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1
Estimating Oxygen Uptake during Non-Steady-State
Activities and Transitions Using Wearable Sensors
Marco Altini
1
, Julien Penders
2
and Oliver Amft
3
Abstract—In this paper, we present a method to estimate
oxygen uptake (VO
2
) during daily life activities and transitions
between them. First, we automatically locate transitions between
activities and periods of non-steady-state VO
2
. Subsequently, we
propose and compare activity-specific linear functions to model
steady-state activities and transition-specific non-linear functions
to model non-steady-state activities and transitions. We evaluate
our approach in study data from 22 participants that wore a
combined accelerometer and heart rate (HR) sensor while per-
forming a wide range of activities (clustered into lying, sedentary,
dynamic/household, walking, biking and running), including many
transitions between intensities, thus resulting in non-steady-
state VO
2
. Indirect calorimetry was used in parallel to obtain
VO
2
reference. VO
2
estimation error during transitions between
sedentary, household and walking activities could be reduced by
16% on average using the proposed approach, compared to state
of the art methods.
Index Terms—Accelerometers, Energy Expenditure, Heart
Rate, Non-Steady-State, VO
2
I. INTRODUCTION
Ubiquitous sensing technologies that objectively and non-
invasively monitor human behavior, started to provide insights
into the relation between physical activity (PA) and health.
Among the parameters used to objectively quantify PA, energy
expenditure (EE) is the most commonly used single metric
[1], [2], [3]. The measurement of steady-state oxygen uptake
(VO
2
) is considered to be the gold standard for estimating
EE during light to moderate steady-state exercise [4], [5],
where aerobic pathways are predominant. In this context, VO
2
measurements are proportional to metabolic heat production
[4]. Due to the practical limitations of measuring VO
2
in free
living, different methods to estimate VO
2
using miniaturized
wearable sensors have been developed in the past.
VO
2
estimation methods are typically based on activity-
specific linear regressions developed using steady-state data
and therefore can describe the variations within each modeled
activity during steady-state. However, transitions to activities
with other VO
2
levels cannot be accurately estimated, since
VO
2
dynamics differ during steady-state and non-steady-
state periods. Proper modeling of non-steady-state transitions
including transitions of activity types (e.g. sitting to walking)
and activity intensities (e.g. walking at different speed) are
necessary in order to provide accurate VO
2
estimation in free
1
M. Altini is with Bloom Technologies, Agoralaan Building Abis 2.13,
3590 Diepenbeek, Belgium, and Eindhoven University of Technology, Eind-
hoven, The Netherlands (e-mail: marco.altini@imec-nl.nl)
2
J. Penders is with Holst Centre/imec The Netherlands, Eindhoven, Nether-
lands, (e-mail: julien.penders@imec-nl.nl)
3
O. Amft is with University of Passau, Germany, and Eindhoven University
of Technology, The Netherlands (e-mail: amft@ieee.org)
living conditions. Accurate identification of non-steady-state
periods as well as quantifications of VO
2
during transitions
could improve EE estimation because during non-steady-state
periods total EE is composed of aerobic and anaerobic compo-
nents. [4]. Earlier work on VO
2
transitions analysis focused
mainly on Post-Exercise Oxygen Consumption (EPOC) [6],
or VO
2
estimation for single activities [7], [8]. However
non-steady-state VO
2
is very frequent during varying low
intensities activities of daily living (ADLs). Studies showed
that most activities performed in free living last shorter than
the time needed to reach steady state. For example, 60% of
all walking bouts last shorter than 30 seconds [9]. Identifying
non-steady-state VO
2
can provide more insights on the aerobic
and anaerobic dynamics during the onset of exercise as well as
during ADLs characterized by short duration. While solutions
have been proposed to model non-steady-state VO
2
for spe-
cific activities [7], [8] or transitions [6], a unified approach able
to continuously estimate VO
2
is missing. Thus, we propose
a novel VO
2
estimation method, which combines activity-
specific VO
2
estimation using linear regression, with non-
steady-state detection and transition-specific VO
2
estimation
using non-linear equations.
This paper provides the following contributions:
1) We introduce a method to automatically locate periods
of non-steady-state VO
2
by analyzing the coefficient
of variation (CV) of the predicted VO
2
. Using the
CV allows for detection of transition both between and
within activities. Then, we compare linear, exponential
and logistic transfer functions to model non-steady-state
VO
2
during individual transition types.
2) We evaluate the proposed approach on a dataset ac-
quired from 22 participants performing a wide set of
physical activities, including many transitions between
activities and changes of intensity within activities. We
show that the transition-specific modeling could reduce
VO
2
estimation error by 16% during activity transitions,
compared to state of the art methods.
II. RELATED WORK
Accelerometer and HR monitors are the most commonly
used single sensor devices in epidemiological studies. Ac-
celerometers use features representative of whole body motion,
as independent variables in the linear regression model devel-
oped to predict EE. However there are limitations due to the
inability of a single linear model to fit all activities, since the
slope and intercept of the regression model change based on
the activity performed while data is collected [3]. On the other
2
hand, the high correlation between HR and EE within one
individual changes substantially between individuals [1]. The
latest EE estimation algorithms extended approaches based
on simple linear regression models performing activity recog-
nition over a predefined set of activities, and then applying
different methods - typically regression models - to predict
EE, based on the activity [2], [3]. The regression models use
accelerometer features and anthropometric characteristics as
independent variables. Some authors included HR features as
well in the activity-specific linear models, showing consistent
improvements in EE estimation accuracy compared to algo-
rithms using accelerometer only features [1]. However, none
of these models explicitly models non-steady-state VO
2
.
A. Non-Steady-State VO
2
Estimation
Non-steady-state EE is often defined as periods of time
where VO
2
and carbon dioxide production vary by more
than 5-10% [10]. Previous research on non-steady-state VO
2
focused mainly on metabolic responses to exercise (EPOC,
[6]). However, VO
2
estimation is intrinsically a temporal
problem and non-steady-state VO
2
is very common during
low intensity ADLs as well. While VO
2
increases rapidly,
normally reaching steady-state within 1-4 minutes, most ac-
tivities performed in free living last less than the time required
to reach steady state [9]. Most EE models are developed
deriving EE from VO
2
, and discarding the first 1 or 2
minutes of data [1], [3], to isolate steady-state. Thus, the
predictions of these models will be negatively affected by the
real life nature of ADL activities. Other models incorporate
non-steady-state VO
2
but without providing details on the
models accuracy during transitions [11], thus limiting our
understanding of the models performance in non-steady-state
conditions. Using physiological data to predict VO
2
involves
slower dynamics present in both physiological changes (e.g.
HR slowing increasing) and aerobic pathways (VO
2
reaching
steady-state). However, these dynamics are different, typically
with HR being much slower than VO
2
[12], [13].
Few attempts to model non-steady-state VO
2
are found in
literature [14], [15], [16], [7], [8]. In [14], [15], the proposed
system relies on HR data only, suffering from all limitations
of non-activity-specific models, while [7], [8] analyzed walk-
ing data only. In [16], the authors used mono-exponential
functions to better capture the relation between movement
and EE during transitions between activities. However, the
EE prediction ignores the fact that during non-steady-state
EE cannot be derived from VO
2
alone, since total EE is
composed of both aerobic (estimated via VO
2
) and anaerobic
components. Finally, one single mono-exponential equation
might not be sufficient to model energy deficit and energy debt
situations between different activities [5]. While solutions have
been proposed to model non-steady-state VO
2
for specific
activities [7], [8] or transitions [6], a unified approach able
to continuously estimate VO
2
is missing.
III. ANA LY S IS A N D ESTIMATION APPROACH
This section describes the problem of non-steady-state VO
2
estimation and our approach to such problem.
5.0
7.5
10.0
12.5
15.0
17.5
0 20 40 60
VO2 (ml/kg/min)
State
steady−state
non−steady−state
a)
5
10
15
0 20 40 60
time windows (4 seconds each)
VO2 (ml/kg/min)
Activity Type
sedentary
dynamic
walking
b)
Fig. 1. Example of non-steady-state VO
2
. a) Non-steady state reference
VO
2
. b) Predicted VO
2
as estimated by steady-state activity-specific models.
In this work, non-steady state modelling is used combined with classic steady-
state models to better estimate actual VO2.
Our approach combines detection of non-steady-state VO
2
,
activity-specific linear models and non-steady state transition-
specific non-linear functions. Fig. 1 shows typical non-steady
state dynamics in activities of daily living, such as transitions
between sedentary activities (e.g. sitting or standing), walking
and then sedentary again. Fig. 1.b shows color-coded activities
as detected by an activity recognition system, while Fig. 1.a
shows steady-state and non-steady-state-data. Non-steady-state
VO
2
is present when the participant starts walking and when
the participant stops walking. Fig. 1.a show measured VO
2
while Fig. 1.b shows VO
2
as predicted by state of the art
activity specific models. Prediction models (Fig. 1.b) jump
between one value to the other as soon as a new activity starts,
while transitions shown in Fig. 1.a are much slower. Thus, a
different modeling technique is required during non-steady-
state.
A. Estimation Architecture
VO
2
predictions are generated by a sequence of steady-state
and non-steady-state models (see, e.g. Fig. 2):
...W
1
,V
1
,W
2
,V
2
,W
1
,V
3
...
where W
i
are activity-specific models used when steady-
state is detected and V
i
are transition-specific non-steady-state
models used when non-steady-state is detected. Each state W
i
or V
i
comprises t predictions based on the time spent in a
specific activity or transition duration:
W
i
= {VO2
Wi
SS
1
,...,VO2
Wi
SS
t
}
V
i
= {VO2
Vi
NS
1
,...,VO2
Vi
NS
t
}
In the following sections, we describe W
i
, V
i
and model
selection.
1) Activity-Specific Steady-State Models - W
i
: W
i
are com-
posed of two parts: activity recognition and activity-specific
multiple linear regression equations. Assuming n clusters of
activities:
C = {c
1
,...,c
n
}, 8c
i
2 C, 9 W
i
3
Activity
Recognition
State
1
model
State
n
model
VO2
ss
Activity-specific VO
2
models
Transition
1
model
Transition
n
model
Transition-specific VO
2
models
Model
Selection
VO2
ns
VO2
Physiological
Features
Anthropometric
Features
activity
class
c
i
W
1
W
n
V
1
V
n
VO2
ss
Accelerometer
Features
Fig. 2. Block diagram of out approach using activity-specific linear models
and transition-specific non-linear functions to estimate VO2. Features are used
for activity recognition and activity-specific VO
2
models. Activity recognition
is used to select the proper activity-specific or transition-specific model.
where the parameters of the activity-specific model W
i
are
derived from VO
2
values for a specific cluster of activities c
i
:
VO2
Wi
SS
= X
act
i
act
i
+ ✏ (1)
is the vector of regression coefficients, and X
act
i
is the
vector of input features. Features are grouped into accelerom-
eter, physiological and anthropometric features (see Fig. 2).
2) Transition-Specific Non-Steady-State models - V
i
: We
compare linear, exponential and logistic functions as V
i
.
Assuming r types of transitions:
Tr = {tr
1
,...,tr
r
}, 8tr
i
2 Tr, 9 V
i
Linear functions: for a transition type V
i
from steady-state
W
j
to steady-state W
k
, a linear model is derived as follows:
VO2
Vi
NS
= ↵ + t + VO2
Wj
SS
+ ✏ (2)
where VO2
Vi
NS
are target VO
2
values during non-steady-state
for the transition V
i
, defined by transition-specific linear func-
tions. The predictor t is the time elapsed since the transition
started. VO2
Wj
SS
is the VO
2
of the steady-state before the
transition (W
j
). Parameters ↵ and are the slope and intercept
of the linear model.
Logistic functions: for a transition type V
i
, a non-linear
model is derived as follows:
VO2
Vi
NS
=
✓
1
1+exp
(✓
Vi
2
+✓
Vi
3
t)
+ VO2
Wj
SS
+ ✏ (3)
where VO2
Vi
NS
are target VO
2
values during non-steady-state
for the transition V
i
, defined by transition-specific logistic
functions. The predictor t is the time elapsed since the tran-
sition started. VO2
Wj
SS
is the VO
2
of the steady-state before
the transition (W
j
). Transitions between activities of different
type and intensity will have different dynamics [5], [17], thus
require transition-specific functions. The parameter ✓
1
is the
asymptote of the logistic function, and can be automatically
derived as the difference between the steady-state VO
2
before
(W
j
) and after (W
k
) the transition:
✓
1
= VO2
Wk
SS
VO2
Wj
SS
. (4)
Parameters ✓
Vi
2
and ✓
Vi
3
control the shape of the logistic curve
(e.g the transition speed), and were determined by fitting
Recognized*ac,vity*
sedentary* walking* sedentary*
0
25
50
75
0 20 40 60
CV (%)
State
steady−state
non−steady−state
Time*windows*(4*s)*
Fig. 3. Example waveform of the CV of the estimated VO
2
for a sequence
of sedentary, walking and sedentary activities. State is non-steady when
CV > 15%. The CV captures transitions between activities as well as within
activities, thus detecting non-steady-state VO
2
.
for each transition type. Thus, ✓
Vi
2
and ✓
Vi
3
are transition-
specific. The transition type (i.e. V
i
) depends on the activities
recognized by the activity recognition system during steady-
states W
j
and W
k
.
Exponential functions: a transition model for a transition
type V
i
is derived as follows:
VO2
Vi
NS
= ✓
1
exp
↵+t
+ VO2
Wj
SS
+ ✏ (5)
where VO2
Vi
NS
are target VO
2
values for the transition V
i
,
defined by transition-specific exponential functions. The pre-
dictor t is the time elapsed since the transition started. VO2
Wj
SS
is the VO
2
of the steady-state before the transition (W
j
). The
parameter ✓
1
is the same as for the logistic function, indicating
the asymptote of the exponential, and can be automatically
derived as shown in Eq. 4.
3) Model Selection: Non-steady-state is detected using the
CV of the predicted VO
2
over the last minute of data,
according to a preselected threshold:
CV
VO2
SS
=
VO2
SS
µ
VO2
SS
(6)
where
VO2
SS
and µ
VO2
SS
are the standard deviation and
mean of a 60 s sliding window of predicted VO
2
values.
Non-steady-state is detected if CV
VO2
SS
>CV
T hres
, where
CV
T hres
was set to 15%. Fig. 3 shows the CV for the predicted
VO
2
data. CV can be used to locate non-steady-states, such
as when activity intensity changes, thus even when there is no
transition between two activities.
IV. EVA L UAT I O N STUDY
A. Participants and Data Acquisition
Participants were 22 (17 male, 5 female), mean age
30.4 ± 5.7 years, mean weight 71.2 ± 12. 4 kg, mean height
1.76 ± 0.09 m, mean BMI 23.0 ± 2.8 kg/m
2
. Imec’s IRB
approved the study. Each participant signed an informed con-
sent form. The sensor platform used was the ECG Necklace, a
wearable sensor acquiring one lead ECG data at 256 Hz, and
three-axial accelerometer data at 32 Hz. Activity type was
annotated manually by experimenter. Breath-by-breath data
were collected using the Cosmed K4b
2
indirect calorimeter.
We interpolated calorimeter data at 0.25 Hz to align it with
the ECG Necklace data, and applied a moving average with
window size 4 elements to reduce high frequency noise.
4
B. Experiment Design
Participants reported at the lab after refraining from drink-
ing, eating and smoking in the two hours before the experi-
ment. Activities were grouped into six clusters to be used for
activity classification. The six clusters were lying (lying down),
sedentary (sitting, standing, desk work, reading, writing, PC
work), dynamic (stacking groceries, washing dishes, cleaning,
sweeping, vacuuming), walking (treadmill flat at 3,4,5,6 km/h,
inclined 3-5%, 3-5 km/h), biking (cycle ergometer, low medium
and high resistance level), running (treadmill 7,8,9, and 10
km/h). Activities were carried out for a period of at least 4
minutes, with the exception of running (1 to 4 minutes). All
transitions were manually annotated.
C. Statistics and Performance Measure
Models were derived using leave-one-participant-out cross
validation. The same training set, consisting of data from
all participants but one, was used to perform feature selec-
tion, activity recognition, activity-specific VO
2
estimation and
transition-specific VO
2
estimation models. The data from the
remaining participant was used for validation. This procedure
was repeated n (n = number of participants) times, and re-
sults were averaged. All parameters used in transition-specific
functions were determined in the same way, no data used for
model building was used for model evaluation. Performance
of the activity recognition models was evaluated using the
class-normalized accuracy. Results for VO
2
estimates are
reported in terms of Root-mean-square error (RMSE), where
the outcome variable was VO
2
in ml/kg/min. Paired t-tests
were used to compare RMSE between models.
V. I MPLEMENTATION
A. Features Extraction and Selection
Features extracted from the sensors’ raw data were used
to derive activity recognition and VO
2
estimation models.
Activity recognition was performed to classify the six activity
clusters introduced in Section IV-B. Accelerometer data were
segmented in 4 s windows, band-pass filtered between 0.1
and 10 Hz, to isolate the dynamic component caused by
body motion, and low-pass filtered at 1 Hz, to isolate the
static component, due to gravity. Feature selection for activity
type recognition was based on mutual information. The final
feature set included: mean of the absolute signal, inter-quartile
range, median, variance, main frequency peak, low and high
frequency band signal power. Feature selection for VO
2
estimation was based on how much variation in VO
2
each
feature could explain within one cluster. The process was
automated using linear forward selection.
B. Activity Recognition
We selected a time window of 4 s, which is short enough
to detect short breaks in sedentary time, and long enough to
capture the repetitive patterns of some activities (e.g. walking
or running). Given the positive results in past research on
activity recognition, we selected Support Vector Machines
(SVMs) as classifiers. For the SVMs, we used a polynomial
kernel with degree 5 ( = 10, C = 1).
C. Activity-Specific Steady-State Models - W
i
Within one activity cluster, VO
2
can be estimated using
features representative of VO
2
changes within the activity
cluster [3], [1]. We used the mean of the absolute signal
to model changes in intensity within an activity, together
with HR. Anthropometrics features (body weight and resting
metabolic rate (RMR), estimated with the Harris-Benedict
formula) were added depending on the activity cluster.
D. Non-Steady-State Detection
The CV over one minute windows was computed to locate
non-steady-state segments of data. When the CV was higher
than CV
T hres
, a new non-steady-state transition was detected.
CV
Thres
was derived from previous literature on detection
of non-steady-state VO
2
, and empirically cross-validated on
our dataset, since no definition of non-steady-state is widely
accepted [10]. Once a non-steady-state transition V
i
was
detected between two steady-states W
j
and W
k
, the system
compared the steady-state VO
2
levels and enables the non-
steady-state models only if the difference in VO
2
was greater
than a threshold. This filter avoids activating the non-steady-
state models for transitions that are too small or short.
E. Transition-Specific Non-Steady-State models - V
i
Transition-specific non-steady-state models V
i
were devel-
oped for the most common transitions. More specifically,
logistic functions were derived by fitting the parameters ✓
2
and ✓
3
while linear and exponential functions were derived by
fitting the parameters ↵ and of the respective models, for
the following transitions: sedentary to walking (SW), walking
to sedentary (WS), sedentary to dynamic/household (SD),
dynamic/household to sedentary (DS), walking fast to walking
slow (WWDOWN), walking slow to walking fast (WWUP).
Data used for model development was not used for validation.
VI. RESULTS
We report results for activity recognition, activity-specific
steady-state models, non-steady-state detection and transition-
specific non-steady-state models, together with summary
statistics on the specific transitions considered in this work.
An example of the proposed method applied to a transition
between sedentary behavior and walking is shown in Fig. 4.
5
10
15
0 20 40 60 80
Samples
VO2 − ml/kg/min
type
Act−Spec ACC−HR
Act−Spec ACC−HR + Logistic
referenceVO2
ac#vity(
sedentary(
walking(
sedentary(
Fig. 4. Example of the results obtained when combining activity-specific
steady state models and transition-specific non-stead-state models (Act-Spec
ACC-HR + Logistic), as proposed by our method, for a transition between
sedentary to walking and walking to sedentary. Act-Spec ACC-HR show the
inability of steady-state models to predict VO
2
accurately during transitions.
5
Fig. 5. RMSE for VO
2
estimation using different sensing modalities and
methods for steady-state data. Activity-specific (Act-Spec) models outperform
all others, combined accelerometer and heart rate (ACC-HR) data improves
performance compared to accelerometer (ACC) or heart rate (HR) only.
A. Activity Recognition
Activity recognition accuracy was 94% on average across
all participants using the validation procedure detailed in Sec.
IV-C. More specifically, accuracy was 100% for lying down,
96% for sedentary, 81% for dynamic/household, 99% for
walking, 91% for biking and 98% for running.
B. Activity-Specific Steady-State Models
RMSE for activity-specific steady-state VO
2
estimation
models using combined accelerometer and HR data was 3.5
ml/kg/min. More specifically, RMSE was 1.16 ml/kg/min for
lying down, 1.75 ml/kg/min for sedentary, 3.93 ml/kg/min
for walking, 4.55 ml/kg/min for dynamic/household, 4.24
ml/kg/min for biking and 5.81 ml/kg/min for running. Sim-
ilarly to what was reported in literature for EE estimation
models, activity-specific VO
2
estimation models combining
accelerometer and HR data outperformed single regression
models relying on accelerometer only (46% RMSE reduc-
tion, p =4e
11
<↵), HR only (23% RMSE reduction,
p =0.0002 <↵), combined accelerometer and HR data
(17% RMSE reduction, p =0.001 <↵) and activity-specific
estimation models relying on accelerometer data only (10%
RMSE reduction, p =0.002 <↵). Fig. 5 provides an
overview.
C. Non-Steady-State Detection
221 transitions were analyzed in total (45 SW, 28 WS, 42
SD, 53 DS, 39 WWUP, 14 WWDOWN). 85% of all transitions
were correctly identified by the transition detection system.
Transition detection was more accurate for transitions between
sedentary to walking activities (98%) and for transitions be-
tween walking to sedentary activities (100%). Transition detec-
tion accuracy dropped to 78% and 84% for transitions between
sedentary to dynamic/household and dynamic/household to
sedentary respectively. Transitions in VO
2
within activities
(e.g. following changes in walking speed or inclination), that
were smaller than 1 ml/kg/min were not considered. All other
within activities transitions were correctly identified (100% ).
Fig. 6. RMSE for VO
2
estimation using different methods for non-steady-
state data. While standard activity-specific models that combine acc and
HR (Act-Spec ACC+HR) perform better than other models during steady-
state (see Fig .5), they offer poor performance during transitions. Linear,
exponential and logistic functions progressively reduce RMSE, with logistic
functions providing the lowest errors. Logistic Generic refers to logistic
functions were parameters did not vary depending on the transition type.
D. Transition Types
There was a significant relation between transition time
and VO
2
change between the starting and target activities
during a transition (correlation coefficient r =0.68, p =
0.0015 <↵). VO
2
difference between the starting and target
activities during a transition was 6.40 ml/kg/min for SW, 9.25
ml/kg/min for WS, 7.47 ml/kg/min for SD, 7.46 ml/kg/min
for DS , 4.38 ml/kg/min for WWUP and 5.80 ml/kg/min
for WWDOWN. Average transition duration was 97 s for
SW , 108 s for WS, 88 s for SD, 98 s for DS, 87 s for
WWUP and 125 s for WWDOWN. VO
2
estimation error
for steady-state models during transitions involving sedentary
and household activities was 4.62 ml/kg/min (SD) and 4.50
ml/kg/min (DS ), even though error during steady-state was
only 1.75 ml/kg/min for sedentary and 4.55 ml/kg/min for
household. VO
2
estimation error for steady-state models
during transitions involving sedentary and walking activities
was 5.63 ml/kg/min (SW) and 4.23 ml/kg/min (WS), even
though error during steady-state was only 1.75 ml/kg/min for
sedentary and 3.93 ml/kg/min for walking.
E. Transition-Specific Non-Steady-State models
Fig. 6 shows VO
2
RMSE during transitions for the best
performing steady-state models (i.e. activity-specific models
combining accelerometer and HR data) and non-steady-state
models. VO
2
RMSE during transitions for steady-state models
was 4.38 ml/kg/min. Linear models reduced RMSE to 4.27
ml/kg/min (3% RMSE reduction, p =0.5 >↵), expo-
nential functions to 4.07 ml/kg/min (7% RMSE reduction,
p =0.2 >↵), and logistic functions to 3.68 ml/kg/min (16%
RMSE reduction, p =0.0007 <↵). Thus, logistic functions
were the best performing non-steady-state models for activities
transitions. For comparison, we evaluated logistic functions
were parameters were not fitted to specific transitions, but were
held constant for all transitions, denoted as Logistic Generic in
Fig. 6 and Table I. Logistic generic results were VO
2
RMSE
of 3.77 ml/kg/min (14% RMSE reduction, p =0.002 <↵).
6
TABLE I
VO
2
RMSE FOR TRANSITIONS MODELS CONSIDERING PERFECT TRANSITION DETECTION (ML/KG/MIN)
Transition Activity-Specific Linear Exponential Logistic Logistic Generic
Sedentary to walking (SW) 5.42 ± 1.46 5.79 ± 1.86 4.67 ± 3.18 4.27 ± 2.20 4.94 ± 2.40
Walking to sedentary (WS) 3.84 ± 1.12 4.10 ± 1.62 3.26 ± 2.60 2.43 ± 1.59 2.48 ± 1.33
Sedentary to dynamic (SD) 4.28 ± 1.25 3.81 ± 1.54 4.07 ± 1.99 3.30 ± 1.29 3.29 ± 1.36
Dynamic to sedentary (DS) 4.20 ± 1.48 3.17 ± 1.43 3.32 ± 1.28 3.57 ± 1.31 3.42 ± 1.23
Walking slow to fast (WWUP) 4.10 ± 2.06 4.97 ± 2.43 3.15 ± 1.79 4.05 ± 2.10 4.06 ± 2.10
Walking fast to slow (WWDOWN) 4.03 ± 2.17 3.69 ± 2.32 4.87 ± 3.01 4.4 ± 2.28 3.95 ± 2.14
Mean 4.38 ± 0.80 4.27 ± 1.05 4.07 ± 1.28 3.68 ± 1.10 3.77 ± 1.03
VII. DISCUSSION
In this paper we introduced a method to estimate VO
2
dur-
ing ADLs. Our method combines non-steady-state detection
and transition-specific VO
2
estimation non-linear equations.
It is misleading to assume that EE can be derived from
VO
2
alone. Proper modeling of non-steady-state transitions
is important since both anaerobic and aerobic EE result in
heat production, which is the true EE. However, only aerobic
EE results in VO
2
consumption. To tackle non-steady-state
VO
2
estimation, we proposed a method to locate periods of
non-steady-state VO
2
using the CV over the predicted VO
2
level. Our results showed that the CV can be used for detecting
transitions between and within activities. Then, we showed that
modeling non-steady-state transitions using non-linear logistic
functions for individual transition types could reduce VO
2
estimation error by 16%.
A. Activity Recognition and Transition Detection
In previous research both unsupervised and supervised
methods for activity recognition were proposed in the context
of VO
2
estimation, with supervised methods providing better
results [18]. For this reason, we opted for supervised methods
typically able to provide good accuracy on big clusters of
activities as confirmed by our results, where 94% average
accuracy was obtained in leave-one-participant-out validation
design. Transition detection was highly accurate for all tran-
sitions including the walking activity (98 100%). However,
transition detection was less accurate for transitions involving
dynamic/household activities (78 84%), since these activities
are both more difficult to recognize and highly variable in
VO
2
. In literature, several approaches have been proposed
to detect transitions between activities [19], [20]. Detecting
transitions based on the CV of the predicted VO
2
provides
the advantage to detect not only transitions between activities,
but also changes in intensity within the same activity (e.g.
walking at a lower speed). Various definitions of steady-state
have been reported [10]. Some researchers defined steady state
as 5 consecutive 1-minutes intervals where O
2
consumption
changes by less than 10%. However this definition resulted
from assessments of basal metabolic rate and is not directly
applicable to free living conditions, where we are interested in
detecting much shorter transitions. Our analysis shows that one
minute windows and a slightly less strict CV (i.e. 15%), are a
good trade-off for non-steady-state and transitions detection.
B. Transition-Specific Non-Steady-State Models
Our analysis focused on sedentary, dynamic/household and
walking activities, since our objective is to improve VO
2
estimation in common transitions during ADLs, where current
methods lack proper modeling.
Thus, we have not considered transitions during intense
activities (e.g. biking or running), which are less frequent in
daily life and well studied in literature. The ADLs considered
are characterized by similar levels of VO
2
for both the starting
and target activity of a transition. Thus, the VO
2
change
during a transition and the time required to reach steady
state are similar. While parameters differ between transitions,
and transition-specific logistic functions provided the best
results, generic logistic functions which do not vary parameters
based on the transition were sufficient to significantly reduce
RMSE compared to steady-state models (14% RMSE reduc-
tion, p =0.002 <↵). Logistic functions were proposed in
literature to model HR recovery after intense exercise [21], due
to the ability to model different dose-response relationships
between two relatively stable levels. While we applied this
technique to model transitory oxygen uptake during ADLs,
the methodology could be extended to other physiological
parameters undergoing similar changes. For comparison, we
also fitted linear and exponential functions, as previously
reported in literature [16]. However we found suboptimal
results compared to logistic functions.
Another advantage of the proposed technique is that at
runtime VO
2
estimations during transitions are only dependent
on the previously fitted parameters and on the parameter ✓
1
,
representing the difference in VO
2
between the starting and
the target activity. Thus, these models could be applied to
systems based on accelerometers only, and do not depend on
other predictors or sensing modalities.
Performance of non-steady-state VO
2
models should be
assessed outside of the lab [22]. However, there is currently no
unobtrusive reference system that is able to measure breath-by-
breath VO
2
in unconstrained settings. Only by using indirect
calorimetry and supervised settings we can record data, which
allows us to analyze how non-steady-state models can improve
VO
2
estimations during transitions. In our evaluation protocol,
we could not elicitate abrupt VO
2
changes within one activity,
e.g. when changing the treadmill speed and inclination level,
there was a gradual change, which could last up to 30
seconds. Hence, it was difficult to even collect representative
data that could benefit from non-steady-state modeling within
an activity (e.g. walking at different speeds) and the VO
2
7
estimation did not provide improvements over the steady-state.
A set of thirty activities of varying intensities was used in
this study and further work could extend the set, for example
including activities involving carrying loads. However, we
believe that the lifestyle activities used here are representative
and relevant to assess VO
2
estimation in non-stationary daily
life conditions. The generalized method proposed in this work
is able to model abrupt within-activity changes in VO
2
without
modifications to the model, since it detects transitions relying
on the CV, instead of the activity type. While it is not feasible
for us to robustly detect activities such as carrying a weight
using a wearable sensor on the chest, the use of HR partially
solves the problem. Carrying a load would create higher
strain, thus raise HR, which is used in the estimation models,
and therefore result in higher predicted VO
2
. In this work,
CV changes were shown to even indicate intensity changes
within the same activity confirming the method’s sensitivity.
By properly modeling VO
2
during transitions and locating
periods of non-steady-state, we quantified VO
2
for aerobic
dynamics during the onset of exercise, as well as during ADLs
characterized by short duration, with 16% error reduction
compared to current methods.
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Marco Altini received the M.Sc. degree in engi-
neering and computer science from the University of
Bologna in 2010. He is currently pursuing the Ph.D.
degree with the Technical University of Eindhoven,
Eindhoven, The Netherlands. His current research
interests include machine learning techniques for
the development and implementation of biomedical
applications using wearable sensors data.
Julien Penders received the M.Sc. degree in systems
engineering from the University of Liege, Belgium,
and the M.Sc. degree in biomedical engineering
from Boston University, in 2004 and 2006, respec-
tively. He is currently the Program Manager with the
Holst Centre/IMEC, Eindhoven, The Netherlands.
He has authored or co-authored over 30 papers in
journals and conference proceedings on body area
networks and autonomous wireless sensor networks.
Oliver Amft received the M.Sc. from TU Chem-
nitz in 1999 and the Ph.D. from ETH Zurich in
2008, both in Electrical Engineering and Information
Technology. Oliver is a Full Professor (W3) and
Chair of Sensor Technology at University of Passau.
He is also affiliated with the Wearable Computing
Lab, ETH Zurich (CH) and the Signal Processing
Systems section at TU Eindhoven (NL). Oliver is
interested in multi-modal activity recognition and
human behaviour inference algorithms and has co-
authored more than 90 publications in this field.
