Vehicle positioning plays an important role in the design of protocols, algorithms, and applications in the intelligent transport systems. In this paper, we present a new framework of spatiotemporal local-remote sensor fusion (ST-LRSF) that cooperatively improves the accuracy of absolute vehicle positioning based on two state estimates of a vehicle in the vicinity: a local sensing estimate, measured by the on-board exteroceptive sensors, and a remote sensing estimate, received from neighbor vehicles via vehicle-to-everything communications. Given both estimates of vehicle state, the ST-LRSF scheme identifies the set of vehicles in the vicinity, determines the reference vehicle state, proposes a spatiotemporal dissimilarity metric between two reference vehicle states, and presents a greedy algorithm to compute a minimal weighted matching (MWM) between them. Given the outcome of MWM, the theoretical position uncertainty of the proposed refinement algorithm is proven to be inversely proportional to the square root of matching size. To further reduce the positioning uncertainty, we also develop an extended Kalman filter model with the refined position of ST-LRSF as one of the measurement inputs. The numerical results demonstrate that the proposed ST-LRSF framework can achieve high positioning accuracy for many different scenarios of cooperative vehicle positioning.