5.2 Physical Anti-Collision Based on Support Vector Machine (SVM)
179
where P is the perimeter of tag image and A is its area. The more the value of C,
the more complicated the shape of tag. Therefore, the shape index of RFID tag is
roughly 16 and the shape index of laser point is roughly 12.56, as shown in Fig. 5.18d.
According to the marked tags and laser point, the position of coordinate and tags
could be obtained, as shown in Fig. 5.18e, d.
5.2.3 Predict Model of RFID Tags’ Distribution Based
on SVM
The dynamic reading performance of RFID multiple tags system is not only influenced by algorithm, but also affected by tags’ geometry distribution. Establishing
geometric model and predicting optimal geometric distribution using SVM could
improve reading performance of RFID system.
(1) SVM regression algorithm
The support vector machine is established at the foundations of Vapnik-Chervonenkis
(VC) dimension and structural risk minimization (SRM) [31].
Consider one has a training data set {(x i , y i )|i = 1, 2, . . . k }, where x i are the
training examples and y i are the class labels. The class label of x is obtained by
considering the sign of y = f (x). Consider using g(x) = ω · x + b to fit the
training examples realizing that the distance of f and g is minimum. In other words,
the loss function R( f, g) =
L( f, g)dx is minimum. According to structural risk
minimization,
J =
1
2
ω
2
+ C
k
i=1
L(g(x i ), y i )
(5.35)
The optimization problem can be written as
min
1
2
ω
2
+ C
k
i=1
(ξ i , ξ
∗
i )
s.t.
⎧
⎨
⎩
y i − ω · x − b ≤ ε + ξ i
ω · x + b + y i ≤ ε + ξ
∗
i
ξ i , ξ
∗
i ≥ 0
(5.36)
where ε>0 is fitting precision, ξ i is the value above target, ξ
∗
i is the value under target,
and C>0 is a constant. The solution of this problem is obtained using the Lagrange
theory:
179
where P is the perimeter of tag image and A is its area. The more the value of C,
the more complicated the shape of tag. Therefore, the shape index of RFID tag is
roughly 16 and the shape index of laser point is roughly 12.56, as shown in Fig. 5.18d.
According to the marked tags and laser point, the position of coordinate and tags
could be obtained, as shown in Fig. 5.18e, d.
5.2.3 Predict Model of RFID Tags’ Distribution Based
on SVM
The dynamic reading performance of RFID multiple tags system is not only influenced by algorithm, but also affected by tags’ geometry distribution. Establishing
geometric model and predicting optimal geometric distribution using SVM could
improve reading performance of RFID system.
(1) SVM regression algorithm
The support vector machine is established at the foundations of Vapnik-Chervonenkis
(VC) dimension and structural risk minimization (SRM) [31].
Consider one has a training data set {(x i , y i )|i = 1, 2, . . . k }, where x i are the
training examples and y i are the class labels. The class label of x is obtained by
considering the sign of y = f (x). Consider using g(x) = ω · x + b to fit the
training examples realizing that the distance of f and g is minimum. In other words,
the loss function R( f, g) =
L( f, g)dx is minimum. According to structural risk
minimization,
J =
1
2
ω
2
+ C
k
i=1
L(g(x i ), y i )
(5.35)
The optimization problem can be written as
min
1
2
ω
2
+ C
k
i=1
(ξ i , ξ
∗
i )
s.t.
⎧
⎨
⎩
y i − ω · x − b ≤ ε + ξ i
ω · x + b + y i ≤ ε + ξ
∗
i
ξ i , ξ
∗
i ≥ 0
(5.36)
where ε>0 is fitting precision, ξ i is the value above target, ξ
∗
i is the value under target,
and C>0 is a constant. The solution of this problem is obtained using the Lagrange
theory: