International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 4
Number 3
September 2010
295
1 MEASUREMENTS
In order to assess how measurement time affects the
accuracy of horizontal position determination in
GPS and GPS/EGNOS systems, more than thirty
measurement sessions were performed. Observations
during each session lasted at least 24 hours. The
tests were carried out with two identical MiniMAX
receivers made by CSI. The use of two receivers of
the same type (with the same software) was aimed at
eliminating possible errors that otherwise result from
measuring instruments of various types. The GPS
antennas were mounted on the antenna platform of
the Maritime University of Szczecin. The antennas’
positions were determined by geodetic methods.
The receivers were operated by using PocketMax_
PC_Ver.2.2. software, which makes it possible to
record data from MiniMAX receivers by PC com-
puters. The data were recorded at 1 Hz frequency in
NMEA-0183: $GPGGA, $GPGGL, $GPGSA,
$GPGST, $GPGSV and $GPZDA formats. Observa-
tions lasted from November 2007 to November
2008.
2 MEASUREMENT RESULTS ANALYSIS
The assessment of measurement duration effect on
the accuracy of horizontal position obtained by GPS
and GPS/EGNOS systems based on registered data
required current calculations, i.e. after each meas-
urement, of the following quantities:
− mean latitude,
− mean longitude,
− circular error of position M (for P = 0.95),
− latitude shift of mean position relative to geodetic
position (Δφ [m]),
− longitude shift of mean position relative to geo-
detic position (Δλ [m]),
− distance between mean position and geodetic po-
sition (R [m]).
Table 1 presents calculation results for selected
ten 24-hour measurement sessions.
Table 1. Ten 24-hour measurement sessions by GPS and
GPS/EGNOS receivers.
Measure-
ment type
Eleva-
tion
Measure-
ment date
M(95%)
[m]
Δφ
[m]
Δλ [m]
R [m]
1
GPS
20°
18.06.08
2.11
-0.73
-0.64
0.972
2
GPS/
EGNOS
25°
19.06.08
29.17
-1.12
-0.58
1.262
3
GPS
20°
18.08.08
20.21
-0.58
-0.13
0.605
4
GPS
5°
19.11.08
1.88
-0.55
-0.80
0.973
5
GPS/
EGNOS
5°
20.11.08
2.02
-0.66
-0.56
0.868
6
GPS/
EGNOS
5°
21.11.08
2.54
-0.54
-0.61
0.733
7
GPS/
EGNOS
5°
22.11.07
2.90
-0.48
-0.62
0.795
8
GPS
5°
25.11.08
2.94
-0.41
-0.60
0.725
9
GPS
5°
26.11.08
3.49
-0.33
-0.55
0.639
10
GPS
5°
27.11.08
3.09
-0.67
-0.63
0.913
Figures 1, 2 and 3, show the data from three ses-
sions:
− changes of the circular error in time M (95%),
− changes of latitude shift of mean position in time
relative to geodetic position (Δφ [m]),
− changes of longitude shift of mean position in
time relative to geodetic position (Δλ [m]),
− changes in time of mean position distance to geo-
detic position (R [m]).
Effect of Measurement Duration on the
Accuracy of Position Determination in GPS and
GPS/EGNOS Systems
R. Bober, T. Szewczuk & A. Wolski
Maritime University of Szczecin, Szczecin, Poland
ABSTRACT: The authors have analyzed the effect of measurement duration on the accuracy of ship’s hori-
zontal (2D) position obtained by GPS and GPS/EGNOS receivers. Also, the influence of measurement dura-
tion on the mean position determination error in relation to a reference (geodetic) position has been examined.
296
Figure 1. Changes of circular error after n seconds. Time scale x 5. Measurements of 22.11.2008
Figure 2. Changes of mean position shift after n seconds relative to geodetic position. Time scale x 5. Measurements of 22.11.2008
GPS/EGNOS ( elevation 5
0
)
1
744
1487
2230
2973
3716
4459
5202
5945
6688
7431
8174
8917
9660
10403
11146
11889
12632
13375
14118
14861
15604
16347
17090
17833
Time [ s ]
0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
Circular error for p=0,95
GPS/EGNOS ( elevation 5
0
)
∆ϕ [ m ]
∆λ [ m ]
∆R [ m ]
1
744
1487
2230
2973
3716
4459
5202
5945
6688
7431
8174
8917
9660
1040
1114
1188
1263
1337
1411
1486
1560
1634
1709
1783
Time [ s ]
-1,2
-1,0
-0,8
-0,6
-0,4
-0,2
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
Distance [ m ]
297
Figure 3. Changes of circular error after n seconds. Time scale x 5. Measurements of 23.11.2008
Figure 4. Changes in mean position shifts after n seconds relative to geodetic position. Time scale x 5. Measurements of 23.11.2008
GPS/EGNOS ( elevation 5
0
)
1
384
767
1150
1533
1916
2299
2682
3065
3448
3831
4214
4597
4980
5363
5746
6129
6512
6895
7278
7661
8044
8427
8810
9193
Time [ s ]
-0,2
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
Circular error for p=0,95
GPS/EGNOS ( elevation 5
0
)
∆ϕ [ m ]
∆λ [ m ]
∆R [ m ]
1
384
767
1150
1533
1916
2299
2682
3065
3448
3831
4214
4597
4980
5363
5746
6129
6512
6895
7278
7661
8044
8427
8810
9193
Time [ s ]
-1,5
-1,0
-0,5
0,0
0,5
1,0
1,5
2,0
Distance [ m ]
298
Figure 5. Changes of circular error after n seconds. Measurements of 27.11.2008
Figure 6. Changes of mean position shifts after n seconds relative to geodetic position. Measurements of 27.11.2008
GPS ( elevation 5
0
)
1
3503
7005
10507
14009
17511
21013
24515
28017
31519
35021
38523
42025
45527
49029
52531
56033
59535
63037
66539
70041
73543
77045
80547
84049
Time [ s ]
-2
0
2
4
6
Circular error for p=0,95
GPS ( elevation 5
0
)
∆ϕ [ m ]
∆λ [ m ]
∆R [ m ]
1
3503
7005
1050
1400
1751
2101
2451
2801
3151
3502
3852
4202
4552
4902
5253
5603
5953
6303
6653
7004
7354
7704
8054
8404
Time [ s ]
-3
-2
-1
0
1
2
3
Distance [ m ]
299
3 CONCLUSIONS
1 In the first stage of measurements (one hour) both
the position error determined from current
readouts of the receiver and the mean position
shift relative to the geodetic position show signif-
icant fluctuations. The position shift exceeds two
meters.
2 After about 12 hours the mean position relative to
the geodetic one seems to be stable. After that
time the distances between the mean position and
the geodetic position do not change more than 19
centimetres.
3 Even if there occur major disturbances during the
measurements (2nd and 3rd measurement series)
the mean position for a long period of measure-
ments does not differ significantly from the mean
position obtained from undisturbed measure-
ments. This refers to both GPS and GPS/EGNOS
measurements.
4 The accuracy of positions determined for long
measurement series is similar for GPS and GPS/
EGNOS systems.
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