# Kinematics of gait: new method for angle estimation based on accelerometers.

**ABSTRACT** A new method for estimation of angles of leg segments and joints, which uses accelerometer arrays attached to body segments, is described. An array consists of two accelerometers mounted on a rigid rod. The absolute angle of each body segment was determined by band pass filtering of the differences between signals from parallel axes from two accelerometers mounted on the same rod. Joint angles were evaluated by subtracting absolute angles of the neighboring segments. This method eliminates the need for double integration as well as the drift typical for double integration. The efficiency of the algorithm is illustrated by experimental results involving healthy subjects who walked on a treadmill at various speeds, ranging between 0.15 m/s and 2.0 m/s. The validation was performed by comparing the estimated joint angles with the joint angles measured with flexible goniometers. The discrepancies were assessed by the differences between the two sets of data (obtained to be below 6 degrees) and by the Pearson correlation coefficient (greater than 0.97 for the knee angle and greater than 0.85 for the ankle angle).

**0**Bookmarks

**·**

**79**Views

- [Show abstract] [Hide abstract]

**ABSTRACT:**Measuring the kinematic parameters in unconstrained human motion is becoming crucial for providing feedback information in wearable robotics and sports monitoring. This paper presents a novel sensory fusion algorithm for assessing the orientations of human body segments in long-term human walking based on signals from wearable sensors. The basic idea of the proposed algorithm is to constantly fuse the measured segment's angular velocity and linear acceleration via known kinematic relations between segments. The wearable sensory system incorporates seven inertial measurement units attached to the human body segments and two instrumented shoe insoles. The proposed system was experimentally validated in a long-term walking on a treadmill and on a polygon with stairs simulating different activities in everyday life. The outputs were compared to the reference parameters measured by a stationary optical system. Results show accurate joint angle measurements (error median below 5°) in all evaluated walking conditions with no expressed drift over time.Computer methods and programs in biomedicine 12/2013; · 1.56 Impact Factor - SourceAvailable from: Fermin MartinezFermín Martínez-Solís, Abraham Claudio-Sánchez, José M Rodríguez-Lelis, Sergio Vergara-Limon, Víctor Olivares-Peregrino, Marciano Vargas-Treviño[Show abstract] [Hide abstract]

**ABSTRACT:**Gait analysis and research have been developed to obtain characteristics of movement patterns of people while walking. However, traditional measuring systems present different drawbacks that reduce their use and application. Among those drawbacks one can find: high price, low sampling frequency and limiting number of steps to be analyzed. Traditional measuring gait systems carry out their measurement at frequencies oscillating between 60 to 100 Hz. It can be argued about the need of higher sampling rates for gait measurements. However small displacements of the knee or hip for example, cannot be seen with low frequencies required a more detailed sampling and higher frequency sampling. Bearing this in mind, in this paper is presented a 250 Hz system based on accelerometers for gait measurement, and the particularities of knee and hip angles during gait are highlighted. The system was designed with a PCI data acquisition card instrumented with an FPGA to achieve a rate sample of 250 Hz. The accelerometers were placed in thighs and legs to calculate the joint angles of hip and knee in the sagittal plane. The angles were estimated using the acceleration polygon method without integrating the acceleration and without filters. The gait of thirty healthy people of Mexican phenotype was analyzed over a flat floor free of obstacles. The results showed the gait phases and particularities associated with the walking style and people's laterality; the movement patterns were similar in the thirty persons. Based on the results, the particularities as the maximum amplitude in the angles and the shape in the movement patterns were related to the anthropometry and people phenotype. The sampling frequency was essential to record 340 samples in single gait cycle and so registering the gait cycle with its particularities. In this work were recorded an average of 8 to 10 gait cycles, and the results showed variation regarding works carried out in biomechanics laboratories; this variation was related to the method and reference frame used to obtain the joint angles and the accuracy of measurement system.Fermin Martinez-Solis, Abraham Claudio-Sanchez, J.M. Rodriguez-Lelis, Sergio Vergara-Limon, Victor Olivares-Peregrino and Marciano Vargas-Trevino are contributed equally to this work.BioMedical Engineering OnLine 03/2014; 13(1):34. · 1.61 Impact Factor - SourceAvailable from: PubMed Central[Show abstract] [Hide abstract]

**ABSTRACT:**The paper presents a multifunctional joint sensor with measurement adaptability for biological engineering applications, such as gait analysis, gesture recognition, etc. The adaptability is embodied in both static and dynamic environment measurements, both of body pose and in motion capture. Its multifunctional capabilities lay in its ability of simultaneous measurement of multiple degrees of freedom (MDOF) with a single sensor to reduce system complexity. The basic working mode enables 2DOF spatial angle measurement over big ranges and stands out for its applications on different joints of different individuals without recalibration. The optional advanced working mode enables an additional DOF measurement for various applications. By employing corrugated tube as the main body, the sensor is also characterized as flexible and wearable with less restraints. MDOF variations are converted to linear displacements of the sensing elements. The simple reconstruction algorithm and small outputs volume are capable of providing real-time angles and long-term monitoring. The performance assessment of the built prototype is promising enough to indicate the feasibility of the sensor.Sensors 01/2013; 13(11):15274-89. · 2.05 Impact Factor

Page 1

Sensors 2011, 11, 10571-10585; doi:10.3390/s111110571

sensors

ISSN 1424-8220

www.mdpi.com/journal/sensors

Article

Kinematics of Gait: New Method for Angle Estimation Based on

Accelerometers

Milica D. Djurić-Jovičić 1,2*, Nenad S. Jovičić 1 and Dejan B. Popović 1,3

1 School of Electrical Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, Belgrade,

Serbia; E-Mails: nenad@etf.rs (N.S.J.); dbp@etf.rs (D.B.P.)

2 Tecnalia Serbia, Vladetina 13/6, Belgrade, Serbia

3 Center for Sensory Motor Interaction, Aalborg University, Fredrik Bajers Vej 7, Aalborg, Denmark

* Author to whom correspondence should be addressed; E-Mail: milica.djuric@etf.rs;

Tel.: +381-11-3218-348.

Received: 1 October 2011; in revised form: 24 October 2011 / Accepted: 25 October 2011 /

Published: 7 November 2011

Abstract: A new method for estimation of angles of leg segments and joints, which uses

accelerometer arrays attached to body segments, is described. An array consists of two

accelerometers mounted on a rigid rod. The absolute angle of each body segment was

determined by band pass filtering of the differences between signals from parallel axes

from two accelerometers mounted on the same rod. Joint angles were evaluated by

subtracting absolute angles of the neighboring segments. This method eliminates the need

for double integration as well as the drift typical for double integration. The efficiency of

the algorithm is illustrated by experimental results involving healthy subjects who walked

on a treadmill at various speeds, ranging between 0.15 m/s and 2.0 m/s. The validation was

performed by comparing the estimated joint angles with the joint angles measured with

flexible goniometers. The discrepancies were assessed by the differences between the two

sets of data (obtained to be below 6 degrees) and by the Pearson correlation coefficient

(greater than 0.97 for the knee angle and greater than 0.85 for the ankle angle).

Keywords: accelerometers; ambulatory system; angles; gait assessment

OPEN ACCESS

Page 2

Sensors 2011, 11

10572

1. Introduction

Gait analysis is important for objective assessment of the effects of rehabilitation interventions. The

most accurate systems for gait analysis are camera-based systems with reflective markers [1]. These

systems acquire spatial movement (3D) of many markers positioned on the body, while a software

outputs the joint angles and/or other gait parameters. However, camera-based systems require a

dedicated laboratory and limit the length of the analyzed walking distances. Gait laboratories also use

force platforms to measure the ground reaction forces which typically record from only one or two

steps in the middle of the gait sequence. The platforms are 60 × 60 cm, so that aiming for the platforms

hinders the subjects’ natural gait patterns. The alternative to camera-based systems are ultrasound

systems [2] and magnetic tracking systems [3], which allow complete 3D kinematic analysis of human

movements.

Over the last decade, many gait analysis systems using non-traditional methods have been developed.

These systems, for example, use laser technology or measure near-body air flow [4,5] in order to

estimate kinematics and spatial gait parameters. Also, electronic carpets or wearable force sensors are

used for estimation of ground reaction forces, centre of pressure, and temporal gait parameters [6,7].

Since there is often a need for gait recording in various environments, portable body-mounted systems

are preferred [8,9].

Portable body-mounted systems allow data acquisition from many steps. The portable systems for

kinematics data acquisition directly measure joint angles, or they can record accelerations or angular

velocities of the body segments that carry the sensors. Measurement of joint angles can be done with

various electrogoniometers [9-11]. Particularly convenient are flexible goniometers, which measure

the relative angle between two small blocks that are fixed to the body segments (e.g., Biometrics

flexible Penny & Giles sensors). The advantages of flexible goniometers are: their output is directly

proportional to the angle and their mounting is simpler compared to some other measurement systems.

However, they are not sufficiently robust for daily clinical usage.

An alternative to goniometers, offered by the progress made in micro-electromechanical systems

(MEMS), is the use of accelerometers and gyroscopes. The advantages of these sensors include their

small size and robustness when compared with goniometers. However, the disadvantages of the

accelerometers (and gyroscopes) are computational problems for determining the angles [12-15].

Accelerometers are used for long-term monitoring of human movements, for assessment of energy

expenditure, physical activity, postural sway, fall detection, postural orientation, activity classification

and estimation of temporal gait parameters [16-21]. However, only a few papers report using only

accelerometers for angle estimation, or position and orientation estimation. In most papers some

additional types of sensors are included (gyroscopes, magnetometers, etc.) [22-25].

One method to calculate the angle is to double integrate the measured angular acceleration.

However, the double integration leads to a pronounced drift [13,14]. Several techniques have been

presented in literature for minimization of this drift. For example, Morris [26] identified the beginning

and the end of each walking cycle and made the signals at the beginning and the end of the cycle equal.

Tong et al. [27] applied a low cut high pass filter on the shank and thigh inclination angle signals.

However, these methods also removed the static and low-frequency information about the angles and

they cannot be applied to real-time processing.

Page 3

Sensors 2011, 11

10573

The other method for estimation of joint angles from the measured accelerations is the estimation of

the inclination angles between the segments (sensor) and the vertical, followed by the subtraction of

the angles for neighboring body segments. The results are acceptable only if the segment accelerations

are small compared to the gravity [28].

Adding Kalman filtering to the integration procedure decreases the drift and provides for

real-time applications, but it requires calibration and data from other sensors (accelerometers,

gyroscopes, and magnetic sensors in most cases) for error minimization, as well as noise statistics and

good probabilistic models [29-31]. These algorithms can be applied in real-time and seem to give

excellent accuracy for motions which exhibit lower accelerations than the leg segments, and which are

not exposed to impacts like those of heel contacts. For the lower extremities, the performance of the

Kalman filter is considerably reduced when measuring the orientation angles of segments that move

fast [28]. Inertial sensors that consist of accelerometers, gyroscopes, and magnetometers, along with

Kalman filtering, allow a good accuracy for estimation of lower limb angles [32]. However, good

accuracy of angle estimation can also be achieved using fewer sensors and much simpler algorithms

that are not sensitive to the presence of metals and ferromagnetic materials such as those that comprise

magnetometers [23].

Willemsen et al. [32] developed a technique to estimate joint angles without integration. This

method is based on comparison of weighted accelerations of the joint (e.g., knee or ankle) obtained

from two accelerometer pairs mounted on two adjacent segments of the leg. The method requires

adequate low-pass filtering, which introduces a delay and to a certain extent hinders the real-time

applicability. Further, the accelerometer pairs need to be precisely oriented, so that their axes intersect

at the joint, which is very difficult to achieve considering that the human joints are polycentric. Also,

the distances between sensors and the joints are required for computation.

We have developed an accurate, yet simple method and instrumentation for estimation of absolute

segment and joint angles during the gait (assuming kinematics in the sagittal plane) which minimizes

the effects of drift. The proposed system is based only on accelerometer sensors, which is advantageous

because their calibration is static and less complex than the dynamic calibration required for

gyroscopes. Additional motivation for this paper was the “bad reputation” of accelerometers due to the

pronounced drift. We wanted to investigate if it is possible to use only accelerometers for angle

estimations and evaluate the precision of the results.

2. Experimental Section

2.1. Sensor System

The acquisition system that we developed for gait analysis is designed as a distributed wireless

sensor network. A set of battery powered sensor nodes is placed on the subject, one sensor node for

each leg segment of both legs. Sensor nodes establish communication with the coordinator node

through a low power 2.4 GHz wireless communication link. The coordinator node is connected using a

USB interface to the computer. Wireless communication is bidirectional, with a coordinator node

acting as a master, and the sensor nodes as slaves. The coordinator node manages network traffic and

Page 4

Sensors 2011, 11

10574

the USB connection with the computer. Data streams from the sensor nodes are synchronized and the

system operates with a 100 Hz sampling rate.

Sensor nodes are realized as a sandwich structure of processor and sensor board with a

Li-ion battery placed between the boards. The compact size design of sensor nodes, with dimensions

70 × 25 × 15 mm and 27 grams weight, enables comfortable wearing and does not hinder the subject’s

movements. Hardware design is based on the Texas Instrument’s CC2430 microcontroller, which

integrates a RF front end and a 8051 core in the same case. Standard microcontroller peripherals

enable interfacing to analog and digital sensors, and different sensor boards can be combined with the

same processor board.

In the configuration used in this research, the sensor board comprises two high performance 12-bit

digital accelerometers LIS3LV02 (SGS-Thomson Microelectronics, USA). The range of the sensors is

either ±2 g or ±6 g, which can be selected in the acquisition software. Accelerometers are aligned to

y axes with distance of 55 mm between centers. This configuration requires the clinician only to fix the

sensor array along the body segment, approximately at the mid section of lateral side of leg (Figure 1).

Figure 1. Setup of the sensor system. (a) photo of the sensors mounted on the body during

the gait analysis, (b) schematic of the system configuration with the coordinate systems.

Goniometers were attached to the leg segments by using double sided adhesive tape and secured

with elastic bands with Velcro endings, mounted over the sensors and around the leg segment. Sensor

nodes were placed in custom made tight sensor node-size elastic pockets placed on elastic bands with

Velcro at their ends.

Page 5

Sensors 2011, 11

10575

The custom-designed software, created in CVI (LabWindows, National Instruments, USA), is used

for online monitoring and storing of the acquired data.

2.2. Algorithm

The mechanics of importance for the analysis considers two sensors (denoted by S1 and S2), which

are mounted on a rigid rod (Figure 2). The distance between the sensors is l. The rod is freely moving

with respect to the fixed global coordinate system (O'x'y'z'), shown in Figures 1(b) and 2. The axis x' of

the global coordinate system is walking direction, and the axis y' is vertical. The center of the rod (O)

is determined by the position vector

)('OOr

=

.

To analyze the movement in the sagittal plane, we consider the case when the rod moves in the

O'x'y' plane (2D model). We define the vector l, which connects the centroids of the two sensors. The

positions of the accelerometers are

2/

01

lrr

−=

and

0t

2/

02

lrr

+=

, respectively.

Figure 2. Rod with two accelerometers and the coordinate system for analysis of

movement in the sagittal plane.

Each accelerometer measures the two Cartesian components of the acceleration vector, with respect

to the local coordinate system Oxy attached to the rod. The equivalent accelerations measured by the

two sensors are:

g

l

2

rg

r

2

a

−−=−=

d

d

..

0

..

1

2

1

t

(1)

and:

g

l

2

rg

r

2

t

a

−+=−=

d

d

..

0

..

2

2

2

(2)

where g is the gravity acceleration.

The difference of the signals from these two sensors is proportional to the amplitude of the vector

..

laa

−=−

. In this way, we cancel out the influence of the movement of the rod centroid and of the

gravity, and retain information only about the changes of the vector l. The second derivative of the

vector l is:

21

Page 6

Sensors 2011, 11

10576

yx

llll

? ?

iilul

2

0

2

0

ω−α=φ

?

−φ=

? ?

,

(3)

where φ is the angle between the axes x and x', ω and α are the absolute angular velocity and angular

acceleration of the rod, respectively, xi ,

rod, respectively,

l

=

l ,

y

lill

== /

0

, and

0

iu

=

z

rotation).

The difference of the outputs from the accelerometers in the direction along the rod axis (

proportional to the square of the angular velocity, and the difference between the outputs from the

accelerometers in the perpendicular direction (

Δ

segment. The proportionality coefficient is equal to the distance between the centers of the

accelerometers. In this way we eliminated the gravity component from the signal, and eliminated the

need for precise positioning of the rod on the body segment and calibration of the system.

As explained in the introduction, one of the main problems with accelerometers is significant drift

after integration, whether the integration is performed numerically or by means of analog integrators.

A characteristic example of the drift, which resulted even with carefully calibrated accelerometers, is

presented in Figure 3.

yi , and zi are the unit vectors of the x, y, and z axes of the

l

×

(where

0

zi is the unit vector of the axis of

y

a

Δ

) is

x a

) is proportional to the angular acceleration of the

Figure 3. Joint angle (bottom panel) and angular velocity (middle panel) obtained by

numerical integration of the measured acceleration of the segment (top panel). Dashed line

envelope on the bottom panel is fitted through the points where the knee should be fully

extended with zero degree joint angle. However, due to the integration drift, instead of

remaining approximately constant, this line has a parabolic shape.

We introduce a method for estimation of the joint angles based on digital filtering. In order to

explain the method, we use the frequency domain. According to the Laplace transform, the integration

in the time domain corresponds to multiplication by

integration corresponds to multiplication by

/ 1 s , where s is the complex frequency. On the frequency

axis (i.e., in the Fourier-transform domain, where

22

/ 1)j /(1

ω−=ω

.Hence, we use a second-order low-pass filter, which mimics this multiplication.

Further in the paper, we shall write

/ 1 ω−

instead of

this multiplicative term is purely real (although negative).

s / 1

in the frequency domain, and the double

2

ω= js

), this corresponds to multiplication by

22

/ 1 s , because we wish to emphasize the fact that

Page 7

Sensors 2011, 11

10577

Without the loss of generality, we can assume that the signal

has pronounced spectral components at

spectral components of

tax

/ )(

Δ

function is proportional to

/ 1 ω−

filter is:

lt/ )(ax

Δ

is nearly periodic. Hence, it

,...2 , 1

=

,/

=

iTifi

, where T is the stride period. All relevant

l

should be in the roll-off region of the filter, where its transfer

2

. For example, the transfer function of the second-order Butterworth

12

1

)(

0

2

0

2

+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

ω

+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

ω

=

ss

sB

(4)

where

00

2 f π=ω

is the cutoff angular frequency. On the imaginary axis, when

0

||

ω>>

s

, we get:

2

2

0

2

2

0

2

)(

ω

ω

−=

ω

s

≈

sB

(5)

In order to approximate the double integration, we pass the signal through the filter and divide the

output by

0

ω .

The filter is, however, dispersive. Various spectral components have various delays and the filtered

signal will only barely resemble the actual function

bi-directional filtering, using the filtfilt function in Matlab. First, the signal is filtered in the forward

direction. Then, the filtered sequence is reversed and run back through the filter. This procedure results

in a real and positive transfer function (zero-phase distortion and zero group delay), whose order

corresponds to double the filter order. For example, if we use the first-order Butterworth filter, whose

transfer function is

) 1/ /(1)(

01

+ω=

ssB

, the result of the bidirectional filtering is the transfer function

22

00

/ ) 1)/ /((1

ωω≈+ωω

when

0

ω >>ω

. Hence, to obtain the

first-order Butterworth filter with the filtfilt function and divide the result by

normalized spectrum of the angular acceleration, along with the

the transfer characteristic of the low-pas filter (Bode plot), low-pass filter combined with a high-pass

filter obtained by the filtfilt function.

2

)(t

φ

. A zero-delay filter can be obtained by

2

2

/ 1 ω−

transfer function, we use the

2

0

ω−

. Figure 4 shows the

function, and the magnitude of

2

2

0/ s

ω

Figure 4. Normalized spectrum of the angular acceleration for knee angle (shown in

Figure 3) and magnitudes of the function

ω

Butterworth low-pass filter (lpf), and function of this low-pass filter combined with a

high-pass filter (lpf + hpf).

2

2

0/ s

, transfer function of a second-order

Page 8

Sensors 2011, 11

10578

The choice of

similar to the numerical integration. On the other hand, in order to keep the spectral components in the

roll-off region of the filter, the condition

ff

gc0

<

respected and

gc

f

(where

spectral components are within the pass band of the filter, where the transfer function of the filter is

approximately constant and close to 1. Increasing further the filter bandwidth, i.e., increasing

components are not affected by the filter. However, their magnitudes are divided by

level of these components is reduced, and the result is distorted. On the contrary, the magnitudes of the

spectral components that are in the roll-off region of the filter are insensitive to the modifications of

Since filtering should replace the integration, all relevant spectral components of the gait should be in

the roll-off region of the filter, i.e., well above the cutoff frequency of the filter. By comparing the

filter amplitude characteristic, which is the modulus of (4), and

between these two functions is less than 1 dB for spectral components that are above two times the

cutoff frequency of the filter. Similarly, the error is less than 0.5 dB for spectral components above

three times the cutoff frequency. Hence, the cutoff frequency

lowest relevant spectral component of the signal is positioned between

0f followed the heuristics (Figure 5). If

0f is too low, joint angles exhibit drifting

T / 1

=

should be fulfilled. If this condition is not

is the gait cycle frequency), one or more

0f is taken to be higher than

gc

f

0f , these

2

0

ω , so that the

0f .

22

0ωω

, it can be verified that the error

0f of the filters is determined so that the

2 f and

0

3f .

0

Figure 5. Influence of

0f on angle estimation: filtering for several cutoff frequencies

compared with angle acquired from goniometers.

The drift can be additionally reduced if a high-pass filter is used in conjunction with the low-pass

filter. The cutoff angular frequency of the high-pass filter should be below

of the low-pass filter is not affected. The order of the high-pass filter can be selected as an additional

parameter to help keep the drift under control.

As an example, Figure 4 shows the magnitude of the transfer characteristic of the combined low-pas

filter and a high-pass filter of 8th order, which is an actual filter used in computations in this paper.

Since filtering distorts the DC level, we restore this information through the self-calibration in the

following way. Before gait initiation, the subject needs to remain standing still (and sensors immobile)

for at least two seconds. During this interval, the initial conditions are determined for each pair of

accelerometers by using them as inclinometers.

The procedure of approximating the double integration can be applied both for reconstruction of

absolute angles (the angles between the rod axes and the vertical axis of the fixed coordinate system)

0

ω , so that the major role

Page 9

Sensors 2011, 11

10579

and the reconstruction of the joint angles. For example, the knee angle is obtained directly from the

difference:

lta

x

/ )(

thigh

−Δ

lta

x

/ )(

shank

Δ

(6)

by performing the bi-directional filtering, and divide the result by

2

0

ω−

. An analogous procedure is

performed for the ankle angle.

2.3. Experiments

The algorithm was tested on 27 healthy subjects walking on the ground at their natural pace.

In order to provide a more systematic validation, we additionally recorded 10 subjects (age: 26 ± 1.5

mean ± SD) walking at various speeds on treadmills (Life Fitness 9500HR and Panatta Advance Lux

1AD003), whose results are presented in this paper.

Four trials per subject were recorded. Besides walking, recording sequence also included standing

still for at least 2 s before and after each walking sequence, which was used for self-calibration and

checking. Subjects were walking with various velocities on a treadmill, starting from 0.15 m/s and

incremented by 0.05 m/s up to 2 m/s. As the reference system for this study, we used SG110 and

SG150 flexible goniometers with the joint angle units for signal conditioning (Biometrics, Gwent,

UK). Goniometers were mounted on the lateral side of the leg (at the ankle and knee joints) following

the instructions of the manufacturer. Simultaneously, the sessions were recorded with a video camera

for later analysis.

2.4. Processing of Measured Data

Based on the recorded accelerometer data, the joint angles were estimated by the proposed algorithm.

Joint angles recorded by goniometers were also computed. The accuracy of our algorithm was

evaluated in terms of the root-mean-square error (RMSE) as well as the Pearson’s correlation

coefficients (PCCs) between the goniometer results and angles provided by the proposed method.

RMSE is expressed in degrees. PCC values range between −1 and 1, where 1 represents the best

possible similarity between the two sets of angles (identical shapes). The first and the last stride were

excluded from each trial, and comparison between goniometer signals and angles provided by our

method was done on the remaining sequence. The data processing was done offline using Matlab 7.5

(Mathworks, USA).

3. Results

Two typical examples for the knee and ankle angles are shown in Figure 6. The error was defined as

the difference between the angles obtained by the proposed method and the angles obtained from

goniometers.

Based on the results obtained from treadmill recordings, the cutoff frequency for the knee angles

should be in the range [

gc

f /3,

gc

f /2], where

gc

f is the gait cycle frequency. The blue area in Figure 6

shows the family of curves estimated by our method when filtered with various frequencies in the

range [

gc

f /3,

gc

f /2].

Page 10

Sensors 2011, 11

10580

Figure 6. Knee and ankle joint angles measured with goniometers and estimated from

accelerometers. Thick lines represent angles from goniometers (dashed line) and

accelerometers (solid line) for optimal filter frequency. Blue areas show the range of angle

values estimated from accelerometers when filtered with various frequencies in the range

[

gc

f /3,

gc

f /2].

Figure 7 shows the optimal filtering frequency versus gait cycle frequency. The squares represent

optimal points obtained by maximizing Pearson’s correlation coefficient and minimizing RMSE

between our results and the angles obtained by goniometers for each walking trial (different gait

velocity). The straight lines are obtained by fitting these data. It is obvious from Figure 7 that signals

for the estimation of the ankle angles should be filtered with about two times higher cutoff frequency

than the signals used for the estimation of the knee angles. These findings are in agreement with the

theoretical background from the previous section.

Figure 7. Optimal filtering frequencies for knee and ankle angles versus gait cycle frequency.

Page 11

Sensors 2011, 11

10581

The higher cutoff frequency of the filter for the ankle angle can be used because the spectrum of the

ankle angle has a very pronounced second harmonic. This is convenient, because the influence of the

drift is further suppressed.

Using the proposed algorithm, for each subject and each trial, we evaluated the PCC and RMSE

values between the angles estimated by our method and goniometer outputs. Figure 8 shows the PCC

and RMSE, respectively, as a function of normalized frequency, for various velocities. Although we

recorded velocities from 0.15 to 0.2 m/s in the steps of 0.05 m/s, Figure 8 shows results for a subset of

the recorded velocities.

Figure 8. Pearson’s correlation coefficient (PCC) and RMSE between goniometers

and estimated angles, for knee and ankle angles, vs. filtering frequency in the range

[

gc gc

corresponds to different gait velocity (in m/s).

f /3,

f /2]. The normalization is with respect to the optimal frequency. Each curve

As shown in Figure 8, all RMSE curves have broad minima, which are, on average about 1. These

results are in accordance with PCC curves, confirming that the optimum normalized cutoff frequency

is 1. Cumulative results for all walking trials and all subjects are presented in Figure 9.

Page 12

Sensors 2011, 11

10582

Figure 9. Boxplots presenting comparison between joint angles (for knee and ankle

angles) calculated from accelerometers and goniometers. Left: Pearson’s correlation

coefficient (PCC). Right: root-mean-square error (RMSE).

4. Discussion and Conclusions

The presented results are based on a model which assumes that the lower limbs move in the sagittal

plane. For healthy subjects, this 2D model has proven to be sufficient, because the sagittal plane is the

plane where the majority of movement takes place. Generally, for clinical applications, the proposed

method provides an acceptable accuracy for angles and high correlation coefficients with the

measurements obtained from goniometers.

In particular, PCCs for the knee angle are higher than 0.97 and RMSE is within 6º for the angle

values. Further, our results showed that a 5° RMSE is obtained for walking speeds in the frequency

range

gc

f

∈ [0.35, 1.15]. This corresponds to all velocity curves in Figure 8 except for v = 0.15 , 1.8 ,

and 2.0 m/s (the slowest and fastest recorded walking). Regarding the ankle angles, PCCs are slightly

lower and in the range from 0.85 to 0.97, while RMSE is from 2° to 4.7°.

For both estimated joint angles (except for the extreme velocities for the knee angle), this error is in

the range of 5° mean error limit accepted by the American Medical Association to consider the

measurements reliable for the evaluation of movement impairments in a clinical context [9]. The

accuracy of our simple system is comparable to the accuracy demonstrated in plots presented in [25],

which were obtained by much more complex hardware and software.

Joint angles were determined by subtracting the absolute angles of the neighboring leg segments.

The error of our method was estimated based on joint angles and includes errors from the two segments.

In this way, the total error of the joint angle estimation is different than the error of the absolute angles.

Hence, comparison of the absolute angles with a camera system would be more appropriate for

validation of the proposed method. However, such a comparison was not possible in our experiments

because the treadmill would present a visual obstacle between cameras and markers. Since our main

goal was to investigate how our method performs for various gait velocities, the treadmill was the

important part of the experiments. Therefore, we selected goniometers as the reference system, which

have ±2° accuracy and 1° repeatability [33]. Although electrogoniometers are prone to errors due to

potential misalignment with the femur and tibia segment in the sagittal plane, this does not affect the

validation of our method since we secured sensor units to be aligned with goniometer blocks.

Page 13

Sensors 2011, 11

10583

Skin motion artifacts cause errors to all body-fixed sensors. Sensors placed on thighs are more

susceptible to skin and soft tissue related motion, because the majority of femur is concealed by a

substantial amount of soft tissue. However, the errors that we report here are much smaller than errors

due to rod misalignment in the procedure proposed by Willemsen [32].

Another limit for this algorithm is the speed of the subject’s gait. As it can be seen from Figures 7

and 8, if the gait is very slow, the quality of our method decreases. This is due to very low angular

accelerations, whose major component comes from the impacts. This suggests that for a very slow

walk, e.g., for subjects with high levels of disability, the quality of the angle estimation may not be

acceptable. However, for very slow gait, accelerometers can be used as inclinometers and angles can

be successfully estimated in this way [17].

Our method does not need information about the distances to joint centers or distances between

sensor rods placed on different segments, which is one of the benefits of this algorithm. The only

condition for mounting the sensors is that they follow the segment line (to be aligned with a line

connecting adjacent joints, viz. hip and knee, knee and ankle, and along the foot and parallel to the

ground).

This algorithm could be used not only for level walking, but also for estimation of angles during

slope walking, stair climbing, or any other rhythmical (periodic) leg movements. It can also be used for

estimation of other segment and joint angles, as long as the movements are in 2D. However,

movements should be fast enough so that the angular acceleration signal is sufficiently above the noise

floor. The proposed method is suitable for postprocessing of raw data. However, it can also be

included into real-time algorithms to estimate the angles of the leg segments with a delay of one stride.

The proposed method is simple and computationally efficient. We have demonstrated that it yields

accurate shapes of the ankle and knee angles. The accuracy of the method is sufficient for quick

diagnostics of gait, as well as for applications of gait control.

Acknowledgments

The work on this project was partly supported by the Serbian Ministry of Education and Science,

Grant No. 175016.

References

1. Furnee, H. Real-time motion capture systems. In Three-Dimensional Analysis of Human

Locomotion; Allard, P.; Cappozzo, A.; Lundberg, A.; Vaughan, C.L., Eds.; Wiley: New York,

NY, USA, 1997; pp. 85-108.

2. Kiss, R.M.; Kocsis, L.; Knoll, Z. Joint kinematics and spatial-temporal parameters of gait

measured by an ultrasound-based system. Med. Eng. Phys. 2004, 26, 611-620.

3. Kobayashi, K.; Gransberg, L.; Knutsson, E.; Nolén, P. A new system for three-dimensional gait

recording using electromagnetic tracking. Gait Posture 1997, 6, 63-75.

4. Bonomi, A.; Salati, S. Assessment of human ambulatory speed by measuring near-body air flow.

Sensors 2010, 10, 8705-8718.

5. Pallejà, T.; Teixidó, M.; Tresanchez, M.; Palacín, J. Measuring gait using a ground laser range

sensor. Sensors 2009, 9, 9133-9146.

Page 14

Sensors 2011, 11

10584

6. Yun, J. User identification using gait patterns on UbiFloorII. Sensors 2011, 11, 2611-2639.

7. Liu, T.; Inoue, Y.; Shibata, K. A wearable ground reaction force sensor system and its application

to the measurement of extrinsic gait variability. Sensors 2010, 10, 10240-10255.

8. Allet, L.; Knols, R.; Shirato, K.; Bruin, E. Wearable systems for monitoring mobility-related

activities in chronic disease: A systematic review. Sensors 2010, 10, 9026-9052.

9. Zheng, H.; Black, N.D.; Harris, N.D. Position-sensing technologies for movement analysis in

stroke rehabilitation. Med. Biol. Eng. Comp. 2005, 43, 413-420.

10. Legnani, G.; Zappa, B.; Casolo, F.; Adamini, R.; Magnani, P.L. A model of an electro-goniometer

and its calibration for biomechanical applications. Med. Eng. Phys. 2000, 22, 711-722.

11. Shiratsu, A.; Coury, H.J.C.G. Reliability and accuracy of different sensors of a flexible

electrogoniometers. Clin. Biomech. 2003, 18, 682-684.

12. Mayagoitia, R.E.; Nene, A.V.; Veltink, P.H. Accelerometer and rate gyroscope measurement of

kinematics: An inexpensive alternative to optical motion analysis systems. J. Biomech. 2002, 35,

537-542.

13. Aminian, K.; Najafi, B.; Bnla, C.; Leyvraz, P.F.; Robert, P. Spatio-temporal parameters of gait

measured by an ambulatory system using miniature gyroscopes. J. Biomech. 2002, 35, 689-699.

14. Dejnabadi, H.; Jolles, B.M.; Aminian, K. A new approach to accurate measurement of uniaxial

joint angles based on a combination of accelerometers and gyroscopes. IEEE Trans. Biomed. Eng.

2005, 52, 1478-1484.

15. Luczak, S.; Oleksiuk, W.; Bodnicki, M. Sensing tilt with MEMS accelerometers. IEEE Sensors J.

2006, 6, 1669-1675.

16. Yang, C.C.; Hsu, Y.L. A review of accelerometry-based wearable motion detectors for physical

activity monitoring. Sensors 2010, 10, 7772-7788.

17. Mizuike, C.; Ohgi S.; Morita S. Analysis of stroke patient walking dynamics using a tri-axial

accelerometer. Gait Posture 2009, 30, 60-64.

18. Eng, J.J.; Winter, D.A. Kinetic analysis of the lower limbs during walking: What information can

be gained from a three-dimensional model? J. Biomech. 1995, 28, 753-758.

19. Takeda, R.; Tadano, S.; Todoh, M.; Morikawa, M.; Nakayasu, M.; Yoshinari, S. Gait analysis

using gravitational acceleration measured by wearable sensors. J. Biomech. 2009, 42, 223-233.

20. Takeda, R.; Tadano, S.; Natorigawa, A.; Todoh, M.; Yoshinari, S. Gait posture estimation using

wearable acceleration and gyro sensors. J. Biomech. 2009, 42, 2486-2494.

21. Yang, C.; Hsu, Y.; Shih, K.; Lu, J. Real-time gait cycle parameter recognition using a wearable

accelerometry system. Sensors 2011, 11, 7314-7326.

22. Favre, J.; Jolles, B.M.; Aissaoui, R.; Aminian, K. Ambulatory measurement of 3D knee joint

angle. J. Biomech. 2008, 41, 1029-1035.

23. O’Donovan, K.J.; Kamnik, R.; O’Keeffe, D.T.; Lyons, G.M. An inertial and magnetic sensor

based technique for joint angle measurement. J. Biomech. 2007, 40, 2604-2611.

24. Williamson, R.; Andrews, B.J. Detecting absolute human knee angle and angular velocity using

accelerometers and rate gyroscopes. Med. Biol. Eng. Comp. 2001, 39, 294-302.

25. Ferrari, A.; Cutti, A.G.; Garofalo, P.; Raggi, M.; Heijboer, M.; Cappello, A.; Davalli, A. First in

vivo assessment of “Outwalk”: A novel protocol for clinical gait analysis based on inertial and

magnetic sensors. Med. Biol. Eng. Comp. 2010, 48, 1-15.

Page 15

Sensors 2011, 11

10585

26. Morris, J.R.W. Accelerometry—A technique for the measurement of human body movements.

J. Biomech. 1973, 6, 729-736.

27. Tong, K.; Granat, M.H. A practical gait analysis system using gyroscopes. Med. Eng. Phys. 1999,

21, 87-94.

28. Dejnabadi, H.; Jolles, B.M.; Casanova, E.; Fua, P.; Aminian, K. Estimation and visualization of

sagittal kinematics of lower limbs orientation using body-fixed sensors. IEEE Trans. Biomed.

Eng. 2006, 53, 1385-1393.

29. Luinge, H.J.; Veltink, P.H. Inclination measurement of human movement using a 3-D

accelerometer with autocalibration. IEEE Trans. Neur. Syst. Rehabil. Eng. 2004, 12, 112-121.

30. Luinge, H.J.; Veltink, P.H. Measuring orientation of human body segments using miniature

gyroscopes and accelerometers. Med. Biol. Eng. Comp. 2005, 43, 273-282.

31. Cooper, G.; Sheret, I.; McMillian, L.; Siliverdis, K.; Sha, N.; Hodgins, D.; Kenney L.;

Howard, D. Inertial sensor-based knee flexion/extension angle estimation. J. Biomech. 2009, 42,

2678-2685.

32. Willemsen, A.T.; van Alste, J.A.; Boom, H.B.K. Real-time gait assessment utilizing a new way of

accelerometry. J. Biomech. 1990, 23, 859-863.

33. Biometrics Goniometers. http://www.biometricsltd.com/gonio.htm (access on 25 October 2011).

© 2011 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article

distributed under the terms and conditions of the Creative Commons Attribution license

(http://creativecommons.org/licenses/by/3.0/).

#### View other sources

#### Hide other sources

- Available from mdpi.com
- Available from Nenad Jovicic · Aug 27, 2014