Methods, apparatuses, and computer programs for estimating the heading of an axis of a rigid body

Method for estimating, or at least for generating information usable to estimate, the heading of at least one axis of interest of a rigid body, wherein the rigid body is equipped with an antenna of a navigation satellite system receiver, hereinafter abbreviated as “NSS receiver”, wherein the antenna's phase center is located at a point, hereinafter referred to as “point B”, which is away from another point, hereinafter referred to as “point A”, wherein point A is either a point of the rigid body or a point being at a fixed position with respect to the rigid body, and wherein the rigid body is further equipped with sensor equipment comprising at least one of:

• a gyroscope,
• an angle sensor measuring the rotation of the rigid body about an Earth-fixed axis, and
• two accelerometers,
• the method comprising:
• subjecting the rigid body to an uninterrupted motion causing point B's horizontal position to change while keeping point A's position fixed relative to the Earth;
• and
• observing, by the NSS receiver, a NSS signal from each of a plurality of NSS satellites during said motion;
• wherein the method further comprises the following operations, carried out by at least one of:
• the NSS receiver, the sensor equipment, and a processing entity capable of receiving data from the NSS receiver and sensor equipment:
• estimating the orientation, at two different points in time, of a body frame of the rigid body with respect to a reference frame based on data from the sensor equipment, wherein the rigid body is subject to the motion at least during a period of time between the two points in time and the rigid body is subject to no other motion between the two points in time;
• computing at least two coordinates of a delta-position vector, in the reference frame, of point B, based on the estimated orientation and on data from the sensor equipment, said delta-position vector being hereinafter referred to as “sensor-based delta-position vector”, and the at least two coordinates being two coordinates containing information about the motion of point B in two independent directions in the local horizontal plane;
• and
• based on the at least two coordinates of the sensor-based delta-position vector and on the NSS signals observed during said motion, and using a computation method which does not, as such, necessitate the use of NSS signals observed during any other motion, at least one of:
• generating information usable to estimate the heading of the at least one axis of interest;
• and
• estimating the heading of the at least one axis of interest.

Method for estimating, or at least for generating information usable to estimate, the heading of at least one axis of interest of a rigid body, wherein the rigid body is equipped with an antenna of a navigation satellite system receiver, hereinafter abbreviated as “NSS receiver”, wherein the antenna's phase center is located at a point, hereinafter referred to as “point B”, which is away from another point, hereinafter referred to as “point A”, wherein point A is either a point of the rigid body or a point being at a fixed position with respect to the rigid body, and wherein the rigid body is further equipped with sensor equipment comprising at least one of:

• a gyroscope,
• an angle sensor measuring the rotation of the rigid body about an Earth-fixed axis, and
• two accelerometers,
• the method comprising:
• subjecting the rigid body to an uninterrupted motion causing point B's horizontal position to change while keeping point A's position fixed relative to the Earth;
• and
• observing, by the NSS receiver, a NSS signal from each of a plurality of NSS satellites at least at a first point in time and at a second point in time, wherein the rigid body is subject to the motion at least during part of the period of time between the first and second points in time and the rigid body is subject to no other motion between the first and second points in time;
• wherein the method further comprises the following operations, carried out by at least one of:
• the NSS receiver, the sensor equipment, and a processing entity capable of receiving data from the NSS receiver and sensor equipment:
• computing an estimate of the horizontal position, or of a position usable to derive the horizontal position, of a point, hereinafter referred to as “point C”, at the first point in time, said estimate being hereinafter referred to as “initial position estimate”, based on the NSS signals observed at least at the first point in time, wherein point C is any one of:
• point A;
• point B;
• and
• another point being either a point of the rigid body or a point being at a fixed position with respect to the rigid body;
• and
• based on the initial position estimate, data from the sensor equipment, and the observed NSS signals, and using a computation method which does not, as such, necessitate the use of NSS signals observed before the first point in time, between the first and second points in time, or after the second point in time, at least one of:
• generating information usable to estimate the heading of the at least one axis of interest;
• and
• estimating the heading of the at least one axis of interest.

Apparatus for estimating, or at least for generating information usable to estimate, the heading of at least one axis of interest of a rigid body, wherein the rigid body is equipped with an antenna of a navigation satellite system receiver, hereinafter abbreviated as “NSS receiver”, wherein the antenna's phase center is located at a point, hereinafter referred to as “point B”, which is away from another point, hereinafter referred to as “point A”, wherein point A is either a point of the rigid body or a point being at a fixed position with respect to the rigid body, and wherein the rigid body is further equipped with sensor equipment comprising at least one of:

• a gyroscope, and
• an angle sensor arranged for measuring the rotation of the rigid body about an Earth-fixed axis;
• wherein the rigid body is arranged to be subject to a motion causing point B's horizontal position to change while keeping point A's position fixed relative to the Earth;
• and
• wherein the NSS receiver is arranged to observe a NSS signal from each of a plurality of NSS satellites during said motion;
• wherein the apparatus comprises hardware and/or software logic configured for:
• estimating the orientation, during said motion, of a body frame of the rigid body with respect to a reference frame based on data from the sensor equipment;
• computing at least two coordinates of a velocity vector, in the reference frame, of point B, based on the estimated orientation and on data from the sensor equipment, said velocity vector being hereinafter referred to as “sensor-based velocity vector”, and the at least two coordinates being two coordinates containing information about the motion of point B in two independent directions in the local horizontal plane;
• and
• based on the at least two coordinates of the sensor-based velocity vector and on the NSS signals observed during said motion, at least one of:
• generating information usable to estimate the heading of the at least one axis of interest;
• and
• estimating the heading of the at least one axis of interest.

Apparatus for estimating, or at least for generating information usable to estimate, the heading of at least one axis of interest of a rigid body, wherein the rigid body is equipped with an antenna of a navigation satellite system receiver, hereinafter abbreviated as “NSS receiver”, wherein the antenna's phase center is located at a point, hereinafter referred to as “point B”, which is away from another point, hereinafter referred to as “point A”, wherein point A is either a point of the rigid body or a point being at a fixed position with respect to the rigid body, and wherein the rigid body is further equipped with sensor equipment comprising at least one of:

• a gyroscope,
• an angle sensor arranged for measuring the rotation of the rigid body about an Earth-fixed axis, and
• two accelerometers;
• wherein the rigid body is arranged to be subject to an uninterrupted motion causing point B's horizontal position to change while keeping point A's position fixed relative to the Earth;
• and
• wherein the NSS receiver is arranged to observe a NSS signal from each of a plurality of NSS satellites during said motion;
• wherein the apparatus comprises hardware and/or software logic configured for:
• estimating the orientation, at two different points in time, of a body frame of the rigid body with respect to a reference frame based on data from the sensor equipment, wherein the rigid body is subject to the motion at least during a period of time between the two points in time and the rigid body is subject to no other motion between the two points in time;
• computing at least two coordinates of a delta-position vector, in the reference frame, of point B, based on the estimated orientation and on data from the sensor equipment, said delta-position vector being hereinafter referred to as “sensor-based delta-position vector”, and the at least two coordinates being two coordinates containing information about the motion of point B in two independent directions in the local horizontal plane;
• and
• based on the at least two coordinates of the sensor-based delta-position vector and on the NSS signals observed during said motion, and using a computation method which does not, as such, necessitate the use of NSS signals observed during any other motion, at least one of:
• generating information usable to estimate the heading of the at least one axis of interest;
• and
• estimating the heading of the at least one axis of interest.

Apparatus for estimating, or at least for generating information usable to estimate, the heading of at least one axis of interest of a rigid body, wherein the rigid body is equipped with an antenna of a navigation satellite system receiver, hereinafter abbreviated as “NSS receiver”, wherein the antenna's phase center is located at a point, hereinafter referred to as “point B”, which is away from another point, hereinafter referred to as “point A”, wherein point A is either a point of the rigid body or a point being at a fixed position with respect to the rigid body, and wherein the rigid body is further equipped with sensor equipment comprising at least one of:

• a gyroscope,
• an angle sensor arranged for measuring the rotation of the rigid body about an Earth-fixed axis, and
• two accelerometers;
• wherein the rigid body is arranged to be subject to an uninterrupted motion causing point B's horizontal position to change while keeping point A's position fixed relative to the Earth;
• and
• wherein the NSS receiver is arranged to observe a NSS signal from each of a plurality of NSS satellites at least at a first point in time and at a second point in time, wherein the rigid body is subject to the motion at least during part of the period of time between the first and second points in time and the rigid body is subject to no other motion between the first and second points in time;
• wherein the apparatus comprises hardware and/or software logic configured for:
• computing an estimate of the horizontal position, or of a position usable to derive the horizontal position, of a point, hereinafter referred to as “point C”, at the first point in time, said estimate being hereinafter referred to as “initial position estimate”, based on the NSS signals observed at least at the first point in time, wherein point C is any one of:
• point A;
• point B;
• and
• another point being either a point of the rigid body or a point being at a fixed position with respect to the rigid body;
• and
• based on the initial position estimate, data from the sensor equipment, and the observed NSS signals, and using a computation method which does not, as such, necessitate the use of NSS signals observed before the first point in time, between the first and second points in time, or after the second point in time, at least one of:
• generating information usable to estimate the heading of the at least one axis of interest;
• and
• estimating the heading of the at least one axis of interest.