Optimal estimation for continuous-time systems with delayed measurements

This note focuses on the traditional problem of the Kalman filtering for linear continuous-time systems. Although the problem has been studied widely in the past decades, little work has been done for the time-delayed systems and some fundamental problems remain to be solved. This note proposes a new tool, namely, reorganization innovation analysis approach , to investigate the filtering problem for systems with delayed measurements. The Kalman filter is given in terms of the solution of standard Riccati equations. The performance is clearly demonstrated through analytical results and simulation. The solved problem in this note is related with some more complicated problems such as H_∞ fixed-lag smoothing, H_∞ control with preview and control with input delays.