Global Positioning System Reference
In-Depth Information
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
The A matrix has as many rows as there are satellites observed, which typically
includes all satellites in view. The superscript i is a sequential identification for the
satellite and not necessarily equal to the PRN number. The symbol e k denotes the
1
3 row vector defined in (5.48). It contains the direction cosines for the vector
from the nominal station location to satellite. The clock error parameter is often set
to
×
cd t k , making the elements in the second column of (7.45) unity. The cofactor
matrix for the adjusted receiver position and receiver clock is
ξ k =
q x
q xy
q xz
q xt
Q x = A T A 1
q y
q yz
q yt
=
(7.46)
q z
q zt
sym
q t
[25
Si nce it is more convenient to interpret results in the local geodetic coordinate system
(w ) (consisting of the coordinates northing n , easting e , and up u ), we transform the
co factor matrix (7.46) using (2.112) and (2.113) of Section 2.3.5.3. The result is
Lin
0.2
——
Nor
PgE
q n
q ne
q nu
Q w =
q e
q eu
(7.47)
sym
q u
The DOP factors are functions of the diagonal elements of (7.46) or (7.47). Table
7.2 shows the various dilution factors: vertical dilution of precision (VDOP) for the
height, horizontal dilution of precision (HDOP) for horizontal positions, positional
dilution of precision (PDOP), time dilution of precision (TDOP) and geometric dilu-
tion of precision (GDOP). GDOP is a composite measure reflecting the geometry of
the position and time estimates.
The DOPs can be computed in advance, given the approximate receiver location
and a predicted satellite ephemeris. The DOPs are useful for finding the best subset
of satellites if a receiver has only four or five channels. Even though most receivers
today observe all satellites in view, the DOPs are still useful to identify a temporal
weakness in geometry in kinematic applications, in particular in the presence of signal
obstruction.
[25
TABLE 7.2 DOP Expressions
VDOP = q u
HDOP = q n +
q e
q u = q x +
PDOP = q n +
q e +
q y +
q z
TDOP = q t
q n +
GDOP
=
q e +
q u +
q t c 2
 
Search WWH ::




Custom Search