6-Degree of Freedom (6DoF) motion estimation with a combination of visual and inertial sensors is a growing area with numerous real-world applications. However, precise calibration of the time offset between these two sensor types is a prerequisite for accurate and robust tracking. To address this, we propose a universal online temporal calibration strategy for optimization-based visual-inertial navigation systems. Technically, we incorporate the time offset td as a state parameter in the optimization residual model to align the IMU state to the corresponding image timestamp using td, angular velocity and translational velocity. This allows the temporal misalignment td to be optimized alongside other tracking states during the process. As our method only modifies the structure of the residual model, it can be applied to various optimization-based frameworks with different tracking frontends. We evaluate our calibration method with both EuRoC and simulation data and extensive experiments demonstrate that our approach provides more accurate time offset estimation and faster convergence, particularly in the presence of noisy sensor data.