CN116295525A - Multi-IMU external parameter calibration method - Google Patents
Multi-IMU external parameter calibration method Download PDFInfo
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- 239000011159 matrix material Substances 0.000 claims description 13
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Abstract
The invention relates to a multi-IMU external parameter calibration method, which comprises the following steps: constructing an IMU output model; calibrating random walk and noise of each IMU on the IMU array; recording IMU array data; taking any IMU from the IMU array as a reference IMU, taking a coordinate system of the reference IMU as a reference coordinate system, establishing a nonlinear least square problem about rotation quaternion between the reference IMU and other IMUs to be calibrated, and solving; generating virtual angular velocity observation values of the rest IMUs to be calibrated according to the calibrated relative rotation external parameters; and establishing a nonlinear least square problem between the reference IMU and the rest IMUs to be calibrated with respect to translation according to the virtual angular velocity observation values of the rest IMUs to be calibrated, and solving. The invention is independent of environment and external sensors, and can rapidly complete calibration.
Description
Technical Field
The invention relates to the technical field of automatic driving, in particular to a multi-IMU external parameter calibration method.
Background
In the field of simultaneous localization and mapping (SLAM), multi-inertial sensor fusion is a hot topic. The inertial measurement unit IMU can output an observed value at a high frequency as a proprioceptive sensor, but has a problem of posture drift in long-time positioning. Thus, the IMU may cooperate with external sensors (e.g., lidar and cameras) to provide global observations. Because of the advantages of compact size, low cost, and the like of microelectromechanical system (MEMS) IMUs, SLAM systems can add more IMUs for master-slave backup or to improve positioning accuracy.
Most SLAM studies ignore the extrinsic accuracy of multiple IMUs, but it plays an important role in fusion algorithms, and most vision-multiple IMU systems assume that the extrinsic between each IMU and sensor module is perfectly calibrated. However, according to simulation experiments, if the sensor external parameters with enough accuracy cannot be ensured, only one IMU is used, and the positioning accuracy is better.
To date, existing external calibration methods for multiple IMUs require accurate self-trajectories, relying on expensive turrets or external sensors (e.g., cameras). While these algorithms may perform well in certain environments, they are limited to the external environment and additional sensor devices.
Disclosure of Invention
The invention aims to solve the technical problem of providing a multi-IMU external parameter calibration method which is independent of environment and external sensors and can quickly complete calibration.
The technical scheme adopted for solving the technical problems is as follows: the multi-IMU external parameter calibration method comprises the following steps:
an IMU output model is built, wherein the output model comprises random walk and noise;
calibrating random walk and noise of each IMU on the IMU array;
recording IMU array data;
taking any IMU from the IMU array as a reference IMU, taking a coordinate system of the reference IMU as a reference coordinate system, establishing a nonlinear least square problem about rotation quaternion between the reference IMU and other IMUs to be calibrated, and solving and completing rotation external parameter calibration of the other IMUs to be calibrated relative to the reference IMU;
generating virtual angular velocity observation values of the rest IMUs to be calibrated according to the calibrated relative rotation external parameters;
and establishing a nonlinear least square problem about translation between the reference IMU and the other IMUs to be calibrated according to the virtual angular velocity observation values of the other IMUs to be calibrated, and solving and completing the translation external parameter calibration of the other IMUs to be calibrated relative to the reference IMU.
The IMU output model is
Wherein I represents a sensor coordinate system, W represents a world coordinate system, < >>
And->
Respectively representing a triaxial angular velocity value output by a gyroscope and a triaxial linear acceleration value output by an accelerometer in the IMU at the time t; omega (t) and a (t) represent the observed value of the gyroscope and the observed value of the accelerometer in the IMU at time t, respectively; b g (t) and b a (t) representing the deviation of the observed value of the gyroscope and the deviation of the observed value of the accelerometer in the IMU at time t, respectively, and modeling as a random walk; η (eta) g (t) and eta a (t) modeling as wiener processes, representing noise of the observations of the gyroscopes and noise of the observations of the accelerometers in the IMU at time t, respectively; r represents a rotation matrix in a world coordinate system; g represents a gravity vector.
When the IMU array data is recorded, the IMU array data is excited to each axis in an 8-shaped mode, and 200 frames of data are recorded, wherein the data comprise angular velocity and linear acceleration.
The nonlinear least squares problem between the reference IMU and the remaining IMUs with respect to rotation is:
wherein, A represents a reference IMU, B represents an IMU to be calibrated, B q A representing a rotation quaternion between the reference IMU and the remaining IMUs to be calibrated, T representing a time set of samples, < ->
Is the residual of the angular velocity observation,
χ represents the system state quantity of the IMU to be estimated, +.>
A first covariance matrix is represented by,
wherein sigma g Representing the variance of the gravity estimation +.>
Representing the variance of the bias estimate, Δt represents the time sampling interval, I 3 Representing the identity matrix of 3*3.
The virtual angular velocity observation value of the IMU to be calibrated passes
Calculated, wherein->
Representing the virtual angular velocity observation, freq represents the sampling frequency.
The nonlinear least square problem about translation between the reference IMU and the remaining IMUs to be calibrated is:
wherein,, B p A representing translation parameters between the reference IMU and the remaining IMUs to be calibrated, < >>
Is the residual of the angular velocity and linear acceleration observations,/->
A p B Representing the position of the reference IMU->
A second covariance matrix is represented by a second covariance matrix,
σ a representing the variance of the acceleration noise,
representing the variance of the acceleration bias.
Advantageous effects
Due to the adoption of the technical scheme, compared with the prior art, the invention has the following advantages and positive effects: the invention does not need IMU turntable equipment and the like, and does not depend on an external sensor, and compared with the prior method, the invention can achieve better calibration accuracy within 2 seconds by only collecting 200 frames of data. Compared with the prior art, the method has the advantages of higher speed and higher applicability under the same data, and can be used for successfully calibrating various IMU array experiments.
Drawings
FIG. 1 is a flow chart of a multi-IMU extrinsic parameter calibration method according to an embodiment of the present invention.
Detailed Description
The invention will be further illustrated with reference to specific examples. It is to be understood that these examples are illustrative of the present invention and are not intended to limit the scope of the present invention. Further, it is understood that various changes and modifications may be made by those skilled in the art after reading the teachings of the present invention, and such equivalents are intended to fall within the scope of the claims appended hereto.
The embodiment of the invention relates to a multi-IMU external parameter calibration method, as shown in fig. 1, comprising the following steps:
step 1, an IMU output model is built, the IMU generally comprises a gyroscope and an accelerometer, wherein the gyroscope outputs a three-axis angular velocity value, the accelerometer outputs a three-axis linear acceleration value, and the output model is as follows:
wherein I represents a sensor coordinate system, W represents a world coordinate system,
and->
Respectively representing a triaxial angular velocity value output by a gyroscope and a triaxial linear acceleration value output by an accelerometer in the IMU at the time t; omega (t) and a (t) respectively represent the observed value of a gyroscope and the observed value of an accelerometer in the IMU at the moment t, and R represents a rotation matrix under a world coordinate system; g represents a gravity vector.
b g (t) and b a (t) represents the deviation of the observed value of the gyroscope and the deviation of the observed value of the accelerometer in the IMU at time t, respectively, and is modeled as a random walk:
wherein,,
and->
Noise estimates representing angular velocity and acceleration bias, respectively,/->
And->
Respectively representing angular velocity and acceleration bias variance, I 3 Representing the identity matrix of 3*3.
η g (t) and eta a (t) noise representing the gyroscope observations and the accelerometer observations in the IMU at time t, respectively, modeled as a wiener process:
wherein sigma g Sum sigma a The variances of the angular velocities are respectively represented.
And 2, calibrating random walk and noise parameters of each IMU on the IMU array through Kalibr.
And 3, recording IMU array data, wherein the recorded data comprises angular velocity and linear acceleration, the IMU array data can be excited to each axis by 8 words, the recorded data volume is about 200 frames of data, for example, the IMU with the frequency of 100Hz is required to record 2 seconds of data.
And 4, taking any IMU from the IMU array as a reference IMU, taking a coordinate system of the reference IMU as a reference coordinate system, establishing a nonlinear least square problem about rotation quaternion between the reference IMU and the other IMU to be calibrated, and completing the rotation external parameter calibration of the other IMU to be calibrated relative to the reference IMU by solving the nonlinear least square problem. For example: the A-th IMU is taken as a reference IMU, the B-th IMU is taken as an IMU to be calibrated, and rotation quaternion between the A-th IMU and the B-th IMU is defined B q A Nonlinear least squares problem of (2):
wherein,,
is the residual of the angular velocity observation:
and 5, generating virtual angular velocity observation values of the rest IMUs to be calibrated according to the calibrated relative rotation external parameters, wherein the virtual angular velocity observation values are generated by taking the B-th IMU as an example as follows:
wherein,,
representing the virtual angular velocity observation, freq represents the sampling frequency.
And 6, establishing a nonlinear least square problem about translation between the reference IMU and the other IMUs to be calibrated according to the virtual angular velocity observation values of the other IMUs to be calibrated, and solving and completing the translation external parameter calibration of the other IMUs to be calibrated relative to the reference IMU. For example: the A-th IMU is taken as a reference IMU, the B-th IMU is taken as an IMU to be calibrated, and translation is defined between the A-th IMU and the B-th IMU B p A Nonlinear least squares problem of (2):
wherein,,
is the residual of the angular velocity and linear acceleration observations:
wherein,, A p B representing the location of the reference IMU.
in this embodiment, the nonlinear least squares problem can be solved using Google Ceres or OpenSLAM g2o tools.
It is not difficult to find that the invention does not need IMU turntable equipment and the like, and meanwhile, does not depend on an external sensor, compared with the existing method, the invention can achieve better calibration accuracy within 2 seconds by only collecting 200 frames of data. Compared with the prior art, the method has the advantages of higher speed and higher applicability under the same data, and can be used for successfully calibrating various IMU array experiments.
Claims (6)
1. The multi-IMU external parameter calibration method is characterized by comprising the following steps of:
an IMU output model is built, wherein the output model comprises random walk and noise;
calibrating random walk and noise of each IMU on the IMU array;
recording IMU array data;
taking any IMU from the IMU array as a reference IMU, taking a coordinate system of the reference IMU as a reference coordinate system, establishing a nonlinear least square problem about rotation quaternion between the reference IMU and other IMUs to be calibrated, and solving and completing rotation external parameter calibration of the other IMUs to be calibrated relative to the reference IMU;
generating virtual angular velocity observation values of the rest IMUs to be calibrated according to the calibrated relative rotation external parameters;
and establishing a nonlinear least square problem about translation between the reference IMU and the other IMUs to be calibrated according to the virtual angular velocity observation values of the other IMUs to be calibrated, and solving and completing the translation external parameter calibration of the other IMUs to be calibrated relative to the reference IMU.
2. The multi-IMU extrinsic reference calibration method according to claim 1, wherein said IMU output model is
Wherein I represents a sensor coordinate system, W represents a world coordinate system, < >>
And
respectively representing a triaxial angular velocity value output by a gyroscope and a triaxial linear acceleration value output by an accelerometer in the IMU at the time t; omega (t) and a (t) represent the observed value of the gyroscope and the observed value of the accelerometer in the IMU at time t, respectively; b g (t) and b a (t) representing the deviation of the observed value of the gyroscope and the deviation of the observed value of the accelerometer in the IMU at time t, respectively, and modeling as a random walk; η (eta) g (t) and eta a (t) modeling as wiener processes, representing noise of the observations of the gyroscopes and noise of the observations of the accelerometers in the IMU at time t, respectively; r represents a rotation matrix in a world coordinate system; g represents a gravity vector.
3. The method of claim 1, wherein the recording of IMU array data is performed by exciting each axis in an 8-word manner, and the total recording of 200 frames of data, including angular velocity and linear acceleration.
4. The multi-IMU extrinsic calibration method according to claim 2, wherein a nonlinear least squares problem between the reference IMU and the remaining IMUs with respect to rotation is:
wherein, A represents a reference IMU, B represents an IMU to be calibrated, B q A representing the rotation quaternion between the reference IMU and the remaining IMUs to be calibrated, T representing the time set of samples,
is the residual of the angular velocity observation, +.>
χ represents the system state quantity of the IMU to be estimated, +.>
Representing a first covariance matrix,>
wherein sigma g Representing the variance of the gravity estimation +.>
Representing the variance of the bias estimate, Δt represents the time sampling interval, I 3 Representing the identity matrix of 3*3.
5. The multi-IMU extrinsic calibration method according to claim 4, wherein said virtual angular velocity observation value of said remaining IMU to be calibrated is through
Calculated, wherein->
Representing virtual angular velocityObservations, freq, represent sampling frequency.
6. The multi-IMU extrinsic calibration method according to claim 5, wherein a nonlinear least squares problem between the reference IMU and the remaining IMUs to be calibrated with respect to translation is:
wherein,, B p A representing translation parameters between the reference IMU and the remaining IMUs to be calibrated, < >>
Is the residual of the angular velocity and linear acceleration observations,/->
A p B Representing the position of the reference IMU->
Representing a second covariance matrix,>
wherein sigma a Representing acceleration noise variance->
Representing the variance of the acceleration bias.
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