(Gm-09v – Sol) Page 1 of 11
NTNU
Geomatics
Exam:
TBA4230 GEOMATICS
Date: 8.12.2009
Time: 0900 – 1300
Solution, version 28.11.2010
Question no. 1: GPS, adjustment by parameters, etc.
Here method 1 is used: The calculations are carried out
in the local coordinate system.
NB: Only calculations in the ground plane (horizontal
plane) are done (no estimations of heights).
Results from the estimation in the ground plane (
x
,
y
):
(
)
2
3,84 mgon
pvv
=
=
T
V PV
Figure 1.1 Observations and points
The normal equations:
2,145
0,354
1,910
0,450
719372
1,029
0,400
0,740
1450000
2,717
1,581
0
2,219
1450000
C
C
D
D
x
y
x
y
=
=
⋅
=
T
X
A PF
↑
the
Q
matrix of the estimated coord.
1.1
(a)
State the number of excess measurements (degree of freedom) for the determination of the
new points C and D on figure 1.1.
The number of excess measurements, 5 baselines, 2 unknown points (NB: No calculations of
heights):
n - e
= 5
⋅
2 – 2
⋅
2 = 6
With 2 known points (A and B) we also can choose to have 2 additional unknowns in the
adjustments: Unknown scale and rotation. Normally this is done when GPS baselines calculated
in WGS84 are used as observations in an adjustment in another datum:
n - e
= 5
⋅
2 – 2
⋅
2 – 2 = 4
(b)
The observation with the unit weight is a plane bearing (as GPS is used).
Calculate the standard deviation of the unit weight for the adjustment of the network in
figure 1.1.
Standard deviation of the unit weight, where
n - e
= 6 is used here, a plus if you use
n - e
= 4:
(
)
0
3,84
0,80 mgon
6
pvv
n
e
σ
=
=
=
−
(With
n – e
= 4 we obtain 0,96 mgon)
(c)
Calculate the standard deviation of the estimated x coordinates of C and D.
Calculate the covariance between the x coordinates of C and D.
Calculate the covariance between the y coordinates of C and D.
Interpret the results.
x
y
B
A
D
C

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