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Coordinate Systems

Defining coordinate system is a crucial aspect when working with IMU data. The coordinate system definition of an internal gaitmap library [1].

Hearing Aid Frame (HAF)

• forms a right-handed coordinate system with axes called X, Y, Z

• uses right-hand-rule around each axis for definition of positive direction of the Gyroscope

• axis as defined by the sensor itself, depends on how sensor is located in hearing aid housing

• can be different for different hearing aid firmware versions

Ear Sensor Frame (ESF)

• forms a right-handed coordinate system with axes called X, Y, Z

• uses right-hand-rule around each axis for definition of positive direction of the Gyroscope

• defines axes’ directions as up (Z), to the tip of the shoe (X), and to the left (Y)

Foot Body Frame (FBF)

• consists of the 3 axes ML (medial to lateral), PA (posterior to anterior), and SI (superior to inferior)

• is not right handed and should not be used for any physical calculations

• produces the same sensor signal independent of the ear (right/left) for the same anatomical movement (e.g. lateral acceleration = positive acceleration)

• follows convention of directions from [2].

Ear Frame Overview

The positive directions for the accelerometer (straight arrows) and the gyroscope (circular arrows) for the hearing aid frame (top), ear sensor frame (bottom left) and ear body frame (bottom right). Click here for fullscreen version of image

Table showing the expected signal (positive or negative and in which axis) when a certain movement (displacement or rotation) of a ear happens for the sensor (ESF) and the body frame (EBF).

	ESF		EBF
	Left Ear	Right Ear	Left Ear	Right Ear
Displacements
anterior	+acc_x	+acc_x	+acc_pa	+acc_pa
posterior	-acc_x	-acc_x	-acc_pa	-acc_pa
lateral	+acc_y	-acc_y	+acc_ml	+acc_ml
medial	-acc_y	+acc_y	-acc_ml	-acc_ml
inferior	-acc_z	-acc_z	+acc_si	+acc_si
superior	+acc_z	+acc_z	-acc_si	-acc_si

Algorithmic Implementation

The algorithmic implementation is also based on the internal gaitmap library [2].

Alignment with the Ear Sensor Frame

Aligning the coordinate system of a sensor with the eargait coordinate system can be a complicated, but usually requires prior knowledge about sensor orientation in the housing.

For Signa devices (D11, or D12) the function convert_ear_to_esf can be used to transform hearing aid sensor data into the ear sensor frame.

Note

For D12 a different rotation is required. For all other firmware versions a default ration will be applied.

Transformation into the Foot Body Frame

Once the data is properly aligned to the earmap-ESF, it is very easy to transform it into the respective BF. For this you can use the function convert_ear_to_ebf.

Transformation into the Foot Body Frame and Alignment to Gravity

Some times an alignment with gravity is necessary.

The function aling_gravity_and_convert_ear_to_ebf transforms data into eargait-ESF, then alignes data with gravity and then transforms it into body frame.

Note

Can only be applied for if data is in eargait-HAF.

Reference

[1]

Küderle A., et al. Gaitmap. To be published soon.

[2] (1,2)

Wu, G., Siegler, S., Allard, P., Kirtley, C., Leardini, A., Rosenbaum, D., … Stokes, I. (2002). ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion - Part I: Ankle, hip, and spine. Journal of Biomechanics.