IONOSPHERIC DELAY |
These are the biases that relate mainly to the propagation
link, and affect both pseudo-range and carrier phase measurements.
However, the special characteristic of the integrated carrier phase observable
leads to an additional special type of constant bias known as the
phase ambiguity.
The ionosphere is that band of atmosphere extending from about 50 to 1000 kilometres above the earth's surface. In this layer the sun's ultraviolet radiation ionises gas molecules which then lose an electron. These free electrons in the ionosphere influence the propagation of microwave signals (speed, direction and polarisation) as they pass through the layer. The largest effect is on the speed of the signal, and hence the ionosphere primarily affects the measured range.
The refractive index of microwaves is a function of frequency (and hence the ionosphere has the property of "dispersion") and the density of free electrons, and may be expressed, to a first-order approximation, by (SEEBER, 1993; HOFMANN-WELLENHOF et al, 1998):
 |
(6.2-1) |
where:
| A | is a constant, |
| Ne | is the total electron density (el/m3), and |
| f | is the frequency. |
The sign will depend on whether the range (+) or the phase (–) refractive index is required. The propagation speed v is related to the refractive index according to:
 |
(6.2-2) |
where c is the speed of electromagnetic radiation (EMR) in a vacuum.
Eqns (6.2-2) and (6.2-1) imply that the speed of the carrier wave (the "phase velocity") is actually increased, or "advanced", hence the phase refractive index is less than unity. However, the speed of the ranging codes is decreased (the so-called "group velocity") and therefore the pseudo-range is considered "delayed", and hence the range (or group) refractive index is greater than unity. (The ranging codes modulated on the carrier waves are considered a "group" of waves because they have different frequencies.)
The implication is therefore that the distance as implied by the integrated carrier phase is too short, but the pseudo-range is too long. The correction terms are, of course, quantities with a reversed sign, that is, the carrier phase correction is positive, while the pseudo-range correction is negative (section 6.4.1).
An adequate expression for the ionospheric group
delay dion and the ionospheric phase delay
ion for a microwave propagating from a satellite
to the ground is:
 |
(6.2-3) |
where:
| dion | is the ionospheric group delay in units of metres, |
| ion |
is the ionospheric phase delay in units of cycles, |
| c | is the speed of EMR in a vacuum(m/sec), |
cosec |
is the cosecant of the zenith angle of the line-of-sight to the satellite, |
| f | is the signal frequency (Hz), |
| STEC | is the Slant Total Electron Content, expressed as the number of free electrons per square metre (el/m2), and |
| VTEC | is the Vertical Total Electron Content (zenith direction) (el/m2). |
Note, from eqn (6.2-3), the higher the frequency, the smaller
the ionospheric delay effect. As mentioned earlier, the pseudo-range
measurements appear to be too long (dion must be subtracted),
while the "phase-range" measurements (phase expressed in metric
units) appear to be too short (dion must be added, or ion
must be subtracted). The constant A in eqn (6.2-1) is therefore equal to
the line integral:
 |
(6.2-4) |
There are a number of factors which influence the magnitude of the TEC (either STEC or VTEC), including (KLOBUCHAR, 1991):
Sunspot activity for the last 40 years. (KLOBUCHAR,
1991)
The ionospheric effects therefore are subject to spatial and temporal variations. The spatial variations are usually low in frequency and generally correspond to the various ionospheric latitude zones: tropical, mid-latitude and auroral. The temporal variations can have high frequencies (the so-called "scintillations"), medium frequency (diurnal and seasonal effects), and low frequency (the 11 year solar cycle -- see Figure above). The 11 year solar activity has recently been characterised by minimums during 1986 and 1995, and a severe maximum in 1991. The next solar maximum is around the turn of the century.
TEC is a maximum at low latitudes (the tropical zone) and at the poles (the auroral zone), and is a minimum at mid-latitudes. At night the ionospheric delay is approximately five to ten times less than for day time observations. The diurnal cycle for TEC is such that the maximum occurs two hours after solar noon, and is a minimum before dawn. Ionospheric disturbances, which can occur suddenly and be very severe, also affect the value of STEC (WANNINGER, 1993). One of the phenomena responsible for these are "travelling ionospheric disturbances", another is due to irregularities in the ionosphere causing "scintillations" (especially in the tropical and auroral zones). Under such conditions the ionosphere is so perturbed that single frequency operations may be impossible because the GPS receiver loses lock on the satellite signals. Where tracking is possible, the likelihood of cycle slips and interrupted tracking is increased, both making ambiguity resolution a more difficult and unreliable task.
The range of observed TEC is from about 1016 to 1019
el/m2. The maximum value of vertical range bias
caused by the ionosphere is about 30m on L1 observations, and about 50m
on L2 observations (the magnitude of dion is found by
scaling by a "mapping function" such as 1 / cosec ). The effect
on pseudo-range point positioning can therefore be quite severe. To aid
single receiver navigation users a crude broadcast predicted ionospheric
correction model is included within the transmitted Navigation Message (section 3.3.4). However, this model can only
reduce the RMS of the measurements (comparing observation residuals after
solution, with and without including the ionospheric model correction) by
approximately 50%. It is also possible to apply a correction derived from
the International Reference Ionosphere.
What is the effect on relative positioning of neglecting to account for the ionospheric delay? As expected, it is a function of baseline length. For short baselines, the ionosphere that the signals to two receivers travel through would be essentially the same, hence the ionospheric delay on measurements made by the receivers to the same satellite would be very similar, and effectively cancel in between-receiver differencing (section 6.3.2). According to BEUTLER et al (1989), when observing L1 phase data only, a scale effect will be introduced which will shorten baselines if the ionospheric signal delay is neglected. This effect expressed as a ratio of baseline length, in parts per million (ppm), is represented by the following "rule-of-thumb":
 |
(6.2-5) |
where L is the length of the baseline, and 
L is the error.
The effect of this scale error can range from about 0.4ppm to over 3ppm for baselines determined from L1 observations alone, corresponding to low and high solar activity respectively. Hence this error is only significant for very high accuracy long baseline determination, or in instances where ambiguity resolution is critical (again, in the case of long baselines, or for very short observation sessions as in the "rapid static" techniques, or for "on-the-fly" ambiguity resolution).
The dispersive nature of the ionosphere can be used in actually removing most of the ionospheric delay effect by making pseudo-range and/or carrier phase measurements on both L-band frequencies, and combining them in a special linear relation that results in an "ionosphere-free", or L3, observable (section 6.4.2). However, there are several disadvantages in using this "ionosphere-free" combination:
IONOSPHERIC DELAY BIAS
MAGNITUDE:
Presently in a sunspot minimum period.
OPTIONS:
|
| (L3)
= 2.546 .(L1) - 1.984 .(L2) |
DIFFERENCE data between
sites -- effect of error is minimised due to its high correlation over short
to medium baselines, typically 1-2ppm residual effect.
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© Chris Rizos, SNAP-UNSW, 1999
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