[Ronald J. Muellerschoen]{.underline}, Willy I. Bertiger,

*Jet Propulsion Laboratory, California Institute of Technology\
4800 Oak Grove Drive, Pasadena, CA 91109*

Michael L. Whitehead\
*Satloc, 15990 N. Greenway Hayden Loop\
Suite 800, Scottsdale, AZ 85260*

# BIOGRAPHY

*Ronald Muellerschoen* received a B.S. degree in physics at Rensselaer
Polytechnic Institute and a M.S. degree in applied math at the
University of Southern California. He is currently a Member of the
Technical Staff in the Orbiter and Radiometric Systems Group at the Jet
Propulsion Laboratory (JPL). His work at JPL has concentrated on the
development of filtering software for processing GPS data, real-time GPS
data processing, and development of wide area differential systems.

*Willy Bertiger* received his Ph.D. in Mathematics from the University
of California, Berkeley, in 1976. In 1985, he began work at JPL as a
Member of the Technical Staff in the Orbiter and Radiometric Systems
Group. His work at JPL has been focused on the use of GPS, including
high precision orbit determination, positioning, geodesy, remote
sensing, and wide area differential systems.

*Michael Whitehead* received his Ph.D. in Electrical Engineering from
the University of Florida in 1986. He developed the software that serves
as the backbone for Satloc's wide-area differential system. This
includes clock-filter algorithms, communications, integrity, and user
interfaces. Most of Mike's past work experience has involved a
combination of software, signal processing, and control.

# ABSTRACT

Wide Area Differential GPS (WADGPS) positioning is performed in
real-time during NASA\'s DC-8 AirSAR flights. The goal of the experiment
is to demonstrate absolute positioning in earth-fixed coordinates to
better than one meter in all components in real-time. Results show
dual-frequency real-time RMS (root-mean-square) accuracy in the vertical
to be 50-60 cms with an RMS horizontal accuracy of better than 40 cms.

Augmenting the system with stable Rubidium oscillators both at a
reference ground receiver and on the aircraft allows the user to model
his clock as a predictable process rather than a stochastic white-noise
process. This permits better separation of the clock and vertical
estimates. Results of this experiment demonstrate dual-frequency
real-time RMS accuracy in the vertical to be better than 40 cms RMS.

An important aspect to real-time GPS positioning experiments is
verifying accuracy. Post-processing techniques using only GPS data are
shown to yield truth solutions with an accuracy in all components of
better than 10 cms RMS.

# Satloc's Wide-Area Differential System

Since May of 1997[^1], Satloc has been providing Wide Area Differential
GPS (WADGPS) correction services to commercial users over the
continental United States (CONUS) and parts of Canada and Mexico. Core
software processes of their system were developed at JPL. These codes
additionally serve as a prototype for the Federal Aviation
Administration's (FAA) Wide Area Augmentation System (WAAS) \[1\] being
brought to development by Raytheon \[2\]. These processes provide
real-time estimates of the ionosphere and dynamic GPS orbits, and
one-second GPS clock corrections. Corrections are only needed every 5
minutes for the GPS orbits and ionosphere due to their slower varying
physical behavior.

The source of Satloc's corrections is a network of 15 dual-frequency
Ashtech Z-12 GPS receivers. One-second GPS data is transmitted to two
redundant network control centers (NCCs) over frame-relay communication
links using TCP/IP protocol. One NCC is located in Reston VA, while the
other is in Scottsdale, AZ. Additionally the data stream is also
transmitted to JPL for purposes of development and debugging. At the
NCCs a network of Pentium PCs running Windows NT processes the data and
computes the WADGPS corrections. References \[3\] and \[4\] contain
details of the core algorithms.

These corrections are packaged into a 750 bps data message and then
viterbi encoded to a 1500 bps data stream. This is uplinked to the
American Mobile Satellite Corporation's (AMSC) L-Band communications
satellite where is it is broadcasted in 3 overlapping spot beams over
the United States and parts of southern Canada and northern Mexico.
Reference \[5\] contains additional details of Satloc's NCC operations,
network infrastructure, integrity software, and steps taken to achieve
99.997% availability of their WADGPS signal. In addition, Reference
\[6\] sites Satloc's superior availability in kinematic tests versus
other competing satellite-based commercial systems, including WAAS.

Some of the noteworthy differences between Satloc's WADGPS system and
FAA's WAAS are 1.) network latency is less than 4 seconds versus 6
seconds for WAAS, 2.) clock updates are at 1 second versus \~6 seconds
for WAAS, 3.) 15 stations are used in the Satloc network and only in
CONUS whereas WAAS has a redundant network of 24+ receivers including
Alaska and Hawaii, 4.) to meet stringent availability requirements due
to high integrity prerequisites, WAAS requires two or more Geostationary
satellites to additionally transmit GPS-like ranging tones, 5.) the WAAS
correction signal is 250 bps versus 750 bps for Satloc's signal, both
before viterbi encoding, and 6.) the WAAS corrections are quantized to
1/8 of a meter versus 1/16 of a meter for Satloc's corrections.

# JPL's RTG and RTI SOFTWARE

The software producing the corrections at the Satloc's NCCs is licensed
from JPL. The GPS orbits and the one-second clock corrections are
computed with JPL's Real-Time Gipsy (RTG) software. The ionosphere
vertical delays are computed with JPL's Real-Time Ionosphere (RTI)
software. For redundancy, Satloc developed an alternate one-second clock
process. Common failure modes between the two clock processes are
unlikely because of the independent implementations. Automatic rollover
occurs should the chosen primary process fail.

For the user, Satloc integrated a single-frequency GPS receiver with an
L-Band receiver. The L-Band receiver processes the WADGPS correction
signal and converts it to RCTM Type 1 SC-104. The GPS receiver uses this
differential correction to adjust its measurements to account for errors
in the broadcast GPS orbit and clock, and errors due to the ionosphere.

On the JPL's user side, the RTG and RTI software sets are hosted on a PC
running Linux. Satloc's WADGPS corrections transmitted by the
Geostationary satellite can be directly combined in software with the
measurements from either a dual-frequency Ashtech Z-12 or AOA
Turbo-Rogue GPS receiver, or a single-frequency Ashtech G-12, to compute
the user's position and clock.

For NASA\'s DC-8 AirSAR flights, there is a dual-frequency Ashtech Z-12
GPS receiver along with an L-Band receiver to acquire Satloc's WADGPS
corrections. The receivers are attached to the serial ports of a Toshiba
Tecra PC where the data streams are combined with RTG to compute the
phase center of the GPS antenna located on top of the aircraft.

Extensive use of shared memory and signals are used to communicate among
the different RTG modules hosted on the PC. For example, a GPS data
daemon reads in the byte stream from the GPS receiver and places the
observables into a circular shared memory buffer. Other processes can
read the same data to either write rinex files for subsequent
post-processing, or to compute the user's position and clock with
various options. Multiple user positioning's can be performed
simultaneously, such as dual-frequency versus single-frequency, or with
varying GPS elevation cutoffs of the data. Being able to run different
user positioning processes on the same data sets in real-time allows for
quick debugging and tuning of the algorithms.

# NON REAL-TIME TRUTH SOLUTIONS 

By post-processing the rinex files captured from the PC's shared memory,
a truth solution can be produced to assess the accuracy of the real-time
solutions. For post-processing, JPL's GIPSY OASIS II software (GOA II)
\[7\] \[8\] and precise orbits[^2] and one-second clocks are used to
reduce the data. GOA II has a long history in precise orbit
determination of GPS and other spacecraft equipped with GPS receivers
\[10\]\[11\]\[12\]\[13\]\[14\], and in precise GPS geodetic applications
\[15\]\[16\].

The high accuracy obtainable in the post-processed truth solutions is
the result of 1.) using precise GPS orbits accurate to better than 20
cms RMS, and precise GPS clocks accurate to a few-tenths of a ns, 2.)
robust data-editing algorithms \[17\], and 3.) iteration and smoothing
of the kinematic filtered solution.

On October 16, 1998 AirSAR flight, GPS data was collected onboard the
DC-8 while simultaneously members of JPL's AirSAR group collected 2
hours of GPS data on the ground at Rosamond, CA near Edward's A.F.B.
(Edward's serves as the staging area for the AirSAR flights.) Ground
data was collected with an Ashtech Z-12 receiver, identical to one used
on the DC-8. The purpose of this data was to detect any interference the
AirSAR L-Band radar pulses might have on a typical GPS user. The test
proved negative; no interference was detected. Moreover, the GPS data
collected at Rosamond provided an opportune data set to access the
accuracy of the post-processed aircraft truth solutions.

The strategy to establish the accuracy of the inflight kinematic truth
solution of the aircraft is as follows: First the truth position of the
ground antenna at Rosamond, CA is determined by post-processing with a
stationary assumption and using precise GPS orbits and precise
300-second GPS clock solutions. Next, the location of the ground antenna
is solved for kinematically at a one-second rate, using the same method
and same orbit and clock database that is used to compute the inflight
kinematic truth solution of the aircraft. The scatter in the kinematic
solution of the ground antenna as compared to its static solution should
then represent the precision of the inflight truth solution of the
aircraft, notwithstanding multipath differences between the two
environments. To determine whether aircraft multipath is significant in
the inflight truth solution, ambiguity resolution is performed between
the kinematic solution of the ground antenna and the inflight kinematic
truth solution of the aircraft. If certain conditions are met, then the
accuracy of the inflight truth solution should be within the scatter
that results by differencing the inflight truth solution with the
inflight ambiguity-resolved solution. These conditions are that
ambiguity resolution yields no degradation in the scatter of the
kinematic ground solution, and that the difference between the inflight
truth solution and the inflight ambiguity-resolved solution is
reasonably small.

## Details of the Static Truth Solution

As mentioned, an accurate static solution for the ground antenna is
needed to judge the accuracy of its kinematic solution. Due to
logistics, only 2 hours of data is available to solve for the location
of the ground antenna at Rosamond. It is well known that with 24 hours
of dual-frequency GPS data, the position of a static antenna can be
determined to within 1-2 cms \[18\]. However with only 2 hours of data,
it is not clear what level of accuracy can be expected.

To answer this question, 2 days of data from an Ashtech Z-12 receiver in
Arcata, CA was processed with X hours of data in each arc, at X hour
increments. Table 1 lists the repeatability of the coordinates relative
to its known location. From Table 1, 2 hours of data is sufficient for 3
cm accuracy in horizontal and 4 cm accuracy in vertical. Note that these
are "1-sigma" numbers.

## Details of the Kinematic Truth Solutions

To compute the kinematic solution of the ground antenna, precise orbits
and one-second data from Satloc's ground network are first used to
compute precise one-second GPS clocks. Holding both the orbits and the
solved-for one-second clocks fixed, the one-second ground data from the
GPS receiver at Rosamond is passed through GOA II, kinematically
estimating its position and stochastic clock. The antenna's zenith
troposphere delay is modeled as an exponential function of geodetic
height. It is not estimated since it would correlate strongly with the
vertical component of position. This is in contrast to the static
positioning of the data where the zenith troposphere delay is estimated
as a constrained random-walk. Table 2 summarizes the differences between
the kinematic solution and the static solution.

Table 1. RMS repeatability for X hours of data from a dual-frequency
static GPS receiver.

  ------------- ------------------- ------------------- -------------------
  X             East (cm)           North (cm)          Vertical (cm)

  1 hour        4.3                 2.8                 7.2

  2 hours       2.8                 1.3                 3.7

  3 hours       2.0                 0.6                 2.7

  4 hours       1.2                 0.6                 1.6
  ------------- ------------------- ------------------- -------------------

The mismodeled and un-estimated troposphere delay in the kinematic
solutions is likely the cause of the -7.1 cm mean difference with the
vertical of the static solution. In fact when the solved-for troposphere
delay from the static ground solution is used and held fixed in the
kinematic solution, the mean in the vertical decreases to -3.9 cms. The
substantial 7.8 mean in the East component may be due to using
300-second clocks in the static case versus using the solved-for
1-second clocks with the network data in the kinematic case. When true
IGS quality orbits and 300-second clocks are used in the static
solution, the mean in the East component decreases to 5.8 cms.

Table 2. 2-hours of one-second kinematic position estimates of the
dual-frequency GPS receiver at Rosamond, CA. Difference is with the
static solution.

  -------------- ------------------ ------------------ ------------------
                 mean (cm)          sigma (cm)         RMS (cm)

  East           7.8                1.7                8.0

  North          2.5                1.2                2.7

  Vertical       -7.1               2.8                7.6
  -------------- ------------------ ------------------ ------------------

The same method of kinematically estimating the GPS antenna position at
Rosamond is applied to estimating the position of the GPS antenna on the
DC-8. However, one difference that needs to be accounted for is the
antenna phase wind-up \[19\] of the mobile antenna on the DC-8. In this
case, the x-component of the effective dipole is chosen to lie along the
Earth-fixed velocity vector of the aircraft. The normal to the dipole
plane is in the direction of the velocity crossed with the aircraft's
cross-track direction. For most typical aircraft attitudes, this is a
well defined reference frame.

If the zenith troposphere delay model has similar accuracy for all
altitudes, then the accuracy seen in the kinematic Rosamond solution
should then be the accuracy of the inflight kinematic truth solution of
the aircraft. From Table 2 it is clear that the accuracy in the truth
solutions should be less than 10 cms RMS in all components.

## Building Confidence with Ambiguity Resolution

As an additional measure of confidence in the truth accuracy, the
double-differenced phase ambiguities between the GPS antenna on the
aircraft and the GPS antenna at Rosamond are resolved. The method from
Reference \[20\] is used in which first the wide-lane combinations are
first resolved with a geometry-free approach, and then the narrow-lane
combinations are resolved after applying a precise model to the
observables. Table 3 lists all 18 of the non-redundant
double-differenced phase ambiguities for the two-hour data set.

The Ashtech Z-12 provides high quality code observables, and since the
wide-lane wavelength is 86.2 cms, all the wide-lane ambiguities are
easily resolved to their nearest integer. Deciding whether a narrow-lane
can be resolved is more difficult since the narrow-lane wavelength is
only 10.7 cms. Additional information such as the formal error of the
double-difference estimate, in addition to the difference of the number
from it's nearest integer, is taken into account. A bootstrapping
technique is used to first resolve the obvious narrow-lane ambiguities.
The positions are then recomputed with the resolved ambiguities in
place, and additional narrow-lane ambiguity resolution is attempted. In
the Rosamond/aircraft data, as table 3 indicates, 3 iterations are
required to safely resolve all the double-differenced ambiguities.

Table 3. Double-differenced phase ambiguities between the aircraft and
GPS receiver at Rosamond, CA. Integer nature of the numbers indicate
that the phase ambiguities can be fixed to the nearest integer. After
the 3rd pass, the remaining two computed narrow-lanes are fixed to their
nearest integers.

+-----------------+-----------------+-----------------+-----------------+
| wide-lane       | computed or     |                 |                 |
| (N1-N2)         | fixed           |                 |                 |
|                 | narrow-lane     |                 |                 |
|                 | (N1)            |                 |                 |
|                 |                 |                 |                 |
|                 | 1st pass 2nd    |                 |                 |
|                 | pass 3rd pass   |                 |                 |
+-----------------+-----------------+-----------------+-----------------+
| -4.916          | 19.932          | fixed at 20     | fixed at 20     |
+-----------------+-----------------+-----------------+-----------------+
| -3.943          | -0.672          | -0.801          | fixed at -1     |
+-----------------+-----------------+-----------------+-----------------+
| -14.046         | 40.485          | 40.412          | 40.144          |
+-----------------+-----------------+-----------------+-----------------+
| 5.016           | -22.632         | -22.801         | fixed at -23    |
+-----------------+-----------------+-----------------+-----------------+
| -9.047          | 21.960          | fixed at 22     | fixed at 22     |
+-----------------+-----------------+-----------------+-----------------+
| -19.968         | 55.954          | fixed at 56     | fixed at 56     |
+-----------------+-----------------+-----------------+-----------------+
| -15.006         | 33.321          | 33.198          | fixed at 33     |
+-----------------+-----------------+-----------------+-----------------+
| 24.993          | 34.006          | fixed at 34     | fixed at 34     |
+-----------------+-----------------+-----------------+-----------------+
| -19.991         | 11.373          | 11.198          | fixed at 11     |
+-----------------+-----------------+-----------------+-----------------+
| -10.995         | -12.807         | fixed at -13    | fixed at -13    |
+-----------------+-----------------+-----------------+-----------------+
| -21.992         | 53.450          | 53.198          | fixed at 53     |
+-----------------+-----------------+-----------------+-----------------+
| -26.989         | 76.082          | fixed at 76     | fixed at 76     |
+-----------------+-----------------+-----------------+-----------------+
| 1.994           | 11.470          | 11.198          | fixed at 11     |
+-----------------+-----------------+-----------------+-----------------+
| -2.975          | 34.103          | fixed at 34     | fixed at 34     |
+-----------------+-----------------+-----------------+-----------------+
| -24.026         | 59.267          | 59.198          | fixed at 59     |
+-----------------+-----------------+-----------------+-----------------+
| -28.968         | 81.900          | fixed at 82     | fixed at 82     |
+-----------------+-----------------+-----------------+-----------------+
| -0.998          | 0.757           | 0.906           | fixed at 1      |
+-----------------+-----------------+-----------------+-----------------+
| 2.912           | 10.679          | 10.245          | 9.877           |
+-----------------+-----------------+-----------------+-----------------+

The results of fixing all the double-differenced phase ambiguities and
re-computing the kinematic position of the antenna at Rosamond is
summarized in Table 4. In terms of scatter of the position estimate,
there is significant improvement in the East component. The improvement
in the vertical is inconsequential since the vertical errors are
relatively uncorrelated with the double-differenced phase ambiguities.
The non-zero mean in the East component may in part be due to the
unreliable static estimation of the antenna's actual position as
mentioned above. Note however that these means are still within the
expected "3-sigma" error that a two-hour static data set can be expected
to provide. The mean in the vertical is likely due to modeling the
zenith troposphere delay as an exponential model of the geodetic height
instead of estimating it as a constrained random-walk parameter as in
the static case.

Table 4. 2-hours of one-second kinematic position estimates at Rosamond,
CA after ambiguity resolution with the aircraft data.

  -------------- ------------------ ------------------ ------------------
                 mean (cm)          sigma (cm)         RMS (cm)

  East           8.0                0.7                8.0

  North          0.0                1.2                1.2

  Vertical       -5.4               1.9                5.7
  -------------- ------------------ ------------------ ------------------

Finally, Table 5 summarizes the differences between the aircraft truth
solution and of the aircraft solution with all phase ambiguities
resolved. Note that the aircraft truth solution here refers to the
unresolved solution. It can be argued that the real truth is where all
the ambiguities have been resolved. But to determine the accuracy of the
truth solution, a better truth is needed to compare with. More typically
there is not a secondary receiver in the vicinity of the aircraft that
can be used for ambiguity resolution.

From Table 2 it is argued that the aircraft truth solutions should yield
horizontal accuracy better that 10 cms RMS. The 7.8 cm mean in the East
component and the 8.0 cm mean in East from Table 4, suggest that the
statically determined position of the antenna may be in error. From
Table 5, the horizontal truth accuracy may even be better than 10 cms
RMS.

Table 5. Difference between the aircraft solution with and without all
double-differenced phase ambiguities resolved.

  -------------- ------------------ ------------------ ------------------
                 mean (cm)          sigma (cm)         RMS (cm)

  East           2.1                2.9                3.6

  North          3.4                1.0                3.5

  Vertical       -6.0               4.0                7.2
  -------------- ------------------ ------------------ ------------------

When all phase ambiguities between the ground and the aircraft GPS
antennas are resolved, improvement is seen in the scatter of the
kinematic ground solution. Consequently, the accuracy of the horizontal
components of the aircraft truth solution should be the scatter that
results by differencing the truth solution with the ambiguity-resolved
solution. From Table 5 then, it is likely that the horizontal components
are better than 4 cms RMS.

The same can not be said of the vertical component since it is not very
sensitive to ambiguity resolution. The dominant error in the vertical is
the modeled exponential zenith troposphere delay. At least at
ground-level, from Table 2, the vertical component is accurate to better
than 8 cms RMS. At a flight level of 8.8 kms, the exponential model of
the zenith troposphere delay may be off as much as 10 cms (see
appendix). Some of this mismodeled troposphere delay is absorbed by the
user's clock, and some translates into a vertical bias of aircraft
solution. Pessimistically the expected accuracy of the aircraft's truth
vertical component is greater than 10 cms RMS, but most likely less than
20 cms RMS.

Later AirSAR flights in May and June of 1999, briefly discussed at the
end of this paper, use the external air pressure as input to better
model the zenith troposphere delay in both the real-time and
post-processed solutions. In these cases, the troposphere model is no
longer the dominant error. So again from Table 2, if the external air
pressure is known, the vertical component of the truth solutions should
be accurate to better than 8 cms RMS.

# Accuracy of real-time SOLUTION

Figures 1 and 2 show the 4+ hour flight path of the DC-8 on October 16,
1998. The 680 meter altitude at the beginning and at the end of Figure 2
represents the altitude of the runway at Edward's A.F.B. Figure 3 shows
the vertical difference of the real-time solution with the
post-processed truth solution to be 54 cms RMS. There is a 20 minute gap
in Figure 3 between hours 2 and 3. During this time the GPS pre-amp was
connected to a spectrum analyzer to determine if the L-Band pulses
transmitted by the radar could be detected by the GPS antenna on top of
the aircraft. The last 2 hours which include the racetracks over
Rosamond, CA are used in the above discussed ambiguity resolution
processing. Additionally, Table 6 demonstrates the horizontal accuracy
of the real-time solutions to be from 30 to 40 cm RMS.

## ![](media/image1.wmf){width="3.25in" height="3.25in"} {#section .Figure}

##  {#section-1 .Figure}

## ![](media/image2.wmf){width="3.25in" height="3.25in"} {#section-2 .Figure}

## ![](media/image3.wmf){width="3.25in" height="3.25in"} {#section-3 .Figure}

Table 6. Difference between the real-time aircraft solution and the
truth aircraft solution on October 16, 1998.

  -------------- ------------------ ------------------ ------------------
                 mean (cm)          sigma (cm)         RMS (cm)

  East           18                 22                 28

  North          -29                31                 43

  Vertical       -39                38                 54
  -------------- ------------------ ------------------ ------------------

Reference \[21\] also briefly discusses the results of an earlier AirSAR
flight on June 4, 1998. On this day, the real-time vertical position
error is 63 cm RMS. Both East and North components are less than 30 cm
RMS.

Figure 4 shows the 3.5 hour flight path of the DC-8 on October 22, 1998.
Table 7 lists the RMS difference between the real-time and truth
solutions. In addition to the real-time dual-frequency solution, a
real-time single-frequency solution is also computed. In Figure 5, every
second of the 3.5 hour flight is represented. There are no missed epochs
and no outliers present. The top line of Figure 5 is the 124 cm RMS
vertical error of the single-frequency solution and the bottom line is
the 47 cm RMS vertical error of the dual-frequency solution.

## ![](media/image4.wmf){width="3.25in" height="3.25in"} {#section-4 .Figure}

Table 7. RMS difference between the real-time aircraft solutions and the
truth aircraft solution on October 22, 1998.

  ----------------------- ----------------------- -----------------------
                          dual freq.              single freq.

  East                    15 cms                  30 cms

  North                   35 cms                  49 cms

  Vertical                47 cms                  124 cms
  ----------------------- ----------------------- -----------------------

##  {#section-5 .Figure}

## ![](media/image5.wmf){width="3.25in" height="3.25in"} {#section-6 .Figure}

# SUB 40 cmS RMS vertical accuracy WITH STABILIZED CLOCKS

A receiver's clock is typically modeled as a stochastic white-noise
process. There is a substantial 96% correlation between the clock and
vertical estimates since the partials for both are nearly identical,
particularly for high elevation data. If however the user's clock is
driven with a stable frequency standard, then its clock can be modeled
instead as a predictable process, such as a low-order polynomial. This
allows for separation of the clock and vertical estimates as they
decorrelate over time. Moreover, if the user's WADGPS clock solution is
relative to the WADGPS reference clock, the reference clock too must be
driven by a stable frequency standard.

Before the AirSAR flight of November 13, 1998, Satloc attached a
Rubidium frequency standard to their Ashtech Z-12 receiver in LaJollo,
CA. This receiver, and a backup receiver, are typically steered by an
Hewlett-Packard ovenized crystal oscillator to maintain a near-zero
clock rate relative to GPS time. This is necessary so that the available
dynamic range of the WADGPS corrections relative to the broadcast clock
is not saturated.

Figure 6 shows the precise clock solution at LaJollo, CA relative to a
ultra-stable hydrogen maser at Goldstone, CA. Represented in this plot
is both before and after the installation of the Rubidium frequency
standard. There is brief settling period at turn-on of the oscillator.

## ![](media/image6.wmf){width="3.25in" height="3.25in"} {#section-7 .Figure}

Figure 7 show the stability of the clocks in terms of an Allan variance.
The bottom line in this plot represents the stability of another
hydrogen maser clock at North Liberty, Iowa. With the Rubidium
oscillators, the clocks at the WADGPS reference station and onboard the
DC-8 are stable to a few parts per 1013 for periods on the order of
several tens of minutes.

## ![](media/image7.wmf){width="3.25in" height="3.25in"} {#section-8 .Figure}

With the stable clocks in the system, multiple real-time positionings
with a white-noise clock model and quadratic clock model are performed.
Table 8 shows the difference between the real-time aircraft solutions
and the truth aircraft solution. So as to not over-determine the
coefficients of the quadratic clock model, a small amount of process
noise is added to the quadratic term of the model at each epoch. Results
from this table show sub 40 cm RMS vertical accuracy.

Table 8. RMS difference between the real-time aircraft solutions and the
truth aircraft solution on November 13, 1998.

  ----------------------- ----------------------- -----------------------
                          white-noise clock model quadratic clock model

  East                    27 cms                  33 cms

  North                   32 cms                  26 cms

  Vertical                61 cms                  39 cms
  ----------------------- ----------------------- -----------------------

Figure 8 represents a short 20-minute segment of vertical errors in the
November 13, 1998 solution. The smoother line in this plot represents
the positioning with the quadratic clock model. From this plot it is
evident that in addition to improving accuracy, adding stable clocks to
the system also increases the robustness and smoothness of the
estimates.

## ![](media/image8.wmf){width="3.25in" height="3.25in"} {#section-9 .Figure}

# STATIC GROUND RESULTS, MULTIPATH, anD SMOOTHING

Reference \[4\] demonstrates real-time steady-state few decimeter
position accuracy of static dual-frequency receivers using Satloc's
WADGPS corrections. Furthermore, Figure 9 shows both real-time filtered
and smoothed WADGPS solutions for a static receiver from start-up to 13+
minutes. As evident in this plot, a few minutes is necessary for
convergence of the estimated carrier phase biases. The smooth solution
uses the terminal solved-for carrier phase biases to better estimate the
position of antenna at the beginning of the arc. The few decimeter
steady-state accuracy demonstrated in Reference \[4\], is also
represented in the smoothed solution of Figure 9. In all these static
cases, there is a benign multipath environment of 50-100 cms. Multipath
here is computed as taking the standard-of-deviation of the difference
between the one-second ionosphere-free linear combination of the range
data minus the one-second ionosphere-free linear combination of the
phase data:

2.54 P1 - 1.54 P2 - ( 2.54 L1 - 1.54 L2 )

On the DC-8 aircraft, multipath is typically 2-3 times worse than these
static cases. Consequently the positioning results are expected to be
2-3 times worse until the phase bias estimates have converged. The
position accuracy is particularly worse at the beginning of a data arc.
Figure 10 shows both real-time filtered and smoothed vertical errors
from a recent May 19, 1999 AirSAR flight. The initial non-steady state
vertical accuracy of the DC-8 filtered solution is in fact about 2-3
times worse than the static results, and it requires about 30+ minutes
to reach convergence to the smoothed solution. Since phase breaks are
detected continuously and may occur frequently in an aircraft
environment, the filtered and smoothed solutions have better agreement
towards the end of the data arc; by definition of course they agree
exactly at the end of the arc.

Although smoothing can not be performed in real-time, the RTG smoother
also hosted on the PC running Linux, requires only a few seconds after
the real-time filtered solution is completed to compute a 3+ hour
smoothed solution. For some applications, such as processing SAR data
immediately upon landing, smoothing the real-time filtered solution can
add significant accuracy without waiting for additional data such as
precise GPS orbits and clocks.

## ![](media/image9.wmf){width="3.25in" height="3.25in"} {#section-10 .Figure}

## ![](media/image10.wmf){width="3.25in" height="3.25in"} {#section-11 .Figure}

# Summary

Accurate real-time position solutions have been produced onboard NASA's
DC-8 aircraft using differential corrections transmitted through a
Geostationary satellite. Much of the software used in generating these
corrections is licensed to Satloc by JPL. The differential L-Band
receiver hardware was purchased from Satloc. Other hardware required for
this demonstration is a dual-frequency Ashtech Z-12 GPS receiver for
collecting observables and a laptop computer. The laptop performs
real-time positioning using JPL's Real-Time Gipsy (RTG) software.

Inflight kinematic truth solutions of the aircraft are computed by
post-processing the flight data with precise orbits and precise
one-second GPS clocks. The horizontal accuracy of these truth solutions
are better than 4 cms RMS. The vertical accuracy of these truth
solutions are better than 8 cms RMS if the external air pressure is
known, since it can be used to better model the dry zenith troposphere
delay. If the external air pressure is not known, then the vertical
accuracy of the truth solution may be as worse as 20 cms RMS.

The accuracy of the real-time solutions can be determined by
differencing them with post-processed truth solutions. Results show
dual-frequency real-time RMS accuracy in the vertical to be 50-60 cms
and an RMS horizontal accuracy of better than 40 cms.

Stabilizing the clocks in the system with Rubidium oscillators allows
for better separation of the vertical and clock components. Results of
this experiment demonstrates dual-frequency real-time RMS accuracy in
the vertical to better than 40 cms RMS.

# APPENDIX

In RTG and GOA II, the zenith troposphere delays can be modeled as
exponential functions of geodetic height (h).

![](media/image11.wmf){width="1.4305555555555556in"
height="0.2638888888888889in"}

![](media/image12.wmf){width="1.9027777777777777in"
height="0.2638888888888889in"}

where h is the geodetic height in meters and W(h) and D(h) are
respectively the wet and dry zenith troposphere delays, also in meters.
At typical aircraft altitudes, the wet zenith delay is sub cm and can
therefore be ignored. Moreover, if the external pressure is known, a
more accurate model of the dry zenith delay can be computed by applying
hydrostatic equilibrium equations to a column of dry air. From the ideal
gas law:

![](media/image13.wmf){width="0.7638888888888888in" height="0.125in"}

where P is pressure, V is volume, n is the number of moles, R is the
ideal gas constant 8.31432 joules / degrees K / mole, and T is
temperature in degrees Kelvin. Multiplying both sides by the molecular
weight of dry air M (0.028964 kg/mole) and dividing by the volume, the
density of air can be expressed as:

![](media/image14.wmf){width="1.5in" height="0.2916666666666667in"}

The dry component of the zenith atmospheric delay can be computed by

![](media/image15.wmf){width="1.2083333333333333in"
height="0.6805555555555556in"}

where the refractivity of dry air is given by

![](media/image16.wmf){width="2.5555555555555554in"
height="0.2916666666666667in"}

The hydrostatic equilibrium equation states that

![](media/image17.wmf){width="1.0416666666666667in"
height="0.6805555555555556in"}

where g is the acceleration of gravity. Substituting yields:

![](media/image18.wmf){width="1.3611111111111112in"
height="0.3055555555555556in"}

![](media/image19.wmf){width="3.0555555555555554in"
height="0.20833333333333334in"}

D is now simply a function of the external pressure in millibars; its
units are meters. At an aircraft altitude of 8.8 kms, the atmospheric
pressure outside the aircraft is typically 320 mbar[^3]. The difference
then between this hydrostatic model and the exponential geodetic height
model at this altitude is 10 cms.

# Acknowledgment

The work described in this paper was carried out by the Jet Propulsion
Laboratory, California Institute of Tech­nology, under contract with the
National Aeronautics and Space Administration.

I would like to thank the entire flight crew, pilots, and mission
managers of NASA 817, along with JPL's AirSAR group, particularly Tim
Miller and Walter "Scotty" Skotnicki, for their tremendous assistance.

I would also like to thank George Hajj at JPL for providing the material
for the appendix.

# 

# References

1\. A.J. Van Dierendonck P. Enge. 1994. The Wide Area Augmentation
System (WAAS) signal specification, *Proceedings of ION GPS-94*, Salt
Lake City, UT, September pp. 985-1005.

2\. J. Ceva, "Hughes Aircraft's Architectural Design of the Federal
Aviation Administration Wide Area Augmentation System: An International
System," 48th International Astronautical Congress, Oct. 6-10, 1997,
Turin, Italy, IAF-97-M.6.04.

3\. W. I. Bertiger, Y. E. Bar-Sever, B. J. Haines, B.A. Iijima, S. M.
Lichten, U.J. Lindqwister, A.J. Mannucci, R. J. Muellerschoen, T.N.
Munson, A.W. Moore, L.J. Romans, B.D. Wilson, S.C. Wu, T.P. Yunck, G.
Piesinger, and M. L. Whitehead. 1998. A real-time wide area differential
GPS system, *J. Navigation*, 44(4), 433-447.

4\. W. I. Bertiger, Y. E. Bar-Sever, B. J. Haines, B. A. Iijima, S. M.
Lichten, U. J. Lindqwister, A. J. Mannucci, R. J. Muellerschoen, T. N.
Munson, A. W. Moore, L. J. Romans, B. D. Wilson, S. C. Wu, T. P. Yunck,
G. Piesinger, and M. Whitehead, "A Prototype Real-Time Wide Area
Differential GPS System," ION National Technical Meeting, Santa Monica,
CA, Jan., 1997.

5\. M. L. Whitehead, G. Penno, W.J. Feller, I.C. Messinger, W.I.
Bertiger, R.J. Muellerschoen, B.A. Iijima., A Close Look at Satloc's
Real-Time WADGPS System, *GPS Solutions* Vol. 2, No. 2, John Wiley &
Sons, Inc., pp 46-63, 1998.

6 Gao, Y., Anderson, J., Banadyga, B., Wang, L, Analysis of WADGPS
Services under Operational Conditions, ENGO 500 Final Report, University
of Calgary, April 1999.

7\. F. B. Webb and J. F. Zumberge, (ed.), *An Intro­duction to
GIPSY/OASIS II*, JPL Internal Document D-11088, July 1993.

8\. S.C. Wu, Y.E. Bar-Sever, W.I. Bertiger, G.A.Hajj, S.M. Lichten, R.P.
Malla, B.K. Trinkle, and J.T. Wu. 1990. Topex/Poseidon Project: Global
Positioning System (GPS) precision orbit determination (POD) software
design, JPL Internal Document No. D-7275, March.

9\. http://igscb.jpl.nasa.gov

10\. Muellerschoen, R. J., Lichten, S., Lindqwister, U. J., Bertiger, W.
I., Results of an Automated GPS Tracking System in Support of
Topex/Poseidon and GPSMet, Proceedings of ION GPS-95, Palm Springs, CA,
September, 1995.

11\. Bertiger, W. I., Y. E. Bar-Sever, E. J. Christensen, E. S. Davis,
J. R. Guinn, B. J. Haines, R. W. Ibanez-Meier, J. R. Jee, S. M. Lichten,
W. G. Melbourne, R. J. Muellerschoen, T. N. Munson, Y. Vigue, S. C. Wu,
and T. P. Yunck, B. E. Schutz, P. A. M. Abusali, H. J. Rim, M. M.
Watkins, and P. Willis, GPS Precise Tracking Of Topex/Poseidon: Results
and Implications, *JGR Oceans Topex/Poseidon Special Issue*, vol. 99,
no. C12, pg. 24,449-24,464 Dec. 15, 1994.

12\. Gold, K., Bertiger W. I., Wu, S. C., Yunck, T. P., GPS Orbit
Determination for the Extreme Ultraviolet Explorer, *Navigation: Journal
of the Institute of Navigation*, Vol. 41, No. 3, Fall 1994, pp. 337-351

13\. Haines, B.J., S.M. Lichten, J.M. Srinivasan, T.M. Kelecy, and J.W.
LaMance, GPS-like Tracking (GLT) of Geosychronous Satellites: Orbit
Determination Results for TDRS and INMARSAT, AAS/AIAA Astrodynamics
Conference, Halifax, Nova Scotia, Aug.14-17, 1995 (AIAA, 370 L'Enfant
Promenade, SW, Washington DC 20024).

14\. Muellerschoen, R. J., Bertiger, W. I., Wu, S. C., Munson, T. N.,
Zumberge, J. F., Haines, B. J., Accuracy of GPS Determined
Topex/Poseidon Orbits During Anti-Spoof Periods, Proceedings of ION
National Technical, San Diego, California, January 1994.

15\. Heflin, M.D., Jefferson, D., Vigue, Y., Webb, F., Zumberge, J. F.,
and G. Blewitt, Site Coordinates and Velocities from the Jet Propulsion
Laboratory Using GPS, SSC(JPL) 94 P 01, IERS Tech. Note 17, 49, 1994.

16\. Argus, D., Heflin, M., Plate Motion and Crustal Deformation
Estimated with Geodetic Data from the Global Positioning System,
Geophys. Res. Lett., Vol. 22, No. 15 , 1973-1976, 1995.

17\. Blewitt, G., An automatic editing algorithm for GPS data, *Geophys.
Res. Lett., 17, No 3, pp. 199-202, 1990.*

18\. J.F. Zumberge, M.B. Heflin, D.C. Jefferson, M.M. Watkins, and F.H.
Webb. 1997. Precise point positioning for the efficient and robust
analysis of GPS data from large networks, *J. Geophys. Res.,* 102(B3),
5005-5017.

19\. J.T. Wu, S.C. Wu, G.A. Hajj, W.I. Bertiger, S.M. Lichten, 1991.
Effects of antenna orientation on GPS carrier phase, AAS/AIAA
Astrodynamics Conference, Durango, Colorado, August 19-22, 1991.

20\. G. Blewitt, 1989. Carrier phase ambiguity resolution for the Global
Positioning System applied to geodetic baselines up to 2000 km*, J.
Geophys. Res., vol. 94*, no.. B8, 10187-10203.

21\. Bertiger, W.I., Haines, B., Kuang, D., Lough M., Lichten S.,
Muellerschoen, R., Vigue Y., Wu, S., Precise Real-Time Low Earth Orbiter
Navigation with GPS, ION GPS-98, Nashville, Tenn., Sept 15-18, 1998.

[^1]: ^+^ In April of 1999, OmniSTAR purchased the network from Satloc.

[^2]: ^+^ The orbits and 300-second clocks used in the truth processing
    are JPL's rapid-orbit submission to the International GPS Service
    (IGS) \[9\]. The orbits differ less than 20 cms RMS with the final
    IGS combined solution.

[^3]: ^+^ This number is based on flight information noted on later
    AirSAR flights in May and June of 1999. It is not known what the
    external pressure at 8.8 kms altitude was during the October 16,
    1998 flight.