非线性系统的改进多模型扩展Kalman滤波器

Improved Multi-model Extended Kalman Filter for Nonlinear systems

针对这样一类非线性系统:状态方程由线性部分和非线性部分构成,测量方程为线性方程,提出了一种基于系统模型拆分的多模型扩展卡尔曼滤波器算法(SMMEKF)。首先,在现有方法的基础上提出了一种改进的多模型扩展卡尔曼滤波方法(IMMEKF)。然后,依据状态方程把原系统拆分为线性子系统与非线性子系统;在时间更新阶段,对线性子系统使用卡尔曼滤波算法进行预测,对非线性子系统使用改进的多模型扩展卡尔曼滤波算法进行预测;在测量更新阶段,采用交替式更新的方法逐步对非线性子系统与线性子系统的预测值进行校正。最后的仿真对比分析了两类方法处理非线性系统滤波问题的性能。

A new multi-model extended Kalman filter algorithm is proposed for a kind of nonlinear systems, in which, the state equation includes a linear part and a nonlinear part, the measurement equation is a linear function. Firstly, the multi-model Kalman filter method is improved and named as IMMEKF. Secondly, the original system is divided into a linear part and a non-linear part. Thirdly, in the process of time update, the Kalman filter algorithm is used to predict the state of the linear part, and the improved multi-model extended Kalman filter algorithm is utilized to predict the state of the nonlinear part. Then, in the measurement update process, a sequential updating method is given to correct the predicted value of the linear part and the non-linear part gradually. The final simulation results illustrate the nonlinear filtering property of the two filtering methods.