Interoperability of GNSS Open Services is a significant trend in the development of all the satellite navigation systems, and its performance will directly affect the users' security and reliability. Therefore, the monitoring and assessment of GNSS Open Services has become a focus of attention for all providers and users of GNSS. In this paper the elements and methods for the monitoring and assessment of GNSS Open Services are investigated first. Then the schemes designed for an international GNSS Monitoring and Assessment System (iGMAS) are proposed. The schemes are based on omni-directional antennas, multi-beam antennas and a high-gain paraboloid antenna to achieve Quadruple-overlap and Single-overlap coverage and sophisticated analysis respectively. Moreover, the scheme for the deployment of world-wide monitoring stations is also proposed. Finally, some related works that have been conducted to monitor and assess Beidou Open Services are introduced, which verifies the feasibility of the proposed system.