Global Positioning System Reference
In-Depth Information
ronment. Here, the solution geometry can be significantly degraded relative to
open-sky conditions. Hence, each meter of ranging error can be scaled by a large
multiplier related to the geometry (e.g., HDOP for the HPE), resulting in a signifi-
cant navigation error, which DGPS can reduce.
The approximate altitude of the mobile can be provided as either the altitude
(above the WGS-84 reference ellipsoid) of the serving cell or an average altitude
over the cellular network service area (e.g., the average of the altitudes of each BS in
the network). It is reasonably important that an accuracy measure be provided for
the altitude, generally represented as a 1-sigma error: the applicable standards allow
for this, as discussed in [76]. This error measure is then most readily incorporated
into a WLS solution for the mobile position (see Section 7.3.3 and Appendix A).
Thus, the altitude is added as an additional measurement to the
m
pseudorange
measurements,
z
m
+1
, with an error variance set to the square of the 1-sigma value
from the network:
(
)
−
1
T
−
1
T
−
1
xHRHHRz
=
(9.51)
1 dimensional measure-
ment vector,
z
, and the four-dimensional vector of state corrections,
x
. The mea-
surement gradient matrix
H
is of dimension
m
Note that bold letters denote vectors in (9.51)—the
m
+
1 by 4, with its first
m
rows
corresponding to the
m
pseudorange measurements, and the last row corresponding
to the altitude, and
R
is the
m
+
1 dimensional diagonal measurement error variance
matrix, with each element representing an error variance assigned to the corre-
sponding measurement. The importance of assigning the error variance to the alti-
tude measurement can be illustrated by an example. Suppose the emergency call is
made from the tenth floor of a high-rise building, and the mean altitude of the cellu-
lar network coverage area is only slightly above mean sea level—in this case, the
altitude aiding information is grossly in error, and the only mechanism for inform-
ing the mobile is through the assignment of a large error variance to the altitude aid-
ing. Thus, the communicated network 1-sigma altitude error must reflect the
presence of high-rise buildings in the service area.
The approximate location that is communicated to the mobile can serve two
functions for the navigation solution. The first is simply to
initialize
the WLS solu-
tion, or provide a starting point for its iterations—the
x
value in (9.51)—which is
defined as a set of corrections relative to this initial supplied location. In order for
(9.51) to be valid, the approximate location must be sufficiently accurate such that
the pseudorange measurements are effectively
linearized
. A second function is to
add horizontal position domain constraints to the WLS solution, in the same way in
which the altitude constraint is added. The dimension of the measurement vector,
z
,
is then increased to
m
+
3, where
m
is the number of pseudorange measurements,
and the
R
matrix elements corresponding to the position constraints are assigned
error variances that reflect the accuracy of the approximate location. As referenced
in (9.41), error variances, perhaps in the form of an error ellipse, are communicated
with the approximate position. The error ellipse can be communicated (as an orien-
tation angle and 1-sigma errors in principal axes), as illustrated in Figure 9.44,
when the approximate position is determined from a coarse fix (e.g., based upon
+
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