The inertial navigation system (INS) error compensation for the case of time-correlated measurement errors is proposed in this study. Measurement differences are derived in the filter for the solution of the state estimation problem. In this case, the measurement noise for the derived measurements is no longer correlated in time, but it is correlated with the process noise. Therefore, in this study, the measurement-differencing-approach-based Kalman filter (KF) is designed for the case of correlated system and measurement noise. The innovation properties of the proposed measurement differencing KF (MDKF) are investigated. Conventional KF (CKF), robust adaptive KF (RAKF), and the proposed MDKF were applied to estimate the states of a multi-input/output aircraft model in the presence of time-correlated INS measurements, and the obtained results were compared. It is shown that MDKF is also robust to the noise-increment-type INS errors.