Originated from challenging industrial applications, this paper addresses a soft sensor development problem for linear systems with two types of measurements. One is fast, regular and delay-free measurements. The other is infrequent, irregular measurements with time-varying delays. The approach to be taken is based on the Kalman filter and data fusion technique, avoiding running the full augmented state Kalman filter, and leading to a considerably lower implementation cost. Although it is suboptimal, the loss in performance is minor compared to the optimal filter. Two simulation examples demonstrate the advantages of the proposed approach. An industrial soft sensor application example is also used to demonstrate its practicality. (C) 2014 Elsevier Ltd. All rights reserved.