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The accuracy and integrity of structural deformation monitoring can be improved by the GNSS/accelerometer integrated system, and gross error detection is the key to further improving the reliability of GNSS/accelerometer monitoring. Traditional gross error detection methods assume that real-state information is known, and they need to establish state iterators, which leads to low computational efficiency. Meanwhile, in multi-sensor fusion, if the sampling rates are different, the change in the dimension of the observation matrix must be considered, and the calculation is complex. Based on state-domain consistency theory, this paper proposes the State-domain Robust Autonomous Integrity Monitoring by Extrapolation (SRAIME) method for identifying slow-growing gross errors for GNSS/accelerometer integrated deformation monitoring. Compared with the traditional gross error detection method, the proposed method constructs state test statistics based on the state estimated value and the state predicted value, and it directly performs gross error identification in the state domain. This paper deduces the feasibility of the proposed method theoretically and verifies that the proposed method does not need to consider the dimension change of the observation matrix in gross error detection. Meanwhile, in the excitation deformation experiments of the Suntuan River Bridge in Anhui and the Wilford Bridge in the United Kingdom, the slow gradient of the slope was added to the measurement domain, and the traditional AIME method and the method proposed in this paper were adopted for the gross error identification of the GNSS/accelerometer fusion process. The results demonstrate that both methods can effectively detect gross errors, but the proposed method does not need to consider the dimensional change in the observation matrix during the fusion process, which has better applicability to GNSS/accelerometer integrated deformation monitoring. [ABSTRACT FROM AUTHOR]