<p>In networked control systems (NCSs), random measurement delays and packet dropouts are inevitable consequences of limited communication bandwidth, impacting the reliability of data transmissions. To address this issue, a novel model is proposed in this paper to describe finite random measurement delays and packet dropouts by employing a group of Bernoulli distributed random variables. By utilizing singular value decomposition (SVD), the singular system is transformed into two reduced-order subsystems. Further, the subsystems are reformulated into a stochastic parameterized state space system with correlated noises by augmenting the states with delayed measurements. Based on the new model, the least mean square linear estimators, including filter and predictor, are developed using the innovation analysis approach. These estimators explicitly depend on the probabilities of the stochastic parameters. Consequently, an optimal linear estimator is obtained for a class of singular systems. Furthermore, the stability and steady-state properties of the proposed estimator are also analyzed. Lastly, a simulation example is presented for the performance evaluation of the proposed algorithm.</p>