大范围不确定随机线性系统自适应滤波估计及其若干应用

项目名称： 大范围不确定随机线性系统自适应滤波估计及其若干应用

项目编号： No.61473038

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 马宏宾

作者单位： 北京理工大学

项目金额： 84万元

中文摘要： 滤波估计是一种通用性技术，广泛应用于信号降噪、惯性导航等诸多领域，其典型代表为卡尔曼滤波。滤波估计技术的一个核心困难是系统具有大范围参数不确定性或结构不确定性或先验信息缺乏时如何设计滤波器有效利用可获得的数据保证算法具有稳定性，兼顾精度与实时性。针对随机线性系统，标准卡尔曼滤波算法要求系统模型和噪声统计特性精确已知，但由于建模、测量及量化过程中普遍存在的误差或未建模动态，这一假设在工程实践中常难以满足。已有的自适应卡尔曼滤波、自校正滤波算法可在线估计未知的噪声方差，但由于状态估计和参数辨识相互耦合，其稳定性分析十分困难，理论上尚未完全解决。本项目拟针对这一背景，基于前期对自适应控制以及有限模型滤波算法等方面的研究，对随机线性系统模型中存在大范围参数不确定性或结构不确定性时的滤波估计问题，提出新的滤波估计算法，引入新的数学工具进行理论分析，并将算法在惯导系统、多机械臂系统中加以验证与应用。

中文关键词： 随机系统；不确定性；状态估计；卡尔曼滤波器；自适应控制

英文摘要： Filtering is a basic and general technology, which is widely used in various areas such as signal de-noising applications and inertial navigation systems, and Kalman filter algorithm is a standard filtering method for linear systems. At present one subtle difficulty for filtering technology is how to design a suitable filtering algorithm which can effectively utilize the measurement signal and guarantee the filtering stability and real-time performance at the presence of large parametric or structural uncertainties. For a stochastic linear system state space model, successful application of standard Kalman filter requires that the system parameters and the noise statistical nature must be obtained a priori precisely. However, such requirements are seldom completely satisfied in practice due to the commonly existence of modeling errors, measurement errors, quantitative errors or unmodeled dynamics. The unknown noise covariance matrix could be estimated in real-time by the adaptive Kalman filter (AKF) or self-tuning Kalman filtering algorithm, however for these algorithms, the parameter estimation is coupled with the state estimating process, which makes the close-loop stability analysis of the filtering algorithm very difficult and the mathematical stability analysis has not yet been fully resolved up to now. Considering such background, motivated by our previous research on the adaptive control and finite-model filtering algorithms, a series of new filtering algorithms will be proposed and investigated so as to deal with the problem of state estimation when there exist large uncertainties of system parameters or system structure. And new mathematical analysis techniques will be used to present the stability analysis results for the new algorithms and the new algorithms will be verified in the inertial navigation systems and mechanical manipulator systems.

英文关键词： Stochastic Systems;Uncertainties;State Estimation;Kalman Filter;Adaptive Control