规范状态空间系统辨识方法

因为状态空间模型既包含了未知状态,又包含了未知参数,且二者是非线性乘积关系,使得辨识问题变得复杂.针对这一问题,详细研究了规范状态空间系统的状态与参数联合估计方法.采用交互估计理论,即采用递推方法或迭代方法实现系统状态与参数的交互估计.基本思路是在计算参数估计时,辨识算法信息向量中的未知状态用其估计值代替,然后利用获得的参数估计,设计基于参数估计的状态观测器或基于参数估计的Kalman滤波算法估计系统的状态,二者形成一个交互计算过程(递阶计算过程).沿着这条思路,分别从递推方案和迭代方案,研究和提出了基于状态观测器和基于Kalman滤波状态估计的随机梯度辨识算法、递推最小二乘辨识算法、多新息随机梯度辨识算法、多新息最小二乘辨识算法,以及模型分解的辨识算法,并给出了几个典型算法的计算步骤、流程图和计算量.

Identification methods for canonical state space systems

Because the state space model contains both the unknown states and the unknown parameters,and they involve the nonlinear product relations,which makes the identification problem more complicated. In order to solve this problem,this paper studies the combined state and parameter estimation methods for canonical state space sys-tems.The interactive estimation theory is used to derive the combined state and parameter estimation algorithms by means of the recursive or iterative scheme.When computing the parameter estimates,the unknown states in the infor-mation vector of the identification algorithms are replaced with their estimates,the obtained parameter estimates are used to design the parameter estimates based observer or the parameter estimates based Kalman filtering algorithm to estimate the states of the systems.They form an interactive estimation process （a hierarchical estimation process）. Along this line,from the recursive scheme or the iterative scheme,this paper presents the observer based or the Kal-man filtering based stochastic gradient （ SG） identification algorithm,recursive least squares （ LS） identification al-gorithm,multi-innovation SG algorithm, multi-innovation LS identification algorithm, and the model decomposition based identification methods. Finally, the computational efficiency, the computational steps and the flowcharts of some typical algorithms are discussed.