In this paper, the state estimation problem for discrete-time Markovjump linear systems affected by time correlated measurement noise is considered where the time-correlated measurement noise is described by a linear system model with white noise. As a result, two algorithms are proposed to estimate the state of the system under consideration based on a measurement sequence. The first algorithm is optimal in the sense of minimum mean-square error, which is obtained based on the measurement differencing method, Bayes' rule and some results derived in this paper. The second algorithm is a suboptimal algorithm obtained by using a lot of Gaussian hypotheses. The proposed suboptimal algorithm is finite dimensionally computable and does not increase computational and storage load with time. Computer simulations are carried out to evaluate the performance of the proposed suboptimal algorithm. (C) 2016 Elsevier Ltd. All rights reserved.