Multi-imu extrinsic calibration method

Abstract

This invention relates to a multi-IMU extrinsic parameter calibration method, comprising: constructing an IMU output model; calibrating the random walks and noise of each IMU in the IMU array; recording IMU array data; arbitrarily selecting one IMU from the IMU array as a reference IMU, using the coordinate system of the reference IMU as the reference coordinate system, establishing and solving a nonlinear least squares problem about rotation quaternions between the reference IMU and the other IMUs to be calibrated; generating virtual angular velocity observations for the other IMUs to be calibrated based on the calibrated relative rotation extrinsic parameters; and establishing and solving a nonlinear least squares problem about translation between the reference IMU and the other IMUs to be calibrated based on the virtual angular velocity observations of the other IMUs. This invention does not rely on the environment or external sensors and can complete calibration quickly.

Description

Technical Field

[0001] This invention relates to the field of autonomous driving technology, and in particular to a method for calibrating the extrinsic parameters of multiple IMUs. Background Technology

[0002] In the field of Simultaneous Localization and Mapping (SLAM), multi-inertial sensor fusion is a hot topic. Inertial Measurement Units (IMUs), as proprioceptive sensors, can output observations at high frequencies, but they suffer from attitude drift during long-term localization. Therefore, IMUs can collaborate with external sensors (such as LiDAR and cameras) to provide global observations. Due to the advantages of microelectromechanical systems (MEMS) IMUs, such as compact size and low cost, SLAM systems can add more IMUs for master-slave backup or to improve localization accuracy.

[0003] Most SLAM research neglects the extrinsic accuracy of multiple IMUs, yet it plays a crucial role in fusion algorithms. Most vision-multiple IMU systems assume perfect extrinsic calibration between each IMU and sensor module. However, simulations show that using only a single IMU can achieve better localization accuracy if sufficiently accurate sensor extrinsic parameters cannot be guaranteed.

[0004] To date, existing external calibration methods for multiple IMUs require accurate self-trajectories and rely on expensive turntables or external sensors (such as cameras). While these algorithms can achieve good calibration results in specific environments, they are limited by the external environment and additional sensor equipment. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a multi-IMU extrinsic parameter calibration method that does not depend on the environment and external sensors and can quickly complete the calibration.

[0006] The technical solution adopted by this invention to solve its technical problem is: to provide a multi-IMU extrinsic parameter calibration method, comprising the following steps:

[0007] Construct an IMU output model, which includes random walks and noise;

[0008] Calibrate the random walks and noise of each IMU on the IMU array;

[0009] Record IMU array data;

[0010] Take any IMU from the IMU array as the reference IMU, use the coordinate system of the reference IMU as the reference coordinate system, establish a nonlinear least squares problem about rotation quaternions between the reference IMU and the other IMUs to be calibrated, and solve the rotation extrinsic parameter calibration of the other IMUs to be calibrated relative to the reference IMU.

[0011] Based on the calibrated relative rotation extrinsic parameters, generate virtual angular velocity observations for the remaining IMUs to be calibrated;

[0012] Based on the virtual angular velocity observations of the other IMUs to be calibrated, a nonlinear least squares problem about translation is established between the reference IMU and the other IMUs to be calibrated, and the translational extrinsic parameter calibration of the other IMUs to be calibrated relative to the reference IMU is completed by solving the problem.

[0013] The IMU output model is Where I represents the sensor coordinate system and W represents the world coordinate system. and Let ω(t) and a(t) represent the triaxial angular velocity values ​​output by the gyroscope and the triaxial linear acceleration values ​​output by the accelerometer in the IMU at time t, respectively; ω(t) and a(t) represent the observation values ​​of the gyroscope and the accelerometer in the IMU at time t, respectively; b g (t) and b a (t) represent the deviations of the gyroscope and accelerometer observations in the IMU at time t, respectively, modeled as a random walk; η g (t) and η a (t) represents the noise of the gyroscope observation and the accelerometer observation in the IMU at time t, respectively, and is modeled as a Wiener process; R represents the rotation matrix in the world coordinate system; g represents the gravity vector.

[0014] When recording IMU array data, each axis is excited in a figure-eight pattern, and a total of 200 frames of data are recorded, including angular velocity and linear acceleration.

[0015] The nonlinear least squares problem regarding rotation between the reference IMU and the other IMUs is as follows: In this table, A represents the reference IMU, and B represents the IMU to be calibrated. B q A The rotation quaternion represents the number of times between the reference IMU and the other IMUs to be calibrated, and T represents the time set of sampling. It is the residual of the angular velocity observation. χ represents the system state variables of the IMU to be estimated. Let the first covariance matrix be denoted as . Where, σ g This represents the variance of the gravity estimate. It represents the variance of the bias estimate, Δt represents the time sampling interval, and I3 represents the 3x3 identity matrix.

[0016] The virtual angular velocity observations of the remaining IMU to be calibrated are obtained through... The calculation yielded that, This represents the virtual angular velocity observation value, and freq represents the sampling frequency.

[0017] The nonlinear least squares problem regarding translation between the reference IMU and the other IMUs to be calibrated is as follows: in, B p A This represents the translation parameters between the reference IMU and the other IMUs to be calibrated. It is the residual between the observed angular velocity and linear acceleration. A p B Indicates the location of the reference IMU. Let the second covariance matrix be represented.

[0018] in,

[0019] σ a This represents the variance of acceleration noise. This represents the variance of the acceleration bias.

[0020] Beneficial effects

[0021] By employing the above-described technical solution, this invention has the following advantages and positive effects compared to existing technologies: This invention does not require equipment such as an IMU turntable, and it does not rely on external sensors. Compared to existing methods, this invention only needs to collect 200 frames of data and can achieve better calibration accuracy within 2 seconds. Compared to existing methods, with the same amount of data, this invention is faster and more applicable, and can successfully calibrate in various IMU array experiments. Attached Figure Description

[0022] Figure 1 This is a flowchart of the multi-IMU extrinsic parameter calibration method according to an embodiment of the present invention. Detailed Implementation

[0023] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0024] The embodiments of the present invention relate to a multi-IMU extrinsic parameter calibration method, such as... Figure 1 As shown, it includes the following steps:

[0025] Step 1: Construct the IMU output model. An IMU typically includes a gyroscope and an accelerometer. The gyroscope outputs three-axis angular velocity values, and the accelerometer outputs three-axis linear acceleration values. The output model is as follows:

[0026]

[0027]

[0028] Where I represents the sensor coordinate system and W represents the world coordinate system. and ω(t) and a(t) represent the three-axis angular velocity values ​​output by the gyroscope and the three-axis linear acceleration values ​​output by the accelerometer in the IMU at time t, respectively; R represents the rotation matrix in the world coordinate system; g represents the gravity vector.

[0029] b g (t) and b a (t) represent the deviations of the gyroscope and accelerometer observations in the IMU at time t, respectively, modeled as a random walk:

[0030]

[0031]

[0032] in, and Let represent the noise estimates for angular velocity and acceleration bias, respectively. and I0 and I3 represent the angular velocity and acceleration bias variance, respectively, and I3 represents the 3x3 identity matrix.

[0033] η g (t) and η a (t) represent the noise of the gyroscope observations and the accelerometer observations in the IMU at time t, respectively, modeled as a Wiener process:

[0034]

[0035] Where, σ g and σ a Let each represent the variance of the angular velocity.

[0036] Step 2: Calibrate the random walk and noise parameters of each IMU on the IMU array using Kalibr.

[0037] Step 3: Record IMU array data. The recorded data includes angular velocity and linear acceleration. Each axis can be excited by moving in a figure-eight motion. The amount of data recorded is about 200 frames. For example, for an IMU with a frequency of 100Hz, 2 seconds of data need to be recorded.

[0038] Step 4: Randomly select one IMU from the IMU array as the reference IMU. Using the coordinate system of the reference IMU as the reference coordinate system, establish a nonlinear least squares problem about rotation quaternions between the reference IMU and the other IMUs to be calibrated. By solving this nonlinear least squares problem, the rotational extrinsic parameters of the other IMUs to be calibrated relative to the reference IMU can be calibrated. For example: using the A-th IMU as the reference IMU and the B-th IMU as the IMU to be calibrated, define the rotation quaternion between them. B q A Nonlinear least squares problem:

[0039]

[0040] in, It is the residual of the angular velocity observations:

[0041]

[0042] The corresponding covariance matrix is:

[0043]

[0044] Step 5: Based on the calibrated relative rotation extrinsic parameters, generate virtual angular velocity observations for the remaining IMUs to be calibrated. Taking the Bth IMU as an example, the virtual angular velocity observations are generated as follows:

[0045]

[0046] in, This represents the virtual angular velocity observation value, and freq represents the sampling frequency.

[0047] Step 6: Based on the virtual angular velocity observations of the remaining IMUs to be calibrated, establish a nonlinear least squares problem regarding translation between the reference IMU and the other IMUs to be calibrated, and solve it to complete the translational extrinsic parameter calibration of the remaining IMUs relative to the reference IMU. For example: taking the A-th IMU as the reference IMU and the B-th IMU as the IMU to be calibrated, define the relationship between them regarding translation... B p A Nonlinear least squares problem:

[0048]

[0049] in, It is the residual between the observed angular velocity and linear acceleration:

[0050]

[0051] in, A pB Indicates the location of the reference IMU.

[0052] Here is the corresponding covariance matrix:

[0053]

[0054] The nonlinear least squares problem in this embodiment can be solved using Google Ceres or OpenSLAM g2o tools.

[0055] It is easy to see that this invention does not require equipment such as an IMU turntable, and it does not rely on external sensors. Compared with existing methods, this invention only needs to collect 200 frames of data and can achieve better calibration accuracy within 2 seconds. Compared with existing methods, with the same amount of data, this invention is faster and more applicable, and can be successfully calibrated in various IMU array experiments.

Claims

1. A multi-IMU extrinsic calibration method, characterized in that, The method comprises the following steps: constructing an IMU output model, which comprises random walk and noise; calibrating the 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 the coordinate system of the reference IMU as a reference coordinate system, establishing a nonlinear least squares problem about rotational quaternion between the reference IMU and the remaining IMUs to be calibrated, and solving the rotational extrinsic parameter calibration of the remaining IMUs to be calibrated relative to the reference IMU; generating virtual angular velocity observation values of the remaining IMUs to be calibrated according to the calibrated relative rotational extrinsic parameters; establishing a nonlinear least squares problem about translation between the reference IMU and the remaining IMUs to be calibrated according to the virtual angular velocity observation values of the remaining IMUs to be calibrated, and solving the translational extrinsic parameter calibration of the remaining IMUs to be calibrated relative to the reference IMU.

2. The multi-IMU extrinsic calibration method of claim 1, wherein, The IMU output model is where I denotes the sensor coordinate system, W denotes the world coordinate system, and respectively denote the three-axis angular velocity value and the three-axis linear acceleration value of the gyroscope output and the accelerometer output in the IMU at time t; ω(t) and a(t) respectively denote the observation value of the gyroscope and the observation value of the accelerometer in the IMU at time t; b g (t) and b a (t) respectively denote the bias of the observation value of the gyroscope and the bias of the observation value of the accelerometer in the IMU at time t, and are modeled as random walks; η g (t) and η a (t) respectively denote the noise of the observation value of the gyroscope and the noise of the observation value of the accelerometer in the IMU at time t, and are modeled as Wiener processes; R denotes a rotation matrix in the world coordinate system; and g denotes a gravity vector.

3. The multi-IMU extrinsic calibration method of claim 1, wherein, When recording the IMU array data, each axis is excited in the form of an 8-shaped path, and a total of 200 frames of data are recorded, which includes angular velocity and linear acceleration.

4. The multi-IMU extrinsic calibration method of claim 2, wherein, The nonlinear least squares problem between the reference IMU and the rest of the IMUs with respect to rotations is: where A represents the reference IMU, B denotes the IMUs to be calibrated, B q A denotes the rotation quaternion between the reference IMU and the rest of the IMUs to be calibrated, T denotes the set of time samples, is the residual of the angular velocity observation, χ represents the system state quantities of the IMUs to be estimated, denotes the first covariance matrix, where σ g denotes the variance of the gravity estimate, denotes the variance of the bias estimate, Δt denotes the time sampling interval, I3 denotes the 3*3 identity matrix.

5. The multi-IMU extrinsic calibration method of claim 4, wherein, The virtual angular velocity observation value of the remaining to be calibrated IMU is calculated by wherein, represents the virtual angular velocity observation value, and freq represents the sampling frequency.

6. The multi-IMU extrinsic calibration method of claim 5, wherein, The nonlinear least squares problem in translation between the reference IMU and the rest of the IMUs to be calibrated is: where, B p A denotes the translation parameters between the reference IMU and the rest of the IMUs to be calibrated, is the residual of the angular velocity and linear acceleration observations, A p B denotes the position of the reference IMU, denotes the second covariance matrix, where, a denotes the acceleration noise variance, denotes the variance of the acceleration bias.

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