In this paper, a discrete-time iterative learning Kalman filter scheme is proposed for repetitive processes to reject repeatable disturbances as well as random noises. The proposed state estimator scheme integrates Kalman filter with iterative learning control. The estimation process contains two stages: a conventional Kalman filter is applied in the first stage; the second stage refines the estimates in an iterative learning fashion, leading to a gradual improvement on the estimation performance. According to the estimates that the first stage feeds to the second stage, the optimal design includes two types - posterior type and priori type. In order to reduce the memory and computation load of the optimal design, two suboptimal estimators are provided as well. The stability of the both suboptimal estimators is also studied. Furthermore, a lower bound is given to estimate the ultimate estimation performance before implementing any estimation. Finally, an illustrative example of injection molding is given to verify the performance of the four estimators developed. (C) 2016 Elsevier Ltd. All rights reserved.