State estimation with delayed measurements considering uncertainty of time delay

State estimation problem with time delayed measurements is addressed. In dynamic system with noise, after taking measurements, it often requires some time until that is available in a filter. A filter not considering this time delay cannot be used since a current measurement is related with a past state. These delayed measurements problem is solved with augmented state Kalman filter, and uncertainty of the delayed time is also resolved based on the probability distribution of the delay. The proposed method is analyzed by a simple example, and its consistency is verified.