Connected and Automated Vehicle (CAV) research has gained traction in the last decade due to significant advancements in perception, navigation, communication, and control functions. Accurate and reliable position information is needed to meet the requirements of CAV applications, especially when safety is concerned. With the advent of various perception sensors (e.g. camera, LiDAR, etc.), the vehicular positioning system has improved both in accuracy and robustness. Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I) based cooperative positioning can improve the accuracy of the position estimates, but the integrity risks involved in multi-sensor fusion in a cooperative environment have not yet been fully explored. This paper reviews existing research in the field of positioning Integrity Monitoring (IM) and identifies various research gaps. Particular attention has been placed on identifying research that highlights cooperative IM methods. This analysis helps pave the way for the development of new IM frameworks for cooperative positioning solutions in the future.