自识别自校准Kalman滤波方法
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摘要
在导航滤波、故障诊断等许多工程领域中,受环境因素影响、模型和参数的选取不当等原因,系统状态方程中往往含有未知输入(系统误差),传统的Kalman滤波方法无法消除这种未知输入的影响,导致产生较大的滤波误差。为此,提出一种自识别自校准Kalman滤波方法,并分别对线性系统和非线性系统进行了详细讨论,给出了相应的公式和滤波步骤。该方法能够自动识别状态方程中有无未知输入,当有未知输入时,则能自动估计未知输入,并对它进行补偿和修正。大量实例计算和仿真模拟表明,与传统方法相比,本文方法能够有效提高状态估计精度,且计算简单,便于工程应用。
In many engineering fields, such as deep space exploration, navigation, fault diagnosis and so on, due to the influence of environmental factors, improper selection of models and parameters, the system state equation often contains unknown inputs(systematical errors). Traditional Kalman filters cannot eliminate the influence of unknown inputs, resulting in larger filtering errors. In this paper,a self-recognition and self-calibration Kalman filtering method is proposed. The linear and nonlinear systems are discussed, and the corresponding formulas and filtering steps are given. This method can automatically recognize whether there are unknown inputs in the state equation. When there are unknown inputs, they can beautomatically estimated, compensated and corrected them. A large number of examples and simulation results show that compared with the traditional method,the proposed method can effectively improve the accuracy of state estimations,and the calculation is simple,which is convenient for engineering application.
In many engineering fields, such as deep space exploration, navigation, fault diagnosis and so on, due to the influence of environmental factors, improper selection of models and parameters, the system state equation often contains unknown inputs(systematical errors). Traditional Kalman filters cannot eliminate the influence of unknown inputs, resulting in larger filtering errors. In this paper,a self-recognition and self-calibration Kalman filtering method is proposed. The linear and nonlinear systems are discussed, and the corresponding formulas and filtering steps are given. This method can automatically recognize whether there are unknown inputs in the state equation. When there are unknown inputs, they can beautomatically estimated, compensated and corrected them. A large number of examples and simulation results show that compared with the traditional method,the proposed method can effectively improve the accuracy of state estimations,and the calculation is simple,which is convenient for engineering application.
引文
[1] KALMAN R E. A new approach linear filtering and prediction problems[J]. Journal of Fluids Engineering,1960,82(1):35-45.
[2] SUNAHARA Y. An approximate method of state estimation for nonlinear dynamical systems[J]. Journal of Basic Engineering,1970,92(2):385-393.
[3] FUJIMOTO O,OKITA Y,OZAKI S. Nonlinearity compensation extended Kalman filter and its application to target motion[J]. Oki Technical Review,1997,63(159):1-12.
[4] JULIER S J,UHLMANN J K. A new extension of Kalman filter to nonlinear systems[C]//Proceedings of 11th International Symposium Aerospace/Defense Sensing.Simulation and Controls. Orlando:SPIE,1997.
[5] JULIER S J,UHLMANN J K,DURRANT-WHYTE H F. A new method for the nonlinear transformation of means and covariances in filters and estimators[J]. IEEE Transactions on Automatic Control,2000,45(3):477-482.
[6] JULIER S J,UHLMANN J K. Unscented filtering and nonlinear estimation[J]. Proceedings of the IEEE,2004,92(3):401-423.
[7] SIMON D. Optimal state estimation Kalman H∞and nonlinear approaches[M]. Hoboken,US:John Wiley&Sons,2006.
[8] PITT M,SHEPHARD N. Filtering via simulation:auxiliary particle filters[J]. Journal of the American Statistical Association,1999,94(446):590-599.
[9]傅惠民，肖强，吴云章，等.秩滤波方法[J].机械强度，2014,36(4):521-526.FU H M,XIAO Q,WU Y Z,et al. Rank filter method[J]. Journal of Mechanical Strength,2014,36(4):521-526.
[10]傅惠民，肖强，娄泰山，等.非线性非高斯秩滤波方法[J].航空动力学报，2015,30(10):2318-2322.FU H M,XIAO Q,LOU T S,et al. Nonlinear and non-Guassian rank filter method[J]. Journal of Aerospace Power,2015,30(10):2318-2322
[11] BLANLE M,KINNAERT M,LUNZE J,et al. Diagnosis and faulttolerant control[M]. Berlin,Germany:Springer,2006.
[12] CHEN J,PATTON R. Robust model-based fault diagnosis for dynamic systems[M]. Norwell, MA, US:Kluwer Academic Publishers,1999.
[13] GILLIJNS S,MOOR B D. Unbiased minimum variance input and state estimation for linear discrete-time systems[J]. Automatic,2007,43(1):111-116.
[14]傅惠民，吴云章，娄泰山，等.自校准Kalman滤波方法[J].航空动力学报，2014,29(6):1363-1368.FU H M,WU Y Z,LOU T S,et al. Self-calibration Kalman filter method[J]. Journal of Aerospace Power,2014,29(6):1363-1368.
[15]傅惠民，娄泰山，肖强，等.自校准扩展Kalman滤波方法[J].航空动力学报，2014,29(11):2710-2715.FU H M,LOU T S,XIAO Q,et al. Self-calibration extended Kalman filter method[J]. Journal of Aerospace Power,2014,29(11):2710-2715.
[2] SUNAHARA Y. An approximate method of state estimation for nonlinear dynamical systems[J]. Journal of Basic Engineering,1970,92(2):385-393.
[3] FUJIMOTO O,OKITA Y,OZAKI S. Nonlinearity compensation extended Kalman filter and its application to target motion[J]. Oki Technical Review,1997,63(159):1-12.
[4] JULIER S J,UHLMANN J K. A new extension of Kalman filter to nonlinear systems[C]//Proceedings of 11th International Symposium Aerospace/Defense Sensing.Simulation and Controls. Orlando:SPIE,1997.
[5] JULIER S J,UHLMANN J K,DURRANT-WHYTE H F. A new method for the nonlinear transformation of means and covariances in filters and estimators[J]. IEEE Transactions on Automatic Control,2000,45(3):477-482.
[6] JULIER S J,UHLMANN J K. Unscented filtering and nonlinear estimation[J]. Proceedings of the IEEE,2004,92(3):401-423.
[7] SIMON D. Optimal state estimation Kalman H∞and nonlinear approaches[M]. Hoboken,US:John Wiley&Sons,2006.
[8] PITT M,SHEPHARD N. Filtering via simulation:auxiliary particle filters[J]. Journal of the American Statistical Association,1999,94(446):590-599.
[9]傅惠民，肖强，吴云章，等.秩滤波方法[J].机械强度，2014,36(4):521-526.FU H M,XIAO Q,WU Y Z,et al. Rank filter method[J]. Journal of Mechanical Strength,2014,36(4):521-526.
[10]傅惠民，肖强，娄泰山，等.非线性非高斯秩滤波方法[J].航空动力学报，2015,30(10):2318-2322.FU H M,XIAO Q,LOU T S,et al. Nonlinear and non-Guassian rank filter method[J]. Journal of Aerospace Power,2015,30(10):2318-2322
[11] BLANLE M,KINNAERT M,LUNZE J,et al. Diagnosis and faulttolerant control[M]. Berlin,Germany:Springer,2006.
[12] CHEN J,PATTON R. Robust model-based fault diagnosis for dynamic systems[M]. Norwell, MA, US:Kluwer Academic Publishers,1999.
[13] GILLIJNS S,MOOR B D. Unbiased minimum variance input and state estimation for linear discrete-time systems[J]. Automatic,2007,43(1):111-116.
[14]傅惠民，吴云章，娄泰山，等.自校准Kalman滤波方法[J].航空动力学报，2014,29(6):1363-1368.FU H M,WU Y Z,LOU T S,et al. Self-calibration Kalman filter method[J]. Journal of Aerospace Power,2014,29(6):1363-1368.
[15]傅惠民，娄泰山，肖强，等.自校准扩展Kalman滤波方法[J].航空动力学报，2014,29(11):2710-2715.FU H M,LOU T S,XIAO Q,et al. Self-calibration extended Kalman filter method[J]. Journal of Aerospace Power,2014,29(11):2710-2715.