有限脉冲响应结构下离散随机动态过程的状态估计

状态估计在控制理论发展及工程实践中一直独具魅力，成果丰富，但现有大多数方法均是在Kalman滤波的全局递推结构上所构建的。由于任意时刻系统的观测会在递推结构中向后传播，作用于后续所有的估计值，算法对外界冲击的响应为无限时长，鲁棒性差。有限脉冲响应估计除了能够很好地克服上述缺陷外，还具有抗干扰、对初始误差不敏感、有界输入输出稳定等优点，应用背景极强。然而，将有效脉冲响应结构视为一种状态估计策略现仍处于研究初期，处理实际问题的能力有限。本项目以离散随机动态过程为对象，在有限脉冲响应结构下进行状态估计研究。考虑最小均方意义下无偏有限脉冲响应滤波的迭代形式，减少计算负荷；给出极大似然在有限观测数据下的实现，构建与现有估计算法的桥梁。进一步，求解风险敏感指标与最大估计误差的最小化问题，得到鲁棒有限脉冲响应估计的设计方法。最后对阶段性的成果进行推广，寻求其在离散非线性状态空间下的实现。

State estimation has drawn much attention in control theory and applications, and many useful results have been achieved up to now. However, most of the existing methods are proposed based on the Kalman filter, which estimates the states based on all the past measurements in a recursive manner. Since arbitrary observation will be propagated through recursions and further affects all the subsequent estimates, the resulting algorithm has infinite impulse response and exhibits week robustness. The finite impulse response (FIR) structure can not only overcome this drawback satisfactorily, but also has the advantages such as anti-interference, insensitiveness of initial errors, and the bounded input/bounded output stability, owning a strong application background. Despite these good features, the current research that considers the FIR structure as a state estimation strategy is still in its infancy, which limits the ability of solving practical problems. Therefore, this proposal aims to develop a new filed of FIR filter for discrete stochastic dynamic process. To reduce computational load, the optimal unbiased FIR filter in the minimum mean square error sense is realized iteratively. Then, the maximum likelihood estimate is obtained based on finite measurements, providing a connection between the FIR filters and the existing estimation algorithms. Moreover, robust FIR estimators are developed by minimizing the risk-sensitive cost function and the maximum estimation errors. To have a wider range of application, finally, the results obtained previously are extended to the discrete nonlinear state-space models.