# EEATC: A Novel Calibration Approach for Low-cost Sensors
IEEE-copyrighted material refer doi 10.1109/JSEN.2023.3304366

M V Narayana  Devendra Jalihal  Member, IEEE  Shiva Nagendra S M  M V
Narayana, is a graduate student in the Department of Electrical Engineering,
Indian Institute of Technology Madras, Chennai, India-600036 (e-mail:
ee18d302@smail.iitm.ac.in).Devendra Jalihal, is a professor in the Department
of Electrical Engineering, Indian Institute of Technology Madras, Chennai,
India-600036 (e-mail: dj@iitm.ac.in).Shiva Nagendra S M, is a professor in the
Department of Civil Engineering, Indian Institute of Technology Madras,
Chennai, India-600036 (e-mail: snagendra@iitm.ac.in).

###### Abstract

Low-cost sensors (LCS) are affordable, compact, and often portable devices
designed to measure various environmental parameters, including air quality.
These sensors are intended to provide accessible and cost-effective solutions
for monitoring pollution levels in different settings, such as indoor, outdoor
and moving vehicles. However, the data produced by LCS is prone to various
sources of error that can affect accuracy. Calibration is a well-known
procedure to improve the reliability of the data produced by LCS, and several
developments and efforts have been made to calibrate the LCS. This work
proposes a novel Estimated Error Augmented Two-phase Calibration (EEATC)
approach to calibrate the LCS in stationary and mobile deployments. In
contrast to the existing approaches, the EEATC calibrates the LCS in two
phases, where the error estimated in the first phase calibration is augmented
with the input to the second phase, which helps the second phase to learn the
distributional features better to produce more accurate results. We show that
the EEATC outperforms well-known single-phase calibration models such as
linear regression models (single variable linear regression (SLR) and multiple
variable linear regression (MLR)) and Random forest (RF) in stationary and
mobile deployments. To test the EEATC in stationary deployments, we have used
the Community Air Sensor Network (CAIRSENSE) data set approved by the United
States Environmental Protection Agency (USEPA), and the mobile deployments are
tested with the real-time data obtained from SensurAir, an LCS device
developed and deployed on moving vehicle in Chennai, India.

Air Quality Monitoring, Calibration Approaches, Low-cost Sensors, Machine
Learning, and Mobile and stationary deployment.

##  1 Introduction

L ow-cost sensors (LCS) have gained significant attention in recent years as
valuable tools for air quality monitoring (AQM). These sensors offer several
advantages, including fine-granular measurements, cost-effectiveness, and
portability, making them more popular than conventional reference-grade air
quality monitoring instruments. These advantages enable them to use in various
AQM applications.

LCS have been successfully employed in stationary deployments, where they are
fixed to a specific place for an extended period. These applications include
monitoring air quality in urban areas, indoor environments, or industrial
sites. LCS in stationary applications can provide continuous data collection
and long-term trend analysis [1, 2]. LCS are also suitable for mobile
applications, where they are mounted on moving vehicles such as cars,
bicycles, or drones. This mobility enables monitoring air quality or other
environmental factors in different locations, offering a more comprehensive
understanding of spatial variations[3].

LCS for AQM are designed to detect and measure various pollutants present in
the environment, such as particulate matter (PM), gases like nitrogen dioxide
(NO2), carbon monoxide (CO), and volatile organic compounds (VOCs). They
operate on different principles, including optical, electrochemical, and
metal-oxide-based sensing mechanisms.

Despite these advantages, LCS data may be prone to various sources of error
that can affect accuracy. Some common error sources include temperature
variations, relative humidity changes, and cross-sensitivities [4]. Proper
calibration is crucial to address these issues and improve the accuracy of LCS
data [5]. Calibration involves adjusting the sensor readings to align with
known reference values. This process helps account for sensor drift, non-
linearity, and other factors that can introduce inaccuracies. By calibrating
LCS, the impact of error sources can be minimized, leading to more reliable
and precise measurements.

Calibration approaches for low-cost sensors (LCS) have been an active area of
research, and several developments and efforts have been made to enhance the
accuracy of LCS through calibration, and the notable advancements in LCS
calibration are as follows:

#### Laboratory and field studies

Extensive laboratory and field studies have been conducted to collect data
from LCS in various environments [6, 7, 8, 9, 10, 11]. This collected data
allows for the characterization of sensor responses under varying conditions
and serve as valuable inputs for developing calibration approaches. At the
same, by comparing these LCS measurements with reference instruments or
established air quality monitoring stations, the performance of the LCS can be
validated.

#### Correction factor approaches

The collected data in the field and laboratory makes it possible to develop
correction factors for sensor response, which helps to correct the sensor
response biases. Temperature baseline correction and humidity baseline
correction are the popular correction factor approaches [12, 13, 14, 15, 16,
17, 18, 19, 20, 21, 22, 23, 24, 25]. In contrast to the static correction
factors approach, Aurora [26] first modelled the sensor response under various
temperature and relative humidity values and developed a self-correction
algorithm in order to calibrate the metal oxide LCS.

#### Data driven approaches

In the data-driven approach, LCS are calibrated with the data obtained from
real-time deployments against the reference station observations, often
including other influencing parameters such as temperature and humidity. This
approach is more prevalent due to its simplicity, and the proliferation of
machine learning (ML) and artificial intelligence (AI) catalyzed its adoption
further. Various ML and AI models are explored to calibrate LCS. These models
include single-variable linear regression (SLR) [27, 28, 29, 30], multiple-
variable linear regression (MLR) [31, 32], K-nearest neighbours (K-NN) [31],
random forest (RF) [33, 34, 35], artificial neural networks (ANN) [36, 35, 37,
38, 39], support vector machine (SVM) [40, 41] extreme gradient boosting (XGB)
[42], generalised additive model (GAM) [43].

#### Hybrid models

In addition, a few works explored hybrid models obtained by combining two or
more architectures to calibrate the LCS. Hagan et al. [44] and Malings et al.
[45] combined the regression model with the k-nearest neighbours and random
forest, respectively, to improve the calibration accuracy compared to the
stand-alone models. A similar approach that combines regression models with
ANN was implemented by Cordero et al. [46]. Instead of combining the models,
Ferrer-Cid et al. used multi-sensor data fusion techniques to calibrate the
LCS [47].

However, the calibration approaches discussed above are developed for
stationary applications, which cannot be adopted directly to mobile
applications due to additional error sources, such as mobility effects and
rapid variation of the inputs [48]. Dong et al. [49] identified that vehicle
starts and stops, creates variations in the airflow at the sensors and causes
irregular measurements. They used GPS loggers to identify the samples of the
start and stop positions and then filtered out the respective samples before
calibrating the LCS using SVM and ANN models. Lin et al. [50] applied a moving
average filter to remove the noise pertained due to the vehicle’s movement. In
a recent study, Arman et al. [51] highlight the application of wavelet
transform to address the noise components induced in the LCS data during
mobile air quality monitoring. By utilizing wavelet transform, they aimed to
remove higher frequency components, which are often attributed to the
acceleration and deceleration of the vehicle carrying the LCS. The denoised
data, which represents the lower frequency components associated with the air
quality measurements, was then used to develop land-use regression models.

Furthermore, adaptive calibration algorithms have indeed been developed to
calibrate the LCS in mobile applications. These algorithms utilize feedback
from sensor readings, environmental conditions, and historical data to
continuously refine the calibration process in real time. For instance,
Esposito et al., [52] proposed dynamic neural network architectures which
leverage the past samples of both sensors and reference instruments in order
to calibrate the LCS. Another study by Hasenfratz et al. [53] focused on
preparing urban air pollution maps using mobile sensor nodes. They employed
land-use regression models but found that the accuracy of these models
decreased over a longer duration of deployment. To address this issue, they
incorporated calibration using past samples, which helped improve the accuracy
of the models by accounting for temporal variations and sensor drift.

In this work, we propose a novel Estimated Error Augmented Two-phase
Calibration (EEATC) approach, which combines the advantages of hybrid and
adaptive data-driven calibration approaches to calibrate the LCS in both
stationary and mobile deployments. To the best of our knowledge, EEATC is the
first-of-its-kind calibration approach that works for both stationary as well
as mobile deployments.

EEATC calibrates the LCS in two phases, where the LCS are first calibrated
with a machine learning model, which is then used to generate the calibrated
output. The absolute errors obtained between the calibrated output of the
first phase and reference observations are fed to nannyML, an error estimation
model. The nannyML learns the error distribution and produces estimated
errors. The estimated errors and the LCS data are given to the second phase,
where another machine-learning model is trained to calibrate the LCS in the
final stage. Since the error (the uncertainty of the calibrated values) is
learned in the second phase, which helps to produce better calibration results
in the second phase.

We test the EEATC on LCS data in stationary deployments using the Community
Air Sensor Network (CAIRSENSE) data set approved by the United States
Environmental Protection Agency (USEPA). In order to test EEATC on mobile LCS
data, we conducted a mobile monitoring pilot by deploying SensurAir, an LCS
device that we developed, on a moving vehicle which opportunistically moves in
parts of Chennai, India.

Contributions of this work are summarized as follows,

  * •

It proposes EEATC a novel calibration approach which calibrates the LCS in
both stationary and mobile deployments.

  * •

exhaustively Tests the EEATC on both stationary and mobile deployment data
sets.

  * •

It describes a new design and deployment of an LCS device, SensurAir, for
mobile AQM monitoring.

  * •

It contributes new data sets for mobile AQM with LCS to the research community

  * •

Compares the performance of EEATC with the state-of-art calibration models
such as MLR and RF

Details of the rest of the paper are as follows. Sec. 2 illustrates the EEATC,
the proposed calibration approach. Evaluation of the EEATC on the stationary
deployment of LCS is covered in Sec. 3 and on mobile deployments in Sec. 4.
The future scope and conclusions are covered in Sec. 5.

##  2  Estimated Error Augmented Two-phase Calibration (EEATC) process

In general, the LCS are calibrated with a single-phase calibration approach
shown in Fig. 1. In this approach, a model is trained with the LCS data set
($\mathcal{X}$) against the reference station observations ($\mathcal{Y}$),
such that the root mean squared error between the sensor output
($\mathcal{S}$) and $\mathcal{Y}$ is minimum. Note that $\mathcal{X}$ is an
LCS data set that includes $\mathcal{S}$ and other influencing covariates such
as temperature ($T$) and relative humidity ($Rh$). The model in Fig. 1 may be
a machine learning or deep learning model depending on the characteristics of
the data. Once the model is trained, it can be used to obtain calibrated
sensor values ($\mathcal{\hat{Y}}_{f}$) for the corresponding $\mathcal{S}$

Figure 1: Block diagram representation of single-phase calibration

In extension to the single-phase calibration, a two-phase calibration can also
be used to calibrate the LCS, which can be implemented by cascading two models
as shown in Fig. 2.

Figure 2: Block diagram representation of two-phase calibration

In two-phase calibration, the models are cascaded in such a way that the
residual error vector ($\mathcal{E}$), the difference between the calibrated
output of model 1 ($\mathcal{\hat{Y}}_{f}$) and the reference instrument
values $\mathcal{Y}$, is fed into model 2 along with the input $\mathcal{X}$,
that is given in the first phase. In other words, the two-phase calibration
can also be treated as a single-phase calibration with augmented input
($\mathcal{X}$ $|$ $\mathcal{E}$), where $\mathcal{E}$ is obtained from some
process, here that is obtained from other single-phase calibration.
Augmentation of $\mathcal{E}$ with $\mathcal{X}$ boosts the performance of the
calibration model in the second phase.

####  2.0.1 Importance of error vector $\mathcal{E}$ in boosting the
performance

The calibration of LCS is a regression problem where the calibrated model
returns a value for each sample given to the model, and it can be treated as a
point prediction. Behind the point prediction, there is always a distribution
formed by the model equation and the dimension of the distribution depends on
the number of features the model is trained on.

For instance, in Fig. 1, an MLR model is trained for the calibration of LCS
with two features $\mathcal{S}$ and $Rh$, then post the training MLR predicts
the values ($\mathcal{\hat{Y}}_{f}$) corresponding to the value of
$\mathcal{S}$ and $Rh$ from the posterior distribution formed by the
calibration equation in 1 with calibration coefficients $\beta_{1}$ and
$\beta_{2}$. The blue mesh in Fig. 3 is the plane formed by the calibration
equation 1, and the predicted values ($\mathcal{\hat{Y}}_{f}$) lie on the
plane. However, the predicted values deviate from the reference station
observations ($\mathcal{Y}$), which are the residual errors ($e$) in the model
predictions shown in Fig. 3, and the collection of all such errors forms the
residual error vector $\mathcal{E}$
($\mathcal{E}=\mathcal{\hat{Y}}_{f}-\mathcal{Y})$. The $\mathcal{E}$ has an
evident relation with $\mathcal{Y}$ and can express the uncertainty in the
model predictions. The uncertainty in the model predictions can be estimated
by analyzing the distribution formed by the $\mathcal{E}$

$\mathcal{\hat{Y}}_{f}=\beta_{1}(\mathcal{S})+\beta_{2}(Rh)$ (1)

Figure 3: 3D view of the calibration space formed by MLR equation with $S$ and
$Rh$

Therefore, including $\mathcal{E}$ in the input to the second phase gives the
scope for model 2 to learn the distribution of $\mathcal{E}$ along with $S$
and $Rh$ so that the second phase produces better predictions. Implicitly,
instead of conditioning on two variables $S$ and $Rh$ in the single-phase
calibration, here in the two-phase calibration, we are conditioning on three
variables $\mathcal{E}$, $\mathcal{S}$ and $Rh$, which gives a better estimate
of $\mathcal{\hat{Y}}_{f}$ than the former one.

Then the question arises as to how to obtain $\mathcal{E}$. One way is
subtracting the calibrated output from the first phase with reference station
observations [50]. Obtaining $\mathcal{E}$ in this way is possible only in
training. However, in testing or remote real-time deployments, the LCS are
inaccessible to the reference station observations, which renders the
impossibility of obtaining $\mathcal{E}$ in practical applications. Now the
only possible way is to use its estimate ($\mathcal{\hat{E}}$) instead of
directly using $\mathcal{E}$ in testing or real-time deployments.

####  2.0.2 Estimation of $\mathcal{E}$ using nannyML

Estimation of $\mathcal{E}$ in testing after the first phase can be
hypothesised to estimate first-phase model performance without the ground
truth or reference station observations. NannyML is a recent development in
ML, where an extra ML model is trained on the absolute loss or error of the
monitored model [54]. By doing so, the extra ML model can be used to estimate
the loss of the monitored model in the lack of ground truth observations.
Here, the extra ML model is called the Nanny model, and the monitored model in
two-phase calibration is the model at the first phase. NannyML offers
Confidence-based Performance Estimation (CBPE) for classification problems and
Direct Loss Estimation (DLE) for regression problems. Since the calibration of
LCS is a regression problem, we have adopted the DLE to estimate the
$\mathcal{E}$ after the first phase.

Figure 4: Block diagram representation of EEATC calibration approach

Therefore a NannyML model is placed in between the models of the two-phase
calibration shown in Fig 2 such that the $\mathcal{\hat{E}}$ is fed into the
second phase instead of $\mathcal{E}$. This is a novel way of implementing
two-phase calibration for LCS, and we call this Estimated Error augmented two-
phase calibration (EEATC).

The implementation of EEATC is shown in Fig. 4. Let’s denote the model in the
first phase as $\mathcal{F}$ and the nanny model as $\mathcal{H}$. We are
interested in estimating the mean absolute error of $\mathcal{F}$ for which
reference station observations are unavailable. At first, $\mathcal{F}$ is
trained with data ($\mathcal{X}$) against $\mathcal{Y}$, then it is used to
predict the targets, $\mathcal{\hat{Y}}_{f}$ as shown in the equation 2

$\mathcal{\hat{Y}}_{f}=\mathcal{F}(\mathcal{X})$ (2)

Then the $\mathcal{H}$ is trained with $\mathcal{X}$ and
$\mathcal{\hat{Y}}_{f}$ against the absolute error vector ($\mathcal{E}_{a}$)
formed between $\mathcal{\hat{Y}}_{f}$ and $\mathcal{Y}$ shown in equation 3

$\mathcal{E}_{a}=|\mathcal{Y}-\mathcal{\hat{Y}}_{f}|$ (3)

The trained $\mathcal{H}$ can be used to obtain $\mathcal{\hat{E}}$ vector in
real-time without the ground truth observations as shown in equation 4

$\mathcal{\hat{E}}=\mathcal{F}(\mathcal{X},\mathcal{\hat{Y}}_{f})$ (4)

Where $\mathcal{\hat{E}}$ is the estimated error vector by nannyML. Finally,
the model in the second phase leverages $\mathcal{\hat{E}}$ to produce better
calibration results compared to the existing approaches.

####  2.0.3 When does the performance of the single-phase calibration tend to
equal with EEATC

As we discussed, the two-phase calibration can be represented as single-phase
calibration by including additional input $\mathcal{E}$ in the calibration
features. When $\mathcal{E}$ is zero, that means the errors between the
reference station observations and the calibrated values at the first phase
are zero, which implies that the LCS are 100% calibrated in the first phase
itself; if so it doesn’t require the second phase calibration. Then the
calibration in equation (5) becomes the calibration equation in (1) provided
$\mathcal{E}$ is zero vector. If $\mathcal{E}$ is zero, obviously
$\mathcal{\hat{E}}$ is zero, then EEATC approach converts to single-phase
calibration with model 2, the model in the second phase as shown in Fig. 5.
This can happen only in theory, which is practically impossible.

$\mathcal{\hat{Y}}=\beta_{1}(\mathcal{S})+\beta_{2}(Rh)+\beta_{3}(\mathcal{\hat{E}})$
(5)

Figure 5: EEATC with $\mathcal{E}$ is a zero vector

###  2.1 Practical implementation of EEATC

We have implemented the EEATC by adopting the MLR model in the first phase and
the RF model in the second phase, as shown in Fig. 6. The RF model is a
machine learning algorithm that works by constructing an ensemble of decision
trees utilizing the training data [55], and the MLR is a regression model that
works by fitting a linear function between the input and target in the
training data. The MLR model, in the first phase, learns the linear properties
and the RF model, in the second phase, learns the non-linear properties so
that the EEATC can capture both the properties of data.

We adopted the RF and MLR models from the Scikit-learn library and
exhaustively evaluated them for different parameters of the models. The
information regarding the parameters is provided in the code in the GitHub
link in the resources section.

Figure 6: Practical implementation of EEATC (in training) with MLR in the
first phase and RF in the second phase

Training We have divided the data sets as training data
($\mathcal{X}_{\text{train}}$, $\mathcal{Y}_{\text{train}}$) and testing data
($\mathcal{X}_{\text{test}}$, $\mathcal{Y}_{\text{test}}$) with the split of
75% and 25% respectively, the standard train test split percentage. We first
trained the MLR model with $\mathcal{X}_{\text{train}}$ such that loss in
equation (6), that is the mean square error (MSE) between the predicted
sensors values ($\mathcal{\hat{Y}}_{f\text{train}}$) and the reference
instrument values ($\mathcal{Y}_{\text{train}}$) is minimised.

$\text{loss}_{\text{MLR}}=\frac{1}{P}\sum_{i=1}^{P}\text{{MSE}}(\hat{y}^{i}_{f\text{train}}-y^{i}_{\text{train}})$
(6)

Where $\mathcal{\hat{Y}}_{f\text{train}}$ =
$\\{\hat{y}^{1}_{f\text{train}},\hat{y}^{2}_{f\text{train}},..P\\}$,
$\mathcal{Y}_{\text{train}}$ =
$\\{y^{1}_{\text{train}},y^{2}_{\text{train}},..P\\}$ and $P$ is the number of
samples in training.

Then the trained MLR model is utilized to generate error vector
$\mathcal{E}_{atrain}$ shown in equation (7), which is the absolute difference
between $\mathcal{\hat{Y}}_{f\text{train}}$ and $\mathcal{Y}_{\text{train}}$.

$\mathcal{\hat{Y}}_{f\text{train}}=\text{MLR}(\mathcal{X}_{\text{train}});\mathcal{E}_{a\text{train}}=|\mathcal{\hat{Y}}_{f\text{train}}-\mathcal{Y}_{\text{train}}|$
(7)

Then the NannyML model ($\mathcal{H}$) is trained with
$\mathcal{X}_{\text{{train}}}$ and $\mathcal{\hat{Y}}_{f\text{train}}$ against
the $\mathcal{E}_{a\text{train}}$ obtained in the first phase to learn the
uncertainty in the MLR model predictions which can be used to estimate
$\mathcal{\hat{E}}_{\text{train}}$ as shown in equation (8)

$\mathcal{\hat{E}}_{\text{train}}=\mathcal{H}(\mathcal{X}_{\text{train}},\mathcal{\hat{Y}}_{f\text{train}})$
(8)

Finally, the model in the second phase, RF, is trained by augmenting the
$\mathcal{X}_{\text{train}}$ with $\mathcal{\hat{E}}_{\text{train}}$, to
minimize the loss in equation (9) against $\mathcal{Y}$. Where K is the number
of samples in testing. Therefore, P+K = N, the total number of samples in the
data sets

$\text{loss}_{\text{RF}}=\frac{1}{K}\sum_{i=1}^{K}\text{{MSE}}(\mathcal{\hat{Y}}^{i}_{\text{train}}-\mathcal{Y}^{i}_{\text{train}})$
(9)

Testing

Figure 7: Testing implementation of EEATC with MLR in the first phase and RF
in the second phase

Testing is straightforward as shown in Fig. 7, where we fed the test data,
$\mathcal{X}_{\text{test}}$, into the MVLR model and then the predicted
$\mathcal{\hat{Y}}_{f\text{test}}$ and $\mathcal{X}_{\text{train}}$ is passed
to nannyML to estimate the error vector, $\mathcal{\hat{E}}_{\text{test}}$.
Once the $\mathcal{\hat{E}}_{\text{test}}$ is obtained, it is then augmented
with $\mathcal{X}_{\text{test}}$, which is fed to the RF model. Finally, the
RF model gives the calibrated values corresponding to the input features
values, shown in equation (10)

$\mathcal{\hat{Y}}=\text{RF}(\mathcal{X}_{\text{test}},\mathcal{\hat{E}}_{\text{test}})$
(10)

Algorithm 1 illustrates the step by step procedure of practical implementation
of EETAC

Algorithm 1 Implementation of EEATC calibration

Training
Input $\mathcal{X}_{\text{train}},\mathcal{Y}_{\text{train}}$
Output $\mathcal{\hat{Y}}_{\text{train}}$

1:Train MLR with $\mathcal{X}_{\text{train}}$ against
$\mathcal{Y}_{\text{train}}$

2:$\mathcal{\hat{Y}}_{f\text{train}}$ = MLR($\mathcal{X}_{\text{train}}$)

3:$\mathcal{E}_{a\text{train}}=|\mathcal{\hat{Y}}_{f\text{train}}-\mathcal{Y}_{\text{train}}|$

4:Train nannyML with $\mathcal{X}_{\text{train}}$,
$\mathcal{\hat{Y}}_{f\text{train}}$ against $\mathcal{E}_{a\text{train}}$

5:$\mathcal{\hat{E}}_{\text{train}}=\text{{nannyML}}(X_{\text{train}},\mathcal{\hat{Y}}_{f\text{train}})$

6:Train RF with $\mathcal{X}_{\text{train}}$,
$\mathcal{\hat{E}}_{\text{train}}$ against $\mathcal{Y}_{\text{train}}$

7:$\mathcal{\hat{Y}}_{\text{train}}=\text{{RF}}(\mathcal{X}_{\text{train}},\mathcal{\hat{E}}_{\text{train}})$

Testing or real-time deployments
Input $\mathcal{X}_{\text{test}}$
Output $\mathcal{\hat{Y}}_{test}$, the final calibrated values of
$\mathcal{S}$ in real-time applications

1:$\mathcal{\hat{Y}}_{f\text{test}}=\text{{MLR}}(\mathcal{X}_{\text{test}})$

2:$\mathcal{\hat{E}}_{\text{test}}=\text{{nannyML}}(\mathcal{X}_{\text{test}},\mathcal{\hat{Y}}_{\text{test}})$

3:$\mathcal{\hat{Y}}_{test}=\text{{RF}}(X_{\text{test}},\mathcal{\hat{E}}_{\text{test}})$

###  2.2 Metrics

We considered the root mean square error (RMSE) in equation (11) and
coefficient of determination ($\text{R}^{2}$) in equation (12) to evaluate the
performance of the calibration models. $R^{2}$ describes the proportionality
of variability between independent and dependent variables of the model.
$RMSE$ indicates the deviation between the predicted values and reference
station observations.

$\text{RMSE}(\mathcal{\hat{Y}},\mathcal{Y})=\sqrt{\frac{1}{N}\sum_{j=1}^{N}{(\hat{y}_{j}-y_{j})^{2}}}$
(11)

Here, $\mathcal{\hat{Y}}=\\{\hat{y_{1}},\hat{y_{2}},...\\}_{N}$ are the
calibrated sensor values, $\mathcal{Y}=\\{y_{1},y_{2},....\\}_{N}$ are the
reference instrument values and $N$ is the number of samples.

$\text{R}^{2}=1-\frac{SS_{res}}{SS_{tot}}$ (12)

where

$SS_{tot}=\sum_{j=1}^{N}{(y_{j}-\overline{\mathcal{Y}})^{2}}$
${SS_{res}}=\sum_{j=1}^{N}{(y_{j}-\hat{y}_{j})^{2}}$
$\overline{\mathcal{Y}}=\frac{1}{N}\sum_{i=1}^{N}{y_{j}}$

###  2.3 Notations at a glance

  * •

$\mathcal{S}$, $T$ and $Rh$ are the columns vectors representing the LCS
values, temperature and relative humidity, respectively, and $\mathcal{X}$ is
the data set formed by these vectors after pre-processing.

  * •

$\mathcal{Y}$ is a column vector that represents the time corresponding
reference instrument or reference station observations to the values in
$\mathcal{X}$

  * •

$\mathcal{\hat{Y}}_{f}$ and $\mathcal{\hat{Y}}$ are the calibrated values in
the first and second phases, respectively.

  * •

$\mathcal{E}$ is the residual error vector, and $\mathcal{\hat{E}}$ is the
estimated error vector after first phase.

  * •

train and test in the subscripts indicate training and testing

##  3 Evaluation of the EEATC approach for stationary AQM data sets

Table 1: Evaluation of EEATC approach for different sensors in the CAIRSENSE
data set and comparison with the well-known calibration models such as MLR and
RF. All the approaches are tested with different combinations of input
features, and the outperforming one is indicated with *.

(a) OPCPMF Model |  Variables considered in the calibration process | $\text{R}^{2}$ |  | RMSE |
---|---|---|---|---|---
Training | Testing | Training | Testing
MLR |  $\mathcal{S}$ | 0.16 | 0.16 | 0.92 | 0.93
$\mathcal{S}$, $T$ | 0.21 | 0.21 | 0.89 | 0.91
$\mathcal{S}$, $Rh$ | 0.25 | 0.25 | 0.86 | 0.88
$\mathcal{S}$, $T$, $Rh$ | 0.26 | 0.25 | 0.86 | 0.88
RF |  $\mathcal{S}$ | 0.29 | 0.27 | 0.84 | 0.87
$\mathcal{S}$, $T$ | 0.48 | 0.45 | 0.72 | 0.75
$\mathcal{S}$, $Rh$ | 0.46 | 0.44 | 0.74 | 0.76
$\mathcal{S}$, $T$, $Rh$ | 0.55 | 0.53 | 0.67 | 0.7
EEATC |  $\mathcal{S}$ | 0.3 | 0.27 | 0.84 | 0.86
$\mathcal{S}$, $T$ | 0.58 | 0.47 | 0.65 | 0.74
$\mathcal{S}$, $Rh$ | 0.55 | 0.46 | 0.67 | 0.75
$\mathcal{S}$, $T$, $Rh$ | 0.76* | 0.67* | 0.49* | 0.58*

(b) Speck Model |  Variables considered in the calibration process | $\text{R}^{2}$ |  | RMSE |
---|---|---|---|---|---
Training | Testing | Training | Testing
MLR |  $\mathcal{S}$ | 0.14 | 0.14 | 0.93 | 0.95
$\mathcal{S}$, $T$ | 0.37 | 0.37 | 0.79 | 0.82
$\mathcal{S}$, $Rh$ | 0.37 | 0.36 | 0.8 | 0.82
$\mathcal{S}$, $T$, $Rh$ | 0.43 | 0.42 | 0.75 | 0.78
RF |  $\mathcal{S}$ | 0.15 | 0.15 | 0.92 | 0.95
$\mathcal{S}$, $T$ | 0.53 | 0.52 | 0.68 | 0.71
$\mathcal{S}$, $Rh$ | 0.43 | 0.43 | 0.75 | 0.78
$\mathcal{S}$, $T$, $Rh$ | 0.61 | 0.6 | 0.62 | 0.65
EEATC |  $\mathcal{S}$ | 0.15 | 0.15 | 0.92 | 0.95
$\mathcal{S}$, $T$ | 0.59 | 0.54 | 0.64 | 0.7
$\mathcal{S}$, $Rh$ | 0.52 | 0.46 | 0.69 | 0.75
$\mathcal{S}$, $T$, $Rh$ | 0.77* | 0.73* | 0.48* | 0.5*

(c) TZOA Model |  Variables considered in the calibration process | $\text{R}^{2}$ |  | RMSE |
---|---|---|---|---|---
Training | Testing | Training | Testing
MLR |  $\mathcal{S}$ | 0.46 | 0.39 | 0.73 | 0.82
$\mathcal{S}$, $T$ | 0.55 | 0.47 | 0.67 | 0.77
$\mathcal{S}$, $Rh$ | 0.49 | 0.41 | 0.72 | 0.80
$\mathcal{S}$, $T$, $Rh$ | 0.55 | 0.47 | 0.67 | 0.76
RF |  $\mathcal{S}$ | 0.51 | 0.40 | 0.7 | 0.81
$\mathcal{S}$, $T$ | 0.70 | 0.51 | 0.55 | 0.73
$\mathcal{S}$, $Rh$ | 0.62 | 0.45 | 0.62 | 0.78
$\mathcal{S}$, $T$, $Rh$ | 0.69 | 0.52 | 0.56 | 0.73
EEATC |  $\mathcal{S}$ | 0.51 | 0.4 | 0.7 | 0.81
$\mathcal{S}$, $T$ | 0.81 | 0.54 | 0.43 | 0.71
$\mathcal{S}$, $Rh$ | 0.7 | 0.42 | 0.55 | 0.8
$\mathcal{S}$, $T$, $Rh$ | 0.85* | 0.62* | 0.38* | 0.65*

(d) AirAssure Model |  Variables considered in the calibration process | $\text{R}^{2}$ |  | RMSE |
---|---|---|---|---|---
Training | Testing | Training | Testing
MLR |  $\mathcal{S}$ | 0.56 | 0.56 | 0.67 | 0.67
$\mathcal{S}$, $T$ | 0.57 | 0.57 | 0.66 | 0.66
$\mathcal{S}$, $Rh$ | 0.57 | 0.58 | 0.65 | 0.66
$\mathcal{S}$, $T$, $Rh$ | 0.57 | 0.58 | 0.65 | 0.66
RF |  $\mathcal{S}$ | 0.67 | 0.63 | 0.6 | 0.62
$\mathcal{S}$, $T$ | 0.69 | 0.68 | 0.55 | 0.57
$\mathcal{S}$, $Rh$ | 0.7 | 0.68 | 0.55 | 0.57
$\mathcal{S}$, $T$, $Rh$ | 0.73 | 0.71 | 0.52 | 0.55
EEATC |  $\mathcal{S}$ | 0.64 | 0.63 | 0.6 | 0.62
$\mathcal{S}$, $T$ | 0.73 | 0.69 | 0.6 | 0.62
$\mathcal{S}$, $Rh$ | 0.74 | 0.69 | 0.51 | 0.57
$\mathcal{S}$, $T$, $Rh$ | 0.80* | 0.75* | 0.44* | 0.5*

(e) Shinyei Model |  Variables considered in the calibration process | $\text{R}^{2}$ |  | RMSE |
---|---|---|---|---|---
Training | Testing | Training | Testing
MLR |  $\mathcal{S}$ | 0.48 | 0.46 | 0.72 | 0.75
$\mathcal{S}$, $T$ | 0.55 | 0.53 | 0.67 | 0.7
$\mathcal{S}$, $Rh$ | 0.54 | 0.52 | 0.68 | 0.70
$\mathcal{S}$, $T$, $Rh$ | 0.56 | 0.54 | 0.66 | 0.69
RF |  $\mathcal{S}$ | 0.63 | 0.63 | 0.61 | 0.62
$\mathcal{S}$, $T$ | 0.76 | 0.76 | 0.49 | 0.49
$\mathcal{S}$, $Rh$ | 0.73 | 0.74 | 0.52 | 0.52
$\mathcal{S}$, $T$, $Rh$ | 0.78 | 0.78 | 0.47 | 0.47
EEATC |  $\mathcal{S}$ | 0.63 | 0.63 | 0.61 | 0.62
$\mathcal{S}$, $T$ | 0.79 | 0.76 | 0.46 | 0.50
$\mathcal{S}$, $Rh$ | 0.75 | 0.75 | 0.48 | 0.51
$\mathcal{S}$, $T$, $Rh$ | 0.86* | 0.83* | 0.38* | 0.42*

(f) Aeroqual Model |  Variables considered in the calibration process | $\text{R}^{2}$ |  | RMSE |
---|---|---|---|---|---
Training | Testing | Training | Testing
MLR |  $\mathcal{S}$ | 0.90 | 0.90 | 0.31 | 0.31
$\mathcal{S}$, $T$ | 0.90 | 0.90 | 0.31 | 0.31
$\mathcal{S}$, $Rh$ | 0.90 | 0.90 | 0.31 | 0.31
$\mathcal{S}$, $T$, $Rh$ | 0.90 | 0.90 | 0.31 | 0.31
RF |  $\mathcal{S}$ | 0.93 | 0.93 | 0.26 | 0.26
$\mathcal{S}$, $T$ | 0.94 | 0.94 | 0.23 | 0.23
$\mathcal{S}$, $Rh$ | 0.94 | 0.94 | 0.24 | 0.24
$\mathcal{S}$, $T$, $Rh$ | 0.95 | 0.95 | 0.23 | 0.23
EEATC |  $\mathcal{S}$ | 0.93 | 0.93 | 0.26 | 0.26
$\mathcal{S}$, $T$ | 0.95 | 0.94 | 0.23 | 0.24
$\mathcal{S}$, $Rh$ | 0.94 | 0.94 | 0.24 | 0.26
$\mathcal{S}$, $T$, $Rh$ | 0.96* | 0.95* | 0.2* | 0.23*

In general, LCS for AQM are divided into metal oxide ($MO_{x}$),
electrochemical ($EC$) and optical sensors ($OS$) based on the principle on
which they work. $MO_{x}$ and $EC$ are predominant in gas pollutants
monitoring and $OS$ sensors are known for PM monitoring. Relative
humidity($Rh$) and temperature ($T$) are the prime environmental factors
influencing the accuracy of $MO_{x}$ and $EC$ sensors. These factors influence
the resistance of the heating element under the metal oxide surface in
$MO_{x}$ sensors; thus, changing its sensitivity causes inaccurate
measurements [26, 18]. In the case of $EC$ sensors, $T$ changes the rate of
the chemical reaction and moisture content depletes the sensors’ electrodes,
thus changing the response of the sensors [20, 14]. In addition, the gas
sensors suffer from low selectivity, which means they are cross-sensitive to
other gas pollutants present in the atmosphere [4, 56].

PM sensors work on optical principles severely affected by higher moisture
content since particles experience hygroscopic growth at higher $Rh$, where
the tiny particles floating around tend to stick together more because of the
water vapour [57]. The hygroscopic growth factor can be calculated as the
ratio of PM at a given humidity and temperature to that of the PM at the
temperature and humidity where the reference instrument is reporting the data.
Carl et al. [19] used the same method to correct the hygroscopic growth effect
on particulate matter measured by low-cost sensors working on the light
scattering principle. Later when they used the data-driven approaches, they
used temperature and humidity as explanatory variables of the model to
calibrate the same sensors since the hygroscopic growth factor accounts for
both temperature and humidity, and the ML algorithms take care of the complex
relationship among the variables. A similar procedure is followed by Zheng et
al. [16], Badural et al. [36], Janani et al. [58] to calibrate the low-cost
sensors works on light scattering principle.

In order to test EEATC on different LCS in stationary deployments, we choose
Community Air Sensor Network (CAIRSENSE) data set. The CAIRSENSE data set is
an open repository developed by Feinberg et al. [59] for LCS, and it is
available at the US Environmental Protection Agency (USEPA) data website [60].
The data set contains different LCS measurements ($\mathcal{S}$) and the time
corresponding $T$, $Rh$ and $\mathcal{Y}$ values. The measurements are taken
from the Colorado state at a one-minute resolution for one year.

The list of sensors involves in testing from the CAIRSENSE data set is as
follows,

  * •

Speck - measures PM - optical principle

  * •

Tzoa - Measures PM - optical principle

  * •

Aeroqual - measures $O_{3}$ \- metal oxide principle

  * •

Shinyei - measures PM - optical principle

  * •

OPCPMF - measures PM - optical principle

  * •

AirAssure - measures PM - optical principle

Before applying the calibration procedures, we eliminated the data outliers
based on threshold-based filtering. Then we normalized the data with mean and
standard deviation normalization, which is then separated into training and
testing at 75% and 25 %, respectively. All data cleaning, training and testing
parameters are available in the code at the GitHub link in the resources
section.

Our approach is data-driven, a general setup of any machine learning-based
calibration. The input features on which the model builds are the model’s
explanatory variables, and these are the parameters on which the performance
of the selected sensors gets influenced. Since there exist studies on the
effect of meteorology on the performance of LCS, including sensors that work
on optical principles, as a cautionary note, we tested all the models with
different feature subsets with cross-validation, and the results are presented
in table 1. The outperforming combinations of features are indicated with *.

(a)

(b)

Figure 8: comparison of EEATC approach with MLR and RF in terms of $R^{2}$ and
$RMSE$ for different sensors (a) in training (b) in testing

The plots drawn for the outperforming combination of features from the table 1
in Fig. LABEL:fig:eatc_train and LABEL:fig:eatc_test show the outperformance
of the EEATC approach compared to the well-known calibration models, such as
MLR and RF for all the sensors in training and testing respectively.
Therefore, we conclude that the EEATC performs better than the MLR and RF
approaches in stationary deployments.

However, in the case of Aeroqual sensors, $R^{2}$ of 0.9 and $RMSE$ of 0.31
with the MLR model clearly show the linear relationship among the features
utilized in the calibration process. As we discussed in the section 2.0.3,
when the single phase calibration itself can calibrate the LCS, then the
performance difference between EEATC and single phase approach is less. It can
be verified in Fig. LABEL:fig:eatc_train and LABEL:fig:eatc_test.

##  4 Evaluation of the EEATC approach for mobile AQM data sets

###  4.1 Mobile monitoring

Due to lack of publicly available data sets on mobile monitoring with LCS, we
conducted a pilot in Chennai (the city of Chennai spans nearly 1000
${km^{2}}$), India. For that, we have designed SensurAir, an LCS device which
monitors PM.

The core of the SensurAir is the 32-bit microcontroller, STM-32, by
STMicroelectronics, that integrates our LCS. Two LCSs, SDS011 and BME280, and
a GSM module, SIM900A, are integrated into the STM-32 on a customized printed
circuit board. SDS011 is a well-known LCS [61, 62] to monitor PM and works on
the light scattering principle, where the intensity of scattered light
indicates the PM concentration. The photodiode in SDS011 measures the
intensity of scattered light and converts it into an electrical signal which
is transformed into particle count and size by a predefined algorithm [63].

BME280 is a meteorological sensor specially developed for mobile and wearable
applications [64]. It consumes less power and measures temperature ($T$) and
relative humidity ($Rh$). Though it is an LCS, it is used as a reference
device to measure meteorological parameters in sensor devices since it is
known to be very accurate [65]. The GSM module of the SensurAir device
transfers sensor data to the central server. A GPS logger captures the
vehicle’s location during the monitoring period.

Figure 9: SensurAir mobile monitoring setup

Grimm, a nationally approved instrument for particulate monitoring, was used
as a reference device during the pilot. Grimm continuously samples air through
a pump, measures every 6 seconds, and averages over a minute. Our mobile
monitoring device travels at an average speed of 5.1 kmph (1.4 m/s), shown in
table 2, implying that Grimm captures 60 values within a distance of 84 m and
averages them to obtain one measurement reading. Therefore, the performance of
Grimm is not affected by vehicle speed in our mobile monitoring. Using the
same principle, Wang et al. [66] used Grimm in a mobile laboratory to monitor
on-road air pollutants during the Beijing 2008 summer Olympics. Elen et al.
[67] used Grimm on bicycles to monitor PM. At the same time, Grimm and SDS011,
the LCS in the SensurAir, work on the light scattering principle. Therefore we
can compare the final results of the calibration without any ambiguity. The
widespread use of Grimm motivates its selection as a reference instrument for
mobile monitoring.

We have deployed the SensurAir devices and the reference instrument (Grimm) on
a rickshaw as shown in Fig. 9 and operate opportunistically in parts of
Chennai, India. The route map of mobile monitoring is shown in Figure 10. As
we mentioned, the vehicle moves opportunistically, and the positions of the
vehicle are captured with the GPS module. Whenever there was a dead end in the
roads or the end of the monitoring period on that day, we started the vehicle
from the new positions. We plot the raw GPS positions without tailoring them
on the map, which may be the reason for some sudden jumps on the track shown
in Fig.2. The main reason for selecting a rickshaw is that it is open on the
sides to the atmosphere and provides unrestricted airflow to the instruments.

Figure 10:  Mobile monitoring on Google Maps. The red track is the monitoring
route, and the green markers are the reference stations near the route.

.

Mobile monitoring was conducted over three weeks, in the mornings (usually
between 10.30 am and 12.30 pm) and evenings (between 6.30 and 9.30 pm),
between September and October 2021.

###  4.2 Measurements

During the pilot, we monitored $PM_{25}$, $PM_{10}$, $T$, and$Rh$ parameters.
However, the present work covers the calibration of $PM_{25}$ for the purpose
of illustration, and the same procedure outlined holds for $PM_{10}$. The
sample plots of $PM_{25}$, $T$ and $Rh$ for six consecutive days in the
morning and the evening are shown in Fig. 11 and 12 and Table 2 illustrates
the statistics of these parameters for the entire monitoring period.

From Fig. 11, it can be observed that the $PM_{25}$ concentrations in the
evenings are slightly higher than what is observed in the mornings. This may
be due to the evening after-office rush hour traffic. Further, $T$ values are
higher during the mornings than in the evenings, which is an expected
scenario. The variations in $Rh$ are the exact opposite of $T$, which is a
general tendency of meteorology, and our measurements follow the same.

(a)

(b)

Figure 11:  $PM_{25}$ values of mobile monitoring for six consecutive days for
morning and evening. (a) from LCS (b) from Grimm

(a)

(b)

Figure 12:  Meteorological measurements of mobile monitoring for six
consecutive days for morning and evening. (a) $Rh$ (b)$T$

###  4.3 Data set preparation

All the measurements are collected at a resolution of one second and then
averaged the data over a minute. This averaging process serves two purposes.
Firstly, it allows time synchronization with the reference instrument
measurements, enabling comparisons between the LCS and reference measurements.
Secondly, it helps to smooth out any transient effects in the data caused by
the mobility of the vehicle carrying the LCS [50]. We followed the methodology
of Dong et al. [49] to remove the samples of vehicle start and stop positions
from the data sets using GPS positions. Then, we applied a threshold-based
filtering process to remove the outliers in the data

In order to address the heterogeneity in the data, we normalized all the
parameters using mean and standard deviation normalization. This normalization
ensures all the parameters have a similar scale and distribution, facilitating
faster learning for the calibration models.

Table 2: Statistics of the mobile monitoring data. parameter |  $\mathcal{S}$ ($\mu g/m^{3}$) |  $\mathcal{R}$ ($\mu g/m^{3}$) |  $Rh$ ($\%$) |  $T$ (${}^{\circ}C$) |  VS ($kmph$)
---|---|---|---|---|---
Min | 4.3 | 7.7 | 51 | 26 | 2.4
Max | 59 | 69.9 | 91 | 36.2 | 29.4
Mean | 19.9 | 35.9 | 71.6 | 30.6 | 5.1
Std | 7.8 | 12.3 | 7.5 | 2.6 | 2.38

We then constructed a data set $\phi$ based on the normalized data and it
contains three features $\mathcal{S}$, $T$ and $Rh$. It provides the input
data for the calibration models and this is the mobile LCS data set
contributed to the research community. Therefore, it can be represented in
matrix form as follows, where each row of the matrix corresponds to a specific
observation or measurement, and each column represents a specific parameter or
input.

$\displaystyle\phi=\begin{bmatrix}\mathcal{S}&T&Rh\\\ \end{bmatrix}_{(N\times
3)}$

###  4.4 Evaluation

Following the data set preparation, we tested the MLR and RF models with
$\phi$. The primary purpose of this testing is to check how these models work
with the mobile LCS data, and, at the same time, this helps to compare the
performance of the proposed method with these baseline models. We trained the
models with 75 % of the random data from $\phi$ and tested them with the
remaining data. To show the impact of each variable on the calibration
process, we have trained and tested the models with different combinations of
the variables, and the results are presented in Table 3. The best-performing
combination is highlighted with $*$.

Table 3: Performance of various models in the calibration of mobile LCS with Single-phase calibration  Model |  Variables considered in the calibration process | $\text{R}^{2}$ |  | RMSE |
---|---|---|---|---|---
Training | Testing | Training | Testing
MLR |  $\mathcal{S}$ | 0.12 | 0.13 | 0.93 | 0.81
$\mathcal{S}$+$Rh$ | 0.16 | 0.19 | 0.91 | 0.78
$\mathcal{S}$ +$T$ | 0.27 | 0.27 | 0.85 | 0.74
$\mathcal{S}$+$T$+$Rh$ ($\phi$) | 0.36* | 0.41* | 0.79* | 0.66 *
RF |  $\mathcal{S}$ | 0.35 | 0.14 | 0.80 | 0.81
$\mathcal{S}$+$Rh$ | 0.47 | 0.44 | 0.72 | 0.65
$\mathcal{S}$\+ $T$ | 0.63 | 0.59 | 0.60 | 0.59
$\mathcal{S}$+$T$+$Rh$ ($\phi$) | 0.68 * | 0.64 * | 0.56 * | 0.52 *
EEATC |  $\mathcal{S}$ | 0.66 | 0.50 | 0.57 | 0.61
$\mathcal{S}$+$Rh$ | 0.70 | 0.52 | 0.54 | 0.60
$\mathcal{S}$\+ $T$ | 0.85 | 0.78 | 0.38 | 0.40
$\mathcal{S}$+$T$+$Rh$ ($\phi$) | 0.86 * | 0.82 * | 0.37 * | 0.37 *

The calibration with MLR and RF by utilising only a single variable
$\mathcal{S}$ shows limited performance. This poor performance infers a weak
correlation between the $\mathcal{S}$ and $\mathcal{Y}$, and the scatter plot
in Figure 13 clearly shows this weak positive correlation. This is a common
scenario for mobile LCS due to the unwanted noise induced in mobile monitoring
and the effect of meteorological parameters [51]. When other covariates such
as $T$ and $Rh$ are included in the calibration process along with $S$, both
MLR and RF show improvements, which again follow the established trend in the
literature since these variables influence the performance of the LCS [4].

Figure 13: Scatter plot between PM sensor output and reference instrument
observations of the mobile monitoring data

Between MLR and RF models, the RF work better than the MLR for mobile data
also. However, the maximum $R^{2}$ of 0.64 and the minimum $RMSE$ of 0.52 are
able to achieve with the RF model with $\phi$ which are not attaining the
guidelines of USEPA. According to USEPA at least $R^{2}$ of 0.8 between the
LCS values and reference stations observations is required in order to accept
the LCS data for the indication purpose.

The proposed EEATC is an attempt in that aspect and it is able to attain the
benchmarks. In both training and testing, it is able to maintain the $R^{2}$
more than 0.8 and outperform the MLR and RF in all aspects shown in table 3.

Further, we propose an enhanced data set $\phi\prime$ for calibrating mobile
LCS that encompasses the time-shifted input $\mathcal{S}(t-1)$ and the
parameters included in the previously mentioned $\phi$ data set. The delayed
versions of the inputs help to encounter the sensitivity effects and the
temporal dependencies in the mobile measurements [52, 53]. Our experimentation
works with one unit delayed version, and the users need to test with different
versions as per their setup. Therefore, $\phi\prime$ is the enhanced data set
to calibrate the LCS in mobile deployments and it is represented in the matrix
form as follows,

$\displaystyle\phi\prime=\begin{bmatrix}\mathcal{S}&T&Rh&\mathcal{S}(t-1)\\\
\end{bmatrix}_{(N\times 4)}$

The plots in Fig. LABEL:fig:mobile_eeatc_train and Fig.
LABEL:fig:mobile_eeatc_test show the improvement in $R^{2}$ and $RMSE$ with
$\phi\prime$ compared to $\phi$ in all the aspects.

(a)

(b)

Figure 14: comparison of EEATC approach with MLR and RF in terms of $R^{2}$
and $RMSE$ for different features in the data sets, $\phi$ and $\phi\prime$
(a) in training (b) in testing

##  5 Conclusions and future work

The proposed EEATC can calibrate the LCS in stationary and mobile deployments
and outperform the well-known calibration models such as MLR and RF. This is
proved empirically by comparing the performance of the EEATC with the MLR and
RF in terms of $R^{2}$ and $RMSE$ values. However, in the case of mobile
deployments, it is tested on the data obtained through the pilot conducted in
Chennai, India, for a limited period. Testing with different data sets
obtained for various cities is a work for the future, and we believe that the
EEATC can work for this too. At this point, we would like to add a cautionary
note that models and variables we presented here may need to be suitably
altered for different deployment conditions.

Regarding the practical implementation of EEATC, MLR constitutes the first
phase and RF the second phase. That means the MLR first captures the linear
relationships in the data, and then RF captures the non-linear part. Now, the
order in which the models are cascaded is also an interesting aspect of EEATC
to explore. For example, how the method works when the RF is used as the first
phase and MLR in the second phase. It can also be tested with different linear
and non-linear models other than MLR and RF in future work. Further, using the
same model or the same type of model in both phases of EEATC may not work
since they would capture only the linear or non-linear behaviour in the data,
and this needs to be tested empirically in future work.

##  6 Resources

Use the following GitHub link to access the codes to implement EEATC and other
models discussed in the article https://github.com/mannamn-1/EEATC/upload/main

## Acknowledgments

We thank Mr Aswin Giri, a graduate student, and Mr Vijay Kumar, a project
engineer of Air Quality Lab, IITM, for their help during mobile monitoring

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[]M V Narayana is currently a PhD. scholar in Electrical Engineering
Department, Indian Institute of Technology Madras, India. He received his
masters from Andhra University, Andhra Pradesh, India. His research interests
are sensor and Sensor Systems, Calibration models for sensors, IoT devices
communication, wireless sensor networks, ML and AI. Currently, he is working
on calibration models for low-cost sensors for air quality monitoring.

[]Devendra Jalihal is presently working as a professor in the Department of
Electrical Engineering and Chairman of the Center for Continuing Education
(CCE), Indian Institute of Technology Madras, Chennai, India. He served as
head of the Electrical Engineering Department. He received PhD. from the
University of Duke, Durham. He is a member of IEEE, IEICE and reviewer for
IEEE, Elsevier, IET and IETE journals, and many conferences. His research
interests are statistical signal processing, detection and estimation theory,
digital communication and wireless communication.

[]Shiva Nagendra S M is presently working as professor in Department of Civil
Engineering, Indian Institute of Technology Madras, Chennai, India. He is
author of books titled ‘Urban Air Quality Monitoring, Modelling and Human
Exposure Assessment’ (ISBN:978-981-15-5511-4) and ‘Artificial Neural Networks
in Vehicular Pollution Modelling’ (SCI-41, ISBN-10: 3-540-37417-5) published
by Springer. He is associate editor of the journal Frontiers in Sustainable
Cities, Frontiers and Journal of the Institute of Engineers (India): Series A,
Springer. He is founder chairman of Indian International Conference on Air
Quality Management (IICAQM) series and Vice-President, Society for Indoor
Environment (SIE). His research interests focus on air quality management
includes monitoring, source apportionment, modelling, design and development
of emission control system, development of air quality management system and
personal exposure monitoring.