基于贝叶斯理论FIR状态估计器的设计与分析

长期以来，状态估计算法的设计主要以全时域下的卡尔曼滤波及贝叶斯理论为基础，极少考虑有限时域下状态估计器的设计与分析。现有成果已经表明，相对于全时域、全信息策略，有限时域、局部信息策略下的有限脉冲响应(Finite impulse response, FIR)估计能够对模型参数不确定性、相关噪声统计误差、外界干扰及参数突变等展现出较强的鲁棒性。然而，由于其发展时间较短，现有FIR估计的理论框架并不完善且缺乏面向工程实际的设计。本项目将贝叶斯理论引入到有限时域估计内，围绕实际过程中常见的复杂动态及相关特定需求开展FIR状态估计研究。首先在FIR结构下考虑贝叶斯估计的实现及估计区间的初始化问题，为后续研究作铺垫。进一步，给出快速FIR估计的构建与分析，设计匹配不同概率分布的FIR滤波器，拓展适用范围。最后，在有限估计区间内尝试模型关键参数和系统状态的一体化估计，为实际应用提供工具。

Most of the existing state estimation algorithms have been constructed based on the Kalman filter and Bayesian theory for a long time, and there are few methods for the design and analysis of state estimators in a finite horizon. The existing results have shown that, compared with the full-information strategy, the finite impulse response (FIR) state estimator operating with partial observations can exhibit better robustness against modeling uncertainties, errors of noise statistics, external disturbances, and abrupt change of parameters. Since it is only developed for a short period, the theoretical framework of FIR estimation is far from perfect and there is a lack of practice-oriented designs. In this project, the Bayesian theory is introduced into the finite-horizon estimation, and studies of FIR state estimation are conducted with the purpose of handling some complex features of the practical process and meeting specific requirements. Accordingly, we first consider the realization of the Bayesian theory under the framework of FIR estimation as well as the corresponding initialization approaches, paving the way for further research. To obtain a more extensive scope of applications, the design of fast FIR estimation is proposed, and the FIR filters under different probability distributions are also derived. Finally, we attempt to make an integrated estimation of critical modeling parameters and system states in a finite-horizon manner, which provides tools for practical applications.