Global Positioning System Reference
In-Depth Information
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Figure 4.6
Defining elements of stan-
dard ellipse.
[14
4.
9.6 Properties of Standard Ellipses
Lin
—
6.5
——
Nor
PgE
The positional error
p
of a station is directly related to the standard ellipse, as seen
in Figure 4.7. The positional error is the standard deviation of a station in a certain
di
rection, say
ψ
. It is identical with the standard deviation of the distance to a known
(fi
xed) station along the same direction
, as computed from the linearized distance
eq
uation and variance-covariance propagation. The linear function is
ψ
r
=
z
1
cos
ψ +
z
2
sin
ψ
(4.309)
[14
Because of Equations (4.295) and (4.296), the distribution of the random variable
z
i
is multivariate normal with
z
1
z
2
N
0
0
,
N
0
0
,
a
2
Q
1
λ
0
0
2
0
∼
σ
=
(4.310)
Q
2
b
2
0
λ
0
Fi
gure 4.7
Position error.
