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In Situ Calibration Algorithms for Environmental
Sensor Networks: a Review
Florentin Delaine, Bérengère Lebental, Hervé Rivano
To cite this version:
Florentin Delaine, Bérengère Lebental, Hervé Rivano. In Situ Calibration Algorithms for Environ-
mental Sensor Networks: a Review. IEEE Sensors Journal, Institute of Electrical and Electronics
Engineers, 2019, 19 (15), pp 5968 - 5978. �10.1109/JSEN.2019.2910317�. �hal-02174938v2�
IEEE SENSORS JOURNAL, VOL. X, NO. X, MONTH YEAR 1
In Situ Calibration Algorithms
for Environmental Sensor Networks: a Review
Florentin Delaine, B
´
ereng
`
ere Lebental and Herv
´
e Rivano
Abstract—The recent developments in both nanotechnologies
and wireless technologies has enabled the rise of small, low cost
and energy efficient environmental sensing devices. Many projects
involving dense sensor networks deployments have followed, in
particular within the Smart City trend. If such deployments
are now within economical and technical reach, their mainte-
nance and reliability remain however a challenge. In particular,
reaching, then maintaining, the targeted quality of measurement
throughout deployment duration is an important issue. Indeed,
factory calibration is too expensive for systematic application to
low-cost sensors and as these sensors are usually prone to drifting
because of premature aging. In addition, there are concerns about
the applicability of factory calibration to field conditions. These
challenges have fostered many researches on in situ calibration.
In situ means that the sensors are calibrated without removing
them from their deployment location, preferably without physical
intervention, often leveraging their communication capabilities.
It is a critical challenge for the economical sustainability of
networks with large scale deployments.
In this paper, we focus on in situ calibration methods for
environmental sensor networks. We propose a taxonomy of the
methodologies in the literature. Our classification relies on both
the architecture of the network of sensors and the algorithmic
principles of the calibration methods. This review allow us to
identify and discuss two main challenges: how to improve the
performance evaluation of such methods and how to enable a
quantified comparison of these strategies?
Index Terms—Sensor networks, calibration, algorithms
I. INTRODUCTION
E
NVIRONMENTAL sensors are measuring instruments
designed to measure ambient quantities such as temper-
ature, relative humidity, noise, pressure, wind speed, wind
direction, chemical components concentrations and so on.
Fostered by the emergence of the Internet of Things (IoT)
and of low-cost sensing devices, the interest for these devices
has been growing for the past decades [1].
Depending on the target area to monitor and on the spatial
variability of the measurand, hundreds of devices may be
required, as shown for instance by [2] and [3] in the field of air
quality monitoring. The cost of sensors then becomes a major
factor, which explains the interest for low-cost sensors [4].
These technologies are still emerging and must face several
issues, one of them being the improvement of data quality [1]
[5] [6] [7] [8].
Florentin Delaine and B
´
ereng
`
ere Lebental are with Efficacity, F-77420
Champs-sur-Marne, France, Universit
´
e Paris-Est, IFSTTAR, COSYS, F-
77447 Marne-la-Vall
´
ee, France and Laboratoire de Physique des Interfaces
et Couches Minces (LPICM),
´
Ecole Polytechnique, CNRS, Universit
´
e Paris-
Saclay, F-91128 Palaiseau, France.
Herv
´
e Rivano is with Universit
´
e de Lyon, INSA Lyon, Inria, CITI, F-69621,
Villeurbanne, France.
Corresponding author: Florentin Delaine (florentin.delaine@gmail.com)
More precisely, it is often observed that the sensing quality
of low cost devices decay with time, even under regular
operating conditions [9]. In particular, the calibration relation-
ship may change, hence the need for frequent evaluation. In
metrological terms [10], calibration consists in deriving, under
specified conditions, the relationship between the indication
of the instrument (its raw output) and the measurand (the
quantity intended to be measured). This is a quite well
mastered operation when performed in dedicated laboratory
facilities where most parameters can be controlled and almost
perfectly known. However, in such conditions recalibration
of a deployment of sensors means dismounting and shipping
the whole network from the field to a calibration facility and
re-deploy it afterward. It is not technically and economically
sustainable for dense deployments of low cost devices.
Consequently, calibration procedures suitable for sensor
placed in field conditions have been widely investigated in the
past two decades. This is all the more relevant as the validity
of laboratory calibrations is often questioned in the field [11]
[12]. Furthermore, a significant part of commercial sensor
technologies are sold without initial individual calibration (see
for instance [13]) to reduce cost.
In this paper, we review the literature on in situ calibration
methods for environmental sensor networks. In situ meth-
ods, sometimes called field, in place, remote or online cali-
bration instead, enable to calibrate measuring instruments of a
network while leaving them deployed in the field, preferably
without physical intervention. The literature on the subject
studies under which hypotheses, in which manner and with
which performance the measured values from a sensor network
may be exploited to improve the measurement accuracy of
the whole network through calibration. In a recent survey,
Maag et al. focus on the use case of air pollution monitoring,
addressing operational concerns regarding to calibration [14].
In the present paper, we propose a review of in situ
calibration strategies with a different scope: we address all
environmental sensor networks, regardless of the monitored
phenomenon. We also classify the literature with regard to
the underlying algorithmic approaches. More precisely, we
propose a synthetic taxonomy of the large variety of different
techniques reported under different terms in the literature, such
as ”blind calibration”, ”multi-hop calibration”, ”macro calibra-
tion” and so on. Additionally, we consider the architecture of
the sensor network on which depends the relevance of each
strategy.
The review is organized as follows. Section II defines the
terms used and details the scope of our literature review. A
taxonomy is then proposed for the classification of existing
IEEE SENSORS JOURNAL, VOL. X, NO. X, MONTH YEAR 2
techniques of in situ calibration for environmental sensors
networks in Section III. In Section IV, various contributions
are analyzed and positioned regarding the previous categories.
Section V is dedicated to a discussion on how to bring to
a next level the performance evaluation of in situ calibration
methods and their quantified comparison. Finally, Section VI
gives a conclusion.
II. DEFINITIONS AND SCOPE
An environmental sensor network is a set of measur-
ing systems [10] spatially deployed in order to periodically
measure one or more quantities in an environment. Measuring
systems are also called nodes. Each may be composed of one
or more measuring instrument according to the definition
of a measuring system. A node may be static or mobile. The
set of nodes forms a (most probably wireless) network. It can
be either meshed, with device to device communications, or a
collection of stars centered on gateways. For a given measur-
and, instruments which are known to be more accurate than
the others of the network are called reference instruments.
The terminology used in this paper is inspired by the field
of dependability [15] [16]. In particular, recalibration methods
are contributing to the reliability of the measuring instruments.
Reliability is indeed the ability to continuously deliver a
correct service i.e., accurate values in our settings.
There are other considerations that could matter and interact
with calibration, such as integrity, security or even privacy, in
particular when considering crowdsensing platforms involving
citizens [17]. As a matter of fact, their integration at an early
step of the design of the sensor networks is crucial with respect
to the system architecture. The way these concepts are imple-
mented may have a significant impact on the effectiveness of
some calibration methods. We however do not consider them
in the scope of this survey because our classification relies
on the network architecture and the algorithmic principles
underlying the calibration method, as detailed in the following
section. This viewpoint is hardly influenced by system issues
unless practical implementation details are considered.
III. CLASSIFICATION
The following subsections introduce our taxonomy for the
classification of in situ calibration strategies for sensor net-
works (SN).
The classification is independent from the kind of mesurand:
the groups of categories described are relevant for any envi-
ronmental phenomenon.
We consider network architecture characteristics, namely
the nature of instruments and their potential mobility, and the
algorithmic principles of the calibration techniques, namely
the mathematical structure of the calibration relationship and
to which point the algorithm can be distributed.
Each subsection represents a primary level group of cate-
gories that may have others nested. Categories for each group
are in bold font.
A. Use of reference instruments
One of the first criteria of classification is how the cali-
bration method assumes the presence of reference instrument
within the network.
The calibration of measuring instruments using a suffi-
cient number of reference measurement instruments is called
reference-based calibration. It means that the network is
composed of both reference and non-reference instruments and
that all the non-reference instruments can be calibrated using
at least one reference instrument. The approach postulates
the existence of a calibration relationship between each non-
reference instrument and at least one reference instrument
because there are close enough for instance.
The calibration of measuring instruments in the absence of
reference values is called blind calibration. It means that the
network is composed of only non-reference instruments. These
various methods may or may not assume the existence of a
correlation between the instrument outputs.
The hybrid situation is called partially blind calibration.
In this setting, the network may gather both reference and non-
reference instruments, but a reference based calibration is not
achievable, e.g when some of the non-reference instruments
can never be compared to a reference instrument. It also
capture cases where some non-reference instruments are con-
sidered good enough to approximate a reference instruments
compared to the others.
B. Mobility of the instruments
The second significant aspect of the network architecture is
the potential mobility of nodes.
A first category of methods addresses network with ex-
clusively static nodes. A second one addresses networks
with exclusively mobile nodes. The corresponding methods
rely often strongly on the mobility of the nodes to achieve
calibration. A last group of methods addresses heterogeneous
networks with both mobile and static nodes. In such cases
the mobility of the nodes is not systematically exploited in the
calibration strategy.
C. Calibration relationships
The purpose of calibration is to establish a mathematical
relationship between the indications of the instrument and
the measurand. This category is first based on the number
of kind of quantities as input variables in the relationship: the
measurand, the indications, the influence quantities, and so on.
In terms of algorithmic principles of the calibration methods, it
implies the variety and quantity of data to exchange as well as
the computational effort that are necessary to achieve a target
accuracy.
The most straightforward relationships are called mono-
kind variables without time. They only take a single quantity
as input variable and do not depend on time.
The second category of relationships gathers the ones that
have mono-kind variables with time. It accounts for a
relationship with mono-kind variables which is influenced by
time, for instance in case of sensor drifting due to aging [18].
IEEE SENSORS JOURNAL, VOL. X, NO. X, MONTH YEAR 3
The relationships with multiple-kind variables without
time account for two or more quantities as variables but
remain independent from time. These models are mainly used
to include the effect of influence quantities in the calibration
relationship. In these case, the networks include instruments
measuring the influence quantities. They are not systematically
reference instruments and therefore their calibration may also
be included in the calibration strategy.
Finally, this last approach may be extended into rela-
tionships wind multiple-kind variables with time when
appropriate.
For each of these categories, sub-categories can be defined
based on the kind of mathematical expression used for the
calibration relationship. Popular examples are the following:
• polynomial with constant coefficients [19],
• gain-phase [20],
• variable offset [21],
• neural network [22].
D. Instrument grouping strategies
While the previous categories are mostly driven by op-
erational constraints (deployment strategy, properties of the
measurand and of the selected sensors), the present paragraph
considers the number of nodes involved in each calibration
step and to which point the algorithm can be distributed.
A first approach is pairwise calibration. Two instruments
are used, one providing standard values for the other. It is
classically applied between a reference instrument (or approx-
imation of reference) and each of the nodes related to it. It
can be a distributed or even localized algorithm.
A macro calibration strategy consists in calibrating the
network as a whole. Even if they exist, the node-to-node
relationships are not exploited directly. A centralized algorithm
might be necessary with this grouping strategy.
Group calibration is an intermediate approach consisting
in carrying calibration operation among groups of measuring
instruments among the whole network. In this case, the criteria
defining these groups become essential. This approach may be
used when pairwise calibration induces significant error, while
macro calibration is not fine-tuned enough. This category
notably includes strategies where groups are composed of
instruments measuring additional quantities besides the main
target quantity. These additional quantities are often included
as influence quantities in the calibration relationship. These al-
gorithms can be at least partially distributed e.g., computation
concentrated on an elected group leader, or fully distributed
at the cost of messages broadcasting.
IV. REVIEW OF THE LITERATURE BASED ON THIS
CLASSIFICATION
An application of the classification is provided here with
highlights on the existing literature. Table I sorts a large
number of in situ calibration studies according to this classifi-
cation. Some rows refer to multiple papers as they are related
somehow (same technique or same authors) and consist in
developments of the same initial paper. The current section
focuses on a description of the methods. The topic of per-
formance comparison between methods is addressed in the
next section. The addressed measurands cover a wide range
of environmental quantities: temperature [19], pressure [23],
noise [24], air pollutants [25], light [26]... Most of the reported
studies have generic approaches that can be transposed to other
measurands.
A. Overview
Regarding to pairwise strategies, relatively few papers ad-
dress methodological issues related to reference-based pair-
wise strategies, as this approach is the closest to a ”traditional”
calibration approach with measurement standards and features
less challenges. Partially blind and blind pairwise calibration
methods (often focusing on mobile nodes) are more complex
as they require to define calibration relationships not only
between reference and non-reference nodes, but also between
non-reference nodes only. This translates into error propaga-
tion issues.
Macro calibration approaches were initially developed to
address the absence of reference instruments in a network
and thus are mostly blind or partially-blind. In the absence
of reference, there is a strong challenge in defining valid
calibration relationships based on non-reference sensors data,
which explains the strong interest for these methods.
Group strategies have been generating strong interests as
they appear to outperform both pairwise and macro strategies
with or without reference instruments.
Most methods are based on relationships with mono-kind
variables without time and with a linear expression, but more
complex models are progressively appearing to better address
the complexity of environmental sensing.
Likewise, while most work initially focused on static net-
works, there are now many interests for mobile nodes as they
allow for physical rendez-vous between nodes. Henceforth,
calibration methods are less impacted by the physical vari-
ability of the phenomena.
Finally, an underlying question addressed is the ability to
distribute the computation of calibration relationships [24] [27]
[28] [29] [30] [31] [32]. The topic is of strong interest when
considering privacy preservation issues [17]. The capability to
decentralize is linked to the grouping strategy: pairwise and
group strategies foster more naturally decentralized computa-
tion, under the condition that the nodes are capable of indi-
vidual procession and of bidirectional communication. On the
contrary, macro-calibration strategies tend to be centralized,
except when the characteristics of the parameter identification
methods allow for partially or fully decentralized computation.
However, while distributed computing impacts the computa-
tional performance of algorithm, there is no report on how it
affects calibration performance so far.
B. Mobile and static nodes
Static networks are more frequently studied than mobile
ones. A wide range of solutions is now available to calibrate
them. However, these calibration methods usually require a
high spatial density of nodes to overcome the spatial variability
IEEE SENSORS JOURNAL, VOL. X, NO. X, MONTH YEAR 4
of the phenomena, which is not always viable technically or
economically. The availability of mobile nodes could allevi-
ate this constraint, as calibration operations exploit physical
rendez-vous between nodes. In turn, the methods based on this
principle are challenged when the rendez-vous frequency is too
low compared to the speed of degradation of the measurement
accuracy [33]. In such cases, the addition of a few reference
nodes seems to yield satisfying results [25] [34]. Moreover, a
challenge of mobile sensors is that they face rapid transients.
To address this, methods initially developed for static networks
appear promising, such as the work of De Vito et al. [22]
[35] which uses dynamic and nonlinear supervised machine
learning tools.
C. Calibration relationships
Most reported relationships are of mono-kind variables
without time type and based on linear expressions. Never-
theless, there is a rising interest for models with multiple-
kind variables, which stems from the observation that there
are indeed significant influence quantities for various envi-
ronmental measurands, notably air pollutant concentrations. It
often depends on the technology of the sensors used [36] [37]
[38] [39] [40]. Such relationships gave very interesting results
compared to simpler relationship models:
• for reference-based group calibration in [41] [42] and [43]
• for partially blind group calibration strategies in [38] [44]
[45] [46], including with time-sensitive models in [29]
and [44]
• for blind strategies, either pairwise or group based, in
[35] [47] [48] [49] [50].
On the contrary, relationships with multiple-kind variables
were shown to be unnecessary in [51] and in [52] where
the control of the operating temperature of the device was
sufficient to perform a pairwise calibration without being
influenced by this quantity.
In general, time-dependent approaches are used to address
drift issues. Drift is often modeled as an additive random
variable with a given probability distribution [28] [53], so that
drift-compensation translates as an offset correction.
D. Pairwise strategies
a) Reference-based pairwise: Relatively few papers ad-
dress methodological issues related to reference-based pair-
wise strategies, as this approach is the closest to a ”traditional”
calibration approach with measurement standards. Primarily,
reference instruments may be directly co-located in the field
with non-reference instruments to achieve their calibration [38]
[41] [42] [54] [55].
However, more automated strategies are expected, requiring
less the co-location of instruments. Nevertheless, even in the
simple case of a relatively dense SN, the measurand may
spatially vary too much in general to relate a reference instru-
ment at a given location to an instrument at another location
for calibration purposes. As an elementary solution to this,
Moltchanov et al. [56] proposed to carry out calibration against
the reference node using only the data collected during a
specific time span based on the postulate that the phenomenon
varies less during this time span. This was an idea previously
developed by Tsujita et al. [57] including weather conditions
that were also used to corrected the measured values but not
with a reference-based approach.
b) Partially blind pairwise: Partially blind pairwise cal-
ibration focuses mostly on mobile nodes. Tsujita et al. [58]
tackled it first for mobile nodes by proposing that the device
to calibrate should display either the value of a reference node
that is close enough, or the average measurements between co-
located nodes if no reference node is available. A calibration
parameter is tuned with these values to correct measurements
between rendez-vous.
Y. Xiang et al. [28] later proposed another method. They
also distinguish calibration based on the values of a reference
instrument and on the values of a non-reference instrument.
Their originality relies in the correction of the values that is
performed with an estimator of the drift error of the node.
This error is recalculated at each calibration by minimizing
its variance according to a linear combination of the values of
the sensors involved in the calibration process.
Hasenfratz et al. [25] addressed by various methods the case
of calibration for mobile devices against reference instruments
or not. They notably provided dedicated extensions for the case
where some devices rarely encounter reference instruments.
They also demonstrated a linear dependency between the mea-
surement error and the number of intermediary calibrations
between a given node and the reference node it is calibrated
against. In [33] and [59], Saukh et al. proposed solutions to
this issue of error accumulation by working on the occurrence
of rendez-vous between nodes, in view of maximizing the
opportunities of calibration. An alternative idea was developed
by Fu et al. [60] who proposed the optimization of the
deployment of reference instruments in order to ensure that all
nodes can be calibrated against one of the reference with a path
no longer than k hops. Then Maag et al. [45] [61] and Arfire
et al. [44] extended this work to models with multiple-kind
variables, with and without time dependency. They showed
that the complexity of the model should be tuned based on
the frequency of rendez-vous.
In a similar way, Markert et al. [17] introduced a calibration
strategy based on rendez-vous but with a particular focus on
privacy aspects by design for the exchange of data.
Kizel et al. [62] also proposed a multi-hop calibration
method that consists into collocating two devices for a certain
time, one being the reference to the other, and then moving
the freshly calibrated device close to another non-calibrated,
a reference instrument being introduced in the loop to reset
the error that accumulates. The advantage is that the error is
related to the number of hops that took place like in [25].
Sailhan et al. [24] developed a multi-hop, multi-party cali-
bration scheme with the addition of an assessment protocol for
the relevancy of the calibration, based on a weighted directed
hypergraph of the network, the weights indicating the quality
of the calibration. The presented strategy was applied to blind
networks but as in [25], it could be extended to partially blind
networks.
