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GPS-Based Geodesy Tracking:
Technology Prospects for the Year 2000
W. G. Melbourne
Jet Propulsion Laboratory
California Institute of Technology
Pasadena, California 91109
INTRODUCTION
The twenty-first century is a scant dozen years away, too near for
many landmark advances in technology, yet long enough for a few
surprises to emerge. To put it into focus one need only look backwards
12 years to the way things were in 1976, the year of our bicentennial.
The Navstar/Global Positioning System (GPS) program had already been
underway for two years. Meanwhile, we are still awaiting the launch of
the first Block II satellite, which will mark the onset of the GPS
operational phase. Of course, history is laden with inaccurate
predictions of future technology trends based on current knowledge. My
message is really ambivalent. Don't expect too much progress in the
decade of the 1990s; on the other hand, do expect some surprises because
technology often advances in quantum jumps.
In the case of GPS, the evidence today unmistakably suggests future
trends for high accuracy geodesy and Earth satellite tracking. Given
the current performance of GPS, particularly on regional baselines, one
can say that GPS has arrived. Its attributes of high accuracy and
relatively low cost make it the geodetic technique of choice in the
l990s for most of the regional deformation studies that require high
temporal and spatial resolutions. It has even greater potential for the
future. I would like to discuss this potential in terms of:
a. future accuracies of GPS geodetic systems,
b. future costs for data acquisition equipment, operations and
data analysis, and
c. future applications in ground and satellite geodesy.
PROSPECTS FOR MILLIMETER ACCURACIES IN GPS-BASED GEODESY
What are the limiting error sources today for GPS systems and what
are the prospects for their improvement? I think that we should take
our cues on these questions from experience with VLBI. The horizontal
accuracy from Mark VLBI III systems ranges from around 1/2 - 1 cm on
regional baselines to 1 - 1-1/2 cm on transcontinental baselines (Clark
et al., 1987; see chapter by Rogers) the vertical accuracy is about a
factor of 2-3 worse because of tropospheric water vapor errors and
limitations of observational geometry, i.e., one cannot observe below
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one's horizon. Roughly the same ratio between horizontal and vertical
appears to hold in GPS accuracies. However, there is some suggestion
that the more robust observation scenario with GPS systems, in which GPS
satellite and ground receiver clock instabilities are isolated to
prevent possible corruption of baseline estimates, yields better
accuracies in the vertical component than are obtained with VLBI.
Today's evidence (Blewitt et al., 1988) supports the position that
GPS horizontal accuracies are comparable to VLBI accuracies on regional
baselines. For example, Figure 1 shows the agreement between GPS and
VLBI-determined baselines over a range of lengths up to 2000 km for
several measurement campaigns spanning 1985-1988. Centimeter-level
agreement is the norm for regional baselines. On transcontinental
baselines, GPS systems are not quite as accurate as VLBI because of
current limitations in the control of GPS reference system errors, which
should be remedied in the near future with stronger GPS fiducial and/or
global tracking networks.
The principal errors limiting GPS performance today arise from:
a. mix-modeling and/or mix-calibrating the propagation media,
b. antenna multipath,
c. antenna phase center variability, and
d. reference system errors including the terrestrial reference
frame, limitations in alignment with VLBI and SLR frames,
and the GPS satellite ephemerides.
I will now summarize the present status of these error sources and
try to estimate their future course in the 1990s. To reach the
millimeter level will also require dealing with error sources that are
presently masked by these ''tall poles'' cited above. For example,
seasonal environmental effects such as ground water variability can
certainly affect the height of monuments at the millimeter level in
certain soil conditions. Ocean loading is another. GPS satellite
multipath will have to be dealt with on longer baselines. I will mainly
focus on the current limitations and the prospects for improving them.
PROPAGATION MEDIA
Tropospheric water vapor is the major error source for VLBI and GPS
systems. Small errors can arise from mix-modeling or mix-calibrating
the troposphere and the ionosphere.
Dry Troposphere. The total zenith delay of the dry troposphere is about
2 m and is readily determined barometrically to a precision of about
1 mm using standard atmosphere models. Departures from hydrostatic
equilibrium of the dry component of the troposphere leads to zenith
delay mix-modeling that can amount to a few millimeters in certain
dynamical conditions. For baselines longer than the correlation length
of these departures from hydrostatic equilibrium, differential delay
errors will translate into comparable errors in the horizontal
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components and into larger errors in the vertical component. Bender
(1987) has discussed the potential error arising from the dry component
of the troposphere. To reach 1 mm accuracy it may be necessary to
utilize synoptic meteorological data under some conditions; improved
mapping functions may be required to transfer from the zenith to line-
of-sight delays.
Ionosphere. There are small departures from the standard dual band
plasma frequency correction for group delay and phase advance through
the ionosphere. Also, for equatorial and high latitude observations,
particularly those made during very high solar activity, ionospheric
scintillations can be troublesome. The rapid phase variations and
concomitant signal amplitude in the L-band carriers induces tracking
errors in-the tracking loops of some receivers and even loss of lock; on
the other hand, some receivers of more recent design are capable of
tracking signal frequency accelerations of up to several g's, even in
adverse signal conditions, without significant error at the millimeter
level. Code-tracking receivers definitely have a big advantage over
codeless receivers in weakened and highly variable signal conditions.
Consequently, this aspect of the ionospheric problem is likely to
improve greatly, even with the high solar activities expected in the
early l990s, with the advanced receiver designs expected by then. The
other aspect is the departure from the dual frequency correction
resulting from ionospheric density gradients and from the small
corrections in ionospheric refractivity due to the presence of the
geomagnetic field. These effects, which depend on the third and higher
degrees in carrier frequency, can amount to several millimeters at low
elevations during high ionospheric activity. Another error contribution
arises from the residual LCP component of the GPS signal which is about
a factor of four below the RCP component. The propagation velocities of
the RCP and LCP waves differ slightly in a plasma containing a magnetic
field. The rejection of the LCP component by GPS antennas is not
complete, typically 10-20 db lower (in power). As a result errors
relative to the dual band correction up to a few millimeters can result.
Additional modeling based on the dual frequency correction may be
required to reach the millimeter level (Clynch and Renfro, 1982~.
Water Vapor. Water vapor zenith delays range from 5 cm in dry and cold
conditions, upwards to 50 cm in tropical conditions. Water vapor is not
in hydrostatic equilibrium. As a result, in situ meteorological
measurements to infer total water vapor delay can be in error by as much
as 100% of the actual delay; they have fallen into disrepute.
Currently, stochastic modeling and water vapor radiometry-based
calibration are the only viable techniques for dealing with water vapor.
Using the best technology currently available, mix-modeling and/or mis-
calibrating the differential water vapor delay at the geodetic sites
results in expected horizontal baseline errors that range from a few
millimeters to perhaps a centimeter depending on the strategies used, on
the local meteorological conditions, and on the length of the baseline
(Elgered et al., 19881. At these error levels the correlation length
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127
for water vapor is well below 100 km for many regions (Treuhaft and
Lanyi, 1987~. For the vertical component these error levels should be
increased by a factor of three. State-of-the-art water vapor
radiometers have a stability over several hours of about lK in measuring
sky temperature (Jannsen, 1985~. This translates into an accuracy in
zenith delay of about 0.5 cm. Short period stability can be somewhat
better but this is less important for baseline accuracy than long period
stability. Assuming the WVR error can be characterized as a random walk
process with an expected error accumulation of 0.5 cm after four hours
of tracking, one obtains about 3 mm as the expected error in the
horizontal baseline components.
A meteorologically benign region, such as the relatively dry western
U.S. or even a tropical area with a uniform marine layer, would be
characterized by low temporal and spatial variability in water vapor
delay. For these regions, an equally successful approach is to
stochastically model the tropospheric zenith delay as a piecewise
constant random walk or as a first order Gauss-Markov process. The
values of the constants in this time series are adjusted in a batch-
sequential least squares process in which both the transition from one
value to the next and the length of time over which the vertical delay
is held fixed are a priori constrained by the stochastic model. By
judicious choice of the values of the parameters in the stochastic
model, one can obtain baseline repeatabilities that are competitive with
those obtained with WAR calibrations (Herring et al., 1989; Tralli et
al., 1988~. Whether this approach will prevail in less benign
tropospheric conditions with high spatial and temporal gradients such as
those sometimes prevailing at Kokee Park, Kauai is undetermined.
A general consensus remains elusive on strategies for dealing with
the water vapor problem toward achieving 1 mm horizontal baseline
accuracy. A major reason for this is that the variability of water
vapor delay, both spatially and temporally, is not well understood as a
function of locale, season and current meteorological conditions. Of
particular concern is the spectral power of the variability at periods
of roughly a half hour and longer; these are the components that can
partially mimic the signatures of the geodetic parameters in the
tracking data and thus corrupt their estimates. Continuously operating
arrays of GPS receivers, to be discussed later, offer some promise in
developing a data base that should enable one to quantify the spectral
properties of water vapor variability and to develop strategies for
exploiting this knowledge.
Pushing the WVR-based methodology to yield l mm horizontal baseline
accuracies will~be a major technological challenge. To achieve this,
the current dual channel WAR will have to be expanded to several
channels and the sky temperature measurement accuracies improved to
O.1K, a tough requirement. Current WAR system temperatures are several
hundred Kelvins. Future W7R's using HEMT technology will probably
achieve around NOOK, thus, the precision requirement will be around
0.1%. However, the accuracy requirement of O.1K is more stringent
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Representative terms from entire chapter:
horizontal baseline
128
requiring corresponding instrumental and calibration stability over
several hours. Further, the retrieval algorithms for inversion of the
measured sky temperatures to the water vapor-induced path delay, which
involve similar but different integral equations along the line-of-
sight, will have to be greatly improved over current algorithms; they
are likely to become highly dependent on the region and the local
meteorology. Also, mapping functions to map WVR line-of-sight delays to
the local vertical or to the GPS directions will need further
development.
To achieve millimeter-level performance by WVR calibration is going
to be very expensive in the short term. Current W7R's cost around $125K
and that price is likely to go up unless major strides are made in solid
state digital RF systems; that is an ambitious undertaking today at
these relatively high frequencies (20-60 GHz). However, if present
development trends persist in microwave monolithic integrated circuits
(MMIC technology), the mid-l99Os may see virtually all-digital W7R's
including digital sampling at these RF frequencies enclosed in a highly
stable oven that occupies a volume of less than 106 cm; in addition to
costing an order of magnitude less than current designs, it would also
promise an order of magnitude improvement in instrumental stability.
Using a phased array antenna for sky coverage would also improve
performance and reduce cost. Nevertheless, the cost trend for the WAR
is likely to move opposite to that of the GPS receiver technology in the
early 1990s; the current factor of two in their relative unit cost is
likely to grow to ten. Unless their costs can be reduced by an order of
magnitude, WAR systems will not be affordable in large numbers and would
be concentrated mainly at VLBI fiducial and other sites where the
highest accuracy is sought.
While it may be theoretically possible for GPS-based geodetic
systems to achieve millimeter horizontal baseline accuracies with major
capital outlays, as a practical matter we may be mostly limited to
accuracies attainable with the stochastic modeling approach. Stochastic
modeling will reach an impasse at some accuracy level. The short period
(t
129
ANTENNA MULTIPATH
Antenna multipath refers to the perturbation of the received signal
due to the presence of reflective objects in the vicinity of the
antenna. These spurious signals are characterized by additional delay
and usually smaller amplitude relative to the direct signal, and they
contain phase shifts. They combine interferometrically with the main
signal to cause phase and amplitude variations; these are processed by
the receiver and manifest themselves in the measurements as carrier
phase and group delay errors. Thus, both the carrier phase and the
pseudorange measurements are corrupted by multipath, although in
fundamentally different ways. Their manifestation also depends on the
signal processing architecture of the receiver.
Carrier Phase Multipath. Carrier phase multipath depends on the signal
processing scheme used to recover the carrier. For receivers using a
half chip early/late gate correlation approach multipath can arise from
objects up to distances of 450 m for C/A-based recovery and 45 m for P-
code-based recovery. Figure 2 gives an example of multipath in carrier
phase measurements. Here, the plots are the post-fit smoothed residuals
of double-differenced carrier phase measurements of two GPS satellites
from two ground receivers. Ionospheric effects have been eliminated
with dual band measurements. The residuals are shown for two separate
diurnal passes (an arbitrary vertical offset and the siderial period
adjustment in the abscissa are included for illustrative convenience).
The ground receivers were TI-4100s with the standard TI-4100 antenna.
The RMS variation about zero mean is around 1-1/2 cm. Notice the high
degree of diurnal repeatability; the cross correlation function peaks
strongly for a zero time lag.
Multipath in the carrier phase measurements will certainly have to
be dealt with if 1 mm baseline accuracies are sought. It is the long
period spectral components of multipath variability, hence, reflections
from nearby objects, i.e., roughly 1/2 hour and longer, for which one
needs to be concerned. The shorter period components will tend to
average out over several hours of observations and will have little
corrupting influence on the baseline estimates. The high degree of
diurnal repeatability in multipath suggests that a major fraction of it
could be calibrated out by building up an empirical template from a
number of successive passes.: But one would be vulnerable to
1. The Navstar/GPS Joint Program Office has recently announced that it
is considering raising the GPS satellite altitudes about 50 km,
which would increase their period by two (2) minutes. This would
cause the ground tracks to drift westward 1 degree per day; thus,
exact daily repeatability would no longer hold and would be replaced
with an annual repetition. Near exact repeatability might occur at
intermediate intervals but it would involve different satellites.
Although this adjustment breaks an undesirable resonance and results
in improved station keeping; however, it would be unfortunate for
those wishing to calibrate diurnal multipath effects.
130
environmental changes around the antenna site during the intervening
periods between revisitations with a GPS receiver; these could lead to
different multipath signatures and hence, to multipath-induced baseline
errors that are different on the two visitations. Thus, short-term
baseline repeatability over a few days might be an optimistic measure of
long-term repeatability spanning several years of site revisitations.
These considerations also lead one to require standardization and
configuration control of antenna/backplane assemblies over a span of
years because of internal multipath in these systems. Counting on
common mode error cancellations is a dangerous game when the outcome
depends on the stability of two big numbers that are differenced!
Pseudorange Multipath Errors. Multipath error in the pseudorange
depends on the dispersive character of the multipath effects across the
power spectrum of the pseudorange PRN code. Pseudorange measurements
are made by matching local models of the ranging code generated at the
receiver with codes being received from the GPS satellite. In general,
the received signal is a combination of direct and reflected signals
with different delays, phases and amplitudes. The effect of this
combined input is to distort the shape of the correlation function
between the model and received signals. This shape distortion maps into
error in determining the point of maximum correlation and this mapping
function will depend on the particular correlation scheme used by the
receiver. As an example, for a half chip early/late gate scheme, a peak
error of ~5 ns occurs when a multipath signal is present with an
amplitude of 0.1 and an additional delay of ~0.5 chip (1 P-code chip =
97 us) relative to the direct signal. Because the effective
"wavelength" of P-code pseudorange is two orders of magnitude greater
than the carrier wavelengths, the pseudorange mulipath error is
typically a factor of 100 greater than carrier phase multipath error.
An important exception is the case where the reflecting objects are
within 1 carrier wavelength of the receiving antenna. In this case, the
carrier phase multipath is reduced by less than order of magnitude
relative to pseudorange multipath.
Figure 3 illustrates P-code pseudorange multipath effects for a
typical environment using a TI-4100 antenna. The integration time for
the points in this figure is two minutes; thus, thermal noise is an
insignificant contributor to these residuals. Successive daily plots
will attest to these residuals being primarily multipath-induced. RMS
levels for P-code pseudorange typically are in the 1-2 m range for TI-
4100 measurements; in some cases they are worse, even causing loss of
lock; in some cases they are better but rarely, if ever, are they below
50 cm.
Multipath errors need not be anywhere near as high as those in
Figure 3. With proper care in preparing a site with low multipath
environment and with use of advanced antennas and, most importantly,
backplane designs, multipath can be reduced by over an order of
magnitude. Figure 4 shows the multipath level in a recent experiment
131
using a Rogue receiver which has a Dorne & Margolin antenna coupled with
a choke ring backplane designed at JPL (see insert on Figure 4~. These
results are from a single receiver tracking a single GPS satellite whose
elevation with time is also shown. Here, the residuals are plotted in
the form of two-minute points, the nominal output rate of the Rogue
receiver, and also as half-hour running average points. The ordinate on
this plot is the linear combination of P:, L: and L2 that eliminates
both the ionospheric and range delays, where P: is the L1 pseudorange
and L: and L2 are the carrier phase measurements, all expressed in range
units. This linear combination should be constant with time; variations
are measures of multipath, which for this combination is strongly
dominated by that on P:. Also shown are two bands pertaining to
performance specifications that we have placed on our antenna/backplane
development effort. These specifications can in part be described by
the requirement: multipath spectral power shall not cause P-code
pseudorange residuals to exceed 30 cm for all periods of five minutes or
less, nor exceed 5 cm for all periods of 30 minutes or longer. The
latter condition is the most stringent one and the most relevant to
baseline recovery accuracy. Except for very low elevations this test
amply satisfied our long period multipath requirement. Future
innovations on this design are likely to further improve these results.
The particular test shown in Figure 4 demonstrates two points: (1)
dramatic improvements in multipath can be achieved, so that smoothed P-
code pseudorange accuracies below 5 cm appear feasible, and (2) high
frequency multipath, which tends to originate from more distant objects,
can be averaged down to relatively low levels. The very high
repeatability of these residuals on a daily basis (with peak cross-
correlation values well over 90% for this particular experiment) also
suggests an approach for calibrating multipath effects in a stable
environment.
The Utility of Pseudorange. A brief digression on the value of high
accuracy pseudorange would seem to be in order. Most GPS practitioners
make little use of the P-code pseudorange for high accuracy
applications. The reasons for this have been, (a) its relatively coarse
(meter-level) accuracy, primarily because of multipath and partly
because the architecture of the TI-4100 receiver, the standard of the
1980s, through its multiplexing and baseband processing design, resulted
in effectively SNR-limited P-code performance, and (b) the uncertain
future availability of the P-code on the Block II satellites through
possible actuation of the anti-spoofing (AS) function. Receiver
manufacturers have exploited that uncertainty by developing systems for
the civilian market that avoid use of the P-code, using instead the C/A
code to recover L: and various nonlinear detection schemes (e.g., Costas
loops, signal squaring, delay and multiply, code enhanced squaring) to
recover the second harmonic of L2 and in some cases P1, Pa, L1-L2 and P1-
P2. Codeless recovery pays a price in the form of higher SNR-driven
measurement errors, which is particularly significant for the P-code,
and higher thresholds for signal detection and tracking the L2 carrier.
However, receivers of the late 1980s and the l990s are and will achieve
nearly an order of magnitude improvement in SNR performance through
elimination of multiplexing, use of the P-code, use of double sideband
132
in-phase and quadrature processing, lower system temperatures, and
elimination of interchannel biases through all-digital processing.
Moreover, the average received signal strength (C/No) of the P-code
modulation from the Block II satellites may be about 3 db higher.
The DoD has progressively relaxed and/or clarified its position on
the operation of AS over the last several years; its current announced
position is that, except in times of national emergency, AS will be off
except for periods of test and training which would be scheduled
relatively infrequently and announced in advance. The DoD policy on
Selective Availability (SA) is another matter to be discussed later; but
SA does not normally render inoperative the P-code tracking functions of
receivers without decryption capability. However, receivers without
decryption capability (i.e., without the so-called W-chip and the
crypto-keyed information), regardless of whether they are P-code
trackers or not, would not be able to recover the corrections to SA in
real-time.
The discussion earlier suggests that 5 cm differential P-code
pseudorange accuracies or better on 30-minute averages will be
attainable for receiver and antenna/backplane systems that are well-
designed and well-sited, and that it will be largely available to
civilian users. Of what use is this capability given the already very
high accuracy of carrier phase data which would easily be accurate to
sub-millimeter levels if it were not limited by multipath and the
troposphere? A number of applications come to mind.
1. Tracking GPS satellites with dual band carrier phase and 5 cm
pseudorange would yield highly accurate global ephemerides obtained with
far less tracking per pass than is required today. As a rough estimate,
5 cm is about 1 part in 108 on a baseline between two tracking stations
5000 km apart. If the effect of the satellite multipath on baselines of
this length can be controlled or calibrated to 5 cm or better, one would
expect to obtain ephemerides from a global network of GPS tracking
stations that surpass 20 cm in accuracy, a factor of 5-10 better than
today.
2. Carrier phase data that are phase connected, i.e., that have no
cycle dropouts, provide range change information to nearly perfect
accuracy but cannot measure absolute range unless the cycle ambiguities
are resolved. Pseudorange measures absolute range but cannot compete
with carrier phase in measuring range change. This suggests a
synergistic approach (Hatch, 1982~. By combining these data types one
can map a whole time series of pseudorange observations to a common
epoch with nearly perfect accuracy using the continuous and phase
connected carrier phase observations. Thus, all of the pseudorange
observations made over a span of hours can be brought to bear on a
single time point and their errors thereby averaged down. For that
epoch, geometric positioning is accomplished with an effective ranging
accuracy that should be far better than the accuracy of the individual
133
pseudorange points. This quasi-geometric point positioning approach
will have major applicability to tracking from dynamical platforms such
as ocean platforms and buoys, aircraft and spacecraft, and in kinematic
ground tracking. It will also be used for high accuracy orbit
determination of future Earth satellite missions such as TOPEX/Poseidon
which will carry a GPS flight-rated receiver (Yunck et al., 1985~. This
approach obviates the need for extensive dynamical models to generate
the motion of the user platform.
3. It is well known that accurate pseudorange improves the accuracy
of baseline determinations, particularly the east-west component (for
most regions except very high latitudes) (Melbourne, 1985~. Coarse
pseudorange accuracy, e.g., 100 m, provides sufficient accuracy in clock
synchronization so that negligible error is introduced in the ephemeris
look-up epoch. From that level down to 1 m little improvement is
realized. However, for pseudorange accuracy below a carrier wavelength,
baseline accuracy typically improves by factors of 1 to 5, depending on
the component and the situation. This is because with carrier phase
data alone, the baseline estimation process must include the carrier
cycle ambiguities or biases which can typically be estimated to an
accuracy of about 1/2 carrier wavelength or better. In those situations
where it is not possible to exploit the integer character of the cycle
ambiguities and hence to fix their values, introducing pseudorange with
an accuracy that is comparable to or better than the a posterior) cycle
ambiguity accuracy adds significant information bearing on their values;
it aids in breaking the high correlations that tend to prevail between
the biases and the eastern component of the baseline. Figure 5 gives an
example of the effect of introducing pseudorange into the estimation
process with increasing accuracy ranging from no pseudorange to carrier
range, the latter being the case where the cycle ambiguities are exactly
known.
4. Pseudorange can also greatly assist in resolving the carrier
cycle ambiguities. Cycle ambiguity resolution strategies without highly
accurate pseudorange have had moderate success for well designed
networks that contain a range of different baseline lengths. These
techniques have been applied to networks up to about 1000 km in extent
(Blewitt, 1989; Dong and Bock, 1989~. But these schemes usually have
not been able to correctly fix 100% of the cycle ambiguity integers in
any given measurement session mainly because of ionospheric delay and
ephemeris errors. Aiding the ambiguity resolution process with accurate
pseudorange would virtually assure a 100% success rate at all baseline
lengths. It can be shown (Melbourne, 1982) that the cycle ambiguity
integers for L1 and L2 are given by the expressions:
(1) nigh = 4.091*P: - 3.091*P2 - L:
(2) next = 5.091*P~ - 4.°91*P2 - L2
where L and P are the carrier phase (module 2~) and P-code pseudorange
measurements, respectively, all expressed in range units; and ~ is the
134
carrier wavelength. Here, n, P and L may be considered as residuals,
and/or as singly or doubly differenced.
In the absence of measurement errors the left hand side of these
equations are constants with time for a series of phase-connected
carrier phase observations and P-code measurements. This suggests
reducing the effect of measurement errors by averaging this system over
an entire pass to obtain an ensemble mean for (n:,n21; short period
measurement errors (including multipath) will average out, but long
period effects will likely remain. If the long period effects are
sufficiently low, the ensemble mean should lie close to an integer
doublet and hence can be fixed. However, it can be shown that for a
greater than 95% confidence level of picking the correct integer values
for (n',n2), the standard deviation of the ensemble mean must be less
than 1/4 in each component; inspection of the above system of equations
reveals that this is rather ambitious, requiring that the residual
systematic pseudorange errors and averaged down multipath errors must in
aggregate be no larger than about 1 cm. Nevertheless, Figure 4 suggests
that the Rogue receiver/antenna system came close to achieving this goal
in that particular experiment. The ordinate of Figure 4 is merely the
linear combination of Equations (1) and (2) that eliminates P2. There
exists a similar plot for the combination eliminating P: and it shows
comparable performance. One can infer from these two plots that the
uncertainties in the ensemble means for the double differenced versions
of n: and n2 (for white Gaussian distributed errors) would be around 1/3
for this experiment, close but not quite close enough.
Short of an all-out direct assault on the cycle ambiguity problem as
described above, to what other use could accurate pseudorange be made?
Even if the pseudorange measurement accuracy were not quite sufficient
to reliably resolve ambiguities, it certainly would provide a narrow
bound on their possible integer values. This information should improve
the efficiency of current carrier cycle ambiguity resolution techniques.
Also, most techniques first try to fix the value of the difference, n~-
n2, the so-called wide lane cycle integer. This corresponds to a
wavelength of 86 cm and is therefore relatively easier to resolve.
Without P. and P2 the uncertainty in the differential ionospheric delay
limits the reliability of this fixing to baselines or a maximum length
that depends on solar activity, time of day, elevation angles of the GPS
satellites, and geographical location. About 200-300 km appears to be a
typical upper limit for campaigns that have been conducted in the
continental U.S., Mexico and Central America. For receivers that do not
use the P-code to recover L2, but rather, alternative nonlinear
techniques that recover the second harmonic of L2, a wide lane ambiguity
length of only 43 cm results, which is twice as vulnerable to
ionospheric mix-modeling. With the P-code pseudorange the wide lane
ambiguity can be fixed with very high reliability quite independent of
baseline length (Blewitt, 19891. The above cycle ambiguity equations
can be combined to yield
(3) n:-n2 = 0.00652*P: - 0.00509*P2 - Lo + L2
167
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70
60
50
40
30
20
10
COVARIANCE ASSUMPTIONS
\
\
18 GPS CONSTELLATION
2 DEN BASELINES (3 cm)
3 NON-DSN SITES (1 0 cm)
PSEUDORANGE (5 cm)
CARRIER PHASE (0.5 cm)
RANDOM-WALK ZENITH TROP
\
\
\
\
_, ~
5cm
O I ~I ~I I I ~ I I I I L I I I I
0 6 12 18 24 30
TRACKING ARC LENGTH (hrs)
Figure 7. Predicted Accuracy Versus Tracking Time for Recovery of Geocentric Offset in
Reference Frame Using Full 21-Satellite Block 11 Constellation and a 12-Station
Global Tracking Network. See [30] for Additional Covariance Assumptions
169
BROAD COVERAGE IMPROVES SHORT-TERM
GPS ORBIT DETERMINAT10N
SERVES AS AN INTERMEDIATE OBSERVING POINT
BETWEEN WIDELY SEPARATED RECEIVERS
EXTENDS VERTICAL VIEWING GEOMETRY
REDUCES SENSITIVITY TO TROPOSPHERE
,
LEO/ /
~ J
/
/
Figure 8. Utility of LEO in enhancing accuracies of baselines and GPS ephemerides using a global tracking network.
GPS
Or
170
Rogue GPS Receiver Architecture
Signal Flow (L1-C/A only)
ICY
.
B.P
Fiber
B.P
liter
_ >'
DIGITAL BASE BAND DATA
L-BAND
RF data
-
_ DOWN- CONVERTER AC'C'=~.AOI~
11 1~C~11~1
i ~: I'm 1
~_
DSP BOARD
===
_ ~ ~ Cos 0
_ ~
~ Sin0 ~
_ _
F Gen 1 1~l~
Satellite B
Satellite A
~~ =~
~ D
, a, 1 11 ~ Hey. ~
1 thy ~./A A. ~ IN
1/4 ACCUM. CH IP
~VMX BUS ~
| SATELLITE CPU BOARD (68020)
_
~ ~.j: ~_ ~ ~ ~
:
.
REAL TIME CLOCK BOARD .
..
:
NON-VOLATILE RAM BOARD
.
SERIA :'U ~ ~ ::~1 r:5 '~-D
.
~ :::,:::.,.~7
~ \/ME-BUS
| HOST CPU BOAR[) (68020)
TO USER
Fig. 9a).
Rogue GPS Receiver
Architecture. Only the C/A signal
processing is shown. In actuality there are five processing
streams for C/A, L1, L2, Pi, and P2.
171
~ROGUE TO TURBO ROGUE AFTER
C)OWN-CONVERTER
~ _ _ _ ~11~11T
DIGITAL SIGNAL
PROCESOR
_ _ ~ .'
~ _ _ ,___ ~
. ~ _ _
DIGITAL SIGNAL
PROCESOR
11111
Weight : ~ 30 kg
Size : - 0.16 m 3
Power :~ 250 W
Cost : ~ $80 k
it_ ~
IlIt =~
Ill! _ ..'
.''.'2...2..."'.
......
......
....
......
~ ....
......
.....
......
. ....
. .
·:: L I I . ,
TURBO-ROGUE
Weight : ~1 0 kg
Size :~0.02m3
Power :~25W
Cost : ~ $15 k
Fig. 9b). The Rogue to Turbo-Rogue Transition utilizing the DFE chip
for RF down conversion to baseband digital sampling and the
turbo-chip for baseband signal processing.
... ~
172
n
1
| PREAMP |
TYPICAL ANALOG
DOWN CONVERSION
_
FILTER
| NARROW |
~ FILTER ~
~ it'
-
., 1
T .
~-- -l SYNTH ES IZE R |
~ r
- ~1
_
SAMPLER SYNTHESIZER
1
600 MHz BW
FILTER
600 MHz BW@ LBAND
__ ~-
20 MBS SAMPLED DATA TO BASEBAND PROCE' NOR
.,
ANALOG VS. DIGITAL APPROACH
DIGITAL FRONT END
_ .
rim ~
| CHIP ~
FREQUENCY
REFERENCE
Figure 10. Functional Schematic of an Analog Front End for RF Down-Conversion
to Baseband, A/D Conversion, and Digital Sampling. Digital Front End
Eliminates Analog Components that are Expensive and Sources of Error.
/
173
ANALOG RF IN
-
0.1 TO 8000 MHz
600 MHz BANDWIDTH
SAMPLE R
A N D A D
ONVERTER
(ANALOG !
-:~
SAMPLE RATE
SYNTH E SIZER
(ANALOG AND
DIGITAL)
DIGITAL
SINK X
FILTER AND
DATA RATE
RE SUCTION
_ (D IG ITAL)
~ :~'~2'~
PROD E f
CONTROL
. ~
~(DIGITAL' ~
REFERENCE
FREQUENCY
TO 2C0 MHz
SET-UP
PRESENTLY (JAN 1 989)
BEING DESIGNED AND ;6
SIMULATED
a)
. ~
. ~ ~
...................
..... ~ .
..........................
DIGITAL BASEBAND O
10 - 600 MEGA SAMPLES
4 TO 1 0 BIT QUADRATURE
SAMPLES SELECTABLE
COMPLETED DESIGN
PRELIMINARY FA3RlCATION
IN PROCESS
- mom
b)
Figure 11. a) Functional Layout of Digital Front End Chip for Converting RF
Analog to Baseband Digital Samples.
by Photo of Completed Sections of the DEE Chip.
174
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~.-~;~ Or, stat ~ ons
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i In:: i ^1 Beat i u.ns--ALE. T .~01 } ousted
p' ~.~-~ ~.se~ ~r;e ve~-t;~. ~ availabie
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~:i E; i `~ ~ i r, ~ wa ~ er- `~ap c.r- ~ ad ~ omet er
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c =~-~ i de t-`c~mocenec~`s ~ gI ot~1 di stri b~ on
~ Er~har, _e n7~tc`=i ~ ~ ,; ~ i ~ ~ y
cs Geo~,~t ~ ~ ca1 ~tr-e. '~t! ~
c~ r~ed~nda~-,cy ~nd sy~tem ~ el ~=bil ity
~ F ~ ate tector'~ cs ~ '-, new areas
Low Eart:~-, Ori--, tina Soacecraft
5F ~ Trac t: ~ ng lAet wor ~ Cer~ter
Fur~ t i c~n: Oper at ~ c~ns ~' i mp ~ ementat ~ c:~r'
Coo' d~ nat~ ooer-"ti o~-,s
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GF=* l~eteorolcigiccil ~ W'vn' rloct`, rea1-t~rre
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-Lime ~,~-,i. {:or-~ng of r;etwort oerformar~ce
Rea'
Conf i c~urat ~ on a'-id f ac: ~ 1 i t ~ es ~c: ntr~-~l
:~ _
=cista~ni;-,g er~g~neeri'~y "i~d m~i~atenance
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. ·
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f User s ~i.S-'g product, of the Compc~tational Center- as they star~d)
Cor~ti,-,~s t}per~t.~ '~~o .Res~,~.~1 ~ Nor,i tc~s-ed
~ays (~PlfAi Ne~ wol t-s ~1~;~:~> s~ ale'
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7~-~ - e~ser~-. Ji ~ ~ U~ i r~o ~'ract ~ cai ~rs ar:~
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,
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~enter- i:~ic^~;,~ c,~ t.;~ictf;~t' ^~_;~ct(::v reci~, remer~-= G~ for~ resear- ct
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175
T NTEF<~4AT ~ f'~L'f' ~-F'D~SORED
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Limo ~ ~ <-a t ~ or ~ =~ 1 Herr i: e. - ~ or OF ~ ~ -~ h enter ~ ci e
is-, Re'~rer.ce Frc'.~e ,_~-;~-~1
Fur,i-ti Brie:
Off-' or,; d^~ quay itv .or,t:~;j'
~ ~L,; Or-, a,~d d~stributior~
c; F~rc-~mete. esti that i An-'
E;x,;stem desi Or ar~'d Beset.- t:~
~ Tr~~.i,~~ data ,ur-~du~ts +~r Netwc:'rf; ~e -`ter
lo,
0 ~ U ~ ~ 3
So ~ c~t i c~n s
~4cc~ ~ate wFS ---te} 1 ~ te ept~em=r ~ des ,'~. ~! F'~m-~Ocrr' or better
Tr~c'.ir~g stat ic~r-' loc^tior,~. s;ite ~p~cif i :: infor~n~tic~n
lEr - c [; ~ ~ ~ ~ =t ~t i ;;:~, . ~ e l oc ~. t ~ e~ ' F: 1 ~ ~ ~ '~ ec t c:,n i
Gewc=~-,tr i~ he, er£,~ e ~r a,~.e
o Eartl-, orienta' ton (pol~r `~'uti or ~ 1}11-}17~ r a+~:,
GI ;~1 so] ut ~ c,;-~s ~r~d f u1 ~ c~c,~ ar ~ ar-~e
r ch ~ ved dat~
~ Hi gl~' ctetcsl ~ ty ~Fa norroa, pc'~ r,ts
;a Raw tr-opospher e ca i br- at i on dat~
0 Der ~ed tr-opc; ~,~-~er i~ path! de1 ~y c: c~rr ect ~ or~=
IEF
176
1.0
4
0.01 9
4
2
0.001
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1, 1 1
6 t / / ~
, ,
3 _ AN/ / _
2 / / ~(n)/csk(n)
0.1 4: /
=o 3t / / ~
Pr / / ~
1 1/1 1 1 1 1 1 ~ 1 1 1 1 1 1, 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 10 20 30 40 50
60 70
1 000.0
100.0
10.0
AN
(cm)
1.0
0.1
0.01
Figure 13. Predicted Gravity Recovery from GP-B Using a TOPEX/Poseidon Class GPS Flight Receiver
in Conjunction with a GPS Global Tracking System. Mission Duration is 6 Months. aLn)
is Based on Combined Tracking and A Priori Kaula Model Information. ok~n) is Based on
Kaula Model.
176
1.0
4
0.01 9
4
2
0.001
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1, 1 1
6 t / / ~
, ,
3 _ AN/ / _
2 / / ~(n)/csk(n)
0.1 4: /
=o 3t / / ~
Pr / / ~
1 1/1 1 1 1 1 1 ~ 1 1 1 1 1 1, 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 10 20 30 40 50
60 70
1 000.0
100.0
10.0
AN
(cm)
1.0
0.1
0.01
Figure 13. Predicted Gravity Recovery from GP-B Using a TOPEX/Poseidon Class GPS Flight Receiver
in Conjunction with a GPS Global Tracking System. Mission Duration is 6 Months. aLn)
is Based on Combined Tracking and A Priori Kaula Model Information. ok~n) is Based on
Kaula Model.
