RNP navigation without GNSS

A computer readable storage medium containing non-transitory instructions that, when executed by a computer, execute a method implemented in an aircraft comprising at least one computer, the aircraft comprising a flight management system for determining a flight plan associated with a trajectory to be followed by an aircraft, the flight management system comprising one or more databases, wherein the method comprises:

• a first step of obtaining, by said at least one computer, distances of the aircraft from at least four radio transmitters each having a fixed position in a geographical reference frame;
• a second step of converting, by said at least one computer, the positions of the radio transmitters into a terrestrial reference system;
• a third step of defining, by said at least one computer, in matrix form, a system of redundant equations linking, in the terrestrial reference system, the position of the aircraft and the positions of the radio transmitters;
• a fourth step of solving, by said at least one computer, said system of equations, in order to obtain an estimated position of the aircraft and a covariance matrix of a position error in the terrestrial reference system;
• a fifth step of converting, by said at least one computer, the estimated position of the aircraft and the covariance matrix of the position error into the geographical reference frame;
• and
• a sixth step of computing, by said at least one computer, based on the covariance matrix of the position error in the geographical reference frame, a radius, said radius corresponding to the radius of a sphere centered around the estimated position of the aircraft and within which the actual position of the aircraft is located with a probability equal to or greater than a predefined threshold,
• wherein the flight management system uses said estimated position and said radius.

A system implemented in an aircraft comprising:

• at least a computer and a flight management system, wherein the system is configured to execute a method implemented in an aircraft for determining a flight plan associated with a trajectory to be followed by an aircraft, the flight management system comprising one or more databases, wherein the method comprises:
• a first step of obtaining, by said at least one computer, distances of the aircraft from at least four radio transmitters each having a fixed position in a geographical reference frame;
• a second step of converting, by said at least one computer, the positions of the radio transmitters into a terrestrial reference system;
• a third step of defining, by said at least one computer, in matrix form, a system of redundant equations linking, in the terrestrial reference system, the position of the aircraft and the positions of the radio transmitters;
• a fourth step of solving, by said at least one computer, said system of equations, in order to obtain an estimated position of the aircraft and a covariance matrix of a position error in the terrestrial reference system;
• a fifth step of converting, by said at least one computer, the estimated position of the aircraft and the covariance matrix of the position error into the geographical reference frame;
• and
• a sixth step of computing, by said at least one computer, based on the covariance matrix of the position error in the geographical reference frame, a radius, said radius corresponding to the radius of a sphere centered around the estimated position of the aircraft and within which the actual position of the aircraft is located with a probability equal to or greater than a predefined threshold,
• wherein the flight management system uses said estimated position and said radius.