Spaceborne radars play an important role in early warning defense systems because of their unique advantages such as wide detection range, long distance and all-weather surveillance capability. Due to the high-speed movement of the platform and the strong nonlinear observation function, high-accuracy target tracking for spaceborne radars is difficult. In this paper, we propose a variational Bayes-based nonlinear filtering method, which transforms the nonlinear state estimation problem into an optimization problem. The analytical solution is obtained via a closed-loop iteration manner. Moreover, a pitch angle estimation method is presented using the a priori information of target height. Simulation results show that, compared with the extended Kalman filter, unscented Kalman filter, and the converted measurement Kalman filter, the proposed variational Bayes-based nonlinear filtering method achieves the best estimation accuracy.
YAN Wenxu
,
LAN Hua
,
WANG Zengfu
,
JIN Shuling
,
PAN Quan
. Nonlinear filtering for spaceborne radars based on variational Bayes[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020
, 41(S2)
: 724395
-724395
.
DOI: 10.7527/S1000-6893.2020.24395
[1] EINICKE G A, WHITE L B. Robust extended Kalman filtering[J]. IEEE Transactions on Signal Processing, 1999, 47(9):2596-2599.
[2] BELL B M, CATHEY F W. The iterated Kalman filter update as a Gauss-Newton method[J]. IEEE Transactions on Automatic Control, 1993, 38(2):294-297.
[3] HU J, WANG Z, GAO H, et al. Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements[J]. Automatica, 2012, 48:2007-2015.
[4] HU X, BAO M, ZHANG X, et al. Generalized iterated Kalman filter and its performance evaluation[J]. IEEE Transaction on Signal Processing, 2015, 63:3204-3217.
[5] JULIER S J, UHLMANN J K. A new extension of the Kalman filter to nonlinear systems[C]//Proceedings of Spie, 1997:182-193.
[6] Wan E A, VAN DER MERWE R.The unscented Kalman filter for nonlinear estimation[C]//Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium. Piscataway:IEEE Press, 2000:153-158.
[7] JULIER S J,UHLMANN J K. Unscented filtering and nonlinear estimation[J]. Proceedings of the IEEE, 2004, 92(3):401-422.
[8] GUSTAFSSON F,HENDEBY G. Some relations between extended and unscented Kalman filters[J]. IEEE Transaction on Signal Processing, 2012,60:545-555.
[9] ARASARATNAM I, HAYKIN S. Cubature Kalman filters[J]. IEEE Transaction on Automatic Control, 2009,54:1254-1269.
[10] ARASARATNAM I, HAYKIN S, HURD T R. Cubature Kalman filtering for continuous-discrete systems:Theory and simulations[J]. IEEE Transaction on Signal Processing, 2010,58:4977-4933.
[11] MERWE R V D,WAN E A. Sigma-point Kalman filters for integrated navigation[C]//60th Annual Meeting of the Institute of Navigation, 2004:641-645.
[12] 杨春玲,刘国岁,倪晋麟.基于转换坐标卡尔曼滤波算法的雷达目标跟踪[J].现代雷达,1988, 20(5):48-54. YANG C L, LIU G S, NI J L. Radar target tracking based on transformed coordinate Kalman filter algorithm[J].Modern Radar, 1988, 20(5):48-54(in Chinese).
[13] LERRO D, BARSHALOM Y. Tracking with debiased consistent converted measurement vs. EKF[J]. IEEE Transactions on Aerospace and Electronic systems, 1993,29(3):1015-1022.
[14] SONG X,ZHOU Y,BARSHALOM Y. Unbiased converted measurement for tracking[J]. IEEE Transactions on Aerospace and Electronic systems, 1998,34(3):1023-1027.
[15] GORDON N J,SALMOND D J,SMITH A F. Novel approach to nonlinear/non-Gaussian Bayesian state estimation[C]//IEEE Proceedings F-Radar and Signal Processing, 1993,140:107-113.
[16] DOUCET A,GODSILL S,ANDRIEU C. On sequential Monte Carlo sampling methods for Bayesian filtering[J]. Statistics and Computing, 2000,10(3):197-208.
[17] CAPPE O,GODSILL S J,MOULINES E. An overview of existing methods and recent advances in sequential Monte Carlo[J]. Proceeding of the IEEE, 2007,95:899-924.
[18] BEAL M J. Variational algorithms for approximate Bayesian inference[D].Cambridge:Cambridge University,2003.
[19] SMIDL V,QUINN A. Variational Bayesian filtering[J]. IEEE Transactions on Signal Processing, 2008,56(10):5020-5030.
[20] FRIGOLA R,CHEN Y,RASMUSSEN C. Varoational Gaussian process state-space models[C]//Advances in Neural Information Processing Systems, 2014:3680-3688.
[21] AIT-E1-FQUIH B,HOTEIT I. A variational Bayesian multiple particle filtering scheme for large-dimensional systems[J]. IEEE Transactions on Signal Processing, 2016,64(20):5409-5422.
[22] GULTEKIN S,PAISLEY J. Nonlinear Kalman filtering with divergence minimization[J]. IEEE Transactions on Signal Processing, 2017:65,6319-6331.
[23] HU Y M,WANG X Z,LAN H,et al. An iterative nonlinear filter using variational bayesian optimization[J]. Sensors, 2018,18(12):4222.
[24] TSENG P. An analysis of the EM algorithm and entropy-like proximal point methods[J]. Mathematics of Operations Research, 2004, 29:27-44.
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