algorithm is applied to a practical logistics warehouse.
Finally, section ‘ ‘Conclusion’’ concludes our work and
discusses future directions.
Related work
The LANDMARC algorithm is a classic localization
method of RSSI technology.
14
The LANDMARC algo-
rithm assumes that there are n readers, m reference tags,
and u tracking tags in the localization system. The read-
ers could detect the signal strength and identify it as
one of eight levels. The scanning frequency of readers is
30 times per second. Working under these conditions,
the localization process of LANDMARC is as follows.
Suppose that n readers received the signal strength
of a tracking tag, denoted as S =(s
1
, s
2
, ..., s
n
), and
received the signal strength of a reference tag, denoted
as a =(a
1
, a
2
, ..., a
n
), where s
i
and a
i
denote the
tracking tag and the reference tag’s signal strength per-
ceived on reader i (1 ł i ł n), respectively. For each
individual tracking tag p (1 ł p ł u), we define a
Euclidean distance formula as equation (1)
E
j
=
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
n
i = 1
a
ji
S
i
2
q
, j 2 1, ..., mðÞð1Þ
In equation (1), the Euclidean distance of the signal
strength between the tracking tags and the reference
tags is denoted as vector E =(E
1
, E
2
, ..., E
m
). In the
vector, a smaller E
j
value means a smaller signal
strength difference between a tracking tag and a refer-
ence tag. We select k smallest values in vector E to
express the k-nearest neighbor tags, which is called k-
nearest neighbor algorithm. Then, the tracking tags’
position coordinate is estimated. Empirically, a larger k
value does not guarantee good performance, and k =4
or k = 5 is a suitable choice. The coordinate estimated
expression of the tracking tag is defined as equation (2)
x, yðÞ=
X
k
i = 1
w
i
x
i
, y
i
ðÞ ð2Þ
where (x, y), w
i
, and (x
i
, y
i
) denote the coordinate of
tracking tag, the weighting factor, and the coordinate
of reference tag i, respectively. Intuitively, the selection
of w
i
should depend on the value of the k-nearest neigh-
bors. The smaller the value, the larger the weight. The
expression of w
i
is defined as equation (3)
w
i
=
1
E
2
i
P
k
j = 1
(1=E
2
j
)
, i 2 1, ..., kðÞð3Þ
In equation (3), E
j
denotes the jth component of the
vector in the k-nearest neighbor RSSI value because
the k value is estimated by the experience value, and w
i
is influenced by the density of the tags and other
factors. The LANDMARC algorithm has low localiza-
tion accuracy sometimes. Improving the density of the
reference tags in a localization area could increase the
localization accuracy, but it will lead to interference if
there are too many tags. In contrast, localization accu-
racy will decrease. To resolve these issues, the VIRE
algorithm is proposed.
The VIRE algorithm is an improved method based
on the LANDMARC algorithm, where the layout
assumption of readers and tags is the same as that in
the LANDMARC algorithm.
16
The basic idea is to
improve the localization accuracy by excluding small
probability position rather than adding additional
hardware, such as readers or tags. Virtual reference
tags based on the reference tags are utilized in this algo-
rithm. Virtual reference tags are arranged according to
some distributed rules. Generally, in an n 3 n actual
reference tag grid, n – 1 virtual reference tags are inter-
polated between two adjacent actual tags. For example,
in a 4 3 4 actual reference tag grid, every two adjacent
actual tags are inserted by three virtual reference tags,
so it is summarized as a 13 3 13 reference tag grid. The
RSSI values of the virtual reference tags are calculated
by the linear interpolation method, and the RSSI val-
ues of the horizontal direction virtual reference tags are
calculated as equation (4)
S
k
T
p, b
= S
k
T
a, b
ðÞ+ p 3
S
k
T
a + n, b
ðÞ
S
k
T
a, b
ðÞ
n
=
p 3 S
k
T
a + n, b
ðÞn + 1 pðÞS
k
T
a, b
ðÞ
n + 1
ð4Þ
The RSSI values of vertical direction and virtual ref-
erence tags are calculated as equation (5)
S
k
T
a, q
= S
k
T
a, b
ðÞ+ q 3
S
k
T
a, b + n
ðÞS
k
T
a, b
ðÞ
n + 1
=
q 3 S
k
T
a, b + n
ðÞn + 1 qðÞS
k
T
a, b
ðÞ
n + 1
ð5Þ
In a two-dimensional plane, the RSSI values of the
virtual reference tags are calculated as equation (6)
S
k
T
i, j
=
S
k
T
p, b
+ S
k
T
p, b + n
+ S
k
T
a, q
+ S
k
T
a + n, q
2
ð6Þ
In equations (4)–(6), S
k
(T
i, j
) denotes the virtual ref-
erence tags’ RSSI value of reader k and its coordi-
nate value is (i, j); corresponding parameters are
a = i=n, b = j=n, 0 ł (p = imodn) ł n 1,and
0 ł (q = jmodn) ł n 1.
After setting all the virtual reference tags, the RSSI
values combined with the actual reference tags consti-
tute a reference tag grid. The concept of a proximity
Wen et al. 3