EXERCISE RATE ESTIMATION USING A TRIAXIAL
ACCELEROMETER
Teddy M. Cheng, Andrey V. Savkin, Branko G. Celler
School of Electrical Engineering and Telecommunications, the University of New South Wales, Sydney, NSW 2052, Australia
Steven W. Su
Faculty of Engineering, the University of Technology, Sydney, NSW 2007, Australia
Ning Wang
School of Electrical Engineering and Telecommunications, the University of New South Wales, Sydney, NSW 2052, Australia
Keywords:
Wearable sensors, Accelerometer, Exercise intensity, Fundamental frequency estimation, Data fusion, Kalman
filtering.
Abstract:
In this paper, we propose an algorithm for the estimation of exercise rate during a variety of exercises by
using measurements from triaxial accelerometry. The algorithm involves the detection of the periodicity of the
body’s accelerations, and the detected periods are then fused to form an estimate of exercise rate. Experimental
results demonstrate that the algorithm is effective in different modes of exercise. The proposed algorithm
will be useful in monitoring training exercises for healthy individuals and rehabilitation exercises for cardiac
patients.
1 INTRODUCTION
Measuring an exerciser’s body movements provides
a simple and direct way for monitoring and quanti-
fying the intensity of the exercise that is being per-
formed. Accelerometry, in this respect, gives a con-
venient mean of measuring the body’s movements, as
well as identifying and classifying movements per-
formed by an exerciser. In particular, portable tri-
axial accelerometers (TA) are commonly employed
(see, e.g., (Chen and Sun, 1997; Kim and Kim, 2008;
Karantonis et al., 2006; Tanaka et al., 2007; Asano
et al., 2005)). By analyzing the TA measurements,
the rate of exercise or activity being performed can
be determined. In turn, the exercise rate provides a
measure of exercise intensity which is then useful for
exercise monitoring.
The objective of this paper is to propose an algo-
rithm for determining the rate of an exercise using a
wearable TA. In this study, the exercise rate is termed
as the fundamental periodicity or frequency of the lo-
comotion of an exercise, e.g., the stride rate in walk-
ing and paddle rate in cycling. The algorithm is uni-
versal in the sense that it is capable of estimating the
rate regardless of the mode of exercise, and the lo-
cation of the TA is fixed no matter what exercise is
being performed. The algorithm contains two main
parts: the first part is to detect the periodicities of the
TA measurements, and the second part of the algo-
rithm is to estimate the exercise rate through the use of
data fusion techniques. The proposed algorithm can
be applied to exercise monitoring in athletics training,
monitoring activities of the elderly, and rehabilitation
program for the cardiac patients.
2 METHODS
2.1 Equipment
In this study, the TA for measuring the body acceler-
ations during an exercise is a wireless, single, waist-
mounted unit, and it measures accelerations in three
axes. The sampling rate of the measurements is 50Hz
535
M. Cheng T., V. Savkin A., G. Celler B., W. Su S. and Wang N. (2009).
EXERCISE RATE ESTIMATION USING A TRIAXIAL ACCELEROMETER.
In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing, pages 535-538
DOI: 10.5220/0001776605350538
Copyright
c
 SciTePress

per channel. The location of the TA is fixed and
always mounted on the right-hand-side of the waist
of an exerciser. The measurements from the TA are
transmitted using a Bluetooth class 1 radio that gives
a typical radio range of 100 meters and 30 meters in
outdoor and indoor environments respectively. The
sampling rate of the measurements is 50Hz per chan-
nel. To remove any abnormal noise spikes produced
by the TA, the raw signals are first median-filtered
with a 5-second window. Next, the signals are filtered
by a low-pass filter with a cutoff frequency 20Hz for
removing any high-frequency noises.
2.2 Exercise Rate Estimation
To detect the exercise rate, we first estimate the funda-
mental frequency of each acceleration measurement
from the TA. Next, the information of the funda-
mental frequencies or periodicities of the acceleration
measurements are fused together using the Kalman
filtering technique.
2.2.1 Fundamental Frequency Estimation
The problem of estimating the fundamental frequency
of a signal is actively studied in the field of speech
processing. Fundamental frequency, or pitch, de-
tection is important for measuring prosodic fea-
tures in speech for speech recognition and enhance-
ment (Hess, 1983). For these reasons, there are a
number of pitch detection algorithms (PDA) reported
in the literature (see, e.g. (Ross et al., 1974; Rabiner
et al., 1976; Rabiner and Schafer, 1978; de Cheveigne
and Kawahara, 2002)). One of the most widely used
methods for detecting pitch or fundamental frequency
is to use the average magnitude difference function
(AMDF) (Ross et al., 1974).
Alternate approaches to estimating the frequency
of signals are also proposed in other engineering com-
munities. For instance, in control society, the ex-
tended Kalman filtering (EKF) technique is used for
estimating the frequency of the fundamental compo-
nent as well as the amplitudes and phases of the first m
harmonic components (Parker and Anderson, 1990).
However, such a technique requires a large amount of
computationalefforts and it is undesirable in real-time
applications.
The AMDF of a discrete signal x
t
is defined by
e
t
(d) =
1
N
N
∑
i=1
|x
t
(i) − x
t
(i− d)| (1)
where e
t
(d) is the AMDF of lag d calculated at
time index t and N is the summation window size
in terms of samples. When the lag d is very close
or equal to the fundamental period of the signal x
t
,
the AMDF (1) will form a dip or a strong local min-
imum. The AMDF method simply requires one to
search for the lowest dip within a given range of lags
D := [d
min
, d
max
]. Therefore an estimate of the period
of the signal x
t
is given by:
τ =
ˆ
d × T
s
(2)
where
ˆ
d := min
d∈D
{e
t
(d)} ,
and T
s
is the sampling period of the discrete signal
x
t
. Since the above search may result in the so-
called sub-harmonic errors (see e.g., (de Cheveigne
and Kawahara, 2002)). These error create undesir-
able spikes in the period estimates. Therefore, to im-
prove the reliability of the estimates, a causal median-
filter with window length L is employed for removing
spikes in the period estimates.
2.2.2 Data Fusion
The above procedure allows us to estimate the fun-
damental periods of 3 acceleration measurements,
namely τ
x
(t), τ
y
(t), and τ
z
(t) at time instant t. Us-
ing the information of these periods and the data fu-
sion technique (Hall and Llinas, 1997; Smyth and Wu,
2007; Tan et al., 2008), an exercise period T(t) (i.e.,
the inverse of the exercise rate) is to be estimated.
Here we have one TA unit mounted on the waist,
but it measures accelerations in 3 different directions,
giving us 3 measurements for extracting information
about the body movement of an exerciser.
In order to perform data fusion for estimating
the exercise period T(·), we consider the following
discrete-time fusion model
T(k + 1) = T(k) + w(k) for k = 0, 1, 2, . . .
y(k) =


y
1
(k)
y
2
(k)
y
3
(k)


=


τ
x
(k)
τ
y
(k)
τ
z
(k)


=


1
1
1


T(k) +


v
x
(k)
v
y
(k)
v
z
(k)


=: cT(k) + v(k),
(3)
where T(·) ∈ R is the exercise period to be estimated;
y(·) ∈ R
3
is the measurement vector consisting of the
noisy period measurements τ
x
(·), τ
y
(·) and τ
z
(·) ob-
tained from Section 2.2.1; w(·) is a fictitious model
noise; and v
x
(·), v
y
(·) and v
z
(·) are the noises on the
period measurements. The noise processes {w(k)}
and {v(k)} are assumed to be zero mean white Gaus-
sian noise with covariance σ
w
(k) and covariance ma-
trix R(k) respectively:
E[v(k)v( j)
T
] = R(k)δ(k− j), and E[v(k)w( j)] = 0.
BIOSIGNALS 2009 - International Conference on Bio-inspired Systems and Signal Processing
536

Our goal is to estimate T(k) using the noisy pe-
riod measurements y(k) via the Kalman filtering tech-
nique (Simon, 2006).
Let
ˆ
T(k) be the estimate of T(k) at time instant k.
The Kalman filter for the fusion model (3) is given by
the following equations, which are computed for each
time step k = 1, 2, . . .:
ˆ
T(k) =
ˆ
T(k − 1) + K(k)

y(k) − c
ˆ
T(k− 1)

K(k) = p
−
(k)c
T

cp
−
(k)c
T
+ R(k)

−1
p
−
(k) = p
+
(k− 1) + σ
w
(k− 1)
p
+
(k) = (1− K(k)c)p
−
(k)
(4)
where c := [1 1 1]
T
. The filter (4) is initialized as
follows:
ˆ
T(0) = T
0
and p
+
(0) = E[(T
0
−
ˆ
T(0))
2
].
The covariance of {w(k)} is assumed to be constant
σ
w
(k) = σ
w
, and the covariance matrix R(k) of the
measurement noise v(k) is time-varying and defined
as follow:
R
i, j
(k) =
(
0, for i 6= j
r
i
(k) = exp(η|y
i
(k) − ¯y(k)|), for i = j
(5)
where η > 0 and ¯y(k) := mean(y(k)). The R(k) (5)
allows us to pay less attention on any measurement
y
i
(k) that is far way from the mean ¯y(k).
3 EXPERIMENTAL RESULTS
An experimental study was performed to validate the
proposed estimation algorithm. Two experimental
subjects were requested to exercise on a treadmill and
a cycle ergometer. For each kind of exercise, two ex-
ercise rates, in terms of period in seconds, were spec-
ified. To follow the specified exercise rates, the sub-
jects were instructed to exercise following the peri-
odic audio beeps generated from a digital metronome
(Intelli Digital IMT-202 Metronome). The subjects
had been given a training session for them to famil-
iarize with the equipments and to get used to exercis-
ing at a specific rate given by the digital metronome.
We therefore assumed that the subjects could follow
the periodic audio beeps from the digital metronome
closely throughout the exercise, and the exercise rates
were approximately equal to the frequencies of the
audio beeps from the digital metronome.
Each subject completed 2 sessions of walking and
cycling exercises. In each session, the subject was re-
quested to exercise on an equipment at 2 given rates
for 6 minutes continuously: first 3 minutes for one
fixed rate and the next 3 minutes for another fixed
rate. During the exercise, the body accelerations of
0 50 100 150 200 250 300 350
1
1.1
1.2
1.3
1.4
1.5
Time (sec)
Period T (sec)
Subject 1 (walking)
0 50 100 150 200 250 300 350
1
1.1
1.2
1.3
1.4
1.5
Time (sec)
Period T (sec)
Subject 2 (walking)
Figure 1: Estimation of walking stride rate using a triax-
ial accelerometer (at 2 exercise rates: 1.25 and 1.07 secs).
(Top) Subject 1, (Bottom) Subject 2.
the subject were recorded by the TA unit as described
in Section 2.1.
Table 1 summaries the design parameters for the
proposed algorithm in the fundamental frequency de-
tection and data fusion stages.
Table 1: Design parameters for the exercise rate estimation
algorithm.
AMDF search range in seconds:
D = [0.5, 4]
Causal median filter window length:
L = 5
Kalman filter parameters:
ˆ
T
0
= 2, p
+
(0) = 4,
σ
w
= 0.01, η = 10
As shown in Figures 1–2, the proposed algorithm
demonstrated to perform well, as the exercise rate
estimates from the algorithm closely match with the
specified exercise rates for both subjects and for all 2
exercises. The algorithm was able to track the change
of exerciserate at the 3-minute mark and settled to the
new rate in a reasonable short transient period.
One concern is that the estimated exercise rate of
Subject 1 during the first 3 minutes of cycling exercise
appears to have some fluctuations (see Figure 2), but
this kind of fluctuations were not observed in other
exercise rate estimates. This is currently under inves-
tigation, it might due to the fact that Subject 1 did not
concentrate on following the demands from the digi-
tal metronome during the cycling exercise in the first
3 minutes or there is a sensitivity issue of the algo-
rithm that may need to be resolved.
EXERCISE RATE ESTIMATION USING A TRIAXIAL ACCELEROMETER
537

0 50 100 150 200 250 300 350
0.7
0.8
0.9
1
1.1
Time (sec)
Period T (sec)
Subject 1 (cycling)
0 50 100 150 200 250 300 350
0.7
0.8
0.9
1
1.1
Time (sec)
Period T (sec)
Subject 2 (cycling)
Figure 2: Estimation of cycling pedal rate using a triax-
ial accelerometer (at 2 exercise rates: 1.07 and 0.83 secs).
(Top) Subject 1, (Bottom) Subject 2.
4 CONCLUSIONS
An algorithm for the estimation of exercise rate from
triaxial accelerometer measurements was proposed in
this paper. The proposed algorithm is universal re-
gardless of the mode of exercise, and it has been ex-
perimentally verified in determining the exercise rates
of walking and cycling. The algorithm can readily be
applied to the monitoring of rehabilitation exercise for
the cardiac patients, and training exercise for the ath-
letics. Also, it will be useful in monitoring activities
of the elderly and the obese.
ACKNOWLEDGEMENTS
This work was supported by the Australian Research
Council.
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