Assessing the Validity of Attitude and Heading Reference

Systems for Biomechanical Evaluation of Motions

A Methodological Proposal

Karina Lebel

1,2,3

, Patrick Boissy

1,2,3

, Christian Duval

4,5

, Mandar Jog

, Mark Speechley

Anthony Karelis

, Claude Vincent

, James Frank

and Roderick Edwards

Faculty of Medicine and Health Sciences, Université de Sherbrooke, Sherbrooke, Quebec, Canada

Research Center on Aging, Sherbrooke, Quebec, Canada

Interdisciplinary Institute for Technological Innovation (3IT), Université de Sherbrooke, Sherbrooke, Quebec, Canada

Department of Kinesiology, Université du Québec à Montréal, Montréal, Quebec, Canada

Centre de Recherche Institut Universitaire de Gériatrie de Montréal, Montreal, Quebec, Canada

Department of Clinical Neurological Sciences, Neurology, Schulich School of Medicine & Dentistry,

University of Western Ontario, London, Canada

Department of Epidemiology and Biostatistics, University of Western Ontario, London, Canada

Department of Rehabilitation, Université Laval, Quebec, Canada

Faculty of Human Kinetics, University of Windsor, Windsor, Canada

Department Mathematics and Statistics, University of Victoria, Victoria, Canada

Keywords: Attitude and Heading Reference System, AHRS, 3-D Orientation Tracking, Mobility, Validation, Inertial,

Optical Motion Tracking System.

Abstract: Background: Attitude and Heading Reference Systems’ (AHRS) popularity in biomechanics has been

growing rapidly over the past few years. However, the limits of operation and performances of such systems

for motion capture are highly dependent upon their conditions of use and the environment they operate in.

The objectives of this paper are to: (1) propose a methodology for the characterization of the criterion of

validity of accuracy of AHRS in a human biomechanical context; and (2) suggest a set of outcome measures

to assess the accuracy of AHRS. Methods: The criterion validity of accuracy is established using an optical

motion tracking gold standard under standardized human motions. Results: Global assessment of accuracy

is derived by comparing the orientation data provided by the AHRS to those given by the gold standard

using a coefficient of multiple correlation. Peak values and RMS difference between both sets of orientation

data are also analysed to complete the accuracy portrait. The methodology proposed herein is verified for

the knee during regular walk. Conclusion: The proposed methodology and analyses take into consideration

the complexities and processes required to assess the accuracy of AHRS in their context of use and provide

a standardized approach to report.

1 INTRODUCTION

Functional mobility is a fundamental aspect of

quality of life. The evaluation of mobility

impairments is therefore crucial to many clinical

decisions in fields ranging from rehabilitation to

geriatrics. Traditional approaches for biomechanical

evaluation of motion include optical motion capture

systems and magnetic trackers. Although well

known for their capacity to provide a highly accurate

tracking within a given capture volume, accurate

tracking for optical motion capture systems is

limited to portions of the capture volume with a

clear line of sight between the cameras and the

markers. The size of the capture volume is often

further constrained by the number and the resolution

of the cameras used. Furthermore, optical motion

capture systems can’t be used easily outside of a

laboratory environment. Magnetic trackers offer

excellent accuracy but are sensitive to magnetic

perturbations in the capture volume and their

accuracy is limited to short operating ranges

between transmitter and receivers due to the decay

of the magnetic field. Traditional motion capture

230

Lebel K., Boissy P., Duval C., Jog M., Speechley M., Karelis A., Vincent C., Frank J. and Edwards R..

Assessing the Validity of Attitude and Heading Reference Systems for Biomechanical Evaluation of Motions - A Methodological Proposal.

DOI: 10.5220/0004911202300237

In Proceedings of the International Conference on Biomedical Electronics and Devices (BIODEVICES-2014), pages 230-237

ISBN: 978-989-758-013-0

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

approaches all have limitations and trade-offs in

terms of accuracy, validity/reliability, time/cost,

training/expertise and real-world generalizability.

3D inertial motion tracking devices, also referred

to as Attitude and Heading Reference Systems

(AHRS), have been gathering interests by

researchers and end-users as an alternative to

traditional optical and magnetic motion capture and

analysis systems for biomechanical evaluation of

motion. AHRS are composed of inertial sensors

(accelerometers, gyroscopes and magnetometers)

which outputs are fed into a fusion algorithm in

order to determine the orientation of a rigid body in

a global reference frame, defined by gravity and

magnetic North. An AHRS attached on a limb will

therefore enable assessment of changes in

orientation for that limb over time. Analysis of

orientation variations can be used, for example, to

study trunk kinematics of older adults during

transfer activities and assess muscle and postural

control impairments (Giansanti et al., 2007; Horak et

al., 2013). The AHRS ability to express their

orientation in a global reference frame also allows

them to be used in pairs, to reconstruct joint

kinematics. In the past few years, such approach has

also been used, for example, to study gait parameters

(Ferrari et al., 2010a; Horak et al., 2013) as well as

upper limb kinematics (Cutti et al., 2008,

Luinge et

al., 2007

). The long-term recording capabilities of

AHRS makes them suitable to appraise changes and

variability of mobility features during specific

scenarios such as sustained walking or stair climbing

over one floor.

The use of AHRS for biomechanical evaluation

of motion also has limitations. The required

measurement accuracy, depending on the scenario

and biomechanical features studied is a determining

factor in choosing to use AHRS. Several studies

have explored the validity of AHRS orientation

measurement on market-available systems (Brodie et

al., 2008; Cutti et al., 2006; De Agostino et al.,

2010; Picerno et al., 2011; Lebel et al., 2013). Some

studies focussed on assessment of accuracy using a

Plexiglas plank on which multiple units of the same

AHRS model were aligned. Using such setup,

Picerno et al. (2011) concluded that under multiple

static conditions, the tested modules define their

orientation differently, with a worst-case

discrepancy of 5.7

. Using a similar setup under

dynamic conditions, Cutti and al. (2006) revealed an

effect of velocity and direction of motion on the

precision of the orientation measurement. The

concepts evoked in these studies for a single system

were confirmed in a recent study from Lebel et al.

(2013) which used an instrumented Gimbal table in

order to assess, under controlled conditions of

motions, the criterion of accuracy of the orientation

measurement of different types of commercially

available AHRS. This study has shown a significant

effect of velocity for all three systems tested,

although the extent of the effect varied among the

different systems. The discrepancies between the

numerical results observed throughout those studies

suggests an effect of the environment on the

accuracy of the results. Indeed, the orientation data

provided by AHRS is estimated from inertial sensors

data using a fusion algorithm. Although the type of

fusion algorithm varies between AHRS models and

companies, they all face the same challenge: the

filter must autonomously differentiate between true

motion, change in environment and environmental

perturbations. Hence, the tuning of the filter as well

as the magnetic compensation used significantly

affect the computation of the estimated orientation at

a given time, and variations in either conditions

(environment or type of motion) is subject to impact

the precision of the orientation data provided.

The variation in accuracy due to the type of

motion, the velocity and the environment reported in

all those study motivates the definition of a

methodological approach for validating the accuracy

of AHRS in its actual biomechanical context of use.

To do so, a step-wise approach is suggested in order

to separate the validation of the technology itself

from the validation of the biomechanical model used

to interpret those measurements. The present paper

focuses on the technology validation portion and

therefore does not consider the use of any

biomechanical model in the validation process.

The scope of the present paper is (1) to propose a

protocol for the characterization of the criterion of

validity of AHRS in a biomechanical context; (2) to

suggest a set of outcome measures for

biomechanical features precision assessment; and (3)

to present typical validation results obtained using

this protocol.

2 MATERIALS AND METHOD

2.1 General Setup and Assumptions

The proposed methodology aims at validating the

data provided by AHRS in a biomechanical context.

Measurement validation refers to the description of

the quality of the measurement which can be

characterized according to different concepts,

namely the accuracy, the precision and the trueness

AssessingtheValidityofAttitudeandHeadingReferenceSystemsforBiomechanicalEvaluationofMotions-A

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231

of the measurement (Menditto et al., 2006).

According to the ISO nomenclature, accuracy of

measurement refers to the “closeness of agreement

between a quantity value obtained by measurement

and the true value of the measurand” (CAN/CGSB-

158.1-98, 1998) while the precision can be defined

as “the closeness of agreement between independent

test results obtained under stipulated conditions”

(ISO 3534-1,1993). Finally, the trueness refers to

“the closeness of agreement between the average

value obtained from a large series of test results and

an accepted reference value” (ISO 3534-1, 1993).

The validation of AHRS measurements is therefore

accomplished by evaluating the accuracy of AHRS

data compared to an optical motion capture gold

standard while a subject executes a set of pre-

determined tasks. Furthermore, accuracy evaluation

between the gold standard and the AHRS relies upon

the underlying assumptions that both systems are

exposed to the exact same movement at the same

time and that the gold standard is accurate.

2.2 Optical Markers Rigid Body and

AHRS

The assumption that both systems undergo the same

motion at the same time is addressed with the use of

non-ferrous rigid bodies incorporating markers and

AHRS units tested (Figure 1). The number of

markers to be included in each rigid body depends

upon the cameras visibility during motion and the

nature of the markers (passive or active). In the case

of passive markers, a minimum set of four markers

is suggested to allow redundancy and to provide

more flexibility in the configuration of the rigid

bodies. Chosen configurations shall ensure easy

differentiation between the different rigid bodies

used simultaneously for enhanced tracking

capabilities. Each AHRS is then solidly affixed to a

rigid body (Figure 1, panel B) and the created

bundle is ready to be placed on the body segment

targeted for evaluation.

Figure 1: Rigid Body (A) General View (B) with AHRS.

2.3 Gold Standard Accuracy

Assessment

Optical motion capture systems are often considered

the reference for accurate kinematic assessment of

motion in biomechanics. Very few studies however

report on the accuracy of these systems for specific

contexts of use. Indeed, their accuracy vary

according to the cameras lens distortion, the

resolution, the position and the number of cameras

available for the defined volume of acquisition, the

calibration procedure and the markers properties

(Windolf et al., 2008). In order to ensure an

acceptable level of truthfulness to compare the

accuracy of AHRS to a given gold standard in the

defined set-up, the following quality check

procedure is proposed.

The first step of the process is performed at the

markers’ position level and is based on the

assumption that the relative distances between

markers on a specific rigid body is constant.

Referring to the definitions listed in section 2.1, the

precision of the system in locating the position of a

marker can be estimated by computing the variation

in the relative distances between rigid bodies’

markers. To do so, relative distances between all

markers comprised within the same rigid body shall

be computed for all valid orientation data recorded

during a representative trial (i.e. if an orientation

data is provided for a rigid body at a specific

timestamp, it is then relevant to compute the

distances between its markers). The mean relative

distance, computed for each segment, defines the

reference value for that segment. It is indeed

reasonable to do so since the rigid body markers are

close enough to assume that a bias affecting the

measured position of a specific marker will affect its

companions in a similar manner, hence cancelling

the effect of the bias on the relative distance

measurement. Although the computation of the

standard deviation on the markers’ relative distance

measurements provides an idea of the overall

accuracy of the system in its specific context of use,

the impact of such variations on the orientation data

needs to be further addressed.

The second part of the procedure therefore

focuses on the evaluation of the accuracy of the

optical system at the orientation level through a

worst-case Monte Carlo analysis where only the

closest three markers of a rigid body will be used by

the system to reconstruct the rigid body’s attitude.

This step requires the identification of those three

markers and the definition of a sphere of uncertainty

around each of those markers, which radius is

BIODEVICES2014-InternationalConferenceonBiomedicalElectronicsandDevices

232

equivalent to the mean standard deviation computed

on relative markers distances for that rigid body.

Orientation of the rigid body can be assessed from

the vectors defined by those three points. A Monte

Carlo analysis then enables the assessment of the

precision of the optical gold standard for the specific

context of use by computing the standard deviation

on the rigid body’s orientation estimate. The

difference between the mean rigid body’s attitude

(computed from Monte Carlo results) and the

reference orientation value (computed from the

reference segment distances defined) constitute the

level of trueness of the system. A global

appreciation of the accuracy of the optical system in

its conditions of use can finally be derived by

combining the computed trueness and precision of

the system in a 95% confidence interval.

2.4 Comparison of Orientation

Measurement from Different

Systems

A rigid body’s orientation is commonly represented

using a set of three elemental and independent

rotations allowing the definition of the current

spatial orientation of the rigid body based on a

known initial reference frame. Euler angles are a

good example of such approach. Although intuitive,

these representations are subject to gimbal lock, a

problem caused by the alignment of two of the

rotational axes during the independently-segmented

rotational process, affecting the overall ability to

describe the rigid body’s orientation.

An alternate representation to elemental rotations

for the definition of a rigid body’s attitude is the

quaternion. A quaternion is an angle-axis orientation

representation which defines the change in

orientation of a rigid body in a single step, using a

four-component vector. Although far less instinctive

than elemental rotations, the intrinsic redundancy

contained within the quaternion’s definition ensures

avoidance of singularities otherwise referred to as

gimbal lock. The current protocol proposes to use

the global range of motion (ROM) computed

directly from the quaternion’s first vector

component, as a comparison baseline between the

inertial and the optical motion tracking systems

instead of trying to decompose the motion using a

3D descriptive approach. From the definition of

quaternion:

cos( / 2)

sin( / 2)

()

sin( / 2)

, cos( / 2) sin( / 2)

,2cos(0) ()

where and a

OM a q ii











  











 













The assessment of accuracy using any 3D

descriptive approach would require an alignment

protocol between the two systems’ reference frame,

which accuracy can be debated. Theoretically, the

inertial reference frame can be defined by measuring

the local magnetic North and the gravity. The optical

reference frame being known to the user, one can

then deduce the alignment relationship between the

inertial and the optical reference frame. However,

such alignment procedure presents certain flaws

which may affect its accuracy. First of all, it assumes

intrinsic knowledge of the AHRS algorithm

regarding the global reference definition: Is the

algorithm compensating for the angle between the

gravity and the Earth’s magnetic North according to

the location? Does the definition considers the

theoretical value for the Earth’s magnetic field or

does it consider the initial measured value? Perhaps

a mixture of both approaches? Furthermore, typical

biomechanical lab, just like regular environments,

present certain magnetic variations (De Vries et al.,

2009; Bachmann et al., 2004). In order to adapt to

such changes in environment, AHRS are known to

allow slight deviations of their inertial frame

definition under constrained conditions. Hence, one

cannot assume the measured relationship between

the inertial reference frame and the optical reference

frame, would it be accurate, to be constant in time as

the module is moved in the environment. Expressing

accuracy using the global ROM as a baseline for

comparison over any other descriptive 3D quantities

is therefore proposed in an effort to concentrate the

evaluation on the ability of the module to detect

movement while minimizing any other sources of

errors.

2.5 Absolute and Relative Accuracy of

Orientation Measurements from

AHRS

In biomechanics, inertial sensors are sometime used

solely, to measure the variation in the orientation of

a segment, or in pairs, to measure the angle at a

specific joint. In order to fully address the question

AssessingtheValidityofAttitudeandHeadingReferenceSystemsforBiomechanicalEvaluationofMotions-A

MethodologicalProposal

233

of accuracy for AHRS in biomechanics, we

therefore propose to divide the accuracy notion into

absolute and relative accuracy, which concepts are

further detailed in the following sub-sections. The

term accuracy is herein used as both concepts refers

to a general appreciation of the quality of the

measurement.

2.5.1 Absolute Accuracy

In the current context, the concept of absolute

accuracy is directly linked to the ability of a system

to measure a variation in the orientation of a

segment over time. Assessment of absolute accuracy

criterion is therefore verified by comparing the

global change in orientation measured by an AHRS

to the global change in orientation measured by the

optical motion tracking system for a specific

segment.

2.5.2 Relative Accuracy

Relative accuracy assessment refers to the capability

of a pair of module to measure joint angle changes

(i.e. joint angle accuracy). In addition to the ability

of the involved modules to track accurate motion of

the segments around the specific joint, the relative

accuracy concept includes the ability of both

modules to express the independently-measured

motion in a matching reference frame so to

accurately define joint motion. The concept of

relative accuracy therefore relies upon a

combination of the inter-sensors consistency and the

trueness of the reference system of each sensor. The

direct repercussion of this type of accuracy on

biomechanical measurement motivates the

introduction of the relative accuracy concept.

3 OUTCOMES AND DATA

REDUCTION FOR

ORIENTATION ACCURACY

EVALUATION

The concept of accuracy of angular measurement

within a context of a biomechanical evaluation of

motion varies according to the evaluation’s purpose.

The following sub-sections describe how both

concept of accuracies are considered in the proposed

protocol in an effort to provide a validation process

as complete as possible.

3.1 Global Assessment of Validity and

Fidelity

Global assessment of validity refers to the capacity

of the system to measure the motion performed. This

criterion is verified using the coefficient of multiple

correlation (CMC) adapted for the evaluation of the

similarity of biomechanical data acquired

synchronously through different Medias (systems or

protocols) by Ferrari et al. (2010b).

,where P corresponds to the number of

waveforms to evaluate through G cycles, F

relates

to the number of frames measured by gait cycle,







is the average ordinate of frame f of the g

cycle

over the P waveforms, and 





is the overall mean

ordinate for the g

cycle over the P waveforms.

This specific version of the CMC is a measure of

the overall similarity of two waveforms which takes

into consideration the effect of offset, correlation

and gain in its similarity assessment, while ignoring

inter-cycle variability.

The definition of the CMC can be used as an

accuracy index in both absolute and relative

accuracy concepts, through the analysis of the

orientation waveform issued by a single AHRS

module with its matching waveform from the optical

system (e.g. trunk variations during sit-to-stand) or

looking at the variation in the joint angle waveform

computed from the related AHRS modules to the

joint angle waveform computed from the optical

system measurements (e.g. knee angle during

sustained walking).

The global assessment of fidelity is evaluated

using the RMS error between the two waveforms in

order to give an appreciation of the precision of the

measurement within a given trial. The combination

of the CMC and the RMS error reported for a

specific context of evaluation therefore gives a

global appreciation of the quality of the

measurement for that context.

3.2 Peak Accuracy

Orientation data is estimated by AHRS from inertial

sensors data using a fusion algorithm (e.g. Kalman

filter). Although powerful, the effectiveness of



)(

-1 =CMC

iii

PFG

PGF

ggpf

gpf













































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234

fusion algorithms is known to be directly related to

the quality of the algorithm parameters’ adjustment.

Indeed, optimal tuning not only considers the quality

of the sensors over the filter prediction capacity, but

also the desired filter’s reactivity to a change in

motion versus its robustness to a perturbation in the

environment. According to the quality of the filter’s

tuning, the accuracy of the orientation data provided

by an ARHS is therefore expected to fluctuate

during a given motion, with situations such as

motion initiation and changes in direction being

identified among the most challenging

circumstances.

Maximal range of motion is one of the feature of

interest in biomechanical evaluations of motion

which involves measurements at those particularly

challenging situations. Analysis of accuracy at these

specific moments is therefore essential. To define

this error, we propose to compute the mean absolute

difference as well as the RMS error between the

orientation provided by the AHRS and the

orientation measurement provided by the optical

motion tracking system for these change in

direction. Combination of those values gives an

appreciation of the accuracy at these specific peak

situations.

4 IN VIVO APPLICATION

The proposed methodology was applied in the

validation of a specific AHRS under human

conditions of motions with 21 adults. For this

specific application, the protocol was based on a

clinical test recognized as reliable for mobility

capabilities assessment, the Timed Up and Go

(TUG). This test includes a sit-to-stand transfer, a

walking portion, a 180

turn and ends with a stand-

to-sit transfer. For illustration purpose of the

concepts and methods presented before, results from

one subject only are reported.

The AHRS used to illustrate the evaluation

procedures is the IGS-180 motion capture suit

(Animazoo, 2013). The system includes 17 AHRS,

allowing full body kinematics reconstruction. A joint

targeted for evaluation in the study which intends to

use the IGS-180 is the knee. The validation protocol

therefore focussed on the AHRS placed on the thigh

and the shank.

The current protocol used the Vicon optical

motion capture system with 12 cameras as a gold

standard (Vicon, 2013). Each targeted AHRS was

coupled with a rigid body as explained in Section

2.2. Since the selected optical motion capture system

uses passive markers, specific care was given to the

design of the rigid bodies so to ensure optimal

tracking. AHRS were solidly affixed to their

matching rigid body and then, to the subject, as

shown in

Figure 2.

Figure 2: IGS-180 with Vicon Rigid Bodies.

5 VALIDATION RESULTS

Preliminary results for knee angle validation are

presented herein to illustrate the feasibility of the

proposed methodology to assess accuracy of AHRS

in a biomechanical context. The analysis of the

accuracy of the optical gold standard was performed

for the rigid bodies located on the thigh and the

shank. As explained in section 2.3, the variation in

the relative distances between the four markers

comprised within each of the rigid body was first

computed during a typical trial. In this case, the rigid

body on the thigh and the shank has shown a

standard deviation in the markers’ relative distances

of 1.04mm and 1.02mm respectively. A sphere of

uncertainty with a radius equivalent to the computed

standard deviation (1.04mm for the thigh and

1.02mm for the shank) was then defined around the

three closest points of each rigid body. A Monte

Carlo analysis revealed a trueness close to 0º (thigh:

0.0014º; shank:-0.0002º) and precision of 0.35º

(thigh: 0.3339º; shank: 0.355º), giving a 95%

confidence interval of [-0.7, 0.7].

Figure 3 illustrates the knee angle measured

synchronously by the two systems, the Vicon and

the IGS180, during a slow walk. The different cycles

measured by both system are visually very alike,

which similarity is reflected in the computed CMC

value of 0.995. Analysis of the difference between

the curves shows that the accuracy varies along the

motion with the maximum errors being reached at

the change in direction.

AssessingtheValidityofAttitudeandHeadingReferenceSystemsforBiomechanicalEvaluationofMotions-A

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Table 1 reports the chosen indexes for global and

peak accuracy assessment, all for the knee angle

during sustained walking (12 to 18 cycles of walk),

but varying either the speed or the path (i.e. the

environment) of the walk. Increasing the pace of the

walk slightly decreased the CMC (0.991) and

increased both the RMS difference and the mean

difference at maximum ROM (respectively, 3.1

and

2.6

). Similarly, slow walking along a magnetically

perturbed path also affects the validation indexes.

Table 1: Accuracy Assessment in Different Conditions.

SLOW

WALK

FAST

WALK

SLOW

WALK

PERTURBED

CMC 0.995 0.991 0.911

RMS

difference

2.4º 3.1º 8.8º

∆





 2.0º 2.6º 12.3º

RMSE

peak

2.5º 3.3º 12.5º

Nb c

cles

18 12 18

Figure 3: Knee Angle during Walk.

6 DISCUSSION

Optical motion capture systems are often considered

the reference for accurate kinematic assessment of

motion in biomechanics. Although their accuracy is

known to vary according to a number of factors,

very few studies report on the accuracy of these

systems for specific contexts of use. The

methodology proposed herein is intended to be

implemented in the system actual context of use,

hence considering both the material constraints

(cameras, settings, calibration, markers properties,

etc.) as well as the type of motion performed.

Reported accuracy of AHRS also vary according

to their conditions of use, including the environment

and the type of motion performed. The proposed

protocol is specifically designed to verify the

accuracy of AHRS in their context of use and the

chosen indexes were shown appropriate to assess the

impact of velocity, environment and time on the

accuracy of the features of interest. Preliminary

validation of the protocol confirms the feasibility

and added value of this evaluation strategy.

7 CONCLUSIONS

The proposed protocol and analyses take into

consideration the complexities and processes

required to assess the accuracy of AHRS in their

context of use and provide a standardized approach

to report.

ACKNOWLEDGEMENTS

This study was conducted as part of the EMAP

project funded by the Canadian Institutes of Health

Research (CIHR).

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AssessingtheValidityofAttitudeandHeadingReferenceSystemsforBiomechanicalEvaluationofMotions-A

MethodologicalProposal

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