CA2847951A1 - A method and system of determining an inertial sensor orientation offset - Google Patents
A method and system of determining an inertial sensor orientation offset Download PDFInfo
- Publication number
- CA2847951A1 CA2847951A1 CA2847951A CA2847951A CA2847951A1 CA 2847951 A1 CA2847951 A1 CA 2847951A1 CA 2847951 A CA2847951 A CA 2847951A CA 2847951 A CA2847951 A CA 2847951A CA 2847951 A1 CA2847951 A1 CA 2847951A1
- Authority
- CA
- Canada
- Prior art keywords
- chassis
- inertial sensor
- imu
- sensor measurement
- determining
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Abandoned
Links
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
- G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
- G01P21/00—Testing or calibrating of apparatus or devices covered by the preceding groups
Abstract
Inertial sensors are typically mounted at an angular offset relative to a chassis, such as a vehicle chassis or electronic device chassis. This offset can influence the measurements of the angular orientation of said chassis derived from inertial sensors. There is provided a method of determining a sensor orientation offset relative to a chassis by obtaining a first inertial sensor measurement, rotating the chassis approximately 180°, obtaining a second inertial sensor measurement; and then determining the offset from the two inertial sensor measurements.
Description
A METHOD AND SYSTEM OF DETERMINING AN INERTIAL SENSOR ORIENTATION
OFFSET
FIELD OF THE INVENTION
The invention relates to a method and system of determining a sensor angular offset. More particularly the invention relates, but is not limited, to determining the orientation of an inertial sensor relative to a chassis, preferably the chassis of a vehicle.
BACKGROUND TO THE INVENTION
Reference to background art herein is not to be construed as an admission that such art constitutes common general knowledge in Australia or elsewhere.
Inertial sensors are used in many applications to measure movement of objects. For example, vehicles, such aeroplanes and automated vehicles, and many electronic devices, such as smart phones, have inertial sensors to determine orientation, movement, and/or other relevant variables.
Inertial sensors typically include gyroscopes, which measure the rate of change of angle with time, and accelerometers, which measure linear acceleration. Often such sensors are collectively packaged into an inertial measurement unit (IMU). A typical IMU will contain at least a three-axis accelerometer, and often includes one or more gyroscopes. IMUs sometimes also contain a 2 or 3 axis magnetometer for sensing the Earth's magnetic field (although not actually an inertial sensor).
OFFSET
FIELD OF THE INVENTION
The invention relates to a method and system of determining a sensor angular offset. More particularly the invention relates, but is not limited, to determining the orientation of an inertial sensor relative to a chassis, preferably the chassis of a vehicle.
BACKGROUND TO THE INVENTION
Reference to background art herein is not to be construed as an admission that such art constitutes common general knowledge in Australia or elsewhere.
Inertial sensors are used in many applications to measure movement of objects. For example, vehicles, such aeroplanes and automated vehicles, and many electronic devices, such as smart phones, have inertial sensors to determine orientation, movement, and/or other relevant variables.
Inertial sensors typically include gyroscopes, which measure the rate of change of angle with time, and accelerometers, which measure linear acceleration. Often such sensors are collectively packaged into an inertial measurement unit (IMU). A typical IMU will contain at least a three-axis accelerometer, and often includes one or more gyroscopes. IMUs sometimes also contain a 2 or 3 axis magnetometer for sensing the Earth's magnetic field (although not actually an inertial sensor).
Inertial sensing is often used to determine an 'attitude' of an object or a vehicle (i.e. the rotation of object or vehicle with respect to a reference frame, usually a theoretical perfectly level ground surface). In many applications, accurate inertial sensing is critical. For example, in precision agriculture, knowledge of 'attitude' of a vehicle is required to compensate for movements of a Global Navigation Satellite Systems (GNSS) antenna through terrain level changes and undulation.
In machine control applications, such as autonomous vehicles, sensor precision is often high enough that an offset induced by the tilting of a GNSS
antenna mounted on a vehicle can produce a measurable positioning error (e.g. of at least the same order of magnitude as the GNSS system itself). As a result, tilt angle is sometimes compensated with the use of angular estimates derived from sensor measurements produced by an IMU mounted in the vehicle.
The inertial sensors within the IMU are normally mounted in an orthogonal configuration and produce measurements in the sensor frame (i.e.
a coordinate system fixed to the senSor axes), whereas the location of the antenna relative to the vehicle is generally known in the vehicle frame (i.e.
a coordinate system attached to a fixed point on the vehicle). Therefore, unless the sensor frame is precisely aligned with the vehicle frame, there is a fixed angular offset between the sensor frame and the vehicle frame.
.
Typically, an estimate of the attitude of the vehicle is desired and hence the angular offset between the vehicle frame and the sensor frame is required. In applications where the IMU is installed by the manufacturer, the 3=
angular offset between the sensor frame and the vehicle frame can be determined from the design drawings. However, in applications where the IMU is retrofitted after the manufacture of the vehicle (for example, from a third-party supplier of guidance equipment), the IMU must be installed either with the sensor axes precisely aligned with the vehicle, or the angular offset must be measured as part of the installation procedure.
Aligning the sensor axes with the vehicle axes introduces significant limitations on where the device can be mounted within the vehicle. For example, it can be mounted to a flat floor or wall. However, such an aligned position may not be suitable or convenient to mount the device. Furthermore, if the device is not mounted exactly orthogonal to the vehicle then an error in = the measurements may be introduced.
If the device is mounted on a surface that is not aligned with the =vehicle axes, the angular offset may be physically measured. However, this requires high-precision measurements using specialist equipment, such as a theodolite, which is not only time consuming, but impractical for many installations, particularly where an end-user installs the equipment.
OBJECT OF THE INVENTION
It is an aim of this invention to provide a method and= system of determining a sensor offset which overcomes or ameliorates one or more of the disadvantages or problems described above, or which at least provides a useful alternative.
In machine control applications, such as autonomous vehicles, sensor precision is often high enough that an offset induced by the tilting of a GNSS
antenna mounted on a vehicle can produce a measurable positioning error (e.g. of at least the same order of magnitude as the GNSS system itself). As a result, tilt angle is sometimes compensated with the use of angular estimates derived from sensor measurements produced by an IMU mounted in the vehicle.
The inertial sensors within the IMU are normally mounted in an orthogonal configuration and produce measurements in the sensor frame (i.e.
a coordinate system fixed to the senSor axes), whereas the location of the antenna relative to the vehicle is generally known in the vehicle frame (i.e.
a coordinate system attached to a fixed point on the vehicle). Therefore, unless the sensor frame is precisely aligned with the vehicle frame, there is a fixed angular offset between the sensor frame and the vehicle frame.
.
Typically, an estimate of the attitude of the vehicle is desired and hence the angular offset between the vehicle frame and the sensor frame is required. In applications where the IMU is installed by the manufacturer, the 3=
angular offset between the sensor frame and the vehicle frame can be determined from the design drawings. However, in applications where the IMU is retrofitted after the manufacture of the vehicle (for example, from a third-party supplier of guidance equipment), the IMU must be installed either with the sensor axes precisely aligned with the vehicle, or the angular offset must be measured as part of the installation procedure.
Aligning the sensor axes with the vehicle axes introduces significant limitations on where the device can be mounted within the vehicle. For example, it can be mounted to a flat floor or wall. However, such an aligned position may not be suitable or convenient to mount the device. Furthermore, if the device is not mounted exactly orthogonal to the vehicle then an error in = the measurements may be introduced.
If the device is mounted on a surface that is not aligned with the =vehicle axes, the angular offset may be physically measured. However, this requires high-precision measurements using specialist equipment, such as a theodolite, which is not only time consuming, but impractical for many installations, particularly where an end-user installs the equipment.
OBJECT OF THE INVENTION
It is an aim of this invention to provide a method and= system of determining a sensor offset which overcomes or ameliorates one or more of the disadvantages or problems described above, or which at least provides a useful alternative.
Other preferred objects of the present invention will become apparent from the following description.
SUMMARY OF INVENTION
According to an aspect of the invention there is provided a method of determining a sensor orientation offset relative to a chassis, the method including:
obtaining a first inertial sensor measurement;
rotating the chassis approximately 180 ;
obtaining a second inertial sensor measurement; and determining the sensor orientation offset relative to the chassis using the first inertial sensor measurement and the second inertial sensor measurement.
Preferably the first inertial sensor measurement and the second inertial sensor measurement are conducted by an inertial measurement unit (IMU).
Preferably the IMU includes at least a three-axis accelerometer. Preferably the first inertial sensor measurement and the second inertial sensor measurement consist of a measurement of gravity only.
Preferably the step of determining the sensor orientation offset relative to the chassis includes estimating a rotation between the first =and second inertial sensor measurements. The rotation estimate is preferably a rotation matrix.
= Preferably the step of determining the sensor orientation offset relative to the chassis includes determining possible solutions for rotation of the sensor relative to the chassis and/or eliminating impossible and implausible solutions. Alternatively the step of determining the sensor orientation offset relative to the chassis may include determining a region of viable solutions and selecting a solution from within that region or determining the most 5 plausible sensor orientation offset relative to the chassis directly from a rotation estimate.
Preferably any bias in the IM,U is negligible or known.
Preferably the chassis, preferably a vehicle chassis, is either rotated in the same location or is returned to the location of the first inertial sensor measurement after rotating the chassis for the second inertial sensor measurement. The method may include measuring the rotation of the chassis between the first inertial sensor measurement and the second inertial sensor measurement. Measurement of the rotation of the chassis between the first inertial sensor measurement and the second inertial sensor /5 measurement may include using a yaw sensor and/or manually measuring the rotation.
Preferably the step of estimating a rotation matrix between the first and second inertial sensor measurements includes calculating a least squares estimate for the rotation matrix between the first and second inertial sensor measurements. The least squares estimate for the rotation matrix between the first and second inertial sensor measurements may be rank deficient.
SUMMARY OF INVENTION
According to an aspect of the invention there is provided a method of determining a sensor orientation offset relative to a chassis, the method including:
obtaining a first inertial sensor measurement;
rotating the chassis approximately 180 ;
obtaining a second inertial sensor measurement; and determining the sensor orientation offset relative to the chassis using the first inertial sensor measurement and the second inertial sensor measurement.
Preferably the first inertial sensor measurement and the second inertial sensor measurement are conducted by an inertial measurement unit (IMU).
Preferably the IMU includes at least a three-axis accelerometer. Preferably the first inertial sensor measurement and the second inertial sensor measurement consist of a measurement of gravity only.
Preferably the step of determining the sensor orientation offset relative to the chassis includes estimating a rotation between the first =and second inertial sensor measurements. The rotation estimate is preferably a rotation matrix.
= Preferably the step of determining the sensor orientation offset relative to the chassis includes determining possible solutions for rotation of the sensor relative to the chassis and/or eliminating impossible and implausible solutions. Alternatively the step of determining the sensor orientation offset relative to the chassis may include determining a region of viable solutions and selecting a solution from within that region or determining the most 5 plausible sensor orientation offset relative to the chassis directly from a rotation estimate.
Preferably any bias in the IM,U is negligible or known.
Preferably the chassis, preferably a vehicle chassis, is either rotated in the same location or is returned to the location of the first inertial sensor measurement after rotating the chassis for the second inertial sensor measurement. The method may include measuring the rotation of the chassis between the first inertial sensor measurement and the second inertial sensor measurement. Measurement of the rotation of the chassis between the first inertial sensor measurement and the second inertial sensor /5 measurement may include using a yaw sensor and/or manually measuring the rotation.
Preferably the step of estimating a rotation matrix between the first and second inertial sensor measurements includes calculating a least squares estimate for the rotation matrix between the first and second inertial sensor measurements. The least squares estimate for the rotation matrix between the first and second inertial sensor measurements may be rank deficient.
Preferably the step of determining possible solutions for rotation of the sensor relative to the chassis includes performing an eigendecomposition of =
the estimated rotation matrix.
Preferably the step of eliminating impossible and implausible solutions includes eliminating solutions with a determinant of -1. Preferably the step of eliminating impossible and implausible solutions further includes estimating pitch and roll of the chassis using coarse levelling. Preferably the step of eliminating impostible and implausible solutions even further includes selecting a remaining plausible solution. Selecting the remaining plausible solution may include selecting the solution that corresponds to the smallest roll.
Preferably the chassis is located on a generally flat surface for the first and second inertial sensor measurements. The generally flat surface may be at an angle to perfectly flat or level ground. The sensor orientation offset may be determined without knowing the angle of the generally flat surface with respect to perfectly flat ground.
According to another aspect of the invention there is provided a system configured to determine a sensor orientation offset relative to a chassis, the system including;
an inertial measurement unit (IMU); and a computing resource in communication with the IMU and including a processor and memory;
wherein the memory of the computing resource is programmed to instruct the processor to:
the estimated rotation matrix.
Preferably the step of eliminating impossible and implausible solutions includes eliminating solutions with a determinant of -1. Preferably the step of eliminating impossible and implausible solutions further includes estimating pitch and roll of the chassis using coarse levelling. Preferably the step of eliminating impostible and implausible solutions even further includes selecting a remaining plausible solution. Selecting the remaining plausible solution may include selecting the solution that corresponds to the smallest roll.
Preferably the chassis is located on a generally flat surface for the first and second inertial sensor measurements. The generally flat surface may be at an angle to perfectly flat or level ground. The sensor orientation offset may be determined without knowing the angle of the generally flat surface with respect to perfectly flat ground.
According to another aspect of the invention there is provided a system configured to determine a sensor orientation offset relative to a chassis, the system including;
an inertial measurement unit (IMU); and a computing resource in communication with the IMU and including a processor and memory;
wherein the memory of the computing resource is programmed to instruct the processor to:
obtain a first inertial sensor measurement from the IMU;
obtain a second inertial sensor measurement from the IMU after the chassis has been rotated approximately 180 ; and determine the sensor orientation offset relative to the chassis using the first inertial sensor measurement and the second inertial sensor measurement.
According to another aspect of the invention there is provided a system of determining a sensor orientation offset relative to a chassis, the system including:
an IMU mounted on a chassis; and a computing resource in communication with the IMU and including a processor and memory; wherein the IMU:
obtains a first inertial sensor measurement; and obtains a second inertial sensor measurement after the chassis has been rotated approximately 1800;
and wherein the processor of the computing resource:
receives the first inertial sensor measurement and the second inertial sensor measurement from the IMU; and determines the sensor orientation offset relative to the chassis using the first inertial sensor measurement and the second inertial sensor measurement.
Preferably the computing resource is an embedded system. The computing resource may automatically determine when the chassis has been rotated or, alternatively, the computing resource may provide a prompt adapted to receive an input from a user to confirm when the chassis has been rotated. The prompt may be graphical on a display and may assist the user in determining rotation of the chassis.
The IMU preferably includes a three-axis accelerometer. The IMU may ' 5 further include one or more angular rate sensors and/or a 2 or 3 axis magnetometer. The system preferably also includes a global navigation satellite systems (GNSS) component connected to the processor. Output from the GNSS component may be utilised to assist in determining the sensor orientation offset relative to the chassis. The GNSS component preferably includes a GPS receiver.
The sensor orientation offset relative to the chassis may be determined according to the aforementioned method.
Further features and advantages of the present invention will become apparent from the following detailed description.
By Way of example only, preferred embodiments of the invention will be described more fully hereinafter with reference to the accompanying figures, wherein:
Figure 1 is a flow chart illustrating steps of a method according to the invention; and Figure 2 is a flow chart illustrating sub-steps of step 130 of the flow chart in figure 1.
obtain a second inertial sensor measurement from the IMU after the chassis has been rotated approximately 180 ; and determine the sensor orientation offset relative to the chassis using the first inertial sensor measurement and the second inertial sensor measurement.
According to another aspect of the invention there is provided a system of determining a sensor orientation offset relative to a chassis, the system including:
an IMU mounted on a chassis; and a computing resource in communication with the IMU and including a processor and memory; wherein the IMU:
obtains a first inertial sensor measurement; and obtains a second inertial sensor measurement after the chassis has been rotated approximately 1800;
and wherein the processor of the computing resource:
receives the first inertial sensor measurement and the second inertial sensor measurement from the IMU; and determines the sensor orientation offset relative to the chassis using the first inertial sensor measurement and the second inertial sensor measurement.
Preferably the computing resource is an embedded system. The computing resource may automatically determine when the chassis has been rotated or, alternatively, the computing resource may provide a prompt adapted to receive an input from a user to confirm when the chassis has been rotated. The prompt may be graphical on a display and may assist the user in determining rotation of the chassis.
The IMU preferably includes a three-axis accelerometer. The IMU may ' 5 further include one or more angular rate sensors and/or a 2 or 3 axis magnetometer. The system preferably also includes a global navigation satellite systems (GNSS) component connected to the processor. Output from the GNSS component may be utilised to assist in determining the sensor orientation offset relative to the chassis. The GNSS component preferably includes a GPS receiver.
The sensor orientation offset relative to the chassis may be determined according to the aforementioned method.
Further features and advantages of the present invention will become apparent from the following detailed description.
By Way of example only, preferred embodiments of the invention will be described more fully hereinafter with reference to the accompanying figures, wherein:
Figure 1 is a flow chart illustrating steps of a method according to the invention; and Figure 2 is a flow chart illustrating sub-steps of step 130 of the flow chart in figure 1.
DETAILED DESCRIPTION OF THE DRAWINGS
The invention generally relates to determining sensor orientation offset relative to a chassis. Sensors are nearly always mounted at an angle relative to a chassis it is measuring. Even when a sensor is mounted relatively straight and level in the chassis, it is likely to have at least a small offset. The offset can be expressed as a rotation matrix, R.v, , which includes yaw, pitch, and roll values for the sensor relative to the chassis which, in the example embodiment, is a vehicle chassis.
A chassis is considered to be a frame, body, or plane of an article such = as a vehicle or electronic device. Although the invention is primarily described with reference to vehicles, and even more particularly with reference to land vehicles, no limitation is meant thereby and the invention could be applied to other chassis including, for example, in electronic devices such as electronic and electromechanical tools, mobile phones, consoles, game controllers, remote controls, etc.
Although rotation matrices are used in the determination of the sensor orientation offset in the preferred embodiment, it will be appreciated that other' representations of rotations may be utilised including, for example, Euler angles, quaternions, and axis angles.
= Figure 1 illustrates a flow chart that has steps (110 to 130) that outline a method according to an embodiment of the invention. A first inertial sensor measurement ( f ) is obtained (step 100) by collecting and processing data from one or more sensors, typically in an inertial measurement unit (IMU). In a preferred embodiment the IMU will be part of a navigation system which includes a computing resource, typically including a processor and memory.
At a point when the vehicle is stationary the sensor data is received by the system.
5 For a stationary vehicle, an accelerometer sensor will measure the following:
=,3 f = Rõ f" + bõ +6 (1) where i3 is the specific force measurement in the body frame, 11: is the rotation from the navigation (locally level) frame to the sensor frame, 10 f" = [0 - gr is the gravity vector in the navigation frame, ba is the accelerometer bias, and i is a non-fixed perturbation on the measurement.
= The sensor data is typically processed using signal processing to determine an estimate =of the specific force at the location. The estimate of the specific force includes signal processing to account for other factors such as, for example, removal of engine vibration (if the engine is running) or other disturbances. The processed estimate of the specific force results in a first =inertial sensor measurement is, .
The chassis, in this case vehicle chassis, is then rotated 180 (step 110). In a preferred embodiment the system prompts a user to turn the chassis around 180 once sufficient data has been collected at the first point. =
Some vehicles, such, as excavators, may be able to turn 180 on the same point. However, other vehicles have to be driven and returned to the same location facing the other way. In this case, positional equipment, such as a GPS, may be able to assist the user in returning to the same location.
Once rotated 1800, a second inertial sensor measurement (î2) is obtained (step 120) by collecting data from the sensors. Like the first inertial sensor measurement (V ) the sensor data is processed using signal processing to determine an estimate of the specific force which results in a second inertial sensor measurement f2.
Figure 2 illustrates step 130 of figure 1 in more detail. First, at step 132, the first and second sensor measurements are considered. Considering equation (1) supra, the relationship of the first and second measurements =
with gravity is:
= Kir +b0 +El (2) = lea2f + ba + E2 (3) Rõ , which is the rotation from the navigation (locally level) frame to the sensor frame, can be broken down into two parts: R, which is the rotation from the vehicle frame to the sensor frame (desired value) and Rõ which is the rotation from the navigation to the vehicle frame (i.e. the attitude of the vehicle). Accordingly, R can be expressed as:
s v Rõ =RRõ (4) which can be substituted into equations (2) and (3):
The invention generally relates to determining sensor orientation offset relative to a chassis. Sensors are nearly always mounted at an angle relative to a chassis it is measuring. Even when a sensor is mounted relatively straight and level in the chassis, it is likely to have at least a small offset. The offset can be expressed as a rotation matrix, R.v, , which includes yaw, pitch, and roll values for the sensor relative to the chassis which, in the example embodiment, is a vehicle chassis.
A chassis is considered to be a frame, body, or plane of an article such = as a vehicle or electronic device. Although the invention is primarily described with reference to vehicles, and even more particularly with reference to land vehicles, no limitation is meant thereby and the invention could be applied to other chassis including, for example, in electronic devices such as electronic and electromechanical tools, mobile phones, consoles, game controllers, remote controls, etc.
Although rotation matrices are used in the determination of the sensor orientation offset in the preferred embodiment, it will be appreciated that other' representations of rotations may be utilised including, for example, Euler angles, quaternions, and axis angles.
= Figure 1 illustrates a flow chart that has steps (110 to 130) that outline a method according to an embodiment of the invention. A first inertial sensor measurement ( f ) is obtained (step 100) by collecting and processing data from one or more sensors, typically in an inertial measurement unit (IMU). In a preferred embodiment the IMU will be part of a navigation system which includes a computing resource, typically including a processor and memory.
At a point when the vehicle is stationary the sensor data is received by the system.
5 For a stationary vehicle, an accelerometer sensor will measure the following:
=,3 f = Rõ f" + bõ +6 (1) where i3 is the specific force measurement in the body frame, 11: is the rotation from the navigation (locally level) frame to the sensor frame, 10 f" = [0 - gr is the gravity vector in the navigation frame, ba is the accelerometer bias, and i is a non-fixed perturbation on the measurement.
= The sensor data is typically processed using signal processing to determine an estimate =of the specific force at the location. The estimate of the specific force includes signal processing to account for other factors such as, for example, removal of engine vibration (if the engine is running) or other disturbances. The processed estimate of the specific force results in a first =inertial sensor measurement is, .
The chassis, in this case vehicle chassis, is then rotated 180 (step 110). In a preferred embodiment the system prompts a user to turn the chassis around 180 once sufficient data has been collected at the first point. =
Some vehicles, such, as excavators, may be able to turn 180 on the same point. However, other vehicles have to be driven and returned to the same location facing the other way. In this case, positional equipment, such as a GPS, may be able to assist the user in returning to the same location.
Once rotated 1800, a second inertial sensor measurement (î2) is obtained (step 120) by collecting data from the sensors. Like the first inertial sensor measurement (V ) the sensor data is processed using signal processing to determine an estimate of the specific force which results in a second inertial sensor measurement f2.
Figure 2 illustrates step 130 of figure 1 in more detail. First, at step 132, the first and second sensor measurements are considered. Considering equation (1) supra, the relationship of the first and second measurements =
with gravity is:
= Kir +b0 +El (2) = lea2f + ba + E2 (3) Rõ , which is the rotation from the navigation (locally level) frame to the sensor frame, can be broken down into two parts: R, which is the rotation from the vehicle frame to the sensor frame (desired value) and Rõ which is the rotation from the navigation to the vehicle frame (i.e. the attitude of the vehicle). Accordingly, R can be expressed as:
s v Rõ =RRõ (4) which can be substituted into equations (2) and (3):
= R1/1 fn ba + Et (5) '2 = re2 Rnv2 fn ba E2 (6) As the IMU is mounted in a fixed location in the vehicle, there is no rotation change between the first sensor measurement and the second sensor measurement for Ry . Accordingly:
= R.,' = R2 (7) vz Utilising equation (7), equation (5) can be rewritten to include Rsv :
, j7 =R, Rõ2f" + bc, + E, (5) and since the rotation of the vehicle chassis frame to the navigation frame at the second measurement (Rvõ2 ) is the same as the rotation of the vehicle chassis frame to the navigation frame at the first measurement (R ) further rotated by the rotation of the vehicle frame from each measurement (R,v,l2) (assuming the measurements are taken at the same position and, hence, the navigation frame is constant between the measurements) equation (8) may be rewritten as:
=R; W2R,',1 fn + ba +E2 (9) Because the rotation of the vehicle frame from each measurement ) is known to be a 1800 manoeuvre, it can be shown as:
= R.,' = R2 (7) vz Utilising equation (7), equation (5) can be rewritten to include Rsv :
, j7 =R, Rõ2f" + bc, + E, (5) and since the rotation of the vehicle chassis frame to the navigation frame at the second measurement (Rvõ2 ) is the same as the rotation of the vehicle chassis frame to the navigation frame at the first measurement (R ) further rotated by the rotation of the vehicle frame from each measurement (R,v,l2) (assuming the measurements are taken at the same position and, hence, the navigation frame is constant between the measurements) equation (8) may be rewritten as:
=R; W2R,',1 fn + ba +E2 (9) Because the rotation of the vehicle frame from each measurement ) is known to be a 1800 manoeuvre, it can be shown as:
= 0 -1 0 (10) Notably it is the vehicle which is rotated about its z-axis and not the terrain, although on perfectly flat ground the two will coincide.
Solving equation (9) for Raw', , substituting into equation (5), and assuming El 0 and E2 0 results in:
(1'6,2 _ ba )=- - :2 12 vs (isl ba (11) For the purposes of determining the offset it can be assumed that ba O, therefore, the following relation between vehicle manoeuvres is:
i'2 = Rts, Ity'Rv, i (12) = Rf (13) where R = R R2R, which represents a rotation in the form of a rotation matrix between the first and second sensor measurements. R is both a special orthogonal matrix (SO(3)) and a symmetric matrix, properties which can be utilised to estimate R (step 134 of figure 2) which can be expressed as /5 a 3x3 matrix as follows:
R= R12 R22 R23 (14) _R13 R23 R33 _ = Since R is symmetric, it can be appreciated that there are only 6 elements. However, there are only three degrees of freedom in any SO(3) matrix and, accordingly, they are not all independent.
Since R = RI we can also state:
is? = (15) =Rî2 (16) which appears to yield 6 equations with 6 unknowns but a least-squares estimate constructed from equation (15) is only rank 5 and, accordingly, a further constraint is needed. R=R: 11:2R: is also a similarity transform (i.e.
is of the form B =13-1AP ) and, therefore, the trace of the matrix is preserved and the final constraint can be determined as:
/o AI+ R22 + R33 = -1 (17) A linear least squares estimate of R is constructed from equations (15) and (17) as:
Ax = b (18) where f:' 0 0 0 0 f:' 0 4' f 0 0 Of 0 fp f:
/5 A = f:2 4'2 f:2 o o= o (19) o f:2 o 4:2 f:2 0 0 0 f:2 0 f;2 f:2 = [fx52 /2 f:2 f:1 fy81 f:1 (20) x = 2 R 3 R22 R23 R33 17 (21) Once R has been estimated, the next step is to determine possible solutions for rotation of the sensor orientation relative to the vehicle chassis ( Rõ ). Any symmetric matrix, such as:
RR:
=
R=R (22) has an eigendecomposition, which may be utilised in order to extract R, from 5 the estimate of R, in the form of:
A = QAQT (23) where A is a diagonal matrix of eigenvalues and Q is an orthogonal matrix of the eigenvectors corresponding to the eigenvalues. Since the eigendecomposition is also a similarity transform, A and A share the same /o eigenvalues. The eigenvalues for Rv4 can be determined:
eig(Rv4 )= [-1 -1 1] (24) Hence, the diagonal matrix formed by the eigenvalues of R2 is itself, which results in the eigendecomposition of R providing a set of possible solutions for R, when the eigenvalues are arranged in such a way as to 15 match R
v2 . Since the eigenvalues in Q are not unique, each may be multiplied by -1 and still maintain orthogonality, which leads to 8 possible solutions.
Impossible and implausible solutions are eliminated (step 138) through a process of elimination. First, although Q can have a determinant of 1, the determinant of a special orthogonal matrix must be +1 and, accordingly, half of the solutions with a determinant of -1 can be eliminated. Of the four remaining solutions, there are only two unique pairs of pitch and roll (yaw will be ambiguous) corresponding to a 'twisted pair' of solutions.
= Rearranging equation (2):
Rvs:(is' ¨b0 ¨E,)---- Raviir (25) an estimate of the pitch and roll of the vehicle (i.e. ) can be determined using coarse levelling. Assuming the bias and noise are small:
Pitch: O = atan2(f (26) Roll: =atan2(¨fy",¨f:) (27) One of the twisted pair of solutions will correspond to the desired solution and the other will correspond to an implausible situation, such as where the vehicle is 'hanging from the roof', and therefore the solution with the smallest absolute roll corresponds to the physically possible solution.
Instead of determining the solutions and then eliminating impossible and implausible solutions a region of viable solutions could be determined first and then the desired solution could be determined from within that range.
An alternative approach to that described is to directly determine the most plausible solution from the rotation estimate.
The sensor measurements ( ) are utilised to accurately determine two degrees of freedom of the desired angular offset, namely roll and pitch. Yaw (rotation about the vertical axis) can easily be determined from further sensors, if available, or alternatively by being input manually.
For example, a graphical display showing the device with two degrees of freedom =
Solving equation (9) for Raw', , substituting into equation (5), and assuming El 0 and E2 0 results in:
(1'6,2 _ ba )=- - :2 12 vs (isl ba (11) For the purposes of determining the offset it can be assumed that ba O, therefore, the following relation between vehicle manoeuvres is:
i'2 = Rts, Ity'Rv, i (12) = Rf (13) where R = R R2R, which represents a rotation in the form of a rotation matrix between the first and second sensor measurements. R is both a special orthogonal matrix (SO(3)) and a symmetric matrix, properties which can be utilised to estimate R (step 134 of figure 2) which can be expressed as /5 a 3x3 matrix as follows:
R= R12 R22 R23 (14) _R13 R23 R33 _ = Since R is symmetric, it can be appreciated that there are only 6 elements. However, there are only three degrees of freedom in any SO(3) matrix and, accordingly, they are not all independent.
Since R = RI we can also state:
is? = (15) =Rî2 (16) which appears to yield 6 equations with 6 unknowns but a least-squares estimate constructed from equation (15) is only rank 5 and, accordingly, a further constraint is needed. R=R: 11:2R: is also a similarity transform (i.e.
is of the form B =13-1AP ) and, therefore, the trace of the matrix is preserved and the final constraint can be determined as:
/o AI+ R22 + R33 = -1 (17) A linear least squares estimate of R is constructed from equations (15) and (17) as:
Ax = b (18) where f:' 0 0 0 0 f:' 0 4' f 0 0 Of 0 fp f:
/5 A = f:2 4'2 f:2 o o= o (19) o f:2 o 4:2 f:2 0 0 0 f:2 0 f;2 f:2 = [fx52 /2 f:2 f:1 fy81 f:1 (20) x = 2 R 3 R22 R23 R33 17 (21) Once R has been estimated, the next step is to determine possible solutions for rotation of the sensor orientation relative to the vehicle chassis ( Rõ ). Any symmetric matrix, such as:
RR:
=
R=R (22) has an eigendecomposition, which may be utilised in order to extract R, from 5 the estimate of R, in the form of:
A = QAQT (23) where A is a diagonal matrix of eigenvalues and Q is an orthogonal matrix of the eigenvectors corresponding to the eigenvalues. Since the eigendecomposition is also a similarity transform, A and A share the same /o eigenvalues. The eigenvalues for Rv4 can be determined:
eig(Rv4 )= [-1 -1 1] (24) Hence, the diagonal matrix formed by the eigenvalues of R2 is itself, which results in the eigendecomposition of R providing a set of possible solutions for R, when the eigenvalues are arranged in such a way as to 15 match R
v2 . Since the eigenvalues in Q are not unique, each may be multiplied by -1 and still maintain orthogonality, which leads to 8 possible solutions.
Impossible and implausible solutions are eliminated (step 138) through a process of elimination. First, although Q can have a determinant of 1, the determinant of a special orthogonal matrix must be +1 and, accordingly, half of the solutions with a determinant of -1 can be eliminated. Of the four remaining solutions, there are only two unique pairs of pitch and roll (yaw will be ambiguous) corresponding to a 'twisted pair' of solutions.
= Rearranging equation (2):
Rvs:(is' ¨b0 ¨E,)---- Raviir (25) an estimate of the pitch and roll of the vehicle (i.e. ) can be determined using coarse levelling. Assuming the bias and noise are small:
Pitch: O = atan2(f (26) Roll: =atan2(¨fy",¨f:) (27) One of the twisted pair of solutions will correspond to the desired solution and the other will correspond to an implausible situation, such as where the vehicle is 'hanging from the roof', and therefore the solution with the smallest absolute roll corresponds to the physically possible solution.
Instead of determining the solutions and then eliminating impossible and implausible solutions a region of viable solutions could be determined first and then the desired solution could be determined from within that range.
An alternative approach to that described is to directly determine the most plausible solution from the rotation estimate.
The sensor measurements ( ) are utilised to accurately determine two degrees of freedom of the desired angular offset, namely roll and pitch. Yaw (rotation about the vertical axis) can easily be determined from further sensors, if available, or alternatively by being input manually.
For example, a graphical display showing the device with two degrees of freedom =
may be utilised and the user may visually rotate the device about the vertical to input the third degree of freedom.
Advantageously, where the sensor bias ba is either very small or known, as is the case where the IMU is being installed after a calibration procedure (for example, factory calibration), the method according to the present invention allows a device with an IMU to be installed at any orientation within a chassis and then, via a simple 1800 rotation manoeuvre, determine the orientation of the IMU to correct for the sensor orientation offset relative to the chassis. This removes the need for the device with the NU to be mounted orthogonal to the chassis or for the installation orientation to be measured and input manually.
Not having to mount the device with the IMU orthogonal to the chassis =provides significantly more mounting options for the device. For example, it can be mounted on an angled wall, or onto any portion of the body such as, for example, the wheel arch of a road vehicle. Furthermore, any error previously introduced by not having the device mounted perfectly orthogonal is removed as the exact orientation is determined.
Not having to manually measure the orientation of the device relative to the chassis after installation also reduces costs, particularly labour costs, and downtime. Furthermore, specialised equipment is not required and the mounting location is not limited to locations which have to be able to be measured externally.
=
Advantageously, where the sensor bias ba is either very small or known, as is the case where the IMU is being installed after a calibration procedure (for example, factory calibration), the method according to the present invention allows a device with an IMU to be installed at any orientation within a chassis and then, via a simple 1800 rotation manoeuvre, determine the orientation of the IMU to correct for the sensor orientation offset relative to the chassis. This removes the need for the device with the NU to be mounted orthogonal to the chassis or for the installation orientation to be measured and input manually.
Not having to mount the device with the IMU orthogonal to the chassis =provides significantly more mounting options for the device. For example, it can be mounted on an angled wall, or onto any portion of the body such as, for example, the wheel arch of a road vehicle. Furthermore, any error previously introduced by not having the device mounted perfectly orthogonal is removed as the exact orientation is determined.
Not having to manually measure the orientation of the device relative to the chassis after installation also reduces costs, particularly labour costs, and downtime. Furthermore, specialised equipment is not required and the mounting location is not limited to locations which have to be able to be measured externally.
=
In this specification, adjectives such as first and second, left and right, top and bottom, and the like may be used solely to distinguish one element or action from another element or action without necessarily requiring or implying any actual such relationship or order. Where the context permits, reference to an integer or a component or step (or the like) is not to be interpreted as being limited to only one of that integer, component, or step, but rather could be one or more of that integer, component, or step etc.
The above description of various embodiments of the present invention is provided for purposes of description to one of ordinary skill in the related art. It is not intended to be exhaustive or to limit the invention to a single disclosed embodiment. As mentioned above, numerous alternatives and variations to the present invention will be apparent to those skilled in the art of the above teaching. Accordingly, while some alternative embodiments have been discussed specifically, other embodiments will be apparent or relatively /5 easily developed by those of ordinary skill in the art. The invention is intended to embrace all alternatives, modifications, and variations of the present invention that have been discussed herein, and other embodiments that fall within the spirit and scope of the above described invention.
In this specification, the terms 'comprises', 'comprising', 'includes', 'including', or similar terms are intended to mean a non-exclusive inclusion, such that a method, system or apparatus that comprises a list of elements does not include those elements solely, but may well include other elements not listed.
The above description of various embodiments of the present invention is provided for purposes of description to one of ordinary skill in the related art. It is not intended to be exhaustive or to limit the invention to a single disclosed embodiment. As mentioned above, numerous alternatives and variations to the present invention will be apparent to those skilled in the art of the above teaching. Accordingly, while some alternative embodiments have been discussed specifically, other embodiments will be apparent or relatively /5 easily developed by those of ordinary skill in the art. The invention is intended to embrace all alternatives, modifications, and variations of the present invention that have been discussed herein, and other embodiments that fall within the spirit and scope of the above described invention.
In this specification, the terms 'comprises', 'comprising', 'includes', 'including', or similar terms are intended to mean a non-exclusive inclusion, such that a method, system or apparatus that comprises a list of elements does not include those elements solely, but may well include other elements not listed.
Claims (28)
1. A method of determining a sensor orientation offset relative to a chassis, the method including:
obtaining a first inertial sensor measurement;
rotating the chassis approximately 180°;
obtaining a second inertial sensor measurement; and determining the sensor orientation offset relative to the chassis, including at least pitch and roll, using the first inertial sensor measurement and the second inertial sensor measurement.
obtaining a first inertial sensor measurement;
rotating the chassis approximately 180°;
obtaining a second inertial sensor measurement; and determining the sensor orientation offset relative to the chassis, including at least pitch and roll, using the first inertial sensor measurement and the second inertial sensor measurement.
2. The method of claim 1, wherein the first inertial sensor measurement and the second inertial sensor measurement are conducted by an inertial measurement unit (IMU).
3. The method of claim 2, wherein the IMU includes a three-axis accelerometer.
4. The method of claim 2, wherein any bias in the IMU is known and used in the step of determining the sensor orientation offset relative to the chassis.
5. The method of claim 2, wherein any bias in the IMU is negligible.
6. The method of any one of the preceding claims, wherein the first inertial sensor measurement and the second inertial sensor measurement consist of a measurement of gravity only.
7. The method of any one of the preceding claims, wherein the step of determining the sensor orientation offset relative to the chassis includes estimating a rotation between the first and second inertial sensor measurements.
8. The method of claim 7, wherein the rotation estimate is a rotation matrix.
9. The method of claim 8, wherein estimating the rotation matrix includes calculating a least squares estimate for the rotation matrix.
10. The method of claim 9, wherein the least squares estimate for the rotation matrix is rank deficient.
11. The method of any one of the preceding claims, wherein the step of determining the sensor orientation offset relative to the chassis includes determining possible solutions for rotation of the sensor relative to the chassis.
12. The method of claim 11, wherein the step of determining possible solutions for rotation of the sensor relative to the chassis includes performing an eigendecomposition.
13. The method of claim 12, wherein the step of determining the sensor orientation offset relative to the chassis includes eliminating impossible and implausible solutions.
14. The method of claim 13, wherein the step of eliminating impossible and implausible solutions includes eliminating solutions with a determinant of -1.
15. The method of claim 13, wherein the step of eliminating impossible and implausible solutions includes estimating pitch and roll of the chassis using coarse levelling.
16. The method of claim 15 wherein the step of eliminating impossible and implausible solutions further includes selecting a solution that corresponds to the smallest roll.
17. The method of any one of the preceding claims, wherein the chassis is rotated in the same location.
18. The method of any one of claims 1 to 16, wherein the chassis is moved from, and returned to, the location of the first inertial sensor measurement after rotating the chassis.
19. The method of any one of the preceding claims wherein the chassis is a vehicle chassis.
20. The method of any one of the preceding claims, wherein the attitude of the chassis is unknown.
21. A system configured to determine a sensor offset relative to a chassis, the system including;
an inertial measurement unit (IMU); and a computing resource in communication with the IMU and including a processor and memory;
wherein the memory of the computing resource is programmed to instruct the processor to:
obtain a first inertial sensor measurement from the IMU;
obtain a second inertial sensor measurement from the IMU after the chassis has been rotated approximately 180°; and determine the sensor offset relative to the chassis, including at least pitch and roll, using the first inertial sensor measurement and the second inertial sensor measurement.
an inertial measurement unit (IMU); and a computing resource in communication with the IMU and including a processor and memory;
wherein the memory of the computing resource is programmed to instruct the processor to:
obtain a first inertial sensor measurement from the IMU;
obtain a second inertial sensor measurement from the IMU after the chassis has been rotated approximately 180°; and determine the sensor offset relative to the chassis, including at least pitch and roll, using the first inertial sensor measurement and the second inertial sensor measurement.
22. A system of determining a sensor orientation offset relative to a chassis, the system including:
an IMU mounted on a chassis; and a computing resource in communication with the IMU and including a processor and memory; wherein the IMU:
obtains a first inertial sensor measurement; and obtains a second inertial sensor measurement after the chassis has been rotated approximately 180°;
and wherein the processor of the computing resource:
receives the first inertial sensor measurement and the second inertial sensor measurement from the IMU; and determines the sensor orientation offset relative to the chassis, including at least pitch and roll, using the first inertial sensor measurement and the second inertial sensor measurement.
an IMU mounted on a chassis; and a computing resource in communication with the IMU and including a processor and memory; wherein the IMU:
obtains a first inertial sensor measurement; and obtains a second inertial sensor measurement after the chassis has been rotated approximately 180°;
and wherein the processor of the computing resource:
receives the first inertial sensor measurement and the second inertial sensor measurement from the IMU; and determines the sensor orientation offset relative to the chassis, including at least pitch and roll, using the first inertial sensor measurement and the second inertial sensor measurement.
23. The system of claim 21 or 22, wherein the computing resource is an embedded system.
24. The system of any one of claims 21 to 23, wherein the computing resource automatically determines when the chassis has been rotated.
25. The system of any one of claims 21 to 24, wherein the computing resource provides a prompt adapted to receive an input from a user to confirm when the chassis has been rotated.
26. The system of claim 25, wherein the prompt is graphical on a display and assists the user in determining rotation of the chassis.
27. The system of any one of claims 21 to 26, wherein the IMU
comprises a three-axis accelerometer.
comprises a three-axis accelerometer.
28. The system of any one of claims 21 to 27, wherein the processor determines the sensor orientation offset without needing to know an attitude of the chassis.
Applications Claiming Priority (3)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| AU2011903631A AU2011903631A0 (en) | 2011-09-06 | A method and system of determining a sensor offset | |
| AU2011903631 | 2011-09-06 | ||
| PCT/AU2012/001010 WO2013033756A1 (en) | 2011-09-06 | 2012-08-29 | A method and system of determining an inertial sensor orientation offset |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA2847951A1 true CA2847951A1 (en) | 2013-03-14 |
Family
ID=47831341
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA2847951A Abandoned CA2847951A1 (en) | 2011-09-06 | 2012-08-29 | A method and system of determining an inertial sensor orientation offset |
Country Status (7)
| Country | Link |
|---|---|
| EP (1) | EP2753939A4 (en) |
| CN (1) | CN103765226A (en) |
| AR (1) | AR087797A1 (en) |
| AU (1) | AU2012307070A1 (en) |
| BR (1) | BR112014005060A2 (en) |
| CA (1) | CA2847951A1 (en) |
| WO (1) | WO2013033756A1 (en) |
Families Citing this family (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7859392B2 (en) | 2006-05-22 | 2010-12-28 | Iwi, Inc. | System and method for monitoring and updating speed-by-street data |
| US9067565B2 (en) | 2006-05-22 | 2015-06-30 | Inthinc Technology Solutions, Inc. | System and method for evaluating driver behavior |
| US9129460B2 (en) | 2007-06-25 | 2015-09-08 | Inthinc Technology Solutions, Inc. | System and method for monitoring and improving driver behavior |
| US9117246B2 (en) | 2007-07-17 | 2015-08-25 | Inthinc Technology Solutions, Inc. | System and method for providing a user interface for vehicle mentoring system users and insurers |
| US7876205B2 (en) | 2007-10-02 | 2011-01-25 | Inthinc Technology Solutions, Inc. | System and method for detecting use of a wireless device in a moving vehicle |
| US8963702B2 (en) | 2009-02-13 | 2015-02-24 | Inthinc Technology Solutions, Inc. | System and method for viewing and correcting data in a street mapping database |
| US9172477B2 (en) | 2013-10-30 | 2015-10-27 | Inthinc Technology Solutions, Inc. | Wireless device detection using multiple antennas separated by an RF shield |
| CN111207736B (en) * | 2016-07-26 | 2021-11-30 | 广州亿航智能技术有限公司 | Method, system, equipment and readable storage medium for calibrating yaw angle of unmanned aerial vehicle |
Family Cites Families (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE60139881D1 (en) * | 2001-11-13 | 2009-10-22 | Nokia Corp | Method, apparatus and system for calibrating angular rate sensors |
| US7835880B2 (en) * | 2007-09-29 | 2010-11-16 | Imu Solutions, Inc. | Methods for improving accuracy of measurement and calibration of accelerometer parameters |
| US20100318257A1 (en) * | 2009-06-15 | 2010-12-16 | Deep Kalinadhabhotla | Method and system for automatically calibrating a three-axis accelerometer device |
-
2012
- 2012-08-29 CA CA2847951A patent/CA2847951A1/en not_active Abandoned
- 2012-08-29 EP EP12830003.5A patent/EP2753939A4/en not_active Withdrawn
- 2012-08-29 AU AU2012307070A patent/AU2012307070A1/en not_active Abandoned
- 2012-08-29 BR BR112014005060A patent/BR112014005060A2/en not_active Application Discontinuation
- 2012-08-29 WO PCT/AU2012/001010 patent/WO2013033756A1/en active Application Filing
- 2012-08-29 CN CN201280042067.0A patent/CN103765226A/en active Pending
- 2012-09-06 AR ARP120103293 patent/AR087797A1/en unknown
Also Published As
| Publication number | Publication date |
|---|---|
| BR112014005060A2 (en) | 2017-04-04 |
| AR087797A1 (en) | 2014-04-16 |
| CN103765226A (en) | 2014-04-30 |
| EP2753939A4 (en) | 2015-05-27 |
| WO2013033756A1 (en) | 2013-03-14 |
| EP2753939A1 (en) | 2014-07-16 |
| AU2012307070A1 (en) | 2014-02-27 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CA2847951A1 (en) | A method and system of determining an inertial sensor orientation offset | |
| KR102018450B1 (en) | A method for determining a vehicle attitude of UNS-IENS based on a single antenna | |
| CN106647791B (en) | Three-dimensional attitude measurement and control device, mechanical equipment and three-dimensional attitude measurement and control method | |
| US6205401B1 (en) | Navigation system for a vehicle, especially a land craft | |
| JP6257865B2 (en) | Positioning device and positioning method | |
| US9273967B2 (en) | Bias estimating method, posture estimating method, bias estimating device, and posture estimating device | |
| US20150268045A1 (en) | Surveying system and method | |
| CN104880189B (en) | A kind of antenna for satellite communication in motion low cost tracking anti-interference method | |
| CA2848102A1 (en) | A method and system of recalibrating an inertial sensor | |
| AU2012307067B2 (en) | Method of recalibrating inertial sensors | |
| JP5602070B2 (en) | POSITIONING DEVICE, POSITIONING METHOD OF POSITIONING DEVICE, AND POSITIONING PROGRAM | |
| JP2018047888A (en) | System and method for measuring angular position of vehicle | |
| JP2008535725A (en) | Vehicle control system | |
| WO2016203744A1 (en) | Positioning device | |
| EP3227634B1 (en) | Method and system for estimating relative angle between headings | |
| WO2010030565A1 (en) | Magnetic sensing device for navigation and detecting inclination | |
| Promrit et al. | In-vehicle MEMS IMU calibration using accelerometer | |
| Wongwirat et al. | A position tracking experiment of mobile robot with inertial measurement unit (imu) | |
| US20150145720A1 (en) | Coarse attitude determination from gnss antenna gain profiling | |
| CN114877886A (en) | Vehicle-mounted integrated navigation equipment attitude self-adaptive estimation method | |
| JP5352922B2 (en) | Angular velocity calculation device, navigation device | |
| AU2012307068A1 (en) | A method and system of recalibrating an inertial sensor | |
| US11614329B2 (en) | Method for monitoring the performance of inertial measurement units | |
| Sun et al. | Analysis of the Kalman filter with different INS error models for GPS/INS integration in aerial remote sensing applications | |
| Majumdar et al. | Attitude estimation and compensation in odometric localization of mobile robot using low cost imu |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| EEER | Examination request |
Effective date: 20140306 |
|
| FZDE | Discontinued |
Effective date: 20150831 |