Abstract: The scale and complexity of modern industrial systems, along with their construction and operational costs, are continuously increasing, making the reliability and safety of equipment operation extremely critical. Owing to the highly interconnected and coupled nature of these systems, faults can spread quickly, disrupting operations, destabilizing equipment, and potentially causing major accidents. Fault detection technology is, therefore, essential to ensure the reliable operation of equipment and modern industrial systems. Industrial systems and equipment are inevitably affected by random disturbances, which can degrade the performance of nominal controllers and potentially lead to control algorithm failures and system instability. To effectively address control and fault detection challenges in complex systems, it is crucial to systematically analyze the impact of unknown disturbances. This paper focuses on the state estimation problem for time-varying stochastic systems subject to unknown disturbances. Previous research in fault diagnosis has primarily addressed steady-state systems, with limited studies on systems affected by random disturbances. Besides, in most of the existing published works, many existing observer design methods are only applicable to specific systems and fault structures, severely limiting their use. Furthermore, these methods often lack both robustness and sensitivity, making it difficult to ensure that residuals remain robust to faults within a specific set while remaining sensitive to the faults outside that set. To tackle these challenges, this paper proposes an adaptive disturbance rejection observer that can decouple state estimation errors from unknown disturbances. A novel, easily implementable full-order observer design method is introduced, offering highly adaptable performance across diverse disturbances and control system structures. This significantly enhances the universality of the proposed method. This paper rigorously proves the necessary and sufficient conditions for achieving minimum variance estimation. It also introduces a fault signal and unknown disturbance equivalent transformation strategy. By carefully selecting an appropriate fault distribution matrix, the proposed method designs observers that are both robust to specific faults and sensitive to others, enabling effective fault detection. Finally, a fault diagnosis algorithm based on the designed observer is investigated and validated through simulations, demonstrating the effectiveness of the proposed approach.