WO2022117254A1

WO2022117254A1 - Method for calibrating a tri-axial accelerometer

Info

Publication number: WO2022117254A1
Application number: PCT/EP2021/078442
Authority: WO
Inventors: Hanna BEUCHERT
Original assignee: Robert Bosch Gmbh
Priority date: 2020-12-02
Filing date: 2021-10-14
Publication date: 2022-06-09
Also published as: DE102020215241A1

Abstract

The invention relates to a method for calibrating a tri-axial accelerometer. The accelerometer is spatially oriented in that it is successively brought into four different measurement orientations. The measurement orientations are selected in such a way that the gravitational acceleration in the sensor coordinate system of the accelerometer points in different, non-coplanar directions for the four measurement orientations. At least one measurement value is recorded for each axis of the accelerometer in each of the four measurement orientations when the accelerometer is idle in the relevant measurement orientation. An offset for compensating for an offset measurement error is determined using the recorded measurement values.

Description

description

title

PROCEDURE FOR CALIBRATION OF A THREE-AXIS ACCELERATION SENSOR

State of the art

Microelectromechanical (MEMS) sensors for detecting acceleration (accelerometers) are used in smartphones, hearables and wearables, for example, to recognize gestures or to determine the orientation of the device in space. Due to the manufacturing process, however, these sensors have systematic measurement errors that have a negative effect on the orientation estimation. The measurement errors include offset errors, with the measured values of the sensor for at least one axis having systematic, additive deviations from the actual acceleration experienced by the sensor. As a result, the acceleration detected by the sensor deviates from the acceleration due to gravity even in the absence of external accelerations. The measurement errors also include sensitivity errors, with the measured acceleration deviating from the actual acceleration by a multiplicative factor for at least one axis. Finally, the measurement errors can also include orthogonality errors that arise because the three axes of the acceleration sensor are not exactly orthogonal to one another.

The systematic measurement errors can largely be eliminated by means of a pre-calibration at the end of the manufacturing process in the factory. However, further systematic errors (in particular offset errors) occur when the sensors are soldered on, which make a new calibration necessary. These systematic errors can be estimated using methods similar to those used in factory pre-calibration, typically placing the sensor very precisely in six different orientations and using the deviations between the actually expected acceleration values and the measured acceleration signals for the systematic errors these orientations are determined. In this case, the orientations correspond to an alignment of each sensor axis parallel to the gravitational acceleration vector, in each case in the positive and negative direction.

Furthermore, methods are known in which the acceleration sensor is brought into several (typically at least six) different positions whose exact orientation does not have to correspond exactly to the specified positions. Thus, from Zhang et al., "Improved multi-position calibration for inertial measurement units", Meas. Be. technol. 21, 2010, a corresponding calibration method for inertial measurement units is known. Furthermore, from Ye et al., "Optimum Experimental Design applied to MEMS accelerometer calibration for 9-parameter auto-calibration model", 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2015, a method for minimization of the variance in parameter estimation and prediction. Frosio et al., "Autocalibration of MEMS Accelerometers," IEEE Trans. Instrum. Meas, vol. 58(6), pp. 2034-2041, 2009 describes an autocalibration method for acceleration sensors.

Methods are also known which use the acceleration signals measured during normal use, such as Glueck et al., "Real-Time Autocalibration of MEMS Accelerometers," IEEE Trans. Instrum. Meas, vol 63(1), pp. 96-105, 2014.

Using an algorithm, offset errors and, if necessary, sensitivity and orthogonality errors are measured once or iteratively using the measured values recorded. This exploits the fact that the magnitude of the measured signal in the rest position should correspond to the magnitude of the acceleration due to gravity, regardless of the position.

Disclosure of Invention

The invention provides a method for calibrating a three-axis acceleration sensor with the features of patent claim 1.

Preferred embodiments are the subject matter of the dependent claims.

The invention therefore relates to a method for calibrating a three-axis acceleration sensor. In this case, the acceleration sensor is spatially aligned by successively bringing it into four different measurement orientations. the Measurement orientations are selected in such a way that the gravitational acceleration in the sensor coordinate system of the acceleration sensor points in different, non-coplanar directions for the four measurement orientations. In each of the four measurement orientations, at least one measured value is recorded for each axis of the acceleration sensor when the acceleration sensor is at rest in the respective measurement orientation. An offset to compensate for an offset measurement error is determined using the recorded measurement values.

Advantages of the Invention

The invention makes it possible to estimate offset errors of a three-axis acceleration sensor in such a way that systematic estimation errors of the offset are prevented from occurring as a result of small sensitivity errors. Such sensitivity errors can still remain even after sensitivity errors and orthogonality errors have already been corrected beforehand, with a test-signal-based method being used, for example.

The minimum number of measurement orientations needed to calibrate the offset of a triaxial accelerometer is three. For this purpose, the acceleration sensor is typically aligned in such a way that each of the three sensor axes is aligned once parallel to the gravitational acceleration vector. Due to the sensitivity error, however, the offset determined in this way shows a systematic error, i.e. the distribution of the offset error is not free of mean values. To prevent this, the measurement orientations must be evenly distributed in space. With three measurement orientations, however, such a distribution can only be achieved in one plane, so that the offset can only be determined for two axes of the acceleration sensor. In order to estimate the complete offset in such a way that no systematic estimation errors occur, at least four measurement orientations are required.

The invention makes it possible to use exactly four measurement orientations instead of the six measurement orientations that are usually used (+g and -g for each of the three sensor axes). The offset errors can thus be determined in the shortest possible time, since the calibration time is reduced due to the smaller number of measurement orientations. The number of measurement orientations is thus reduced to a minimum in order to obtain an offset error for all sensor axes that is free of mean values. According to a further embodiment of the method for calibrating the three-axis acceleration sensor, the four measurement orientations are selected in such a way that the gravitational acceleration in the sensor coordinate system of the acceleration sensor for the four measurement orientations is aligned essentially along symmetry axes of a regular tetrahedron centered around a coordinate origin of the sensor coordinate system. These are the lines of symmetry that connect the corners of the tetrahedron to the midpoints of opposite faces. The measurement orientations are thus distributed in space in such a way that the angles between the acceleration vectors are the same for each combination of two measurement orientations. This optimal distribution and alignment of the measurement orientations makes it possible to minimize the systematic influence of sensitivity errors and to obtain an offset error for all sensor axes that is free of mean values.

According to a further embodiment of the method for calibrating the three-axis acceleration sensor, the measurement orientations are selected in such a way that for each measurement orientation the acceleration values of the acceleration signal for each axis of the acceleration sensor essentially have a magnitude of g/[. This ensures that the distribution of the offset error is as equal as possible for all sensor axes.

In practice, however, it is not crucial for the method described that the ideal measurement orientations are adhered to exactly. Similarly good results can be obtained with measurement orientations that deviate slightly from the ideal measurement orientations. For example, it can be provided that for the measurement orientations the direction of the gravitational acceleration deviates from the optimal direction by at most a predetermined angle (approximately 10°). As a result, costs for the required measurement technology can be saved and the measurement duration and the calculation effort can be reduced.

According to a further embodiment of the method for calibrating the acceleration sensor, the sensor signals can be pre-processed for each measurement orientation before the actual estimation, for example by averaging. After the _preprocessed sensor signals a , . According to a further embodiment of the method for calibrating the acceleration sensor, the acceleration sensor is kept stationary in each of the four measurement orientations for a predetermined or predeterminable period of time. A large number of measured values are recorded for each axis of the acceleration sensor in each measurement orientation. For each measurement orientation, the measured values recorded for the individual axes of the acceleration sensor are averaged.

According to a further embodiment of the method for calibrating the acceleration sensor, determining the offset includes solving an optimization problem in order to minimize the sum of quadratic deviations between an amount of offset-compensated acceleration signals and an amount of the acceleration due to gravity. Accordingly, the following optimization problem is solved: min y (||a _n — 0II2 - g) ² . 0<n=l

According to a further embodiment of the method for calibrating the acceleration sensor, the optimization problem is solved using a Gauss-Newton algorithm. The solution can thus be generated within a few iterations.

According to a further embodiment of the method for calibrating the acceleration sensor, acceleration signals from the acceleration sensor are used to identify whether the acceleration sensor is at rest.

According to a further embodiment of the method for calibrating the acceleration sensor, the acceleration sensor is brought into the four different measurement orientations by means of a machine used for the calibration.

According to a further embodiment of the method for calibrating the acceleration sensor, the offset is determined on a microprocessor integrated in the acceleration sensor.

According to a further embodiment of the method for calibrating the acceleration sensor, the method is carried out after the installation of the Acceleration sensor performed in a device, in particular a smartphone, a hearable or a wearable.

According to one embodiment of the invention, the method is carried out in end-of-strip trimming and inspection.

According to one embodiment of the invention, the method can be carried out during use by end users. A user of the method can be assisted in using the method with the aid of visual, audio-visual or other instructions.

According to one embodiment of the invention, the method is carried out on a microprocessor integrated in the sensor module. Provision can also be made for the method to be carried out on a processor of the device in which the sensor is integrated.

From the start of the method, the acceleration sensor can record measurement data continuously or at specific times. Based on the measured data, it is automatically determined when there is a measurement orientation, for example by comparing the variance of several consecutive measured values with a threshold value in order to determine whether the sensor is at rest.

According to a further embodiment of the method for calibrating the acceleration sensor, a user and/or a machine for calibrating the acceleration sensor can initiate the method. The user and/or the machine can use a trigger to signal when a measurement orientation has been reached.

Brief description of the drawings

Show it:

FIG. 1 shows a flow chart of a method for calibrating a three-axis acceleration sensor according to an embodiment of the invention; and FIG. 2 shows a schematic illustration of measurement orientations according to an embodiment of the method for calibrating the three-axis acceleration sensor.

The numbering of method steps is for the sake of clarity and should not generally imply a specific chronological order. In particular, several method steps can also be carried out simultaneously.

Description of the exemplary embodiments

FIG. 1 shows a flow chart of a method for calibrating a three-axis acceleration sensor. The method can be carried out after the acceleration sensor has been installed in a device, in particular a smartphone, a hearable or a wearable.

In the first method step S1, the method for calibrating the three-axis acceleration sensor is started. The calibration process can be started automatically or triggered by a user.

For calibration, the acceleration sensor can be introduced into a machine which can bring the acceleration sensor into predetermined measurement orientations. The machine can also include a computing device for calculating the offset measurement error and is coupled to the acceleration sensor for this purpose in order to receive measurement signals from the acceleration sensor and to send calibration signals to the acceleration sensor.

However, the invention is not limited to this. A microprocessor integrated in the acceleration sensor can also determine the offset.

In a second method step S2, the acceleration sensor is spatially aligned by the machine or by a user in such a way that it is brought into a first measurement orientation. When the accelerometer is at rest, the measurement data captured by the accelerometer can be used for calibration. The acceleration sensor records at least one measured value for each of the three axes of the acceleration sensor, ie at least one measured acceleration value for each axis. Provision can be made for the acceleration sensor to be at rest for a specific period of time before the measurement data used for the calibration is recorded. Whether the acceleration sensor is at rest can also be determined using measurement data from the acceleration sensor. The length of time during which the acceleration sensor should be at rest can depend on the sensor noise, the ambient noise and the desired accuracy of determination of the offset and can be specified or set by a user.

If the acceleration sensor is moved into the measurement orientations by means of a machine, it is also possible to start acquiring the measurement data, which are used for the calibration, directly after the respective position has been reached.

In a further step S3, the measurement data is pre-processed. For this purpose, different measured values can be averaged in order to calculate an averaged measured value for each of the axes of the acceleration sensor. The averaged measured values can be used for the following calculations.

In a method step S4, the averaged measured value is stored after a time interval has elapsed.

In a method step S5, it is determined whether the acceleration sensor is to be brought into further measurement orientations. If this is the case, the machine or the user moves the acceleration sensor into a further remaining measurement orientation and steps S2 to S4 are carried out again for this measurement orientation. This continues until the acceleration sensor has been brought into four different measurement orientations. The four measurement orientations are selected in such a way that the gravitational acceleration in the sensor coordinate system of the acceleration sensor for the four measurement orientations points in different, non-coplanar (ie not in one plane) directions.

After the acceleration sensor has been brought into all four measurement orientations and corresponding measurement values have been recorded, if necessary averaged and stored, in a method step S6 an offset measurement error is calculated using the stored measurement values estimated. The offset can be determined by solving an optimization problem where the sum of squared deviations between a magnitude of offset-compensated acceleration signals and a magnitude of the acceleration due to gravity is minimized. The optimization problem can be solved using a Gauss-Newton algorithm.

The estimated offset is provided in a method step S7. The accelerometer can be calibrated using the provided offset. FIG. 2 shows a schematic illustration of measurement orientations. the

Coordinate axes x, y, z correspond to the three measurement axes and thus specify a sensor coordinate system. Four different measurement orientations RI to R4 are also shown, which are aligned along symmetry axes of a regular tetrahedron T centered around a coordinate origin of the sensor coordinate system. The acceleration values of the acceleration signal for each axis x, y, z of the acceleration sensor preferably have an absolute value of g/[ for each measurement orientation.

Claims

Expectations

1. Method for calibrating a three-axis accelerometer, in which the accelerometer is spatially aligned by successively bringing it into four different measurement orientations, which are chosen such that the gravitational acceleration in the sensor coordinate system of the accelerometer for the four measurement orientations is in different, non-coplanar directions ( R1-R4), in which at least one measured value is recorded in each of the four measurement orientations for each axis (x, y, z) of the acceleration sensor when the acceleration sensor is at rest in the respective measurement orientation, and in which using the recorded Measured values, an offset to compensate for an offset measurement error is determined.

2. The method as claimed in claim 1, in which the four measurement orientations are selected such that the gravitational acceleration in the sensor coordinate system of the acceleration sensor for the four measurement orientations is aligned essentially along axes of symmetry of a regular tetrahedron centered around a coordinate origin of the sensor coordinate system.

3. The method as claimed in claim 2, in which the measurement orientations are selected in such a way that for each measurement orientation the acceleration values of the acceleration signal for each axis (x, y, z) of the acceleration sensor essentially have an absolute value of g/[.

4. The method as claimed in one of the preceding claims, in which the acceleration sensor is kept stationary in each of the four measurement orientations for a predetermined or predeterminable period of time, a large number of measured values being recorded in each measurement orientation for each axis (x, y, z) of the acceleration sensor and in which the measured values recorded for the individual axes (x, y, z) of the acceleration sensor are averaged for each measurement orientation. A method according to any one of the preceding claims, wherein determining the offset comprises solving an optimization problem to minimize the sum of squared deviations between a magnitude of offset-compensated acceleration signals and a magnitude of the acceleration due to gravity. Method according to Claim 5, in which the optimization problem is solved using a Gauss-Newton algorithm. Method according to one of the preceding claims, wherein it is detected on the basis of acceleration signals from the acceleration sensor whether the acceleration sensor is at rest. Method according to one of the preceding claims, in which the acceleration sensor is brought into the four different measurement orientations by means of a machine used for calibration. Method according to one of the preceding claims, in which the determination of the offset is carried out on a microprocessor which is integrated in the acceleration sensor. Method according to one of the preceding claims, wherein the method is carried out after the acceleration sensor has been installed in a device, in particular a smartphone, a hearable or a wearable.