Statistical evaluation of GPS error

1
Statistical evaluation of GPS error

• Amalia Doebbert
• Ninfa Bennington

2
Problem

• Assumed uncertainties in GPS systems
• sHH lt 10 m
• sDGPS lt 1 m

• Big questions
• Do uncertainties we observe in real data agree
  with these estimates?
• Are the distributions of these data Gaussian?

3
Data used

• Field exercise 26 April, 2008
• DGPS
• 3 Trimble rcvrs
• 10 sec. epochs
• HH GPS
• 3 HH rcvrs
• 10 min. tracks
• Variable epochs

4
Methods
5
HH absolute position histograms
m 43.0709º s 3.19 m
6
DGPS relative position histograms
m 1.1574 m s .1286 m
7
Methods
8
Z-distribution (HH)

• Z(x-m)/s
• Hist(Z)

9
Z-distribution (DGPS)

• Z(x-m)/s
• Hist(Z)

10
Methods
11
c2 (Goodness of fit)

• c2 S(O-E)/s2

Diff Locat c2
UW04wrtSAYL (dn) 9.0113E06
UW04wrtSAYL (de) 2.1309E06
UW04wrtSAYL (du) 6.0056E04
A306wrtSAYL (dn) 2.2728E05
A306wrtSAYL (de) 1.8557E05
A306wrtSAYL (du) 9.0394E04
A101wrtSAYL (dn) 4.5513E05
A101wrtSAYL (de) 1.1583E06
A101wrtSAYL (du) 1.5453E05
Position c2
BWSI-Lat 1.5816E13
BWSI-Lon 4.8006E12
KJK-Lat 1.7499E13
KJK-Lon 6.6512E13
BSRB-Lat 1.0013E16
BSRB-Lon 2.5960E15
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Results (DGPS)
Diff Locat A101wrtSAYL (dn) A101wrtSAYL (de) A101wrtSAYL (du)
m (m) 0.4762 1.1574 2.9775
s (m) 0.1822 0.1286 0.2399
c2 4.5513E05 1.1583E06 1.5453E05
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Results (DGPS)
Diff Locat A306wrtSAYL (dn) A306wrtSAYL (de) A306wrtSAYL (du)
m (m) 0.1668 1.2244 2.0585
s (m) 0.1813 0.1128 0.2839
c2 2.2728E05 1.8557E05 9.0394E04
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Results (DGPS)
Diff Locat UW04wrtSAYL (dn) UW04wrtSAYL (de) UW04wrtSAYL (du)
m (m) 0.0172 1.3675 3.0678
s (m) 0.0524 0.0471 0.1665
c2 9.0113E06 2.1309E06 6.0056E04
15
Results (HH)
Station BSRB-Lat BSRB-Lon
m (deg) 43.0699 -89.4102
s (deg) 1.8858E-06 4.2437E-06
s (meters) .21 .35
c2 1.0013E16 2.5960E15
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Results (HH)
Station BWSI-Lat BWSI-Lon
m (deg) 43.0709 -89.41
s (deg) 2.8721E-05 4.5791E-05
s (meters) 3.19 3.73
c2 1.5816E13 4.8006E12
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Results (HH)
Station KJK-Lat KJK-Lon
m (deg) 43.0709 -89.41
s (deg) 4.5756E-05 2.7793E-05
s (meters) 5.08 2.27
c2 1.7499E13 6.6512E13
18
Conclusions

• Positions from DGPS better fit to Gaussian
  distribution than HH
• Assuming Gaussian distribution
• sHH between 0.21 m and 5.06 m
• sDGPS,vert lt 0.2839 m sDGPS,NorE lt 0.1822 m
• DGPS positioning more precise than HH positioning
• Both DGPS and HH have uncertainties w/in
  estimated uncertainty