This paper investigates interval estimation methods for discrete-time linear time-invariant systems. We propose a novel interval estimation method by integrating robust observer design with reachability analysis. By introducing H∞ design into interval estimation, the proposed method provides a systematic and effective approach to improve the accuracy of interval estimation. Moreover, the relationships and comparisons between the existing results and the proposed method are discussed in detail. Finally, simulation results are presented to demonstrate the effectiveness of the proposed method.