Table 1 Airborne remote sensing positioning requirements
Ž . Application area
Position RMS accuracy m Engineering, Cadastral
0.05–0.10 Ž
. Forestry detailed
0.2–1.0 Cartographic mapping 1:10 000
2–5 Resource applications
2–5
a lesser extent, orbital errors. Multipath, or the re- flection of signals off nearby objects, can be miti-
gated through proper antenna selection and place- ment. Atmospheric errors, on the other hand, can be
Ž rather large depending on the weather conditions in
. the case of the troposphere and the activity of the
ionosphere. Ionospheric error and its contribution to the over-
all aircraft positioning error budget is a particularly important topic given that the next solar maximum is
in the year f 2000. At that time, the ionospheric error will increase in magnitude and the occurrence
of geomagnetic storms will be more frequent, partic- ularly for users in northern and equatorial latitudes.
This may result in poor GPS tracking capabilities due to scintillation effects, as well as poorer differen-
tial positioning accuracies due to decreased spatial correlation of the ionospheric effect. This paper fo-
cuses on describing the ionospheric effects on GPS measurements and provides an estimate of the errors
that can be expected at solar maximum, through analysis of a geomagnetic substorm event which
occurred in April 1997. This analysis also includes a discussion of the spatial decorrelation of ionosphere
range delays and the propagation of these errors into expected DGPS position accuracies.
2. Ionospheric effects on GPS
A GPS receiver measures two types of observ- ables: carrier phase in number of cycles, and code
group delay in seconds. These measurements are converted to carrier phase range and pseudorange
measurements, respectively, through multiplication by the speed of light in a vacuum. Implicit in GPS
range measurements, therefore, are the assumptions that the GPS signal travels at the speed of light and
the wavelength of the signal is equal to its wave- length in a vacuum along its entire path length. This
is equivalent to assuming that the phase and group indices of refraction, n
and n , are equal to one
p g
throughout the propagation medium, where the car- Ž .
Ž .
rier phase range F
and pseudorange PR
are calculated as follows:
l l
ct F s
ld Ns d Ns
d
H H
H
ž
n n
l
path path
path
p p
c s
d t 1
Ž .
H
n
path
p
c PR s
Õ d t s
d t 2
Ž .
H H
g
n
path path
g
where Õ is the group velocity, c is the speed of light
g
in a vacuum, l is the true wavelength, l is the
wavelength in a vacuum, d N denotes the differential number of cycles and d t denotes the differential
element of time. F and PR are both measured in Ž
. units of length nominally meters .
The assumption n s n s 1 is incorrect in re-
g p
gions such as the troposphere and ionosphere, where the index of refraction may differ significantly from
one. In the dispersive ionosphere, the phase index of refraction depends on several factors:
Ne
2 2
2p
Ž .
2
ž
m´ 1 v
1
p
n s 1 y s1 y
p 2
2 2
2 2
v 2p
f
Ž .
N s 1 y 40.3
3
Ž .
2
f where N s electron density; e s electron charge s
1.602 = 10
y1 9
C; m s electron mass s 9.1095 = 10
y3 1
kg; ´ s permittivity of free space s 8.854 = 10
y1 2
C
2
rNm
2
; f s frequency of the carrier signal. The phase index of refraction therefore depends
only on the electron density N. A corresponding expression for the group index of refraction can be
derived as follows: d n
N N
p
n s n q f s1 y 40.3
q 80.6
g p
2 3
d f f
f N
s 1 q 40.3 4
Ž .
2
f Ž .
Ž . The second term in Eqs. 3 and 4 causes the
signal velocity to differ from c, giving rise to abso-
Fig. 1. The slant TEC, as measured along the satellite–receiver line-of-sight. The majority of TEC is concentrated in the ionosphere shell, near altitudes of 350 km.
lute range errors associated with GPS signal propa- Ž
gation through the ionosphere as integrated along .
the path length : 40.3
40.3 Nd s s
TEC 5
Ž .
H
2 2
f f
path
where TEC represents the total electron content along a 1 m
2
column along the signal path. The majority of TEC is concentrated near altitudes of 350 km, where
Ž .
the largest electron densities are found Fig. 1 . The Ž
. dispersive nature of the ionosphere d nrd f 0 al-
lows direct calculation of the absolute TEC, if range measurements are available on two separate frequen-
cies:
1 1
1 TEC s
y PR y PR
6
Ž .
Ž .
1 2
2 2
ž
40.3 f
f
1 2
for the case of a dual-frequency GPS receiver, where Ž
. f s 1575.42 MHz herein referred to as L1 and
1
Ž .
f s 1227.60 MHz herein referred to as L2 . The
2
corresponding absolute ionosphere range delay can Ž .
be derived from Eq. 5 . Such range delays, along the slant line-of-sight through the ionosphere shell,
are referred to as slant range delays. For differential GPS applications, the decorrelation of slant iono-
sphere range delay depends directly on the distribu- tion of spatial irregularities in electron density. Such
irregularities can be significant in the auroral region.
3. Auroral region and substorm effects
