WO2013033755A1

WO2013033755A1 - A method and system of recalibrating an inertial sensor

Info

Publication number: WO2013033755A1
Application number: PCT/AU2012/001009
Authority: WO
Inventors: Damien Dusha; Paul Dale
Original assignee: Leica Geosystems Ag
Priority date: 2011-09-08
Filing date: 2012-08-29
Publication date: 2013-03-14
Also published as: AU2012307069A1; EP2753941A4; BR112014005130A2; CN103782180A; AR087800A1; CA2848102A1; EP2753941A1; MX2014002805A

Abstract

There is provided a method and system of recalibrating a sensor, preferably by determining a sensor bias for an Inertial Measurement Unit (IMU) in a vehicle. The sensor bias is determined by taking a measurement from the IMU at a first orientation, and then taking a second measurement from the IMU at a second orientation that is rotated approximately 180° from the first orientation.

Description

A METHOD AND SYSTEM OF RECALIBRATING AN INERTIAL SENSOR

FIELD OF THE INVENTION

The invention relates to calibration of a sensor. More particularly the invention relates, but is not limited, to in field recalibration of inertial sensors. 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), !n 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 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.

For many inertial sensors, notably industrial grade inertial sensors often used in machine control applications, there are error characteristics, known as sensor bias, which change with temperature and age. These errors affect system accuracy and typically require the sensors to be sent back to the manufacturer for recalibration periodically (e.g. once per year). Such recalibration is costly and time consuming as it not only requires the device to be removed, but also requires the device to be returned to the manufacturer for a period of time, resulting in significant down-time.

Furthermore, even a yearly calibration can be insufficient in minimising bias as ambient temperature fluctuates over a year and, accordingly, temperature errors arise when the sensor is used in a different temperature range to what it was calibrated for. For example, if the sensor is calibrated in summer, the temperature errors will !lke!y become prevalent in winter when the ambient temperature is lower.

If the user does not send the device back to the manufacturer for factory calibration in an effort to avoid the costs and downtime then, in addition to the temperature error, age induced errors will also arise meaning that the device will lose accuracy over time.

One approach to assisting with keeping the sensors calibrated, particularly for temperature induced bias, is to add temperature sensing components and a sensor bias model to estimate the sensor bias at measured temperatures. However, this increases the cost and complexity of devices that use the sensors. Furthermore, calibration using such models often only includes temperature variation of the inertial senor over a limited temperature range. The model must also be updated as the inertial sensor ages to account for age induced bias. Updating the model is commonly done by yearly factory calibration or by calibration using additional sensors. These strategies add further cost and complexity to recalibrating the sensors.

OBJECT OF THE INVENTION

It is an aim of this invention to provide a method and system of calibrating a sensor 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 an inertial sensor bias, the method including the steps of: obtaining the orientation of the inertial sensor relative to a chassis; obtaining a first inertial sensor measurement;

• rotating the chassis with the inertial sensor approximately 180°; obtaining a second inertial sensor measurement; and

determining the sensor bias from the first inertial sensor measurement, the second inertial sensor measurement, and the obtained orientation of the sensor relative to the chassis.

Preferably the step of determining the sensor bias includes considering the first and second sensor measurements, determining possible bias values, determining constraints, and determining the sensor bias value from possible bias values within the constraints. Preferably the determined sensor bias value is the only physically possible bias value determined from the possible bias values and the constraints.

Preferably the step of determining possible bias values includes determining an intersection of two spheres of possible bias values, being a circle of values. Preferably the possible bias values are determined from a gravity constraint. Preferably the step of determining possible bias values includes solving a linear algebra problem.

Preferably determining the constraints includes using a sensor orientation rotation that corresponds to the obtained orientation of the sensor relative to the chassis. Preferably the sensor orientation rotation is a rotation matrix. Preferably the step of determining constraints includes producing a line constraint that converges at least once with the possible bias values. Preferably the line constraint is a parametric equation. Preferably a direction vector of the parametric equation is determined from a nullspace solution. Preferably a point on the line constraint is also determined. Preferably the point on the line constraint is determined using a minimum norm solution, even more preferably using a pseudoinverse.

Preferably the step of determining the sensor bias includes determining an intersection between the possible bias values and the line constraint. The line constraint may intersect the possible bias values at two points, and the step of determining the sensor bias preferably includes selecting one point which is physically possible. Preferably the step of selecting one point which is physically possible includes determining which point falls within a predetermined range. Preferably the predetermined range is determined from a range of values provided by the manufacturer of the sensor.

The step of determining the sensor bias may include determining two line constraint intersection solutions for each inertial sensor measurement. If only one line constraint intersection solution falls within the predetermined range then preferably that solution is determined to be the inertial sensor bias value. If more than one line constraint intersection solution falls within the predetermined range, then preferably the smaller of the two bias values is selected. Preferably the first inertial sensor measurement and the second inertial sensor measurement are conducted by an inertial measurement unit (IMU) mounted on the chassis. 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 sensors are contained in the chassis, preferably a vehicle chassis, which 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 measurement may include using a yaw sensor and/or manually measuring the rotation.

According to another aspect of the invention there is provided a method of calibrating an inertial sensor, the method including the steps of: determining a sensor bias according to the aforementioned method; and

calibrating the inertial sensor using the determined sensor bias.

According to another aspect of the invention there is provided a method of determining a location of a chassis, the method including the steps of: determining a sensor bias according to the aforementioned method; and

determining the location of the chassis using a global navigation satellite system (GNSS) component, the inertial sensor, and the determined sensor bias.

According to another aspect of the invention there is provided a system configured to determine a sensor bias, the system including:

an inertial measurement unit (IMU) having one or more sensors mounted at an orientation relative to a chassis; 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 the orientation of the one or more sensors relative to the chassis;

obtain a first inertial sensor measurement from the IMU;

obtain a second inertial sensor measurement from the IMU after the chassis with the IMU has been rotated approximately 180°; and

determine the sensor bias from the first inertial sensor measurement, the second inertial sensor measurement, and the obtained orientation of the one or more sensors relative to the chassis.

According to another aspect of the invention there is provided a system of calibrating an inertial measurement unit (IMU), the system including: an IMU having one or more sensors mounted at an orientation relative to a chassis;

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 with the IMU 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;

obtains an orientation of the one or more sensors relative to the chassis from the memory of the computing resource;

determines a sensor bias from the first inertial sensor measurement, the second inertial sensor measurement, and the obtained orientation of the one or more sensors relative to the chassis; and

calibrates the IMU using the determined sensor bias.

Preferably the computing resource is an embedded system. The computing resource may automatically determine when the chassis with the mounted IMU has been rotated or, alternatively, the computing resource may provide a prompt adapted to receive an input from a user to confirm when said chassis has been rotated. The prompt may be graphical on a display and may assist the user in determining rotation of said chassis.

The IMU preferably includes a three-axis accelerometer. The IMU may further include one or more angular rate sensors and/or a 2 or 3 axis magnetometer. The system may also include a global navigation satellite system (GNSS) component connected to the processor. Output from the GNSS component may be utilised to assist in determining the sensor bias. The GNSS component preferably includes a GPS receiver. The sensor bias may be determined according to the aforementioned method.

Further features and advantages of the present invention will become apparent from the following detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

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;

Figure 2 is a flow chart illustrating sub-steps of step 130 of the flow chart in figure 1 ; and

Figure 3 illustrates a graphic example of determining a bias value from possible values within constraints.

DETAILED DESCRIPTION OF THE DRAWINGS

The invention generally relates to determining sensor bias for an inertial sensor, particularly an accelerometer. Inertial sensors have a bias that changes with temperature and time. Such inertial sensors are used in many applications including vehicles. 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 embodiments including, for example, in electronic devices such as electronic and electromechanical tools, mobile phones, consoles, game controllers, remote controls, etc.

Figure 1 illustrates a flow chart that has steps (100 to 130) that outline a method according to an embodiment of the invention. A first inertial sensor measurement is obtained (step 100) by collecting and processing data

from one or more sensors, typically in an 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 and processed by the system.

For a stationary vehicle, an accelerometer sensor will measure the following:

where

is the specific force measurement in the body frame, is the

rotation from the navigation (locally level) frame to the sensor frame, is the gravity vector in the navigation frame, b₀ is the

accelerometer bias, and ε 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

.

The sensor is then rotated 180° (step 110). In a preferred embodiment the system prompts a user to turn a chassis, preferably a vehicle chassis, that the sensor is mounted on 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 180°, a second inertial sensor measurement

is obtained (step 120) by collecting and processing data from the sensor. Like the first inertial sensor measurement

the sensor data is processed using signal processing to determine an estimate of the specific force which results in a second inertial sensor measurement .

When an accelerometer is stationary, the total force acting on the accelerometer is due to gravity and, accordingly, if scale, misalignment, and noise are known or considered to be negligible, and the only significant error in measurement is sensor bias ( b_fl ), then the following constraint must be satisfied:

Where g is the magnitude of acceleration due to gravity. Accordingly, for multiple positions there are multiple equations:

Expanding equations (3) - (6) for the first and second inertial sensor measurements results in:

Each gravity measurement (equation (7) and equation (8)) form a sphere of possible values for the bias in light of the constraints of gravity. If the sensor is rotated on perfectly flat ground for the two inertial sensor measurements (steps 100 and 1200 then the two spheres will coincide. Otherwise, if the rotation is on uneven ground, as is usually the case, an intersection of the two spheres from the 180° manoeuvre will form a circle of values that fulfil the constraints of gravity. Figure 2 illustrates step 130 of figure 1 in more detail. By considering the measurements (step 132 of figure 2) and determining the sphere, from perfectly flat ground, or the circle, from uneven ground, the possible bias values for the sensor are determined (step 134).

To determine the sensor bias (b_a ) (step 130) from the possible bias values (step 134) certain constraints are determined. Considering equation (1), the relationships of the first and second measurements with gravity are:

, which is the rotation from the navigation (locally level) frame to the

sensor frame, can be broken down into two parts: which is the rotation

from a chassis frame, in the preferred embodiment a vehicle frame, to the sensor frame (known value, typically determined when the sensors are mounted in the chassis) and which is the rotation from the navigation

frame to the vehicle frame (i.e. the attitude of the vehicle). Accordingly,

can be expressed as:

which can be substituted into equations (9) and (10):

As the IMU is mounted in a fixed known location in the vehicle, there is no rotation change for variable between the first sensor measurement and

the second sensor measurement. Accordingly:

Utilising equation (14), equation (13) can be rewritten to include :

and since the rotation of the vehicle chassis frame to the navigation frame at the second measurement is the same as the rotation of the vehicle

chassis frame to the navigation frame at the first measurement further

rotated by the rotation of the vehicle frame from each measurement

(assuming the measurements are taken at the same position and, hence, the navigation frame is constant between the measurements) equation (15) may be rewritten as:

Because the rotation of the vehicle frame from each measurement is known to be a 180° rotation, it can be shown as:

Notably it is the vehicle which is rotated about its z-axis and not the terrain, although the two will coincide on perfectly flat ground.

Solving equation (16) for , substituting into equation (12), and

assuming results in:

which can be simplified to:

where which can be determined from the known (or at

least estimated) mounting orientation offset;. which will typically be obtained from a stored rotation variable that is determined earlier (e.g. when the sensors are installed in the chassis). Rearranging equation (19) for bias results in:

which is of the form:

where

The term (I -R) is rank 2 and, accordingly, the possible bias values from the constraint forms a line in 3-space. The parametric equation of the line in terms of t is therefore determined:

With the direction vector 1 being determinable from the nullspace of A , the nullspace being a set of non-trivial solutions of 'x' to the equation Ax=0 which, in this case, results in one solution from a 3x3 matrix of rank 2:

An arbitrary point on the line x₀ can be found by determining any possible solution to equation (20). In a preferred embodiment a minimum norm solution via the Moore-Penrose pseudoinverse is utilised:

The line constraint (equation 22) is therefore determined using the solutions of equations 23 and 24.

Figure 3 illustrates a graphical representation of the circular gravity constraint 10 (i.e. the intersection of two spheres of possible bias values discussed previously) and the line constraint 20 for a zero-noise and a perfect 180° rotation condition. In order to determine the inertial sensor bias value, the intersection of the gravity constraint 10 and the line constraint 20, being points 40 and 50, need to be determined. Once determined, the intersection 40, 50 that falls within a predetermined range 30, which corresponds to the physically possible bias values determined from the sensor datasheet, is the correct bias value (i.e. intersection 50 in figure 3).

In practice, however, the 180° rotation^'is often not perfect and noise from the sensor is present. Accordingly, the line constraint 20 may only be approximately on the same plane. In order to cater for this, the intersection of the line constraint 20 with each sphere of possible values determined from the gravity constraint (as discussed previously) is determined.

The intersection of the line constraint 20 with each sphere can be determined given a sphere in the form of:

and a line in the form of:

in terms of parameter t by determining the roots of:

where:

The intersection points, may then be determined as:

Where only one of the intersections, , falls within the

predetermined range of physically possible bias values then that intersection represents the correct bias value. Where more than one intersection falls within the predetermined range of physically possible bias values, the intersection that represents the smaller of the two bias values is selected to be the determined bias value.

Advantageously the method and system according to the present invention allows a sensor to be easily calibrated without the need to send the sensor, or equipment containing the sensor, to a third party or back to the manufacturer. The invention can easily be carried out in a vehicle by rotating the vehicle 180°. This allows the sensors to be recalibrated at minimal cost and with minimal downtime to an operator. Additionally, the relative ease of recalibration means that the sensors can be recalibrated frequently ensuring that any sensor bias due to age or temperature is kept to a minimum, even due to seasonal changes, and the like, if desired.

A further advantage of the present invention is that no temperature sensors, or other additional components, are required in order to try to estimate the sensor bias. This reduces costs and complexity of devices utilising the invention compared to those that use bias models, and the like, to estimate the bias. Furthermore, the present invention is typically more accurate than devices that use a bias model as the bias is actually measured and not merely assumed to match the bias model.

The method and system can be utilised to calibrate an IMU in a vehicle on flat and near flat ground by obtaining only two measurements either side of a simple 180° manoeuvre. Operators of vehicles can therefore easily recalibrate the IMU when desired, such as during temperature changes. Although rotation matrices are used in the determination of the sensor 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.

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.

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 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

CLAIMS:

1. A method of determining an inertial sensor bias, the method including the steps of:

obtaining the orientation of the inertial sensor relative to a chassis; obtaining a first inertial sensor measurement;

rotating the chassis with the inertial sensor approximately 180°; obtaining a second inertial sensor measurement; and

2. The method of claim 1 , wherein the step of determining the sensor bias includes considering the first and second sensor measurements, determining possible bias values, determining constraints, and determining the sensor bias value from possible bias values within the constraints.

3. A method according to claim 2, wherein the possible bias values are determined from a gravity constraint.

4. A method according to claim 3, wherein determining possible bias values includes determining an intersection of two spheres of possible bias values.

5. A method according to any one of claims 2 to 4, wherein determining the constraints includes using a sensor orientation rotation that corresponds to the obtained orientation of the sensor relative to the chassis.

6. A method according to claim 5, wherein the sensor orientation rotation is a rotation matrix.

7. A method according to any one of claims 2 to 6, wherein determining constraints includes producing a line constraint that converges at least once with the possible bias values.

8. A method according to claim 7, wherein the line constraint is a parametric equation.

9. A method according to claim 8, wherein a direction vector of the parametric equation is determined from a nullspace solution.

10. A method according to any one of claims 7 to 9, wherein a point on the line constraint is using a minimum norm solution.

11. A method according to any one of claims 7 to 10, wherein the step of determining the sensor bias includes determining an intersection between the possible bias values and the line constraint.

12. A method according to claim 11 , wherein the line constraint intersects the possible bias values at two points, and the step of determining the sensor bias includes selecting one point which is physically possible.

13. A method according to claim 12, wherein the step of selecting one point which is physically possible includes determining which point falls within a predetermined range.

14. A method according to any one of the preceding claims, wherein the first inertial sensor measurement and the second inertial sensor measurement are conducted by an inertial measurement unit (IMU) mounted on the chassis.

15. A method according to claim 14 wherein the IMU includes a three-axis accelerometer.

16. A method according to 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.

17. A method according to any one of the preceding claims, wherein the chassis is a vehicle chassis and the sensors are contained in the vehicle chassis.

18. A method of calibrating an inertial sensor, the method including the steps of:

determining a sensor bias according to any one of the preceding claims; and

calibrating the inertial sensor using the determined sensor bias.

19. A method of determining a location of a chassis, the method including the steps of:

determining a sensor bias according to any one of claims 1 to 17; and determining the location of the chassis using a global navigation satellite system (GNSS) component, the inertial sensor, and the determined sensor bias.

20. A system configured to determine a sensor bias, the system including: an inertial measurement unit (IMU) having one or more sensors mounted at an orientation relative to a chassis; and

obtain the orientation of the one or more sensors relative to the chassis;

obtain a first inertial sensor measurement from the IMU; obtain a second inertial sensor measurement from the IMU after the chassis with the IMU has been rotated approximately 180°; and

21. A system of calibrating an inertial measurement unit (IMU), the system including;

an IMU having one or more sensors mounted at an orientation relative to a chassis; and

wherein the IMU:

and wherein the processor of the computing resource:

uses the determined sensor bias to calibrate the IMU.

22. A system according to claim 20 or 21 , wherein the computing resource is an embedded system.

23. A system according to any one of claims 20 to 22, wherein the computing resource automatically determines when the chassis with the IMU has been rotated.

24. A system according to any one of claims 20 to 22, wherein the computing resource provides a prompt adapted to receive an input from a user to confirm when the chassis has been rotated.

25. A system according to any one of claims 20 to 24, wherein the IMU includes a three-axis accelerometer.

26. A system according to any one of claims 20 to 25, wherein the chassis is a vehicle chassis.