带有色量测噪声的非线性系统 Unscented 卡尔曼滤波器

王小旭; 梁彦; 潘泉; 赵春晖; 李汉舟

doi:10.3724/SP.J.1004.2012.00986

带有色量测噪声的非线性系统 Unscented 卡尔曼滤波器

doi: 10.3724/SP.J.1004.2012.00986

1.
西北工业大学自动化学院控制与信息研究所西安 710072;
2.
中国航天科技集团公司第九研究院第十六研究所西安 710100

详细信息

通讯作者:
梁彦,西北工业大学自动化学院教授.主要研究方向为状态估计,信息融合及目标跟踪.

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出版历程
- 收稿日期: 2011-09-07
- 修回日期: 2012-02-02
- 刊出日期: 2012-06-20

Unscented Kalman Filter for Nonlinear Systems with Colored Measurement Noise

1.
Institute of Control and Information, School of Automation, Northwestern Polytechnical University, Xi'an 710072;
2.
The 16th Institute, the 9th Academy, China Aerospace Science and Technology Corporation, Xi'an 710100

摘要

摘要: 传统Unscented卡尔曼滤波器(Unscented Kalman filter, UKF)要求噪声必须为高斯白噪声, 无法解决带有色噪声的非线性系统滤波问题. 为此, 本文提出了一种带有色量测噪声的UKF滤波新算法. 首先,基于量测信息增广和最小方差估计, 推导出一类带有色量测噪声的非线性离散系统状态的最优滤波框架, 接着采用Unscented变换(Unscented transformation, UT)来计算最优框架中的非线性状态后验均值和协方差, 进而得到有色量测噪声下UKF滤波递推公式. 所设计的UKF新方法能有效地解决传统UKF在量测噪声有色情况下非线性滤波失效的问题, 数值仿真实例验证了其可行性和有效性.
- 非线性 /
- 有色量测噪声 /
- 最优滤波框架 /
- Unscented卡尔曼滤波 /
- Unscented变换 /
- 量测信息增广 /
- 最小方差估计
Abstract: Traditional unscented Kalman filter (UKF) calls for that noise should be Gaussian white one, and can not solve nonlinear filtering problem with colored noise. For this reason, a new UKF filtering algorithm with colored measurement noise is proposed. Firstly, optimal filtering framework for a class of nonlinear discrete-time systems with colored measurement noise is derived on the basis of augmented measurement information and minimum mean square error estimation. Secondly, filtering recursive formula of UKF with colored noise is proposed through applying unscented transformation (UT) to calculation the posterior mean and covariance of the nonlinear state in this optimal framework. The proposed UKF can effectively deal with the issue that traditional UKF is failure under the condition that measurement noise is colored. A numerical simulation example also shows its feasibility and effectiveness.
- Nonlinear /
- colored measurement noise /
- optimal filtering framework /
- unscented Kalman filter (UKF) /
- unscented transformation (UT) /
- augmented measurement information /
- minimum mean square error estimation

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[1]

Julier S, Uhlmann J, Durrant-Whyte H F. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Transactions on Automatic Control, 2000, 45(3): 477-482[2] Julier S J, Uhlmann J K, Durrant-Whyte H F. A new approach for filtering nonlinear systems. In: Proceedings of American Control Conference. Seattle, WA: IEEE, 1995. 1628-1632[3] Pan Quan, Yang Feng, Ye Liang, Liang Yan, Cheng Yong-Mei. Survey of a kind of nonlinear filters --- UKF. Control and Decision, 2005, 20(5): 481-489, 494 (潘泉, 杨峰, 叶亮, 梁彦, 程咏梅. 一类非线性滤波器--- UKF综述. 控制与决策, 2005, 20(5): 481-489, 494)[4] Merwe van der R, Wan E A. Sigma point Kalman filters for integrated navigation. In: Proceedings of the 60th Annual Meeting of the Institute of Navigation (ION). Dayton, USA: Dayton Marriott Hotel, 2004. 641-654[5] Cho S Y, Kim B D. Adaptive IIR/FIR fusion filter and its application to the INS/GPS integrated system. Automatica, 2008, 44(8): 2040-2047[6] Blom H A P, Bar-Shalom Y. The interacting multiple model algorithm for systems with markovian switching coefficients. IEEE Transactions on Automatic Control, 1988, 33(8): 780-783[7] Song Q, Han J D. An adaptive UKF algorithm for the state and parameter estimations of a mobile robot. Acta Automatica Sinica, 2008, 34(1): 72-79[8] Zhao Lin, Wang Xiao-Xu, Sun Ming, Ding Ji-Cheng, Yan Chao. Adaptive UKF filtering algorithm based on maximum a posterior estimation and exponential weighting. Acta Automatica Sinica, 2010, 36(7): 1007-1019 (赵琳, 王小旭, 孙明, 丁继成, 闫超. 基于极大后验估计和指数加权的自适应UKF滤波算法. 自动化学报, 2010, 36(7): 1007-1019)[9] Li Peng, Song Shen-Min, Chen Xing-Lin. Adaptive square-root unscented Kalman filter algorithm. Control Theory and Applications, 2010, 27(2): 143-146 (李鹏, 宋审民, 陈兴林. 自适应平方根无迹卡尔曼滤波算法. 控制理论与应用, 2010, 27(2): 143-146)[10] Hermoso-Carazo A, Linares-Pérez J. Unscented filtering algorithm using two-step randomly delayed observations in nonlinear systems. Applied Mathematical Modelling, 2009, 33(9): 3705-3717[11] Teixeira B O S, Trres L A B, Aguirre L A, Bernstein D S. On unscented Kalman filtering with state interval constraints. Journal of Process Control, 2010, 20(1): 45-57[12] Kols S, Fossa B A, Schei T S. Constrained nonlinear state estimation based on the UKF approach. Computers and Chemical Engineering, 2009, 33(8): 1386-1401[13] Soken Halil Ersin, Hajiyev Chingiz. Pico satellite attitude estimation via robust unscented Kalman filter in the presence of measurement faults. ISA Transactions, 2010, 49(3): 249-256[14] Leven W F, Lanterman A D. Unscented Kalman filters for multiple target tracking with symmetric measurement equations. IEEE Transactions on Automatic Control, 2009, 54(2): 370-375[15] Petsios M N, Alivizatos E G, Uzunoglu N K. Solving the association problem for a multistatic range-only radar target tracker. Signal Processing, 2008, 88(9): 2254-2277[16] Tang X J, Yan J, Zhong D D. Square-root sigma-point Kalman filtering for spacecraft relative navigation. Acta Astronautica, 2010, 66(5-6): 704-713[17] Kim C, Sakthivel R, Chung W K. Unscented FastSLAM: a robust and efficient solution to the SLAM problem. IEEE Transactions on Robotics, 2008, 24(4): 808-820[18] Schopp P, Klingbeil L, Peters C, Manoli Y. Design, geometry evaluation, and calibration of a gyroscope-free inertial measurement unit. Sensors and Actuators A: Physical, 2010, 162(2): 379-387[19] Ning X L, Fang J C. A new autonomous celestial navigation method for the lunar rover. Robotics and Autonomous Systems, 2009, 57(1): 48-54[20] Murshed AKM M, Huang B, Nandakumar K. Estimation and control of solid oxide fuel cell system. Computers and Chemical Engineering, 2010, 34(1): 96-111[21] Wang J L, Feng X Y, Zhao L Q, Yu T. Unscented transformation based robust Kalman filter and its applications in fermentation process. Chinese Journal of Chemical Engineering, 2010, 18(3): 412-418[22] Kim J S, Shin D R, Serpedin E. Adaptive multiuser receiver with joint channel and time delay estimation of CDMA signals based on the square-root unscented filter. Digital Signal Processing, 2009, 19(3): 504-520[23] Tripathy P, Srivastava S C, Singh S N. A divide-by-difference-filter based algorithm for estimation of generator rotor angle utilizing synchrophasor measurements. IEEE Transactions on Instrumentation and Measurement, 2010, 59(6): 1562-1570[24] Simon D. A comparison of filtering approaches for aircraft engine health estimation. Aerospace Science and Technology, 2008, 12(4): 276-284[25] Yuan G N, Xie Y J, Song Y, Liang H B. Multipath parameters estimation of weak GPS signal based on new colored noise unscented Kalman filter. In: Proceedings of IEEE International Conference on Information and Automation. Harbin, China: IEEE, 2010. 1852-1856[26] Ma N, Bouchard M, Goubran R A. Dual perceptually constrained unscented Kalman filter for enhancing speech degraded by colored noise. In: Proceedings of the 7th International Conference on Signal Proceeding. Beijing, China: IEEE, 2004. 2522-2525[27] Yin Wei, Yi Ben-Shun, Shen Xiao-Feng. Speech enhancement based unscented particle filter with non-Gaussian noises. Chinese Journal of Radio Science, 2009, 24(3): 476-481 (尹伟, 易本顺, 沈小丰. 有色噪声下基于Unscented粒子滤波的语音增强方法. 电波科学学报, 2009, 24(3): 476-481)[28] Xiong Wei, Chen Li-Kui, He You, Zhang Jing-Wei. Unscented Kalman filter with colored noise. Journal of Electronics and Information Technology, 2007, 29(3): 598-600 (熊伟, 陈立奎, 何友, 张晶炜. 有色噪声下的不敏卡尔曼滤波器. 电子与信息学报, 2007, 29(3): 598-600)[29] Zhou D H, Frank P M. Strong tracking filtering of nonlinear time-varying stochastic systems with coloured noise: application to parameter estimation and empirical robustness analysis. International Journal of Control, 1996, 65(2): 295-307[30] Wu W R, Chang D C. Maneuvering target tracking with colored noise. IEEE Transactions on Aerospace and Electronic Systems, 1996, 32(4): 1311-1320[31] El-Sayed Abdel-Salam G. Global Positioning System (GPS) Receiver Design for Multipaths Mitigation. Ohio, USA: Air Force Institute of Technology Air University, 1998. 101-103[32] Ito K, Xiong K Q. Gaussian filters for nonlinear filtering problems. IEEE Transactions on Automatic Control, 2000, 45(5): 910-927[33] Wang Xiao-Xu. Research on Nonlinear SPKF Filtering Algorithm and Its Application for Integrated Navigation [Ph.D. dissertation], Harbin Engineering University, China, 2010 (王小旭. 非线性SPKF 滤波算法研究及其在组合导航中的应用 [博士学位论文], 哈尔滨工程大学, 中国, 2010)

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