In this paper, we propose a novel method of attitude determination for spinning vehicles based on standalone GNSS. A baseband algorithm is first developed to resolves the shadowing effect encountered by 4-antenna receivers mounted on spinning vehicles, enabling continuous and precise signal tracking. Then the particular geometry of the 4-antenna configuration is exploited to yield differential ENU-velocity vectors from co-located antennas. By taking the inner product, the vehicle's pose information is derived the orthonormality of rotation matrices, and yields the roll rate in the body frame. Finally, we use the roll rate to devise linearly independent differential vector pairs and solve for the rotation matrix in the linear system relating ENU velocities and body-frame velocities. The attitude information,defined by Tait-Bryan angles, can thereby be resolved. The algorithm presented is implemented in a 4-antenna real-time GNSS receiver and experiments are carried out with a spinning cylindrical platform. The results are confirmed via evaluation of the PVT results and comparisons with the platform's true attitude.