A balloon-borne experiment, flown at 30 km altitude over New Mexico, was used to test dynamic differential Global Positioning System (GPS) tracking in support of gravimetry at high-altitudes. The experiment package contained a gravimeter (Vibrating String Accelerometer), a full complement of inertial instruments, a TI-4100 GPS receiver and a radar transponder. The flight was supported by two GPS receivers on the ground near the flight path. From the 8 hour flight, about a forty minute period was selected for analysis. Differential GPS phase measurements were used to estimate changes in position over the sample time interval, or average velocity. In addition to average velocity, differential positions and numerical averages of acceleration were obtained in three components. Gravitational acceleration was estimated by correcting for accelerations due to translational motion, ignoring all rotational effects

Evans, Alan G.

Lazarewicz, Andrew R.

English

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\GPS-Alded Gravlmetry at 30_Km Altitude from a Balloon-Borne platform _t/
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Air Force Geophysics Laboratory, LWG, Hanscom AFB, MA 01731
ALAN G. EVANS
Naval Surface Weapons Center, K-13, Dahlgren, VA 22448
ABSTRACT
A balloon-borne experiment, flown at 30 Km altitude over New Mexico,
was used to test dynamic differential GPS tracking in support of gravimetry
at high-altitudes. The experiment package contained a gravimeter (Vibrating
String Accelerometer), a full complement of inertial instruments, a TI-4100
GPS receiver and a radar transponder. The flight was supported by two GPS
receivers on the ground near the flight path. From the 8 hour flight, about
a forty minute period was selected for analysis. Differential GPS phase
measurements were used to estimate changes in position over the sample time
interval, or average velocity. In addition to average velocity,
differential positions and numerical averages of acceleration were obtained
in three components. Gravitational acceleration was estimated by correcting
for accelerations due to translational motion, ignoring all rotational
effects.
INTRODUCTION
The primary objective of this flight (named DUCKY II, flown in October
1985) was to test the differential GPS tracking system; the secondary
objective was to improve on the gravity field measurement shown to be
feasible with the previous flight (named DUCKY la, flown in October 1983).
As with DUCKY Ia, a great deal of data were collected, organized, inspected
and analyzed by several different groups. Overall, the flight, data
collection and analysis went very well, but a few problems did complicate
the data analysis sufficiently that the full promise of this experiment was
not fulfilled. Nevertheless, we did succeed in demonstrating GPS tracking
and improving the quality of the gravity measurements from DUCKY Ia.
TEST DESCRIPTION
The principal limitation in high-altitude gravimetry, as concluded from
the flight of DUCKY la, is high accuracy tracking. Since all accelerometers
measure only acceleration and cannot distinguish between gravitational
acceleration and kinematic acceleration, it is critical to add sensors to
aid in separating the two. There are only two known ways in which this can
be done: I) External tracking to directly determine kinematic acceleration;
or 2) Gravity gradiometry to directly detect gravitational acceleration.
External tracking works by measuring position, velocity and acceleration
relative to the tracking device, which is fixed, usually in a non-inertial
frame. We chose external tracking via GPS because it is a lot simpler, and
it has the potential to resolve a few mGal accelerations with available
technology. DUCKY II did have inertial sensors, and when properly combined
with GPS, highly accurate tracking data is possible.
GPS tracking for DUCKY II was accomplished using three DMA versions of
the TI 4100 receivers. One in flight and two on the ground. The two ground
stations were picked to minimize distance between ground receiver and
balloon. For the flight, one ground station was placed at AFGL Det. 1, near
the launch site; and the other was placed on the roof of the Post Office in
Lovington, NM, near the expected landing area. The data from the flight
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receiver' was telemetered and analyzed In real-time, just as the grou_d
statioris; only the hard line was replaced with a radio link.
At the time of flight, GPSwas a pilot program, with only six
satellites in orbit. GPSwill not be a mature service until at least the
late 1980's or early 1990's. WhenGPSis fully operational, this experiment
could be repeated, with good satellite coverage and geometry, from launch to
landing. As GPStime was limited, we intended to put the best coverage at
altitude; future flights will cover the ascent - a time of high interest.
The ascent time covers 25 to 30 Kmof vertical distance, and gravitational
acceleration and gradient data would be most interesting. Currently, we
have demonstrated that this system works.
GPSDATAPROCESSING
The data processing is showndiagrammatically in Figure I. First, a
rough estimate of absolute position was obtained using a KalmanFilter wlth
pseudorangemeasurements. Next, the combined L1 and L2 frequency
pseudorangemeasurementsand change in range from phase measurementswere
combinedto obtain an average estimate of the pseudorange at the first data
time. Here, change in range Doppler measurementswere subtracted from
succeeding pseudorangesfor the entire satellite pass and averaged to obtain
a more accurate estimate of the pseudorangeat the initial start GPS
solution time. Next, the pseudorangevalues were used to obtain the initial
numberof wavelengths betweendouble differenced phase measurements.The
double-differenced phase measurementswere obtained by first differencing
between the two receivers. Then, the phase measurementswere differenced
between two satellites, where for this set of data PRN11 was the reference
satellite. Using data from four satellites (PRNs6, 9, 11 and 12), the
relative position of the balloon was obtained at each 6 second time mark.
This relative positioning procedure corrects the absolute positioning
estimates, discussed above.
The average velocity was determined next using only the very accurate
L1 change in phase measurements. The standard Doppler procedure was used to
obtain change in range values. Using the relative positioning values
obtained above for the correction partials, average position changeswere
estimated over each data interval. Finally, the accelerations, most
importantly the vertical accelerations, were obtained using a basic
numerical difference between successive average velocity values divided by
the time interval. These accelerations represent the acceleration due to
all forces and are represented in the geodetic coordinate frame.
TESTRESULTS
GPSestimates of vertical acceleration were first obtained between the
two static receivers at Holloman and Lovington sites. Here, the Doppler
procedure for obtaining average velocity over a 6 sec interval was used and
numerically differentiated to obtain vertical acceleration. Here, the
estimates had a numerical standard deviation of 39.3 mGals. Whenaveraged
over the 15 minute interval of data available to the two sites (and the
balloon) an error of only 0.087 mGalswas obtained. Even though the
receivers were in a low noise static moderather than a slightly higher
noise low dynamic mode, this is still a very good indication that GPSis
sufficiently precise to obtain accurate gravity estimates.
The GPSdata was then processed for the balloon with respect to both
static sites. However, since Holloman had such a small amountof
simultaneous data with the balloon, only the results of the balloon with
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respect to Lovington are presented. The data wasprocessed as described
above. The relative vertical position as a function of time is presented in
Figure 2. During this time period, the balloon movedwith average
velocities of about 9 m/s in the North direction and about 17.5 m/s in the
East direction. The cyclic vertical motion was due to gas in the balloon
expanding and contracting as the balloon changedaltitude and
correspondingly temperature. Doppler estimates of vertical velocity were
obtained and numerically differentiated to produce the vertical acceleration
given in Figure 3. This can be comparedwith the Vibrating String
Accelerometer (VSA)measurementsgiven in Figure 4.
In order to obtain a gravity value, the 30 kmaltitude of the balloon
trajectory, modeledgravity as a function of height was obtained and removed
from the GPSaccelerations. Also, Eotvos and Earth rotation corrections
were made. A constant value was found for the difference between the
corrected GPSaccelerations and the raw accelerometer measurements. The
value obtained was90 mGal. This value, if all computations were done
correctly, should theoretically be due to the difference between the modeled
gravity and actual gravity at a 30 kmaltitude. However, there appears to
be a bias that has not been accounted for.
SUMMARY
The two flights completed in this program have demonstrated that
gravimetry is possible at 30 Kmaltitudes. Although the original goal of I
mGalaccuracy has not been reached, muchhas been learned from the test.
The key is GPSdifferential tracking, which has been demonstrated with this
flight. The results of the static GPSacceleration estimates indicate that
GPShas sufficient accuracy to obtain satisfactory acceleration estimates.
However, the results of the dynamic high altitude portion of the test
indicate that a bias is in the data. With the information available from
the test, it has been difficult to isolate this bias. That is, the bias
could be in the gravimeter, the gravity model, or computational corrections.
It is recommendedthat further testing be performed in a controlled manner
close or on the Earth's surface to further validate the accuracy of the
GPS/gravimeter procedure. As the GPSconstellation increases in number,
this work will becomemucheasier in planning and scheduling flights. If
and whenthe next flight occurs, we should have good tracking throughout the
ascent and flight; certainly that dataset would be unique as the only
vertical profile over 30 Km.
ACKNOWLEDGEMENTS
Weare indebted to Dr. JamesClynch and others at the Applied Research
Laboratory of the University of Texas at Austin for the collection of the
GPSdata and the time synchronization of measurements. The technical work
of Mr. Ralph Cowle, Mrs. Catherine Rice, Maj Brenda SchiIinski, Dr. Carl
Leyh, Lt Col Pete Carter (all at AFGLat the time), G. Sitzman, L. Miller,
B. Hermann,S. Meyerhoff, M. Holloway, and G Parker (all at NSWC)for their
technical work. Our thanks to Drs. Don Eckhardt and TomRooney (both at
AFGL) for patiently supporting this work through all its crises. Finally,
we thank Amosand Andy for their relentless help and good humor. Without
such support, we certainly would have literally axed the flight payload and
solved all our problems with one fell swoop.
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GPS-aided gravimetry at 30 km altitude from a balloon-borne platform

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