International Core Journal of Engineering 2020-26 | Page 96

T ABLE IV. F IVE - LINE APPROXIMATE POSITIONING ALGORITHM POSITIONING
RESULTS ( UNIT : CM )
Number
1
2
3
4
5
6
Real
coordinates
[65 ,300]
[125,300]
[305,420]
[185,240]
[185,300]
[125,240]
Coordinates by
algorithm
[86.69,287.67]
[147.24,290.90]
[300.17,411.01]
[189.87,227.79]
[185.12,295.38]
[132.57,245.18]
Absolute
error
18.4
21.8
12.6
7.9
6.8
9.6
Error
variance
9.7
10.3
8.9
7.4
9.8
9.6
The experimental results are shown in Fig. 4 by using the
same mobile tag to collect TDOA data walking along the
preset route in the classroom. The dynamic positioning error
is shown in Table . There are three paths for walking in the
classroom. The first path is which the range of the y-axis is
(500.8, 500.8) and the range of x-axis is (103.1, 980.2). The
second path is which the range of the y-axis is (139.1, 500.8)
and the range of x-axis is (103.1, 103.1). The third path is
which the range of the y-axis is (139.1, 139.1) and the range of
x-axis is (103.1, 980.2).
(d)
It can be clearly seen that the five-line approximate
positioning algorithm has better positioning accuracy than the
other positioning methods. It can be well adapted to the
environment and meet the requirements of general indoor
positioning, such as construction sites, chemical plants,
prisons and other scenes.
V. C ONCLUSIONS AND P ROSPECTS
The paper proposes a positioning algorithm that uses line
to approximate the hyperbola based on UWB. It is seen from
static positioning results that the accuracy of five-line
approximate positioning algorithm is improved by 4.8cm
compared with the three-and-four-line approximate
positioning algorithm. The accuracy of the three-and-four-line
approximate positioning algorithm is improved by 6cm
compared with the three-line approximate positioning
algorithm. It is seen from dynamic positioning results that the
accuracy of the five-line approximate positioning algorithm is
improved by 7.9cm compared with the three-and-four-line
approximate positioning algorithm. The accuracy of the
three-and-four-line approximate positioning algorithm is
improved by 20.1cm compared with the three-line segmental
approximate positioning algorithm. While continuing to
increase the number of approximate line segments, the
positioning accuracy is limited, and the upper limit of
accuracy performance has been basically achieved. Therefore,
five-line segmental approximate positioning is adopted.
(e)
Fig. 3: Hardware physical and experimental environment
B. Experimental results
In order to verify the feasibility and correctness of the
algorithm, the same mobile tag is placed in different positions
in the classroom at different time. Then we use the three-line
segmental approximate positioning algorithm, the
three-and-four-line segmental approximate positioning
algorithm and the five-line segmental approximate
positioning algorithm respectively to conduct comparative
experiments. The simulation results are shown from Table to
Table .
T ABLE II. T HREE - LINE APPROXIMATION POSITIONING ALGORITHM
POSITIONING RESULTS ( UNIT : CM ).
Number
1
2
3
4
5
6
Real
coordinates
[65 ,300]
[125,300]
[305,420]
[185,240]
[185,300]
[125,240]
Coordinates by
algorithm
[110.03,277.76]
[158.81,282.76]
[295.73,388.38]
[193.52,231.70]
[189,49,283.66]
[150.15,238.34]
Absolute
error
20.4
33.1
33.6
12.0
17.8
25.2
Error
variance
10.9
13.2
12.4
9.5
11.2
10.5
T ABLE V. D YNAMIC POSITIONING ERROR COMPARISON ( UNIT : CM )
Three-line Three-and-four-line
Five-line
approximation approximation approximation
Max
70.5
72.4
54.7
First path
Min
0.2
0.4
0.1
Average
30.2
23.9
17.3
Max
119.2
28.9
48.8
Second
Min
23.9
0.1
1.0
path
Average
68.9
8.3
17.6
Max
65.9
85.1
76.9
Third
Min
0.1
0.9
0.1
path
Average
31.8
38.5
11.9
Path
T ABLE III. T HREE - AND - FOUR - LINE APPROXIMATE POSITIONING ALGORITHM
POSITIONING RESULTS ( UNIT : CM )
Number
1
2
3
4
5
6
Real
coordinates
[65 ,300]
[125,300]
[305,420]
[185,240]
[185,300]
[125,240]
Coordinates by
algorithm
[81.87,291.67]
[142.96,290.02]
[312.24,386.51]
[189.35,233.52]
[183.09,286.48]
[126.72,249.30]
Absolute
error
19.3
22.9
31.3
8.1
14.8
9.8
Error
variance
10.2
12.6
10.1
8.3
14.1
9.8
74
Error