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In a passive target tracking system, the position and velocity of a target can be estimated based on time difference of arrival (TDOA) and frequency difference of arrival (FDOA) received by different stations. But TDOA and FDOA equations are nonlinear, which make the target tracking become a nonlinear estimation problem. To solve the nonlinear estimation problem, the most extensive research algorithms are those of extended Kalman filter (EKF), particle filter (PF), unscented Kalman filter (UKF), quadrature Kalman filter (QKF), and cubature Kalman filter (CKF). But the existing algorithms all come up with shortcoming in some way. EKF only retains the first order of the nonlinear function by Taylor series expansion, which will bring large error. PF has to face the degeneracy phenomenon and the problem of large computational complexity. The standard UKF is easy to become divergence in a high dimensional state estimation. QKF is sensitive to the dimension of state, and the calculation is of exponential growth with the growth of dimension. Although CKF can effectively improve the shortcomings, the discarded error is proportional to the state dimension, which may be large in high dimensional state. In view of the above problems, this paper presents an orthogonal cubature Kalman filter (OCKF) algorithm. This algorithm reduces the sampling error by introducing special orthogonal matrix to change the method of cubature sampling based on CKF. It eliminates the dimension impact on the sampling error. In the absence of additional computation, it effectively improves the tracking precision. Simulation results show that, based on the TDOA and FDOA, compared with the EKF and CKF algorithms, OCKF algorithm can improve the tracking performance significantly.
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Keywords:
- target tracking /
- cubature Kalman filter /
- time difference of arrival /
- frequency difference of arrival
[1] Lin C M, Hsueh C S 2013 IEEE Transactions on Instrumentation and Measurement 7 2058
[2] Ho K C, Xu W W 2004 IEEE Transactions on Signal Processing 52 2453
[3] Arie Yeredor, Eyal Angel 2011 IEEE Transactions On Signal Processing 59 1612
[4] Wang G, Li Y M, Ansari N 2013 IEEE Transactions On Vehicular Technology 62 853
[5] Luo L, Tian Z S, Chen J Y 2009 Journal of Chongqing University of Posts and Telecommunications(Natural Science Edition) 01 50 (in Chinese) [罗磊, 田增山, 陈俊亚 2009 重庆邮电大学学报(自然科学版) 01 50]
[6] Gustafsson F, Hendeby G 2012 IEEE Transactions on Signal Processing 02 545
[7] Ning X L, Wang H L, Zhang Q, Chen L H 2010 Acta Phys. Sin. 59 4426 (in Chinese) [宁小磊, 王宏力, 张琪, 陈连华 2010 59 4426]
[8] Zhang Q, Qiao Y K, Kong X Y, Si X S 2014 Acta Phys. Sin. 63 110505 (in Chinese) [张琪乔玉坤孔祥玉司小胜 2014 63 110505]
[9] Julier S J, Uhlman J K, Durrant-Whyte H F 2000 IEEE Transactions on Automatic Control 45 477
[10] Julier S J, Uhlman J K 2004 Proceedings of the IEEE 92 401
[11] Liu Y, Wang H, Hou C H 2013 IEEE Transactions on Signal Processing 61 4988
[12] Ienkaran A, Simon H, Robert J E 2007 Proceedings of the IEEE 95 953
[13] Arasaratnam I, Haykin S 2009 IEEE Transactions on Automatic Control 54 1254
[14] ArasaratnamI, Haykin S, HurdTR 2010 IEEE Transactions on Signal Processing 58 4977
[15] Wei X Q, Song S M 2013 Journa1 of Astronautics 34 193 (in Chinese) [魏喜庆, 宋申民 2013 宇航学报 34 193]
[16] Liu X, Jiao S H, Si X C 2011 Journal of Xi An Jiao Tong University 45 137 (in Chinese) [刘学, 焦淑红, 司锡才 2011 西安交通大学学报 45 137]
[17] Chang L B, Hu B Q, Li A, Qin F J 2013 IEEE Transactions on Automatic Control 58 252
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[1] Lin C M, Hsueh C S 2013 IEEE Transactions on Instrumentation and Measurement 7 2058
[2] Ho K C, Xu W W 2004 IEEE Transactions on Signal Processing 52 2453
[3] Arie Yeredor, Eyal Angel 2011 IEEE Transactions On Signal Processing 59 1612
[4] Wang G, Li Y M, Ansari N 2013 IEEE Transactions On Vehicular Technology 62 853
[5] Luo L, Tian Z S, Chen J Y 2009 Journal of Chongqing University of Posts and Telecommunications(Natural Science Edition) 01 50 (in Chinese) [罗磊, 田增山, 陈俊亚 2009 重庆邮电大学学报(自然科学版) 01 50]
[6] Gustafsson F, Hendeby G 2012 IEEE Transactions on Signal Processing 02 545
[7] Ning X L, Wang H L, Zhang Q, Chen L H 2010 Acta Phys. Sin. 59 4426 (in Chinese) [宁小磊, 王宏力, 张琪, 陈连华 2010 59 4426]
[8] Zhang Q, Qiao Y K, Kong X Y, Si X S 2014 Acta Phys. Sin. 63 110505 (in Chinese) [张琪乔玉坤孔祥玉司小胜 2014 63 110505]
[9] Julier S J, Uhlman J K, Durrant-Whyte H F 2000 IEEE Transactions on Automatic Control 45 477
[10] Julier S J, Uhlman J K 2004 Proceedings of the IEEE 92 401
[11] Liu Y, Wang H, Hou C H 2013 IEEE Transactions on Signal Processing 61 4988
[12] Ienkaran A, Simon H, Robert J E 2007 Proceedings of the IEEE 95 953
[13] Arasaratnam I, Haykin S 2009 IEEE Transactions on Automatic Control 54 1254
[14] ArasaratnamI, Haykin S, HurdTR 2010 IEEE Transactions on Signal Processing 58 4977
[15] Wei X Q, Song S M 2013 Journa1 of Astronautics 34 193 (in Chinese) [魏喜庆, 宋申民 2013 宇航学报 34 193]
[16] Liu X, Jiao S H, Si X C 2011 Journal of Xi An Jiao Tong University 45 137 (in Chinese) [刘学, 焦淑红, 司锡才 2011 西安交通大学学报 45 137]
[17] Chang L B, Hu B Q, Li A, Qin F J 2013 IEEE Transactions on Automatic Control 58 252
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