This paper discusses an interval-valued state estimation framework for linear dynamic systems. In particular, we derive an expression of the tightest possible interval estimator in the sense that it is the intersection of all interval-valued estimators for the system of interest. However, from a numerical implementation perspective, this estimator might suffer from a high complexity, at least in the general setting. Therefore, practical implementation might require some over-approximations which would yield a good trade-off between computational complexity and tightness. We discuss a number of such over-approximations. We also consider the general estimation scenario when the system parameters, the initial state, the input signal and the measurement are all uncertain. (C) 2019 Elsevier Ltd. All rights reserved.