Accurate calibration of the installation angles of vehicle-borne inertial navigation systems (INS) is essential for ensuring the precision and robustness of GNSS/INS integrated navigation systems. To address the problem of unknown installation angles, this study proposes an online automatic calibration method for arbitrary installation angles in vehicle-borne GNSS/INS systems. The method adaptively executes static and dynamic alignment based on the detection of stationary, moving, and high-speed straight-driving vehicle states, completing the calibration in three stages. During the stationary phase, a coarse static alignment is performed to compute the horizontal installation angles and estimate the accelerometer and gyroscope biases through static filtering. After the horizontal alignment, dynamic alignment is conducted when vehicle motion is detected, calculating the heading angle and separating it through dynamic filtering. Finally, during high-speed straight driving, the precise online calibration of installation angles is achieved using the relationship between the velocity and body coordinate frames. To verify the effectiveness and generality of the proposed method, two sets of vehicle experiments were conducted using tactical-grade and MEMS-grade IMUs, and the installation angle estimation accuracy was compared with the conventional engineering reference method. Experimental results show that the proposed method achieves rapid convergence under different IMU accuracy conditions, with mean installation angle errors of 0.389° and 0.287°, significantly outperforming the reference methods. Moreover, the method is applicable to devices such as vehicle-mounted smartphones, enabling recalibration when the IMU position changes, thereby enhancing system adaptability and robustness. This approach provides critical technical support for high-precision autonomous positioning in intelligent vehicles.