Orbit Determination with NASA's High Accuracy Real-Time Global
Differential GPS System

Ronald J. Muellerschoen, Angie Reichert, Da Kuang, Michael Heflin, Willy
Bertiger, Yoaz Bar-Sever

Jet Propulsion Laboratory, California Institute of Technology

# Biography

*Ron 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 Senior Engineer in
the Orbiter and Radio Metric Systems Group at the Jet Propulsion
Laboratory (JPL), California Institute of Technology. His work at JPL
has concentrated on the development of filtering software for processing
GPS data and the development of wide area differential systems.

*Angie Reichert* received her Ph.D in Aerospace Engineering Sciences
from the University of Colorado in 1999 and currently works at JPL in
the Orbiter and Radiometric systems Group. Her research interests
include spacecraft orbit and attitude determination and GPS multipath
mitigation.

*Da Kuang* received his Ph.D. in Aerospace Engineering from the
University of Texas at Austin in 1995. He joined JPL\'s Orbiter and
Radio Metric Systems Group in 1996. His work has been focused on
analyzing GPS and GPS-like tracking data for precision satellite orbit
determination and precise relative positioning in spacecraft formation
flight.

*Michael Heflin* received a Ph.D. in physics from the Massachusetts
Institute of Technology. He is currently a senior member of the
technical staff at JPL. His work at JPL involves GPS software
development, data analysis, and scientific interpretation. Michael is a
co-patent holder for JPL\'s award-winning GIPSY-OASIS II software
package and has appeared on NBC Nightly News to discuss GPS crustal
deformation measurements in Southern California.

*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 Radio Metric Earth
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.

*Yoaz Bar-Sever* is a Technical Group Supervisor at JPL. He holds a
Ph.D. in Applied Mathematics from the Technion - Israel Institute of
technology (1987) and a Master in Electrical Engineering from the
University of Southern California (1993). From 1987 to 1989 he was a
post-doctoral fellow at the Department of Applied Mathematics at
Caltech. He joined JPL in 1989 where he has been involved in GPS
technology development and its geophysical applications, and where he
currently manages the development of the NASA Global Differential
System.

# Abstract

GPS orbits and clocks are computed in real-time with data from NASA's
global GPS network. The accuracy of the GPS orbits and reference frame
alignment to ITRF'97 is discussed. The dissemination of the global
correction message is over the Internet, and a signal-in-space (SIS) is
provided by America's Inmarsat satellite. The SIS will soon expand for
global coverage with Inmarsat's ASPAC (Asia/Pacific) and EMEA
(Europe/Africa) satellites yielding coverage over the entire globe
between +/-75 degrees in latitude. The inherent latency in providing the
corrections to the user through the geosynchronous satellites is shown
to have little impact on true real-time positioning. Orbit
determination, post-processed but filtered as if in real-time, of a
low-Earth orbiter\'s GPS data using the real-time orbit and clock
products will be presented. Anticipated plans call for uploading the
code to a space-qualified receiver and performing orbit determination
with the GPS differential global corrections as transmitted by the
Inmarsat beams.

# Introduction

Precise onboard knowledge of a space platform's position and velocity is
a critical component for a variety of Earth observing and remote sensing
applications. These missions range from ocean altimeters, laser and
synthetic aperture radar (SAR) mappers, atmospheric occultation
receivers, and multispectral imagers. Orbit accuracy requirements range
from \<1 meter in the case of the space shuttle's SAR mapper (SRTM)
\[*Bertiger et al., 2000\]*, to a few centimeters in the case of TOPEX's
altimetry mission \[*Bertiger et al., 1994*\]. Additionally, accurate
space platform velocities less than a few tenths of a mm/sec are
necessary to extract atmospheric water vapor from GPS occultation
observations \[*Kursinski et al.*, 2000\]. While for many applications,
precise knowledge is not needed in real-time, the ability to achieve
such accuracy autonomously and on-board would allow science instruments
to generate finished products in real-time, ready for interpretation,
with enormous savings in analysis cost.

The scientific and practical appeal of a seamless worldwide positioning
system offering nearly post-processing performance in real-time can not
be overstated. Other navigation, commercial, and safety services, such
as aircraft navigation, geolocation, fleet management, excavation,
search and rescue, that are currently available only in
infrastructure-rich regions, could readily be extended to any part of
the world, with little performance degradation or cost.

Funded by the Earth Science Technology Office under the Advanced
Information Systems Technology Program, we have set out to develop and
demonstrate a GPS-based technology that will enable Earth-orbit
satellites, airplanes, and terrestrial systems to achieve unprecedented
levels of real-time positional accuracy, anywhere and at any time. The
system promises centimeter-level accuracy for applications with largely
predictable dynamics, such as satellites in Earth orbit. For kinematic
applications, such as airplanes and terrestrial vehicles, we currently
can deliver sub decimeter-level accuracies worldwide.

In developing such a breakthrough capability we are leveraging the
significant investment NASA has made in its Global GPS Network (GGN), as
well as the government investment in the Wide Area Augmentation System
(WAAS) technology developed at JPL \[*Bertiger et al., 1999*\]*.*
Although a number of private and government organizations provide
real-time positioning services in localized regions to users on or near
the ground, a global system such as described here, capable of
supporting global space users, has never been achieved.

# System Overview

Our global differential GPS (GDGPS) system is geared toward users with
dual-frequency receivers, which are flown on a wide variety of remote
sensing low-Earth orbiter missions, and are prevalent in science
applications. Having eliminated the ionosphere as an error source, these
users are susceptible to errors in the GPS ephemerides and GPS clocks.
Ground-based users and aircraft still must cope with tropospheric delay
effects. For slowly moving ground-based users, these errors can be
accounted for by estimating a slowly time-varying troposphere parameter.
For aircraft users in flight, barometric pressure observations are
sufficient to model the dry component of the tropospheric delay
\[*Muellerschoen et al.*, 1999\].

Accurate global corrections to the broadcasted GPS ephemerides and GPS
clocks require a global network of GPS reference sites. We take
advantage of NASA\'s Global GPS Network (GGN) which is operated and
maintained by JPL. The GGN consists of approximately 50 GPS receivers,
mostly operated in batch mode over the Internet. To return data in
real-time, a new software set called Real-Time Net Transfer (RTNT) was
developed. One hertz phase and range observables are returned over the
Internet using User Datagram Protocol (UDP). More than 98% of the data
is returned in less than 2 seconds from sites with good Internet
connections. Currently 25 GGN sites are returning data in real-time to
JPL (see figure 1). The real-time performance and latency of all the
stations in the network can be monitored at
<http://gipsy.jpl.nasa.gov/igdg/demo/>.

The fundamental tenet of our architecture is a *state-space* approach,
where the orbits of the GPS satellites are precisely modeled, and the
primary estimated parameters are the satellite states and clocks. Since
we are estimating real physical parameters, this approach guarantees
that the corrections will be globally and uniformly valid. In contrast,
most differential systems employ a *measurement-space* approach, where
the estimated parameters are range corrections. Positioning error is

![](media/image1.pct)Figure 1.) Network of dual-frequency GPS reference
receivers returning data to JPL in real-time. The current real-time
portion of the GGN network consists of 2 AOA-ACT Benchmarks, 2
Turbo-Rogues, and 21 Ashtech Z-12s. Open circles indicate anticipated
future sites.

dependent on the user's location relative to the reference network.

Additional information on our real-time GPS clock and orbit
determination processes, including estimation of Earth orientation
parameters can be found in \[*Muellerschoen et al.*, 2000\]. On-line
information is available at <http://gipsy.jpl.nasa.gov/igdg>/. A note
worthy difference with the prior reference is the size of the 1 hertz
global differential correction message. The message to the user has been
reduced from 560 bits per second to 224 bits per second and at the same
time the resolution of the clock and orbit corrections has doubled from
1/64 to 1/128 meters.

Current operations are automated and 24/7 at JPL. Down time due to
occasional network issues and building maintenance does occur however.
To support continuous and reliable system operations, an operations
center is being set up in a secure environment with continuous system
administration support. The center will be configured with multiply
redundant computers, backed up by uninterruptible power supplies.

# Communicating the Corrections

The differential corrections produced at the central processing center
are optimally packed to allow for efficient relay to the users. The
corrections are packaged into a 28-byte/second message. Each one-second
message contains xyz orbit and velocity corrections for one prn, and
clock corrections for 16 prns. Clock corrections for a second set of 16
prns is transmitted on alternating seconds. IODE ephemeris changes are
held 2 minutes after new IODEs are observed. This allows the user
sufficient time to accumulate the newest broadcast ephemeris message.

The global differential corrections are made available over the Internet
via either a TCP or UDP server running at JPL. Figure 2 represents a
6-hour plot of a non-moving user in Southern California with the 28-byte
per second correction message. The RMS user errors are 5, 3, and 9 cm in
east, north, and vertical, respectively. An ongoing demonstration of
this can be additionally found at
<http://gipsy.jpl.nasa.gov/igdg/all_demos/>.

![](media/image2.pct)**Figure 2.) 6-hour 1-hertz user position error of
a non-moving antenna positioned with the 28-byte per second global
differential correction message.**

An additional dissemination system is being developed together with a
commercial partner, Navcom Technology Inc., a Division of John Deere, to
address the need for global availability of the signal. The system will
transmit the 28-byte/second message on the three Inmarsat geosynchronous
L-band global beams. The three satellites (at 100˚ W (Americas), 25˚ E
(Europe/Africa), and 100˚ E (Asia/Pacific)) provide global coverage from
latitudes --75˚ to +75˚. Currently the 28-byte/second message is
available only on America's Inmarsat. Options for service beyond these
latitudes are currently being investigated, with potential solutions
including satellite telephony, and ground based repeaters.

# GPS Real-Time Orbit Accuracy

Table 1 lists orbit differences of various orbit products for the first
10 days in August 2001. The orbit differences are with respect to JPL
Flinn products, which are precise post-processed orbits which have
accuracies of better than 3 cm RMS \[*Jefferson et al., 1999*\]. In
Table 1, the QL orbits are the JPL quick-look products \[*Muellerschoen
et al.*, 1995\] which are filtered and smoothed post-processed orbits,
available within 12 hours of UTC midnight. The IGU products are the IGS
Ultra Rapid Orbits, available 3 hours after both UTC midnight and UTC
noon. The IGUP products are the predicted part of the IGS Ultra Rapid
Orbits. The RTG products are the GPS orbits computed from NASA\'s
real-time global network. The RTG orbits are also made available on
anonymous ftp at <ftp://sideshow.jpl.nasa.gov/pub/15min>/ every 15
minutes.

As table 1 shows, the RTG orbits are not as accurate as the
post-processed orbits by a factor of 2, but more accurate than the IGS
predicted orbits which are also available in real-time. It is suspected
that the RTG orbits will improve with a more sophisticated GPS solar
radiation pressure model and better tuning of the GPS dynamic
stochastics. Currently the RTG orbits use a simple T20 and T30 solar
radiation pressure model \[*Fliegel, 1992,1996*\], whereas the JPL QL
and Flinn products use a more advanced modeling of the solar pressure
and dynamic partial computation \[*Bar-Sever, 1997*; *Marguis, 2000*\].
After 24 hours of integration, the difference between the two models is
over 4 meters.

+------------+--------------+-------------+-------------+-------------+
| Date       | QL           | IGU         | IGUP        | RTG         |
|            |              |             |             |             |
|            | (JPL)        | (IGS)       | (IGS)       | (JPL)       |
+------------+--------------+-------------+-------------+-------------+
| 01aug01    | 9            | 11          | 28          | 23          |
+------------+--------------+-------------+-------------+-------------+
| 01aug02    | 10           | 11          | 25          | 24          |
+------------+--------------+-------------+-------------+-------------+
| 01aug03    | 11           | 10          | 34          | 25          |
+------------+--------------+-------------+-------------+-------------+
| 01aug04    | 13           | 14          | 91          | 25          |
+------------+--------------+-------------+-------------+-------------+
| 01aug05    | 10           | 10          | 43          | 23          |
+------------+--------------+-------------+-------------+-------------+
| 01aug06    | 21           | 13          | 77          | 26          |
+------------+--------------+-------------+-------------+-------------+
| 01aug07    | 13           | 13          | 45          | 24          |
+------------+--------------+-------------+-------------+-------------+
| 01aug08    | 11           | 12          | 39          | 23          |
+------------+--------------+-------------+-------------+-------------+
| 01aug09    | 18           | 14          | 104         | 26          |
+------------+--------------+-------------+-------------+-------------+
| 01aug10    | 18           | 13          | 152         | 23          |
+------------+--------------+-------------+-------------+-------------+

Table 1.) RMS accuracy of orbit products; units are in cm. The QL and
IGU orbits are post-processed smoothed products which are not available
in real-time. The IGUP (IGS predicted products) and RTG (real-time GPS
orbits) are both available in real-time. The IGUP are predicted orbits,
whereas the RTG orbits are filtered products (no smoothing).

# Alignment to ITRF\'97 Frame

Fixed station coordinates are used to align the real-time orbits with
ITRF'97. Daily frame offsets with respect to JPL Flinn orbits in ITRF'97
indicate WRMS (weighted RMS) agreement of 0.5 ppb for the scale, 1-2 cm
for the X, Y, and Z geocenter components, and 0.6-2 nrad for the three
rotation angles. The scatter of reference frame offsets is small
compared to the orbit precision. Additionally the real-time orbits and
clocks are also used to compute daily point positions for a global
network of 335 ground receivers. The resulting daily repeatability of
point-position estimates for August 2001 is 2 cm east, 1 cm north, and 3
cm vertical. For comparison, 3-cm precise JPL Flinn products produce
daily repeatability point-position estimates around 0.7 cm east, 0.4 cm
north, and 1.1 cm vertical \[*Zumberge et al., 1997*\].

# Latency of Correction Message 

The majority of the data from the GGN network arrives at the central
processing center within 2 seconds of its GPS time-tag. Data with
latencies that are less than 2 seconds are used in computing the GPS
clocks. Older data, up to 6 seconds in latency, are used to compute the
GPS orbits since they are more predictable than clocks due to their
orbital dynamics. Figure 3 demonstrates the latency of the corrections
to the user accessing the corrections with either an Internet connection
or the SIS from America\'s Inmarsat. As the figure shows, the latency of
the correction message with an Internet connection is around 2.5
seconds, which includes the 2 second latency to accumulate the global
data over the Internet at the central processing center, and 0.5 seconds
to process the clock solution. The Inmarsat latency is around 4.0
seconds, which includes the additional 1.5 seconds delay to uplink the
global correction message to the geosynchronous satellite and down to
the user.

![](media/image3.pct)**Figure 3.) Latency of the global differential
correction message is shown for an Internet connection and a SIS. The
1-minute periodic spikes are a consequence of the 1-minute orbit process
running on the same computer as the 1-hertz clock process. A faster
computer will be used when the processes move to the operations
center.**

![](media/image4.pct)Figure 4.) Clock extrapolation error in cm for
message latencies of 3, 6, and 9 seconds. The cs and rb in the legend
represents Cesium and Rubidium GPS clocks, respectively.

# GPS Clock Extrapolation Error

The user must extrapolate the GPS clocks in order to obtain his position
in true real-time. The goal is to minimize this extrapolation error. We
consider 3 scenarios: global differential corrections to the user with
latencies of 3, 6, and 9 seconds. In addition, we factor in the 1/128
meter resolution of the clock correctors in the global differential
correction message. The effective round-off error of the GPS clocks in
the differential correction message is therefore 1/2 of the resolution,
or +/- 0.39 cm. Figure 4 demonstrates how predictable the GPS clocks are
with a linear fit for latencies of 3, 6, and 9 seconds, and with the
resolved clock corrections taken into account. The x-axis in figure 4
represents the number of clock epochs used in the fit.

We have broken up the computation in terms of Rubidium GPS clocks and
Cesium GPS clocks. The first point of each line represents a simple
sample-and-hold strategy. As is evident in the plot, the Rubidium GPS
clocks are less predictable in the very short term. For long term
predictability however (not demonstrated in the plot), the Rubidium GPS
clocks can be better predicted than the Cesisum GPS clocks. For message
latencies to the user of less than 6 seconds, a 10 point linear fit is
sufficient to keep the extrapolation error under 1 cm.

Figure 5 shows the user\'s position error after extrapolating the GPS
clocks 6 seconds and using the 28 byte/second global differential
message. The same time period as in figure 2 is shown and the RMS user
errors are also 5, 3, and 9 cm in east, north, and vertical. As the plot
shows, the clock extrapolation error to real-time adds little to the
user\'s position error.

![](media/image5.pct)

Figure 5.) 6-hour 1-hertz user position error with the 28 byte per
second global differential correction message and after extrapolating
the GPS clocks 6 seconds.

# Champ Orbit Processing with Real-Time Orbit Products

The Champ spacecraft was launched into a near polar, 450-kilometer
altitude orbit on July 15, 2000. It carries the JPL BlackJack GPS
receiver \[*Kuang et al., 2001*\]. In addition to providing
dual-frequency GPS range and phase measurements, the BlackJack receiver
tracks GPS occulting satellites as they set below the spacecraft's
horizon. Water vapor or temperature profiles with respect to altitude
can be recovered by processing the occulting GPS signal. Orbit
determination is performed routinely at JPL to determine Champ\'s orbit
and in particular its velocity, since it's the residual Doppler
signature of the occulting GPS signal that provides the information in
the science profiles.

We will look at two orbit determination scenarios. In each scenario, we
will compare to truth orbits as determined with JPL\'s Gipsy Oasis II
(GOA II). GOA II has a long history in precise orbit determination of
GPS and other spacecraft equipped with GPS receivers \[*Muellerschoen,
1994*; *Bertiger, 1994*; *Gold, 1994*; *Haines, 1995\]*, and in precise
GPS geodetic applications \[*Heflin, 1994*; *Argus, 1995*\]. Precise
post-processing of the Champ data set with GOA II includes both
filtering and smoothing of the data sets. The precise JPL Flinn orbits
and clocks are held fixed and the Champ data is used to estimate its
orbit and clock. The accuracy of the truth orbits is believed to be 5 cm
based on orbit overlaps and satellite laser ranging residuals \[*Kuang
et al*., 2001\]. The two scenarios are:

1.  GOA II will be used along with the real-time GPS orbits and clocks
    instead of the JPL Flinn orbits and clocks. Smoothing will be used
    to optimally determine the Champ orbit and velocities.

2.  JPL\'s embeddable Real-Time Gipsy (RTG) code is used to simulate
    processing as if in real-time. The real-time GPS orbits and clocks
    are used; no smoothing is performed.

## GOA II Post-Processed Smoothed Orbits

Downlinked GPS data from the spacecraft and the availability of the
real-time orbit and clock products allows a user on the ground to
immediately perform orbit determination. We use GOA II to obtain a
globally smoothed solution. Figure 6 shows the orbit difference with
truth orbits for July 4, 2001, and table 2 shows the orbit difference
for other consecutive days in July. Of note in table 2 is that the
velocity accuracies are sufficient to obtain accurate Doppler residuals
for occulting GPS signals.

![](media/image6.pct)

Figure 6.) Orbit error with GOA II using real-time GPS orbit and clock
products for July 4, 2001. The RMS differences with the truth orbit are
14, 10, 9 cm in radial, cross-track, and down-track, respectively.

+---------+--------+---------+---------+---------+---------+---------+
| July    | H      | C       | L       | Hdot    | Cdot    | Ldot    |
|         |        |         |         |         |         |         |
| 2001    |        |         |         |         |         |         |
+---------+--------+---------+---------+---------+---------+---------+
| 04      | 14     | 10      | 9       | 0.22    | 0.17    | 0.14    |
+---------+--------+---------+---------+---------+---------+---------+
| 05      | 12     | 10      | 9       | 0.20    | 0.18    | 0.14    |
+---------+--------+---------+---------+---------+---------+---------+
| 06      | 13     | 9       | 10      | 0.20    | 0.18    | 0.13    |
+---------+--------+---------+---------+---------+---------+---------+
| 07      | 13     | 10      | 9       | 0.20    | 0.17    | 0.14    |
+---------+--------+---------+---------+---------+---------+---------+
| 08      | 13     | 8       | 10      | 0.20    | 0.18    | 0.12    |
+---------+--------+---------+---------+---------+---------+---------+

Table 2.) Radial (H), cross-track (C), and down-track (L) orbit and
velocity accuracies of smoothed Champ orbits with GOA II and using the
real-time orbit and clock products. Units are in cm and mm/sec.

## RTG Filtered Orbits

RTG or Real-Time Gipsy is the real-time equivalent to JPL's GOA II
software set. It was written entirely in C and has been compiled under
Unix, linux, Sun, VxWorks operating systems, and on Macintosh with Code
Warrior. It includes precise orbital dynamic models to support onboard
orbit determination and implements the precise measurement algorithms
present in the GOA II software package. Yet it is fundamentally
different in its architecture since it was designed for real-time
applications and embedded operations.

To test the dynamic modeling and measurement algorithms of RTG, GPS
tracking data for a Champ-like satellite (450-km altitude) was simulated
with GOA II. The data included 1 cm phase noise and 60 cm pseudorange
noise. Force models for the simulation included the JGM3 50x50 gravity
field, solar pressure modeling, and atmospheric drag. GPS orbits and
clocks are assumed perfect. Figure 7 shows less than 2 cm RMS agreement
between the RTG orbit determination and the GOA II truth orbit.

![](media/image7.pct)**Figure 7.) Orbit agreement between GOA II orbit,
and RTG filtered orbit solution with [simulated]{.underline} data from
GOA II.**

The dynamic models used in RTG to process the Champ data set include:

-   EGM96 70x70 Earth gravity field.

-   DTM94 atmospheric drag model and dynamic partial computation.

-   Solar radiation pressure modeling and partials.

-   Solid, ocean, and pole tide contributions to the accelerations.

-   Relativity acceleration contributions from point-mass, geodesic
    precession, and Lense Thirring effect.

-   Once per rev HCL accelerations and partials.

-   Constant HCL accelerations and partials.

    To make optimal use of both the data strength and of orbital
    dynamics, the HCL acceleration partials are modeled in the filter as
    stochastic processes. This method is often referred to as a
    reduced-dynamic technique and has proven successful for other
    low-Earth orbit missions \[*Muellerschoen, 1994*; *Bertiger, 1994*;
    *Gold, 1994*\].

Figure 8 shows the orbit difference with truth orbits for July 4, 2001,
and table 3 shows the orbit difference for other consecutive days in
July. Since the RTG orbits are filtered only products, the first 100
minutes of the orbit differences have been removed.

![](media/image8.pct)**Figure 8.) Orbit error with RTG using real-time
GPS orbit and clock products for July 4, 2001. The RMS differences with
the truth orbit are 25, 14, 21 cm in radial, cross-track, and
down-track, respectively.**

+---------+--------+---------+---------+---------+---------+---------+
| July    | H      | C       | L       | Hdot    | Cdot    | Ldot    |
|         |        |         |         |         |         |         |
| 2001    |        |         |         |         |         |         |
+---------+--------+---------+---------+---------+---------+---------+
| 04      | 25     | 14      | 21      | 0.47    | 0.27    | 0.21    |
+---------+--------+---------+---------+---------+---------+---------+
| 05      | 20     | 13      | 17      | 0.41    | 0.26    | 0.18    |
+---------+--------+---------+---------+---------+---------+---------+
| 06      | 25     | 15      | 21      | 0.46    | 0.29    | 0.22    |
+---------+--------+---------+---------+---------+---------+---------+
| 07      | 23     | 16      | 20      | 0.48    | 0.26    | 0.23    |
+---------+--------+---------+---------+---------+---------+---------+
| 08      | 24     | 16      | 19      | 0.45    | 0.26    | 0.21    |
+---------+--------+---------+---------+---------+---------+---------+

Table 3.) Radial (H), cross-track (C), and down-track (L) orbit and
velocity accuracies of filtered Champ orbits with RTG and using the
real-time orbit and clock products. Units are in cm and mm/sec.

Due to the low altitude of the Champ orbit, rapid changes in the
tracking geometry result in short phase arcs. Short phase arcs also may
be due to receiver problems in this first generation BlackJack receiver.
Figure 9 shows the number of GPS observed by the Champ BlackJack
receiver. These short phase arcs limit the accuracy of kinematic
tracking, and also how much dynamic process noise can be added in the
reduced-dynamic technique. Higher altitude spacecraft and space-borne
receivers that can hold phase-lock longer on the GPS signal will achieve
much better results than shown here.

![](media/image9.pct)**Figure 9.) Number of GPS spacecraft observed by
the Champ BlackJack receiver. Short phase arcs limit the ability of
kinematic tracking and reduces the orbit accuracy possible from
reduced-dynamic orbit determination.**

# Porting RTG to the BlackJack Space-Qualified Receiver

The RTG orbit determination software has been successfully ported to a
Macintosh with a PowerPC G4 processor. It is currently being ported to
the processor used by the JPL BlackJack receiver. The BlackJack receiver
operates on a similar PowerPC 603e chip as the Macintosh PowerPC G4
processor. Two future flight missions for the RTG orbit determination
software include SAC-C in late 2001 and the ST-5 constellation mission
in 2003. On SAC-C, the BlackJack uses an operating system developed
exclusively for the BlackJack receiver. For ST-5 the real-time processes
will run under the Greenhills Integrity operating system
([http://www.ghs.com/products/rtos/integrity.htm](http://www.ghs.com/products/RTOS_home/)l).

## SAC-C

Satelite de Aplicanciones Cientificas-C (SAC-C) is a cooperative mission
between NASA and the Argentine Commission on Space Activities (CONAE).
It was launched on June 8, 2000 and has a design life of 4 years. At an
altitude of 705 km, SAC-C shares an orbit with three other spacecraft:
Landsat 7, EO-1, and Terra. After the RTG orbit determination module has
been ported to the BlackJack receiver and tested on a simulator, it will
be uploaded to SAC-C and operated in real-time in December 2001. State
solutions from RTG, including position, velocity, and clock, will be
stored and relayed to the ground for verification. Although the
BlackJack on SAC-C is not capable of receiving the global differential
correction message from the geosynchronous satellites, uploading the RTG
software to SAC-C will serve as a useful tool for the initial
demonstration of RTG in a real-time flight scenario. Figure 10
demonstrates processing Champ data with no differential corrections.
Similar accuracies can be expected from the SAC-C receiver once the RTG
code has been uploaded.

![](media/image10.pct)

Figure 10.) Orbit error with RTG using broadcast orbit and clocks for
July 4, 2001. The RMS differences with the truth orbit are 120, 100, 180
cm in radial, cross-track, and down-track, respectively. No differential
corrections are applied to the measurements.

## ST-5 

Space Technology Mission 5 (ST-5) is a constellation of three satellites
that reside in a geosynchronous transfer orbit with a perigee of 200 km
and an apogee of 36,000 km. ST-5 is a mission under NASA's New
Millennium Program with its purpose being to validate eight new
technologies. Launch is anticipated in the year 2003. One of these new
technologies is the Constellation Communication and Navigation
Transceiver (CCNT). A CCNT will be placed on each of the three ST-5
spacecraft, and one on the Earth's surface. While GPS is not considered
as one of the technologies to be demonstrated on ST-5, CCNT will be
equipped with a GPS receiver to validate the performance of the
inter-constellation ranging and positioning provided by the CCNT.
Depending on funding, global differential corrections may be available
on ST-5.

# Summary

A global GPS differential system has been developed and a global
correction message is currently available on America's Inmarsat. The SIS
will soon expand for global coverage with Inmarsat's ASPAC
(Asia/Pacific) and EMEA (Europe/Africa) satellites.

It has also been shown that extrapolating the GPS clock for up to 6
seconds due to correction message latency through the geosynchronous
satellite adds less than 1 cm extrapolation error to the user's
measurement. Current message latency through the geosynchronous
satellite is around 4 seconds.

The global GPS differential system yields real-time GPS orbits with RMS
accuracies of 25 cm. Improvements to the GPS orbits are anticipated with
a more advanced GPS solar radiation pressure model.

Using the GPS orbit and clock corrections, an Earth-based user can
expect RMS position accuracy in real-time of better than **10 cm** in
each component.

It has been shown that the system is capable of supporting real-time
low-Earth orbit determination with an **accuracy of 25 cm** using JPL's
RTG software, which contains precise orbital dynamics and an extended
Kalman filter. The accuracy is limited due to the short phase-connected
arcs in the spacecraft data.

The software is being ported to a JPL BlackJack GPS receiver and is
scheduled for upload to the SAC-C spacecraft as it's first in-flight
test in December 2001. With only broadcast ephemeris and clocks, the
real-time orbit accuracy is expected to be better than 2 meters.

# Acknowledgments

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

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