A space-based or aeronautical augmentation system, adapted to improve the precision and the reliability of data delivered by a global navigation satellite system comprising:.- a space-based or aeronautical segment having a first integer number N, greater than or equal to two of space-based or aeronautical broadcasting means (GEO#j), respectively provided with their transmission/reception means adapted to transmit data respectively received from associated ground-based broadcasting stations (NLES#j) to the same predetermined geographical area;.- a ground-based infrastructure segment comprising:.- N ground-based broadcasting stations (122, 124, 126, NLES#j) respectively associated with N space-based or aeronautical broadcasting means (GEO#j) for transmitting navigation data thereto and respectively numbered by a first integer index j varying from 1 to N; and.- at least one ground-based station for observing and receiving signals transmitted by at least one satellite of the global navigation satellite system and by the N space-based or aeronautical broadcasting means (GEO#j);.- a second number K, greater than or equal to 2, of mutually redundant computation centres (132, 134, 136, CPF#i), respectively numbered by a second index i varying from 1 to K, and configured to compute, from the signals transmitted by the one or more ground-based observation and reception station(s), streams or sequences of NOF i.j navigation messages of augmented navigation frames, with i varying from 1 to K and j varying from 1 to N, ready to be respectively transmitted according to the index j to the N ground-based broadcasting stations (NLES#j); at least two of the K computation centres (132, 134, 136, CPF#i) being respectively located on sites that are geographically remote from each other and are connected by a first communications network; the at least one ground-based reception and observation station, the N ground-based broadcasting stations (NLES#j) being connected to the K computation centres (CPF#i) respectively by a second communications network and by a third communications network; the K computation centres (CPF#i) each being configured to establish a sequence of N i-th parallel streams of NOF i.j messages, with j varying from 1 to N, so that the sequence of all the NOF i.j message streams, independently of the computation centre (132, 134, 136, CPF#i) that establishes them, comprises the same time sequence (MTs) of MTs types of messages independent of the space-based or aeronautical broadcasting means (GEO#j), the MTs types of messages of the sequence (MTs) being included in a predetermined set {Tm} of types Tm of navigation message contents; the space-based or aeronautical augmentation system being characterised in that: each computation centre CPF#i is configured so that the contents of the N streams of NOF i.j data that said computation centre CPF#i generates differ only in the content of messages for which the type(s) of contents relate to the predicted or recently measured trajectories of the N space-based or aeronautical broadcasting means..- a space-based or aeronautical segment having a first integer number N, greater than or equal to two of space-based or aeronautical broadcasting means (GEO#j), respectively provided with their transmission/reception means adapted to transmit data respectively received from associated ground-based broadcasting stations (NLES#j) to the same predetermined geographical area;.- a ground-based infrastructure segment comprising:.- N ground-based broadcasting stations (122, 124, 126, NLES#j) respectively associated with N space-based or aeronautical broadcasting means (GEO#j) for transmitting navigation data thereto and respectively numbered by a first integer index j varying from 1 to N; and.- at least one ground-based station for observing and receiving signals transmitted by at least one satellite of the global navigation satellite system and by the N space-based or aeronautical broadcasting means (GEO#j);.- a second number K, greater than or equal to 2, of mutually redundant computation centres (132, 134, 136, CPF#i), respectively numbered by a second index i varying from 1 to K, and configured to compute, from the signals transmitted by the one or more ground-based observation and reception station(s), streams or sequences of NOF i.j navigation messages of augmented navigation frames, with i varying from 1 to K and j varying from 1 to N, ready to be respectively transmitted according to the index j to the N ground-based broadcasting stations (NLES#j);