Global Positioning System Reference
In-Depth Information
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2
x
1
+σ
2
x
2
=
σ
DRMS
(4.331)
Th
is measure contains 64% to 77% probability. The related measure
2 DRMS
=
2
×
DRMS
(4.332)
contains about 95% to 98% probability.
The three-dimensional equivalent of CEP is the spherical error probable (SEP),
defined as
0
.
5127
σ
x
1
+σ
x
2
+σ
x
3
SEP
=
(4.333)
Ex
pression (4.333) is, strictly speaking, valid in the region
σ
min
/
σ
max
≥
0
.
35. The
co
rresponding 90% probability region,
[15
SAS
=
1
.
626
×
SEP
(4.334)
Lin
—
-
——
No
PgE
is
called the spherical accuracy standard (SAS). The mean radial spherical error
(M
RSE) is defined as
2
x
1
+σ
2
x
2
+σ
2
x
3
MRSE
=
σ
(4.335)
and contains about 61% probability.
These measures of precision are sometimes used to capture the achieved or an-
ticipated precision conveniently using single numbers. However, the geometry of the
adjustment seldom produces covariance matrices that yield circular distribution. Con-
sequently, the probability levels contained in these measures of precision inevitably
are a function of the correlations between the parameters.
[15
4.10 RELIABILITY
Small residuals are not necessarily an indication of a quality adjustment. Equally
important is the knowledge that all blunders in the data have been identified and re-
moved and that remaining small blunders in the observations do not adversely impact
the adjusted parameters. Reliability refers to the controllability of observations, i.e.,
the ability to detect blunders and to estimate the effects that undetected blunders may
have on a solution. The theory outlined here follows that of Baarda (1967, 1968), and
Kok (1984).
4.
10.1 Redundancy Numbers
Following the expressions in Table 4.1 the residuals for the observation equation
model are
v
=
Q
v
P
(4.336)
