The primary means for electronic position fixing currently in use in majority of contemporary merchant ships are shipborne GPS (Global Positioning System) receivers or DGPS (Differential GPS) and IALA (International Association of Lighthouse Authorities) radio beacon receivers. More advanced GNSS (Global Navigation Satellite System) receivers able to process signals from GPS, Russian GLONASS, Chinese Beidou, European Galileo, Indian IRNSS, Japan QZSS, and satellite-based augmentation systems (SBAS), are still relatively rare in maritime domain. However, it is expected that such combined or multi-system receivers will soon become more common in maritime transport and integrated with gyro, inertial, radar, laser, and optical sensors, and they will become indispensable onboard maritime autonomous surface ships (MASS). To be prepared for a malfunction of any position sensors, their state-of-the-art integrity monitoring should be developed and standardized, taking into account the specificity of MASS and e-navigation safety. The issues of existing requirements, performance standards, and future concepts of integrity monitoring for maritime position sensors are discussed and presented in this paper.