Accelerometer based attitude determination
AssigneeCommissariat A L'energie Atomique Et Aux Energies Alternatives
InventorsMikael Carmona, Laurent Jouanet, Nathalie Sprynski
Life of this patent
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Abstract
Determining an object's inclination fixed reference frame relative to a gravity field includes supplying circularly disposed accelerometers rigidly linked by the object and measuring in non-collinear directions. A radius linking it to the circle's center defines an accelerometer's measurement direction. The accelerometers measure components of the field along the measurement directions to provide measurement values. Then, a matrix equation is solved to obtain the object's inclination relative to the reference frame.
Claims9
1-7. (canceled)
A method comprising determining an inclination of an object in a fixed frame of reference relative to a direction of the Earth's gravity field, wherein determining an inclination comprises supplying a plurality of first accelerometers rigidly linked by said object and distributed over a circle, wherein each of said accelerometers is suitable for measuring an acceleration in at least one measurement direction, wherein respective measurement directions of at least two of said accelerometers are non-collinear, wherein at least one of measurement direction of each of said accelerometers is defined by a radius linking said accelerometer to a center of said circle, measuring, by said accelerometers, of components of the Earth's gravity field along said measurement directions, said measurement providing, for each of said directions, a measurement value, mj for a measurement direction of index i, resolving the following matrix equation to determine an inclination Φ of said object relative to a frame of reference:
- M
- =
- A
-
- [
- cos
-
- (
- φ
- )
- -
- sin
-
- (
- φ
- )
-
- sin
-
- (
- η
- )
- -
- sin
-
- (
- φ
- )
-
- cos
-
- (
- η
- )
- ]
- wherein M is vector whose ith component is defined by the measurement mj, wherein A is a matrix defined by measurement directions of said accelerometers in a frame of reference attached to said object, wherein η is an angle of rotation of said attached frame of reference relative to said fixed frame of reference, wherein said accelerometers exhibit a Gaussian and centered measurement statistical noise, wherein resolving comprises minimizing a criterion L(Φ, η) defined by the following equation:
- L(Φ,η)=(sin(φ)f(η)−M)T×Γ−1×(sin(φ)f(η)−M)
- wherein f(η) is a vector whose ith component is equal to −sin(αi+η), wherein αi is a positioning angle, about an axis normal to said circle and passing through said center, of an accelerometer of index i relative to an other of said accelerometers taken as a reference, and wherein Γ is a covariance matrix corresponding to measurement statistical noises of said accelerometers for said measurement directions.
An apparatus comprising an instrumented object, said instrumented object comprising a device for automatically determining inclination of said object in a fixed frame of reference relative to the direction of the Earth's gravity field, wherein said device comprises a plurality of accelerometers and a programmed computation device, wherein said accelerometers are linked rigidly by said object, wherein said accelerometers are distributed over a circle, wherein each of said accelerometers is suitable for measuring a component of the Earth's gravity field in at least one measurement direction to supply a measurement value denoted mj for a measurement direction of index i, the respective measurement directions of at least two of said accelerometers being non-collinear, at least one of the measurement directions of each of said accelerometers being defined by the radius linking said accelerometer to the center of said circle, wherein said programmed computation device is programmed and configured for determining an inclination Φ of said object relative to said frame of reference by resolution of the following matrix equation:
- M
- =
- A
-
- [
- cos
-
- (
- φ
- )
- -
- sin
-
- (
- φ
- )
-
- sin
-
- (
- η
- )
- -
- sin
-
- (
- φ
- )
-
- cos
-
- (
- η
- )
- ]
- wherein M is a vector whose ith component is defined by measurement mj, wherein A is a matrix defined by measurement directions of said accelerometers in a frame of reference attached to said object, wherein η is an angle of rotation of said attached frame of reference relative to said fixed frame of reference, wherein said accelerometers exhibit a Gaussian and centered measurement statistical noise, wherein said computation device is programmed to resolve said matrix equation by minimization of a criterion L(Φ, η) defined by the following equation:
- L(Φ,η)=(sin(φ)f(η)−M)T×Γ−1×(sin(φ)f(η)−M)
- wherein f(η) is a vector whose ith component is equal to −sin(αi+η), wherein αi is a positioning angle about an axis normal to said circle and passing through said center of an accelerometer of index i relative to one of said accelerometers taken as a reference, and wherein Γ is a covariance matrix corresponding to measurement statistical noises of said accelerometers for said measurement directions.
Dependencies are inferred from the claim text.