IMU Calibration

This package provides methods to calculate and apply calibrations for IMUs based on multiple different methods.

So far supported are:

• Ferraris Calibration (Ferraris1995)
• Ferraris Calibration using a Turntable

Installation

pip install imucal

To use the included calibration GUI you also need matplotlib (version >2.2). You can install it using:

pip install imucal[calplot]

Calibrations

Ferraris

This package implements the IMU-infield calibration based on Ferraris1995. This calibration methods requires the IMU data from 6 static positions (3 axis parallel and antiparallel to gravitation vector) and 3 rotations around the 3 main axis. In this implementation these parts are referred to as follows {acc,gry}_{x,y,z}_{p,a} for the static regions and {acc,gry}_{x,y,z}_rot for the rotations. As example, acc_y_a would be the 3D-acceleration data measured during a static phase, where the y-axis was oriented antiparallel to the gravitation.

Creating a new Calibration Object

If the data of all of these sections is already available separately as numpy arrays of the shape (n x 3), where n is the number of samples in each section, they can be directly used to initialize a Calibration object:

from imucal import FerrarisCalibration

sampling_rate = 100 #Hz 
cal = FerrarisCalibration(sampling_rate=sampling_rate,
                          acc_x_p=data_acc_x_p,
                          ...,
                          gyr_z_rot=data_gyr_x_rot)

or via class variables:

from imucal import FerrarisCalibration

sampling_rate = 100 #Hz 
cal = FerrarisCalibration(sampling_rate=sampling_rate)
cal.gyr_z_a = data_gyr_z_a
...

If the data was recorded as a single continuous stream, we first need to identify the different regions in the data. The from_interactive_plot method can be used to extract them manually using a GUI. For this and for most other methods, we expect the data to be a pd.DataFrame with the columns 'acc_x', 'acc_y', 'acc_z, 'gyr_x', 'gyr_y', 'gyr_z', where each column represents the datastream of one sensor axis.

Note: The expected column names can be overwritten

from imucal import FerrarisCalibration

sampling_rate = 100 #Hz 
# This will open an interactive plot, where you can select the start and the stop sample of each region
cal, section_list = FerrarisCalibration.from_interactive_plot(data, sampling_rate=sampling_rate)

section_list.to_csv('./calibration_sections.csv')  # This is optional, but recommended

This method also returns the section_list in addition to the Calibration object. It is advised to save this list, as it can be used recreate the Calibration without performing the manual selection of the regions again:

# At some other day:
from imucal import FerrarisCalibration
import pandas as pd

section_list = pd.read_csv('./calibration_sections.csv', index_col=0)
sampling_rate = 100 #Hz 
# This will recreate the calibration
cal = FerrarisCalibration.from_section_list(data, section_list, sampling_rate=sampling_rate)

Performing the Calibration

When the calibration object was successful initialized, you can obtain the calibration by simply calling compute_calibration_matrix:

cal_mat = cal.compute_calibration_matrix()
print(cal_mat)

This will return an FerrarisCalibrationInfo object, which holds all required calibration information. This object can be saved and loaded to and from hdf5 and json using the respective methods:

cal_mat.to_json_file('./calibration.json')
# some other day:
from imucal import FerrarisCalibrationInfo

cal_mat = FerrarisCalibrationInfo.from_json_file('./calibration.json') 

cal_mat.to_hdf5('./calibration.h5')
# some other day:
from imucal import FerrarisCalibrationInfo

cal_mat = FerrarisCalibrationInfo.from_hdf5('./calibration.h5') 

Applying the Calibration

The FerrarisCalibrationInfo object can be used to apply the Calibration to new data from the same sensor:

calibrated_acc, calibrated_gyro = cal_mat.calibrate(acc, gyro)

acc and gyro are expected to be numpy arrays in the shape (n x 3)

Turntable Calibration

The turntable calibration uses some sort of instumeted turntable to perform the orientation changes and rotations for the Ferraris calibration. It is fundamentally identical to the simple Ferraris calibration, however to indicate the expected difference in precision, this calibration method is implemented as seperate classes. The interface is identical to the Ferraris calibration and all methods shown above can be used.

Note: By default the Turntable calibration expects 720 deg rotations instead of 360 deg

# obtain the calibration
from imucal import TurntableCalibration

sampling_rate = 100 #Hz 
# This will open an interactive plot, where you can select the start and the stop sample of each region
cal, section_list = TurntableCalibration.from_interactive_plot(data, sampling_rate=sampling_rate)
cal_mat = cal.compute_calibration_matrix()
cal_mat.to_json_file('./calibration.json')

# Apply the calibration
from imucal import TurntableCalibrationInfo

cal_mat = TurntableCalibrationInfo.from_json_file('./calibration.json') 

calibrated_acc, calibrated_gyro = cal_mat.calibrate(acc, gyro)