Using different sensors in an autonomous vehicle (AV) can provide multiple constraints to optimize AV location estimation. In this paper, we present a low-cost GPS-assisted LiDAR state estimation system for AVs. Firstly, we utilize LiDAR to obtain highly precise 3D geometry data. Next, we use an inertial measurement unit (IMU) to correct point cloud misalignment caused by incorrect place recognition. The estimated LiDAR odometry and IMU measurement are then jointly optimized. We use a lost-cost GPS instead of a real-time kinematic (RTK) module to refine the estimated LiDAR-inertial odometry. Our low-cost GPS and LiDAR complement each other, and can provide highly accurate vehicle location information. Moreover, a low-cost GPS is much cheaper than an RTK module, which reduces the overall AV sensor cost. Our experimental results demonstrate that our proposed GPS-aided LiDAR-inertial odometry system performs very accurately. The accuracy achieved when processing a dataset collected in an industrial zone is approximately 0.14 m.