In the development of automated driving vehicle, it is important to detect the driving intentions of the remote vehicles, such as if the remote vehicle on left lane intends to keep driving along the same lane (lane keeping) or change to right lane (change to right lane which results in cut in to host lane), or if the lead vehicle intends to follow the vehicle on the adjacent lane and then change to that adjacent lane. In this paper, we have proposed and implemented a remote vehicle driving intention estimation system which specifically detects the driving intentions of remote vehicles in lateral direction. The estimation FOV covers the three lanes (left, ego, right). The main estimated driving intentions include lane keeping, start lane change to left or right side, arriving to left or ego or right lane, etc. To provide the full FOV range objects data, first, we have proposed and implemented an object tracking algorithm, which tracks the objects in the full three lanes to give us the convenience of analyzing the object motion especially when an object is moving from one lane to another lane (the originally provided object data sets only have the object motion information in the specific lane where the object is located). Then, for all objects, the driving intentions, such as lane keeping, lane change to left/right, are derived based on the object deviation and deviation rate data from the ego lane center. Specifically, we have proposed the kinematic models for vehicle lane keeping and lane changing maneuvers, and used the interacting multiple model algorithm to detect if a vehicle is performing a lane keeping or lane change maneuver by calculating probabilities of the vehicle motion is aligned to the lane keeping model and lane changing model. The remote vehicle driving intention detection is implemented in vehicle level with verifications conducted using actual road data which has shown the promising results.