There are several open source IMU instrinsic calibration tools. However the result of those tools varies a lot and the calibration result is difficult to evaluate.
So I create a tool to simulate IMU data by implementing IMU-Noise-Model then use the tools to calibrate simulated IMU data. After comparing IMU simulator configuration and calibration result, I found allan_variance_ros gives a good result.

Experiment steps

1. Simulate IMU Data: Build the branch feature-support-imu-simulation and run rosrun allan_variance_ros imu_simulator imu-sim.bag config/simulation/imu_simulator.yaml to get simulated imu data imu-sim.bag;
2. Compute calibration result: Use calibration tool to get imu.yaml.

Result analysis

Simulator configuration config/simulation/imu_simulator.yaml and result of allan_variance_ros fit very well, especially the noise_density.

config/simulation/imu_simulator.yaml

#Accelerometer
accelerometer_noise_density: 0.0025019929573561175 
accelerometer_random_walk: 6.972435158192731e-05
accelerometer_bias: 0.007

#Gyroscope
gyroscope_noise_density: 0.0001888339269965301 
gyroscope_random_walk: 2.5565313322052523e-06
gyroscope_bias: 0.006

rostopic: '/sensors/imu'
update_rate: 400.0

sequence_time: 11000

imu.yaml

#Accelerometer
accelerometer_noise_density: 0.002514275004256148 
accelerometer_random_walk: 7.839662376685361e-05 

#Gyroscope
gyroscope_noise_density: 0.00018857851446797772 
gyroscope_random_walk: 3.4044926542479456e-06 

rostopic: '/sensors/imu' #Make sure this is correct
update_rate: 400.0 #Make sure this is correct

Log graph of simulated data:

I also test imu_utils, but get a bad result:

%YAML:1.0
---
type: IMU
name: xsens
Gyr:
   unit: " rad/s"
   avg-axis:
      gyr_n: 3.7434416456652866e-03
      gyr_w: 2.6282617430254198e-05
   x-axis:
      gyr_n: 3.7318006434153101e-03
      gyr_w: 2.5886094931213328e-05
   y-axis:
      gyr_n: 3.7504972327004698e-03
      gyr_w: 2.6307730658703765e-05
   z-axis:
      gyr_n: 3.7480270608800802e-03
      gyr_w: 2.6654026700845500e-05
Acc:
   unit: " m/s^2"
   avg-axis:
      acc_n: 4.9111024092767130e-02
      acc_w: 4.7116333895251159e-04
   x-axis:
      acc_n: 5.0225631388534600e-02
      acc_w: 4.2043757646841598e-04
   y-axis:
      acc_n: 4.8325112701115391e-02
      acc_w: 5.1573007305579790e-04
   z-axis:
      acc_n: 4.8782328188651393e-02
      acc_w: 4.7732236733332096e-04

Hi author, Thanks for your sharing so convient tool to community very much. In code we average three axis Accel Random Walk to get accelerometer_random_walk of kalibr. accelerometer_random_walk's unit is m/s^3/sqrt(HZ), namely m/s^2/sqrt(s), but the Accel Random Walk's unit is m/s^2, is there a typo ? The same question exist about Rate Random Walk. Velocity Random Walk and Angle Random Walk units are equal to accelerometer_noise_density and gyroscope_noise_densityof kalibr. Thanks for your help and time! https://github.com/ori-drs/allan_variance_ros/blob/25a33882f1fafddc910dbbdb0e2d4858cde009fc/scripts/analysis.py#L121

I am getting the following on the example simulation:

#Accelerometer
accelerometer_noise_density: 0.0025019929573561175 #true
accelerometer_noise_density: 0.0017989768146338795 

accelerometer_random_walk: 6.972435158192731e-05 #true
accelerometer_random_walk: 5.073249247970349e-05 

#Gyroscope
gyroscope_noise_density: 0.0001888339269965301  #true
gyroscope_noise_density: 0.00013494835013762752 

gyroscope_random_walk: 2.5565313322052523e-06 #true
gyroscope_random_walk: 2.324462789522549e-06 

rostopic: '/sensors/imu' 
update_rate: 400 

The accelerometer_noise_density seems to be almost half what it should be here.

Here is the script I am using to generate this result: simulate_imu.sh.txt

• Hi, I've recorded IMU data (all topics) with SBG Ellipse. When I turn on cookbag. py, I get this error:

> magda@magda-VirtualBox:~$ cd catkin_ws
> magda@magda-VirtualBox:~/catkin_ws$ source devel/setup.bash
> magda@magda-VirtualBox:~/catkin_ws$ rosrun allan_variance_ros cookbag.py --input /home/magda/catkin_ws/src/allan_variance_ros/2022-08-12-12-14-04.bag --output cooked_rosbag
> Failed to load Python extension for LZ4 support. LZ4 compression will not be available.
> Traceback (most recent call last):
>   File "/home/magda/catkin_ws/src/allan_variance_ros/scripts/cookbag.py", line 14, in <module>
>     with rosbag.Bag(args.output, 'w', compression='lz4') as outbag:
>   File "/opt/ros/melodic/lib/python2.7/dist-packages/rosbag/bag.py", line 445, in __init__
>     raise ValueError('compression must be one of: %s' % ', '.join(allowed_compressions))  
> **ValueError: compression must be one of: none, bz2**

• But then I run normally

> rosrun allan_variance_ros allan_variance /home/magda/catkin_ws/src/allan_variance_ros/ /home/magda/catkin_ws/src/allan_variance_ros/config/ellipse.yaml

• this works great and I get allan_variance.csv. Unfortunatelly the next step doesn't work again. I see this error:

> magda@magda-VirtualBox:~/catkin_ws$ rosrun allan_variance_ros analysis.py --data /home/magda/catkin_ws/src/allan_variance_ros/allan_variance.csv
> 
> /home/magda/catkin_ws/src/allan_variance_ros/scripts/analysis.py:23: RuntimeWarning: divide by zero encountered in log
>   logy = np.log(y)
> Traceback (most recent call last):
>   File "/home/magda/catkin_ws/src/allan_variance_ros/scripts/analysis.py", line 101, in <module>
>     accel_wn_intercept_x, xfit_wn = get_intercept(period[0:white_noise_break_point], acceleration[0:white_noise_break_point,0], -0.5, 1.0)
>   File "/home/magda/catkin_ws/src/allan_variance_ros/scripts/analysis.py", line 24, in get_intercept
>     coeffs, _ = curve_fit(line_func, logx, logy, bounds=([m, -np.inf], [m + 0.001, np.inf]))
>   File "/home/magda/.local/lib/python3.6/site-packages/scipy/optimize/minpack.py", line 734, in curve_fit
>     ydata = np.asarray_chkfinite(ydata, float)
>   File "/home/magda/.local/lib/python3.6/site-packages/numpy/lib/function_base.py", line 486, in asarray_chkfinite
>     "array must not contain infs or NaNs")
> **ValueError: array must not contain infs or NaNs**

• Additionally I have created a launch file in which I show IMU topic and frequency. In this topic IMU status, sensors values and computed orientation using Quaternion are listed.

Do you know where is the problem? Thank you very much for the answer

1. uint64_t catkin_build/src/allan_variance_ros/include/allan_variance_ros/ImuMeasurement.hpp:14:3: error: ‘uint64_t’ does not name a type uint64_t t{}; ///< ROS time message received (nanoseconds).

add #include <stdint.h> in ImuMeasurement.hpp file.

2. error: expected unqualified-id before ‘using’ catkin_build/src/allan_variance_ros/include/allan_variance_ros/AllanVarianceComputor.hpp:17:1: error: expected unqualified-id before ‘using’ using EigenVector = std::vector<T, Eigen::aligned_allocator>;

Hello author, I have recorded 3hr 37:31s (13051s) 2021-11-18-14-38-03.bag, it only contains imu data which published by gazebo libgazebo_ros_imu_sensor.so. cooked_rosbag_2021-11-18-14-38-03.bag is located in /home/jxl/jxl/allan_ws/. gazebo_husky.yaml is

imu_topic: "/imu/data"
imu_rate: 50
measure_rate: 50
sequence_time: 13050 #bag in seconds

rosrun allan_variance_ros cookbag.py  --input /home/jxl/2021-11-18-14-38-03.bag  --output  cooked_rosbag_2021-11-18-14-38-03.bag
rosrun allan_variance_ros allan_variance  /home/jxl/jxl/allan_ws/ /home/jxl/jxl/allan_ws/src/allan_variance_ros/config/gazebo_husky.yaml

When createing allan_variance.csv, it reminds me many imu msgs timestamp have somewrong, this is only part of the information output by the terminal.

[ERROR] [1637290175.093369303]: Skipped imu messages 614547
[ INFO] [1637290175.093390054]: 12291 / 13050 seconds loaded
[ERROR] [1637290175.093418470]: IMU message before last imu time. IMU time: 13077039999998 last imu time 93877317622759
[ERROR] [1637290175.093438070]: Skipped imu messages 614548
[ INFO] [1637290175.093457149]: 12291 / 13050 seconds loaded
[ERROR] [1637290175.093483640]: IMU message before last imu time. IMU time: 13077059999998 last imu time 93877317622759
[ERROR] [1637290175.093503903]: Skipped imu messages 614549
[ERROR] [1637290175.093530664]: IMU message before last imu time. IMU time: 13077079999998 last imu time 93877317622759
[ERROR] [1637290175.093551317]: Skipped imu messages 614550
[ INFO] [1637290175.093572197]: 12291 / 13050 seconds loaded
[ERROR] [1637290175.093600659]: IMU message before last imu time. IMU time: 13077099999998 last imu time 93877317622759

[ INFO] [1637290176.968499108]: Computed 0 averages for period 985.5
[ INFO] [1637290176.968519090]: Computed 0 averages for period 985.6
[ INFO] [1637290176.968539519]: Computed 0 averages for period 985.7
[ INFO] [1637290176.968559882]: Computed 0 averages for period 985.8
[ INFO] [1637290176.968580278]: Computed 0 averages for period 985.9
[ INFO] [1637290176.968600411]: Computed 0 averages for period 986
[ INFO] [1637290176.968620740]: Computed 0 averages for period 986.1
[ INFO] [1637290176.968641282]: Computed 0 averages for period 986.2
[ INFO] [1637290176.968661284]: Computed 0 averages for period 986.3
[ INFO] [1637290176.968681675]: Computed 0 averages for period 986.4
[ INFO] [1637290176.968701987]: Computed 0 averages for period 986.5
[ INFO] [1637290176.968721859]: Computed 0 averages for period 986.6
[ INFO] [1637290176.968742431]: Computed 0 averages for period 986.7
[ INFO] [1637290176.968763563]: Computed 0 averages for period 986.8
[ INFO] [1637290176.968783902]: Computed 0 averages for period 986.9
[ INFO] [1637290176.968804266]: Computed 0 averages for period 987
[ INFO] [1637290176.968824155]: Computed 0 averages for period 987.1
[ INFO] [1637290176.968844767]: Computed 0 averages for period 987.2
[ INFO] [1637290176.968865573]: Computed 0 averages for period 987.3

When i rosrun allan_variance_ros analysis.py --data /home/jxl/jxl/allan_ws/allan_variance.csv, program is terminated. Is there something i missing? Every imu msg has a timestamp, does it mean cookbag.py do nothing actually ? Thanks for any your suggestion and help.

➜  [/home/jxl/jxl/allan_ws] rosrun allan_variance_ros analysis.py --data  /home/jxl/allan_variance.csv 
/home/jxl/jxl/allan_ws/src/allan_variance_ros/scripts/analysis.py:25: RuntimeWarning: divide by zero encountered in log
  logy = np.log(y)
Traceback (most recent call last):
  File "/home/jxl/jxl/allan_ws/src/allan_variance_ros/scripts/analysis.py", line 84, in <module>
    accel_wn_intercept_x, xfit_wn = get_intercept(period[0:white_noise_break_point], acceleration[0:white_noise_break_point,0], -0.5, 1.0)
  File "/home/jxl/jxl/allan_ws/src/allan_variance_ros/scripts/analysis.py", line 26, in get_intercept
    coeffs, _ = curve_fit(line_func, logx, logy, bounds=([m, -np.inf], [m + 0.001, np.inf]))
  File "/home/jxl/.local/lib/python3.8/site-packages/scipy/optimize/minpack.py", line 735, in curve_fit
    ydata = np.asarray_chkfinite(ydata, float)
  File "/usr/lib/python3/dist-packages/numpy/lib/function_base.py", line 495, in asarray_chkfinite
    raise ValueError(
ValueError: array must not contain infs or NaNs
➜  [/home/jxl/jxl/allan_ws] 

This is csv file's part info.

0.5 -0 -0 -0 -0 -0 -0 
0.6000000238418579102 -0 -0 -0 -0 -0 -0 
0.6999999880790710449 -0 -0 -0 -0 -0 -0 
0.8000000119209289551 -0 -0 -0 -0 -0 -0 
0.8999999761581420898 -0 -0 -0 -0 -0 -0 
1 -0 -0 -0 -0 -0 -0 
1.10000002384185791 -0 -0 -0 -0 -0 -0 
1.20000004768371582 -0 -0 -0 -0 -0 -0 
1.29999995231628418 -0 -0 -0 -0 -0 -0 
1.39999997615814209 -0 -0 -0 -0 -0 -0 
1.5 -0 -0 -0 -0 -0 -0 

This adds ability to calculate the allan variance values in parallel (halved my processing time on a 8 core machine) If the user's compiler doesn't support OpenMP then it should ignore the pragma.

Some small quality of life improvements for the print statements in a couple places also. Additionally fixed some compile warnings for the try catch exceptions.

Additionally, creating the bag variable locally instead of in the class fixed this error (ubuntu 20.04):

allan_variance: /usr/include/boost/smart_ptr/shared_ptr.hpp:734:
typename boost::detail::sp_member_access<T>::type boost::shared_ptr<T>::operator->() const [with T = rosbag::EncryptorBase; typename
boost::detail::sp_member_access<T>::type = rosbag::EncryptorBase*]: Assertion `px != 0' failed.

Not complaining - trying to plan - but approx. how long should the allan_variance computation process take for say ~3hr long data?

I have a rosbag ~3hrs (11214s) long being processed. The message Computed X averages for period Y is progressing through 1-unit of "period" every ~3.5s real-time. If I take "period" to mean the seconds in the rosbag it looks like my computer will take >10hrs to process... Is just how it is or am I missing something?

Obviously this is dependant on my hardware. I'm on a Ryzen 3600X based machine 16GB if that helps.

Here are some more example bags that you can link to from the readme (feel free to reupload or directly link): https://drive.google.com/drive/folders/1a3Es85JDKl7tSpVWEUZryOwtsXB8793o?usp=sharing

Allow simulator to stop generating on ctrl+c, and some debug printouts to help users see what was read in. Additionally, don't try to process if there is no IMU data extracted from the bag.

Hi,

I record a video and extract IMU metadata like shown below. I need to know the units so i can easily use your tool. Please help !!

"Doc1961:Accelerometer": { "id": "Accelerometer", "table": "QuickTime::Stream", "val": "0.97705078125 -0.775634765625 -0.63134765625" }, "Doc1961:AngularVelocity": { "id": "AngularVelocity", "table": "QuickTime::Stream", "val": "-0.711596667766571 -0.207726567983627 -0.145941227674484"

hi! i got calibration papers:

this is cheap mpu-650 (GY-521). how to understand is it good or not ? what "stars", "circles", "triangles" mean ?

thanks for sharing your work. when I try to run rosrun allan_variance_ros cookbag.py --input workspace/imu_calibration.bag --output workspace/cooked_rosbag.bag I get this error :Failed to load Python extension for LZ4 support. LZ4 compression will not be available. I instaled lz4 and roslz4 package but it still occur.What is the mistake?