一类广义连续-离散系统量测丢失情况下鲁棒滤波算法

Robust algorithm for a class of sampled-data descriptor systems with missing measurements

有噪声的非线性广义连续-离散系统的状态估计问题是目前一个较新的研究领域。量测丢失可能会导致系统动态模型的状态估计值与动态方程真实值产生较大偏差。为解决该问题,针对一类量测丢失情况下的范数有界非线性广义连续-离散系统,提出一种基于鲁棒扩展卡尔曼滤波(REKF)算法的状态估计方法。首先,给出参数并使用欧拉离散化方法将理想化的广义连续-离散系统转化为非奇异离散系统,但这样的处理方式导致转换得到的非奇异离散系统动态模型中存在新增不确定项。针对该问题,提出最优上界以保证卡尔曼滤波误差协方差矩阵收敛。其次,针对转化得到的非奇异离散系统,提出基于该优化上界的扩展卡尔曼滤波方法,用于在量测丢失时对系统的动态模型量进行观测。最后,仿真算例验证了该方法的有效性。

The state estimation of the nonlinear sampled-data descriptor system with noise is a new study domain. In view that the measurement loss of the system would cause large deviation between the estimation and real value of the dynamic model, a robust extended Kalman filter（REKF） algorithm is proposed for the state estimation of a class of non-linear sampled-data descriptor system. Firstly, the parameters are given and the Euler discretization method is used for transforming the descriptor system into non-singular discrete-time one, but this transforming way leads to new uncertainties in the dynamic model of the transformed non-singular system. For solving this problem, an optimal upper-bound is proposed to make sure the covariance matrix of the Kalman filter be convergence. Then, the upper-bound based REKF algorithm is proposed for the transformed nonsingular discrete systems, which is used to observe the dynamic model of the system with missing measurements. Finally, a simulation example is given, which verifies the effectiveness of the proposed method.