基于线性分式变换的U卡尔曼滤波算法

Unscented Kalman Filter Algorithm Based on Linear Fractional Transformation

针对鲁棒控制中存在的线性反馈连接法并不可以将任何非线性映射都转化为线性映射的问题,本文提出反馈连接变量的选取可以根据实际问题,选取为状态变量分量的非线性组合形式,即非线性变量.同时根据U卡尔曼滤波原理,给出线性分式变换U卡尔曼滤波算法步骤(称其为线性分式变换U卡尔曼滤波算法).并将此方法应用到实际非线性测量光电跟踪系统中,与U卡尔曼算法进行性能对比,仿真实验结果证明,其性能优于U卡尔曼滤波算法.

In robust control, not all nonlinear mappings can be transformed into linear mappings through linear feedback connection. For this problem, a method is proposed that feedback connection variables can be chosen as nonlinear combina- tion of the state variable component in practical problems. Meanwhile, according to unscented Kalman filtering principle, the step of linear fractional transformation unscented Kalman filtering is proposed. In the actual nonlinear optical tracking mea- surement system, this method is compared with unscented Kalman filtering. Simulation results indicate that its performance is better than unscented Kalman filtering.