连续时间系统的定常状态估计器

 对于线性定常的连续时间系统,当系统和测量噪声为平稳白噪声过程时,研究了定常的状态估计器的设计方法。为了改进传统的Kalman-Bucy滤波器的瞬态性能,提出了两种新的性能函数的定义,从而给出了两种便于工程应用的修正的Kalman-Bucy滤波器。

A TIME-INVARIANT STATE ESTIMATOR FOR CONTINUOUS TIME SYSTEMS

This paper is intended to present two modified stationary Kalman-Bucy filters with improved transient performance.A linear time-invariant multivariable dynamical system the state of which is to be estimated, is characterized by the equations （1） and （ 2 ）. The linear time-invariant multivariable filter as the same dynamic system is characterized by the equations（ 9 ）and （10）. Firstly, according to unbiasedness, the filter should possess the same number of dimensions and the same structure as the dynamic system, and thus an unbiased filter is formed as shown in equation （22）. Secondly, the optimal filter gain matrix is determined. There are three cases:1.In view of the transient performance, it is a problem of pole assignment and thus a Luenberger's observer is designed.2.In view of the steady-state performance, it is possible to determine the optimal filter gain matrix which minimizes the steady-state filtering error covariance matrix （28）, and thus obtain the stationary Kalman-Bucy filter as shown in Theorem 1 and 2 .3.In view of the compromise between the steady-state and the transient performances, two new performance measures （36） and （46） are defined. The optimal filter gain matrix which minimizes the performance measures （36） or （46） can be determined, and thus two modified stationary Kalman-Bucy filters are obtained as shown in Theorems 3 and 5 or 6 .The method given in this paper is important in design of the state estimator operating in short time.