线性系统初值最小二乘估计的收敛性问题

The Convergence Problem of the Least Squares Estimation of the Initial State of Linear Systems

本文是文献[1]的发展,讨论带随机量测噪声线性离散时间系统的初始状态最小二乘估计的均方收敛性与几乎处处收敛性,给出估计误差约方收敛于零或几乎处处收敛于零的充要条件,并给出收敛速率估计。

This paper deals with the least squares estimation of the initial state of linear systems with zero input and measurement noise, and provides some sufficient and necessary conditions in order to guar-antee the least squares estimation error converging to zero (almost surely or in the mean square sense). The convergence rates are also obtained. And an example is given to show that the convergence rate in the mean square sense can not be improved any more.