一种基于变论域自适应模糊逻辑系统提高卡尔曼滤波器性能的方法
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摘要
实际工程应用中,预测动态系统的状态通常是一类比较重要的问题。卡尔曼滤波器已经被证明是处理该类问题的一个有效的工具。在系统特性能够较好把握的前提下,卡尔曼滤波器的预测准确性很大程度上取决于测量噪声协方差矩阵R的实时取值情况。但由于工作状况的各种不确定性,使得R矩阵的值会持续地受到不确定的干扰,从而极大地影响了卡尔曼滤波器的工作性能。针对上述问题,考虑到变论域自适应模糊逻辑系统的独特优点,提出了一种基于变论域自适应模糊逻辑系统动态实时调整R矩阵的方法。通过对滤波新息序列的实时监测,利用其实际值与理论值之间的偏差,采用变论域自适应模糊逻辑系统动态地对卡尔曼滤波器进行实时调整,通过仿真算例,验证了此种方法的优越性。应用此方法,在提高卡尔曼滤波器的预测精度的同时,也简化了模糊逻辑系统的设计,从而为更加方便、有效地应用卡尔曼滤波器提供了一种新的思路。
In practical applications, it is usually of great importance to predict the states of dynamical systems. Kalman filter has been proven to be an effective tool to solve these prediction problems. With a good understanding of the system characteristics, the prediction accuracy of Kalman Filter is more dependent on the real-time value of the measurement noise covariance matrix. However, because of the uncertainties of working conditions, the values in matrix are disturbed continuously. This case greatly affects the performance of Kalman filter. To solve the problem mentioned above, considering the special advantages of variable universe fuzzy system, a method based on variable universe fuzzy system is proposed to adjust the matrix dynamically in real time. Through monitoring the innovation sequence of Kalman filter, the deviation of the innovation value from the theoretical value is calculated. Based on deviation value, Kalman filter is then adjusted by the variable universe fuzzy system. The benefits of the mentioned method are verified by simulation. It improves the prediction accuracy of Kalman Filter, simplifies the design of fuzzy logic system, and therefore provides a new thinking for applying Kalman filter more conveniently and effectively.
In practical applications, it is usually of great importance to predict the states of dynamical systems. Kalman filter has been proven to be an effective tool to solve these prediction problems. With a good understanding of the system characteristics, the prediction accuracy of Kalman Filter is more dependent on the real-time value of the measurement noise covariance matrix. However, because of the uncertainties of working conditions, the values in matrix are disturbed continuously. This case greatly affects the performance of Kalman filter. To solve the problem mentioned above, considering the special advantages of variable universe fuzzy system, a method based on variable universe fuzzy system is proposed to adjust the matrix dynamically in real time. Through monitoring the innovation sequence of Kalman filter, the deviation of the innovation value from the theoretical value is calculated. Based on deviation value, Kalman filter is then adjusted by the variable universe fuzzy system. The benefits of the mentioned method are verified by simulation. It improves the prediction accuracy of Kalman Filter, simplifies the design of fuzzy logic system, and therefore provides a new thinking for applying Kalman filter more conveniently and effectively.
引文
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[2] Anderson B D O,Moore J B,Eslami M.Optimal filtering[J].IEEE Transactions on Systems Man & Cybernetics,1982,12(2):235～236.
[3] Faragher R.Understanding the basis of the Kalman filter via a simple and intuitive derivation[Lecture Notes][J].IEEE Signal Processing Magazine,2012,29(5):128～132.
[4] Chen S Y.Kalman filter for robot vision:A survey[J].IEEE Transactions on Industrial Electronics,2012,59(11):4409～4420.
[5] Lee S W,et al.Time-varying signal frequency estimation by VFF Kalman filtering[J].Signal Processing,1999,77(3):343～347.
[6] Rezaei S,Sengupta R.Kalman Filter-based integration of DGPS and vehicle sensors for localization[J].IEEE Transactions on Control Systems Technology,2007,15(6):1080～1088.
[7] Jazwinski A H.Adaptive filtering[J].Automatica,1969,5(4):475!485.
[8] Mehra R K.Approaches to adaptive filtering[C]//Adaptive Processes.IEEE,2010:141～141.
[9] Mohamed A H,Schwarz K P.Adaptive Kalman filtering for INS/GPS[J].Journal of Geodesy,1999,73(4):193～203.
[10] Zadeh L A.Fuzzy sets[J].Information & Control,1965,8(3):338～353.
[11] 李洪兴.从模糊控制的数学本质看模糊逻辑的成功——关于“关于模糊逻辑似是而非的争论”的似是而非的介入[J].模糊系统与数学,1995,9(4):1～14.
[12] 李洪兴.Fuzzy控制的本质与一类高精度Fuzzy控制器的设计[J].控制理论与应用,1997,(6):868～872.
[13] 李洪兴,苗志宏,王加银.非线性系统的变论域稳定自适应模糊控制[J].中国科学,2002,32(2):211～223.
[14] 李洪兴等.四级倒立摆的变论域自适应模糊控制[J].中国科学,2002,32(1):65～75.
[15] 李洪兴.模糊控制的插值机理[J].中国科学,1998,28(3):259～267.