Estimating the speed and the heading of an aircraft, independently of a magnetic measurement

A method of estimating speed relative to the ground and heading of an aircraft, wherein the method comprises:

• providing a measurement of a speed vector relative to the ground of the aircraft in a geographical reference frame, by receiving signals from a plurality of satellites, the geographical reference frame including a horizontal plane;
• providing a measurement of an acceleration vector of the aircraft in a fuselage reference frame rigidly associated with the aircraft, together with estimates of attitude angles and a directional estimate of the heading of the aircraft;
• and
• preparing an estimate of an unbounded error affecting the directional estimate of the heading, which preparation is performed in a manner that is linear by combining the measurement of the speed vector relative to the ground with the estimates of the attitude angles, with the directional estimate of the heading, and with the measurement of the acceleration vector.

A device for estimating ground speed and heading of an aircraft, the aircraft having three axes forming a fuselage reference frame rigidly associated with a structure of the aircraft, the device comprising:

• a global navigation satellite system (GNSS) receiver receiving signals from a plurality of satellites and configured to provide a measurement of a speed vector relative to the ground of the aircraft in a geographical reference frame, the geographical reference frame including a horizontal plane;
• an attitude and heading reference system (AHRS) device providing a measurement of an acceleration vector of the aircraft in the fuselage reference frame together with estimates of the attitude angles, and a directional estimate of the heading of the aircraft;
• and
• a first estimator connected to the GNSS receiver and to the AHRS;
• wherein the first estimator is linear and configured to prepare an estimate of an unbounded error affecting the directional estimate of the heading determined by the AHRS device by combining the measurement of the speed vector relative to the ground with the estimates of the attitude angles, with the directional estimate of the heading, and with the measurement of the acceleration vector, independently of any magnetic measurement;
• and
• wherein the device includes a second estimator operating with a model that is linearized by the “small angles” assumption, the first estimator operating during an initial convergence stage and subsequently being replaced by the second estimator for continuing to prepare the estimate of the unbounded error affecting the directional estimate of the heading, and consequently to refine the estimated values and for the horizontal components of the vector of the speed relative to the ground and for a geographical heading of the aircraft.

A method of estimating speed relative to the ground and heading of an aircraft, wherein the method comprises:

• providing a measurement of a speed vector relative to the ground of the aircraft in a geographical reference frame, by receiving signals from a plurality of satellites, the geographical reference frame including a horizontal plane;
• providing a measurement of an acceleration vector of the aircraft in a fuselage reference frame rigidly associated with the aircraft, together with estimates of attitude angles and a directional estimate of the heading of the aircraft;
• and
• preparing an estimate of an unbounded error affecting the directional estimate of the heading, which preparation is performed in a manner that is linear by combining the measurement of the speed vector relative to the ground with the estimates of the attitude angles, with the directional estimate of the heading, and with the measurement of the acceleration vector;
• wherein the preparing the estimate of the unbounded error affecting the directional estimate of the heading comprises the following sub-steps:
• projecting the measurement of the acceleration vector onto a local horizontal reference frame while using the estimates of the attitude angles in order to obtain an estimate of a horizontal component of the acceleration vector, the local horizontal reference frame being formed firstly by a projection of the direction of the fuselage reference frame onto a horizontal plane, and secondly by a direction perpendicular to the projection and situated in the horizontal plane;
• projecting the estimate of the horizontal component of the acceleration vector onto a horizontal pseudo-geographical reference frame in order to obtain a pseudo-geographical estimate of a horizontal component of the acceleration vector, the horizontal pseudo-geographical reference frame being defined from the local horizontal reference frame and from the directional estimate of the heading, the directions of the horizontal pseudo-geographical reference frame each forming an angle equal to the directional estimate of the heading with a respective one of the directions of the local horizontal reference frame;
• linearly transforming the pseudo-geographical estimate of the horizontal component in the pseudo-geographical reference frame of the acceleration vector into an estimate of a horizontal component in the geographical reference frame of the acceleration vector, the estimate being corrected with the estimate of the unbounded error affecting the directional estimate of the heading, by means of the estimated values;
• integrating the estimate of the horizontal component of the acceleration vector in the pseudo-geographical reference frame in order to obtain an estimate of the speed vector relative to the ground in the horizontal geographical reference frame, taking account of the estimate of the unbounded error affecting the directional estimate of the heading;
• comparing the estimate of the speed vector relative to the ground in the horizontal geographical reference frame with the measurement of the speed vector relative to the ground;
• and
• preparing corrections acting on the estimate of the unbounded error and on the estimate of the speed vector relative to the ground;
• and
• wherein, during certain stages, preparing the estimate of the unbounded error affecting the directional estimate of the heading applies a model that is linearized by the “small angles” assumption.