As illustrated in FIG. 1, when the guidance system for an aircraft 10 has to slave the trajectory of the aircraft to a fixed direction 12 which corresponds to an alignment trajectory, the slaving takes place in three phases. In a first phase the pilot positions the aircraft so as to fly according to a trajectory having a known angle predetermined with respect to the direction of alignment. The direction of alignment passes with respect to a determined point 11.
For example, the information relating to the direction of alignment 12 comes from a wireless beacon 11 situated on the ground constituting this determined point, and emitting a radiofrequency signal constituting a directional beam. The useful angular aperture 13 of this beam, which is used during the alignment phase, is typically plus or minus a few degrees, typically +/−2.5° around the direction of alignment 12. The two ends of this angular aperture are designated by the straight lines 121 and 122. The direction of alignment 12 is commonly referred to as the “beam centre”.
These beacons are for example of the runway alignment radio beacon type according to the acronym LOC standing for “Localizer”. These LOC beacons may be for example those of a:                VHF runway alignment radio beacon referred to by the acronym ILS standing for “Instrument Landing System”,        Microwave landing system referred to by the acronym MLS,        Satellite landing system referred to as GLS standing for “GNSS Landing system”,        Landing system with LOC performance and vertical guidance referred to by the acronym LPV standing for “Localizer performance with vertical Guidance”.        
For systems for example of GLS or LPV type, the beacon is a pseudo-beacon which does not have any physical existence. It is a point whose coordinates are stored in a database. The FMS (Flight Managing System), or GPS system, establishes in this case a pseudo-beam on the basis of this datum.
These beacons are for example beacons used for navigation, where the direction of alignment 12 is selected by the pilot with the aid of an onboard control. This navigation system allows the pilot to align himself on radials of an omnidirectional beacon and the beacon is referred to by the acronym VOR standing for “Omni Directional Radio Range”.
The first phase is identified as the capture arming phase. Typically during this phase the pilot positions the aircraft in such a way that its trajectory intercepts the directional beam with a known and predetermined angle commonly referred to as the angle of interception, the angle of interception being defined as the angle formed between the heading of the aircraft and the direction of alignment defined by the directional beam. From the instant t0 at which the aircraft, previously oriented according to the correct angle of interception, cuts the direction 121 or 122, 121 in the example of FIG. 1, at the point 14 in FIG. 1, the alignment process enters its second phase commonly referred to as the capture phase, which corresponds to the alignment phase proper. At the start of the alignment phase the guidance system modifies the trajectory of the aircraft 14 by making it perform a turn.
The instant t0 corresponds for example to the moment from which the detector situated on the aircraft 102, detecting a signal originating from the beacon, exhibits a response proportional to the angular divergence E between the straight line 111 passing through the beacon and the aircraft 102, and the direction of alignment 12. The guidance system controls the positioning of the aircraft so as to cancel this angular divergence E.
When the aircraft is established on a trajectory aligned with the direction 12, starting from the point 15 of FIG. 1, the guidance system enters the third phase commonly referred to as track mode.
The guidance system comprises algorithms which compute the roll angle of the aircraft and are commonly referred to as piloting laws.
Ideally during the alignment phase, the trajectory 16 of the aircraft 102 does not exceed an angle of more than typically 1 to a few degrees with respect to the direction 12 during its turn.
FIG. 2 describes the aircraft's roll command slaving loop during the phase of alignment with the guidance system according to a prior art. These aircraft guidance systems are simply equipped with navigation instruments 22 operating with respect to magnetic North and with respect to the ambient air, for example the systems of attitude and heading platform type according to the acronym AHRS standing for “Attitude and reference system”.
The data accessible in this case to the guidance system are:                the speed vector with respect to the surrounding air Vair/mg referenced by its angle with respect to magnetic North equal to the magnetic heading CM of the aircraft, determined by the navigation instruments 22,        the angular divergence E measured by a receiver 20 situated on the aircraft.        
The guidance system 25 thus computes a roll command 26 on the basis of these data. In this case the algorithms use conventional piloting laws, typically referred to as LOC or VOR (corresponding to the various types of beacons) to slave the trajectory of the aircraft to the beam of the beacon.
In the presence of wind 17 (and particularly when the wind is in a crosswise direction with respect to the direction of alignment), the aircraft equipped with such guidance systems will stray from the optimal trajectory 16, and thus overshoot the typical value by 1 to a few degrees corresponding to about ⅖ of the useful angular aperture 13. This trajectory deviation, referred to as overshoot, leads to a non-optimum trajectory 18 in FIG. 1, posing a problem for the air traffic control. The guidance system 25 is therefore unable to anticipate the deviation of the aircraft due to the wind, which moreover constrains the pilot to aid the guidance system by reducing the angle of interception, thereby lengthening the trajectory of the aircraft before the arming.