Hybrid system and apparatus for calculating the position and monitoring the integrity

The system (1) has an extended Kalman filter (KE1) comprising an extended state vector with a part representing a gap between a first elementary hybrid solution (PPVl 1) and a second elementary hybrid solution. An extended calculation module (100) receives an extended variance/covariance matrix (MHYPE1). The module determines a protection radius (RHG1) of the system from the matrix, based on probability of preset false alarm, preset non-integrity level and preset probability of appearance of a non-detected hardware failure of primary and secondary satellite positioning receivers (10, 80).