含时延和丢失数据不确定系统的FIR滤波器

针对状态空间模型中存在服从伯努利分布的时延和随机观测丢失的情况,基于极大似然法则,分别设计有限脉冲响应(finite impulse response, FIR)滤波器的慢速率批处理形式和快速率迭代形式.首先,将时延和数据丢失情况下的模型表述为服从伯努利分布的概率线性函数;然后,通过极大似然处理从而得到所提出极大似然FIR算法;最后,将在相同条件下的极大似然FIR估计、改进型卡尔曼滤波以及无偏FIR估计3种滤波方法进行对比,从估计误差、均方根误差和不确定性影响等角度进行比较分析.实验部分通过3-DOF直升机模型仿真,可发现所提出极大似然FIR估计方法在处理时延和数据丢失问题时更加有效,鲁棒性更高.

FIR filter for uncertain systems with time delay and data loss

In this paper, we design a slow-rate batch form and a fast-rate iterative form of the finite impulse response (FIR) filter based on the law of great likelihood for the state space model with time delay and random observation loss obeying Bernoulli distribution. Firstly, the model in the case of time delay and data loss is formulated as a linear function of probability obeying Bernoulli distribution, and then the proposed FIR algorithm with great likelihood is obtained by the great likelihood process. Finally, the maximum likelihood FIR estimation, the improved Kalman filter and the unbiased FIR estimation under the same conditions are compared and analyzed in terms of estimation error, root mean square error and uncertainty impact. In the experimental part, the 3-DOF helicopter model simulation shows that the proposed maximum likelihood FIR estimation method is more effective and robust in dealing with time delay and data loss problems.