International Core Journal of Engineering 2020-26 | Page 95

Where ( x 6 , y 6 ) is the intersection coordinate of the
vertical line of hyperbolic focus and the hyperbolic asymptote,
and ( x 7 , y 7 ) is the intersection coordinate of the vertical line
of hyperbolic focus and the hyperbola.
Three-line segmental approximate positioning results
1000
800
700
0
-100
-200
0
200
400
x/cm
800
1000
Three-and-four-line segmental approximate positioning results
1000
Hyperbola
Three-and-four-line
The point by the algorithm
900
800
700
anchor2 anchor3
anchor1 anchor4
600
Five-line segmental approximate results
1000
Hyperbola
Five-line
The point by the algorithm
500
400
300
200
100
anchor3
0
600
-100
500
-200
0
200
400
x/cm
400
600
800
1000
(b)
300
Five-line segmental approximate results
200
1000
100
anchor1
0
-100
600
(a)
The localization results are shown respectively in
anchor4
400
100
The second line is the connected line of ( x 8 , y 8 +L2) and
asymptote. The fourth line is the connected lines of ( x 9 ,
y 9 +L2) and asymptote.
anchor2
anchor1
500
200
coordinates of nodes are ( x 8 , y 8 +L2) and ( x 9 , y 9 +L2).
700
anchor3
300
( x 9 , y 9 ). Then the nodes are translated by L2 (25cm) and the
800
anchor2
600
When we use five lines to approximate hyperbola, the first
line and the fifth line are respectively the asymptotes of which
the original hyperbola is moved some distances. The moved
distance formula is shown in (3). The third line is the vertical
line of hyperbolic focus which translates by L1 (5cm). The
nodes of the vertical line and the hyperbola are ( x 8 y 8 ,) and
900
Hyperbola
Three-line
The point by the algorithm
900
Hyperbola
Five-line
The point by the algorithm
900
anchor4
800
-200
0
200
400
x/cm
600
800
1000
700
anchor2 anchor3
anchor1 anchor4
600
(c)
Fig. 2. Positioning algorithm results
500
400
300
. The most used method for calculating the program
running method is the combination of Tic and Toc. The
classic format is:
200
100
0
Tic;
-100
Intermediate program;
-200
0
200
400
x/cm
600
800
1000
(c)
Toc;
Fig. 2. Positioning algorithm results
From this, the time taken for the Chan algorithm to run
one cycle is 14.5s, and the time taken by the five-line segment
approximation algorithm to run one cycle is 7.9s.
IV. E XPERIMENTAL S IMULATION AND R ESULT A NALYSIS
A. Experimental Environment
3
The experimental site is a 9.8×7.8×3.5 m of indoor
classroom. Four base stations (anchor1, anchor2, anchor3,
anchor4) for transmitting signals are installed in the four
corners of the classroom and the height is about 2m. The
physical hardware and experimental environment are shown
in Fig. 3. In (d), the left is the anchor and the right is the
mobile tag.
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