Instrumentation & Measurement Magazine 23-5 - 54

Fig. 4. (a) The 11 city areas in Salerno, Italy; (b) Zoomed view of the sensor distribution (city area n.7).

implementation of the Reference Method at test sites representative for typical conditions including possible episodes of
high concentrations. The comparison may be performed in the
form of a short campaign, during which a minimum of n=40
valid measurement results (each averaged over 24 hours) shall
be collected.
To fulfill the field test prescriptions, during Autumn 2018,
the PM10 concentration was recorded on an hourly basis over
two months (October-November) by the WSN including N=30
low-cost smart PM10 sensors installed as close as possible
(within 100 m distance) to a regional fixed station in the city of
Salerno. Two similar AMSs (hereinafter denoted as AMS1 and
AMS2) were considered by ordering the sensors according to
the distance from the fixed station and including them alternatively between the systems. Then, thanks to measurement
provided by the regional agency for environmental protection,
a comparison in terms of daily average for the PM10 concentration was made between the n measurement xi obtained on
the basis of the 24 hour data recorded by the fixed station (operating as RM [14]) and the corresponding measurements
yi,AMS1 and yi,AMS2 provided for a single 24-h period by the smart
sensors of the distributed system included, respectively, into
the AMSs under test.
In detail, the between-AMS uncertainty ubs,AMS is computed
according to:

 y

n

	

2
bs ,AMS

u

i 1

i , AMS1

 yi ,AMS 2

2n



2

	(1)

Moreover, the actual relation between the results of the
AMS and the (average) results of the RM is established for each
of the AMS individually using a regression technique, leading
to symmetrical treatment of both variables. A commonly applied technique is the orthogonal regression that leads to the
estimation of the slope b and intercept a of the expected linear relation:
	
54	

yi  a  bxi	(2)

When the slope b differs significantly from 1 and/or the intercept differs significantly from 0, the AMS shall be calibrated
according to the following formula:
yi ,corr 

	

yi  a
	(3)
b

Then, the orthogonal regression shall be again applied to
estimate the linear relation between the (corrected) results of
the AMS and the average concentration by the RM:
yi ,corr  c  dxi	(4)

	

Finally, the uncertainty uyi,corr of the results of the AMS is estimated according to the following formula:
	

uyi2 
,corr

2
RSS
2
 uRM
  c   d  1 L   ua2  L2 ub2	(5)
n  2

where RSS is the residual sum of squares resulting from the orthogonal regression, uRM is the random uncertainty of the RM
(assumed equal to 0.67 μg/m3 when a single reference instrument is adopted), and ub and ua are the standard uncertainty
of the slope b and intercept a, respectively (calculated as the
square root of the corresponding variance).
In the previous formula, the first two terms represent the
random uncertainty of the results of the AMS, whereas the
last terms are the bias at the limit value. Moreover, the covariance term between slope and intercept has not been included
for simplicity.
The combined relative uncertainty wAMS at the relevant limit
value is calculated:
	

w 2AMS 

uyi2 L
L2

	(6)

and the expanded relative uncertainty WAMS is compared with
the previously introduced threshold, having considered a coverage factor k = 2 (in view of the large number of experimental
results).

IEEE Instrumentation & Measurement Magazine	

August 2020
Instrumentation & Measurement Magazine 23-5

Table of Contents for the Digital Edition of Instrumentation & Measurement Magazine 23-5
