signal and Data Processing of Small Target. Bellingham, USA: SPIE, 2009: doi: 10.1117/12.831218.[7] Bordonaro S V, Willett P, Bar-Shalom Y. Tracking with converted position and Doppler measurements[C]//Signal and Data Processing of Small Target. Bellingham, USA: SPIE, 2011: doi: 10.1117/12.895484.[8] 王国宏,毛士艺,何友.均方意义下的最优无偏转换测量 Kalman 滤波[J].系统仿真学报,2002,14(1):119-121. Wang G H, Mao S Y, He Y. Optimal unbiased converted measurement Kalman filtering in the mean-square sense[J]. Journal of System Simulation, 2002, 14(1): 119-121.[9] Daum F E, Fitzgerald R J. Decoupled Kalman filters for phased array radar tracking[J]. IEEE Transactions on Automatic Control, 1983, 28(3): 269-283. [10] Baheti R S. Efficient approximation of Kalman filter for target tracking[J]. IEEE Transactions on Aerospace and Electronic Systems, 1986, 22(1): 8-14.[11] Sung T, Lee J G. A sufficient condition for stability of a decoupled tracking filter in LOS coordinate system[J]. IEEE Transactions on Aerospace and Electronic Systems, 1993, 29(2): 593- 599. [12] Li X R. Canonical transform for tracking with Kinematic models[ J]. IEEE Transactions on Aerospace and Electronic Systems, 1997, 33(4): 1212-1224.[13] 伍明,李琳琳,孙继银.基于概率数据关联交互多模型滤波的移动机器人未知环境下动态目标跟踪[J].机器人, 2012,34(6):668-679. Wu M, Li L L, Sun J Y. PDA-IMM based moving object tracking with mobile robots in unknown environments[J]. Robot, 2012, 34(6): 668-679.[14] Miller M D, Drummond O E. Coordinate transformation bias in target tracking[C]//Signal and Data Processing of Small Target. Bellingham, USA: SPIE, 1999: 409-424.[15] Julier S J, Uhlmann J K. A consistent, debiased method for converting between polar and Cartesian coordinate systems[C]//Conference on Acquisition, Tracking, and Pointing XI. Bellingham, USA: SPIE, 1997: 110-121.[16] 王宏强,黎湘,庄钊文,等.解耦的转换测量Kalman 滤波算法[J].电子学报,2003,31(6):867-870. Wang H Q, Li X, Zhuang ZW, et al. Decoupled converted measurement Kalman filter[J]. Acta Electronica Sinica, 2003, 31(6): 867-870.[17] 林晓君,郭立,熊志伟,等.3 维解耦转换量测Kalman 滤波算法[J].火控雷达技术,2005,34(3):6-12. Lin X J, Guo L, Xiong Z W, et al. 3-D decoupled algorithm based on converted measure Kalman filter[J]. Fire Control Radar Technology, 2005, 34(3): 6-12.[18] Blom H A P, Bar-Shalom Y. The interacting multiple model algorithm for systems with Markovian switching coefficients[J]. IEEE Transactions on Automatic Control, 1988, 33(8): 780- 783. [19] Yaakov B S, Li X R. Estimation and tracking: Principles, techniques, and software[M]. London, UK: Artech House, 1993.
