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In this paper, we present a tightly coupled optimization-based GPS-Visual-Inertial odometry system to solve the trajectory drift of the visual-inertial odometry especially over long-term runs. Visual reprojection residuals, IMU residuals, and GPS measurement residuals are jointly minimized within a local bundle adjustment, in which we apply GPS measurements and IMU preintegration used for the IMU residuals to formulate a novel GPS residual. To improve the efficiency and robustness of the system, we propose a fast reference frames initialization method and an online calibration method for GPS-IMU extrinsic and time offset. In addition, we further test the performance and convergence of our online calibration method. Experimental results on EuRoC datasets show that our method consistently outperforms other tightly coupled and loosely coupled approaches. Meanwhile, this system has been validated on KAIST datasets, which proves that our system can work well in the case of visual or GPS failure.