Journal of Data Analysis and Information Processing, 2013, 1, 46-57 Published Online August 2013 (
Application of Model-Based Data Transmission Techniques
to Gravitational Model Data
Jeremy Straub
Department of Computer Science, University of North Dakota, Grand Forks, USA
Received June 12, 2013; revised July 19, 2013; accepted August 11, 2013
Copyright © 2013 Jeremy Straub. This is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The transmission of scientific data over long distances is required to enable interplanetary science expeditions. Current
approaches include transmitting all collected data or transmitting low resolution data to enable ground controller review
and selection of data for transmission. Model-based data transmission (MBDT) seeks to increase the amount of knowl-
edge conveyed per unit of data transmitted by comparing high-resolution data collected in situ to a pre-existing (or po-
tentially co-transmitted) model. This paper describes the application of MBDT to gravitational data and characterizes its
utility and performance. This is performed by applying the MBDT technique to a selection of gravitational data previ-
ously collected for the Earth and comparing the transmission requirements to the level required for raw data transmis-
sion and non-application-aware compression. Levels of transmission reduction up to 31.8% (without the use maxi-
mum-error-thresholding) and up to 97.17% (with the use of maximum-error-thresholding) resulted. These levels sig-
nificantly exceed what is possible with non-application-aware compression.
Keywords: Spacecraft Communications; Link Budget Reduction; Gravitational Model Data; Gravitational Model Data
Processing; High-Value Transmission; Deep Space Enabling Technologies
1. Introduction
Deep space planetary science missions and those ventur-
ing beyond the solar system are met with a significant
challenge. As a spacecraft journeys away from the Earth,
the power, antenna size and pointing accuracy required,
to transmit a given amount of data in a given amount of
time, increases significantly. While larger spacecraft or
larger, more powerful ground stations are potential solu-
tions to this problem, they are not optimal. The transmis-
sion of raw data, while desirable from a reuse and scien-
tific validity perspective, does not maximize the scien-
tific return for most mission types.
Model-Based Transmission Reduction (MBTR) seeks
to do this. MBTR reduces data throughput via the crea-
tion of a higher-value data product. Model-Based Data
Transmission (MBDT) is the lowest level of MBTR: a
building block for the higher levels. With MBDT, data of
a known level of quality (a maximum discrepancy from
the believed-true value) is transmitted more compactly
via identifying required updates to a pre-existing or co-
transmitted model. Analysis is performed on board the
spacecraft to ensure that the most effective data trans-
mission mechanism is utilized (use of existing model,
co-transmission or raw data transmission), based on that
particular data being prepared for transmission at the
This paper presents the MBTR methodology and re-
views its value. It then presents, in detail, the algorithm
for performing MBDT on gravitational model data and
compares this to the use of MBDT for other data types.
Next, data related to the Earth’s gravitational model is
processed using MBDT and results are presented an ana-
lyzed. Finally, the utility for this technology on board an
interplanetary spacecraft is considered.
2. Background
This paper represents the fusion of four existing areas of
research, which will be discussed in this section. These
include space mission design, Model-Based Transmis-
sion Reduction, MBTR’s Model-Based Data Transmis-
sion component (which has previously been implemented
and demonstrated with image data) and gravitational
modeling (and its associated data products). MBDT for
gravitation modeling combines the MBTR-component,
MBDT, to meet spacecraft communications design needs
for the transmission of gravitational data.
opyright © 2013 SciRes. JDAIP
2.1. Space Mission Needs
Space mission design is the art of balancing competing
needs for limited resources while achieving mission ob-
jectives and operating within mission constraints. For
most spacecraft, budget, volume, mass and schedule are
key constraints [1]. These primary constraints drive sec-
ondary constraints including power limitations (limited
by generation capacity, generally a function of volume)
and link budget (limited by power, frequency and an-
tenna size) restrictions.
Wertz, et al. [1] present a twelve stage mission design
process which flows high-level objectives through re-
quirements and down to system-level design. This proc-
ess is iterative and relies on mission designer ingenuity
and flexibility to create a successful design. Others [2,3]
have proposed similar approaches, with alternate step-
orders and different areas of focus. All, however, share
the immersive approach to mission design.
Communication and onboard processing are key ele-
ments of this mission design process. Communications
capabilities and window availability limits the amount of
data that can be received from the spacecraft, and when it
can be received. A variety of approaches for trading on
board processing time for reduced a communication
needs have been considered [eg, 4-7]. Historically, these
could be subdivided into three categories: loss-causing
compression, lossless compression and removal of ex-
traneous information. Loss-causing compression can
produce a significant reduction in data transmission re-
quirements; however, this is at the expense of quality.
Lossless compression is not able to achieve a high level
of compaction that loss-causing compression can; how-
ever, is suitable for numerous applications that cannot
tolerate the data loss and artificating caused by loss-
causing compression. The removal of extraneous infor-
mation, generally, provides a transmission requirement
reduction benefit commensurate with the amount of in-
formation removed. This category can be very beneficial,
for certain applications; however, is not easily gener-
alizable. All of these techniques require onboard com-
puting resources to be consumed. This requires mass and
volume to be devoted to these subsystems, as well as the
use of power, heat dissipation and other supporting sub-
system capabilities.
2.2. Model-Based Transmission Reduction
The MBTR paradigm has been presented previously
[8,9]. It is a four level approach to reducing the amount
of data that is required to transmit a given amount of
knowledge. Each progressively higher level incorporates
those below it. Each level, thus, requires progressively
more onboard processing capability and produces a data
stream with progressively higher value-per-byte. These
four levels are Model-Based Data Transmission (MBDT),
Model-Based Data Analysis (MBDA), Model-Based
Result Transmission (MBRT) and Model-Based Findings
Transmission (MBFT).
MBDT, the application of which to gravitational data
is the subject of this paper, is the lowest level of MBTR.
With MBDT, a low-resolution data set is utilized as a
model for which a set of updates are created that will
bring it to the higher-resolution level. Ideally, this model
is pre-shared; however, in some circumstances, it may be
effective to co-transmit the model with the update data.
For example, this model may be data remotely sensed
from Earth, prior to mission departure. MBDT is dis-
cussed in greater detail in Section 2.3.
MBDA enhances MBDT by incorporating a new con-
text-aware heuristic for prioritizing data transmission.
While MBDT data might have been prioritized based
upon the magnitude of the variation of the model from
the in-situ collected data, MBDA considers the impor-
tance of the variation, in light of pre-defined heuristics
created based on applicable mission objectives. For ex-
ample, this may include looking for regions of anomaly
and prioritizing these over single large anomalies (which
might be attributable to sensor issues) or looking for cer-
tain patterns of anomaly and prioritizing these.
MBRT considers the scientific thesis that underlies the
mission and prioritizing data for transmission. This in-
cludes considering whether the data provides support or
refutation for each applicable thesis being tested by the
mission, prioritizing the data based upon the thesis that
supports or refutes and by the level of support for refuta-
tion offered by the data. Consideration may also be given,
particularly, to data in a class with limited membership
(e.g., support for thesis without other support).
The top level of MBTR, which provides the highest
value-level Data Products, is MBFT. Under NBFT, the
model of the phenomenon of interest is updated to reflect
conclusions supported by collected data. Assertions made
based upon this revised model are transmitted to control-
lers, along with data that supports the assertions. This
allows controller validation of the proper performance of
the onboard analysis software.
While MBTR offers a significant benefit to planetary
science missions, this is not without cost. This cost is
comprised of two main areas: the requirement for in-
creased onboard processing capabilities (and associated
supporting subsystems) and the loss of raw data for sec-
ondary analysis or validation. This would be particle a
problematic if it was later discovered that the onboard
software was flawed in some way, and its conclusions
cannot be trusted. This risk can be partially mitigated by
causing the spacecraft to retain data for as long as possi-
ble (until the storage is needed for another use), such that
updated software could be used to reprocess the data on-
Copyright © 2013 SciRes. JDAIP
board. Data supporting particularly important conclu-
sions might be stored indefinitely (until the end of the
spacecraft’s useful life).
In [10], it was shown that the MBTR paradigm MFT
technique could be combined with a robotic control ar-
chitecture to produce a multi-robot collaborative data
collection framework. This framework utilizes data fu-
sion techniques to combine data from multiple heteroge-
neous craft with different modes of movement and range-
2.3. Model-Based Data Transmission
MBDT is a technique for reducing data transmission re-
quirements. In [9,11], MBDT was demonstrated to de-
crease the file size of image data. It was shown that
MBDT outperformed common image compression tech-
niques both in cases where a pre-shared model was used
and in cases where co-transmission of the model was
utilized. Unlike most image compression techniques (e.g.,
JPEG) a maximum-possible level of error (and thus a
guaranteed level of quality) was known and could be
relied upon. It was also shown that MBDT could be util-
ized, when updates were co-transmitted with JPEG (or
other) compressed image data to create this guaranteed
maximum level of error. While not considered in [9] or
[11], lossless compression could also be implemented to
compress the model update data, further decreasing the
transmission requirements.
MBDT for image data begins with the acquisition of
high-resolution imaging. This is compared to the lower-
resolution model (created experimentally by reducing the
resolution of the image file) on a pixel-by-pixel basis. A
difference a value for each pixel is obtained (in [11],
black and white imagery was processed). These values
are compared to the minimum guaranteed quality (MGQ)
threshold value. Those exceeding the MGQ are included
in a set of update messages for transmission back to con-
trollers. A low-overhead format for these messages has
been implemented. The update file’s size is compared to
that required to transmit the raw data, as a model that is
particularly inaccurate (or misaligned) may require more
data transmission to correct than the actual data set. The
creation of a co-transmitted model can also be considered,
as in some cases is more efficient to update the low-
resolution model and then supply changes then to pro-
vide changes to a model of limited accuracy. For larger
data sets, model updates could be performed on a re-
gional basis, instead of a global one.
2.4. Gravitational Model Data
Gravitational field data has a multitude of uses in plane-
tary science. This data reflects the local density of the
body, which intensifies are weakens the local gravita-
tional pull. Density data can be used to differentiate be-
tween material types and potentially identify body com-
position and structure.
2.4.1. Use on Earth
Gravitational modeling is used extensively on Earth. It
can be utilized to locate basins of ground water, by those
seeking petroleum, by those that are exploring for natural
resources, to detect geological faults and other hazards or
to detect the internal structure of volcanos [12].
Niu, et al. [13] demonstrate one use for remote-sensed
gravitational field data. They compare gravitational data
from the Gravity Recovery and Climate Experiment
(GRACE) to their Simple Groundwater Model (SIMGM)
which is used as part of a global climate model (GCM).
From this work, they determined that groundwater re-
charge creates a more-wet soil moisture profile and be-
tween 4% and 16% more evaporation than gravitational
free drainage. They attribute this greater evapotranspira-
tion to evaporation from the soil’s surface because it is
Tapley, et al. [14] presents findings derived from grav-
ity modeling performed by the Gravity Recovery and
Climate Experiment (GRACE) spacecraft, which further
demonstrate the utility of a gravity model for under-
standing water flow, on a global scale. In this instance, a
model of known phenomenon was compared to the data
collected by GRACE to identify additional factors that
needed to be accounted for. Tapley, et al. proffer that
water differences represented the largest source of model
and collected-data disparity. This water storage data, the
note, is useful in predicting a plethora of phenomena
including climate change, flooding, weather patterns and
the productivity of agricultural land. The GRACE data
was able to identify very small water-level changes
which effected large bodies of water. The largest varia-
tion was the Amazon basin which varied between 7.7
mm below the average value to 14 mm above it. The data,
they note, had a level of error between 2 and 3 mm, for
features of approximately 600 km in size in 2003 and
1000 km in 2002 (with accuracy increasing due to a
software revision loaded on to the spacecraft). They note
that they found a largely cyclical pattern on a year-to-
year basis with some variations (e.g., the region contain-
ing Africa’s tropical rainforests was found to be drier in
2003 than in 2002). This analysis requires an under-
standing between the interactions of numerous systems
including the atmosphere and ocean. Furthermore, ran-
dom-error-attributable effects must be excluded.
Johnson, et al. [15] discuss their work related to char-
acterizing the Seattle fault in Washington. This fault was
originally identified in 1965 based on the detection of
gravitational data. As late as 1991, additional gravita-
tional data was still being utilized to extend the be-
lieved-scope of the fault (into Elliot Bay). Gravitational
mapping-based work interpreted the fault as a single con-
Copyright © 2013 SciRes. JDAIP
tinuous structure; however, Johnson et al.’s work, based
on seismic reflection, suggests that the fault is more
complex. This, thus, demonstrates the utility of gravita-
tional mapping for fault detection and its limited granu-
larity (requiring refinement from the fusion of in-situ
sensed data, in some cases).
Kauahikaua, et al. [16] proffer that their analysis of
gravitational data has “yielded an unprecedented view of
the substructure of each volcano making up the island” of
Hawai’i. Through this analysis, they believe that they are
gaining a better understanding of how pathways for
magma formed during the process of the formation of
Hawai’i and that future work, based on this data, may
help to understand how seismic energy may be released
and specific causes of large-scale landslides. Kauahikaua,
et al. collected 3300 gravitational measurements over a
1400 × 1400 km area to produce a 250 × 250 km model
of the island, corrected for the effects of the down-
ward-warping of the oceanic crust in the region. They
corrected for known topographic and oceanic features
and produced a 3-d model of the region. Analysis com-
pared a base density of 2300 kg/m3, assigned to above-
water terrain, and 2600 kg/m3, assigned to below-water
terrain, to the higher density (2900 kg/m3) typical of
molten magma and basaltic intrusions. They found the
average density of the island to be approximately 2820
kg/m3. They proffer that this analysis has helped to un-
derstanding the plumbing of the island’s volcanos and
the island’s geologic history.
2.4.2. Use be y ond Ear th
In [17], an outline for a near-Earth asteroid (NEA) inter-
vention mission is presented. NEA intervention can util-
ize several approaches (outlined in [18]). Intervention
strategies include slowly shifting the NEA off of its
Earth-impacting trajectory (either utilizing a NEA-at-
tached propulsion device or gravitational pull of a space-
craft in close proximity), deploying a nuclear charge to
change the momentum and/or break apart the NEA or
causing a kinetic impact to change its trajectory. For
most of these approaches, and to select between them,
characterization of the material composition of the NEA
is required. Additionally, the composition of the NEA
must be known to determine how to best implement in-
tervention strategies which involve close-proximity or
surface operations.
Iess, et al. [19] assess possible structural and material
compositions for Saturn’s largest moon, Titan, using
gravitational field data collected by the Cassini space-
craft. Of Cassini’s over fifty fly-bys of Titan, four were
devoted to gravity field characterization. The gravity
field was measured via tracking the Doppler shift in the
microwave-band transmission from the spacecraft to the
ground. The gravity field was determined via tracking the
spacecraft’s range rate data, which was measured to a
level of accuracy of 7.5 × 105 meters per second. From
this data Iess, et al. theorize about several possible con-
figurations of Titan. They proffer that Titan likely is
comprised of an ice-layer which surrounds a rock core.
They note that there may be an intermediate layer of
ice-rock mixture. They indicate that this data may refute
a previous claim by Zebker, et al. [20], who presumed
that Titan may have frozen at a different altitude from
Saturn than it currently occupies. Iess, et al. note, contra-
dicting this, that Titan’s gravity field closely resembles
that which would be expected from a fluid body.
Smith, et al. [21] combine gravitational and laser al-
timeter data collected by the Mars Global Surveyor
spacecraft to create a model of the seasonal variation of
ice cover on Mars. During the warmer period, much of
this material is in the atmosphere; however, it condenses
back onto the surface of the planet when the temperature
cools. This, Smith, et al. proffer results in an redistribu-
tion of 1/20,000,000 of the planet’s mass on an annual
basis. Using the combined gravitational and laser altime-
ter data, they are able to characterize the density of the
ice formation to 910 ± 230 kg/m3. This, it is noted, is a
higher density than ice on the Earth, despite Mars having
a lesser gravitational pull to compact it. They proffer that
this is an expected result, given the composition of the
CO2 and dust (representing 10 ± 40% of the deposited
mass) ice.
Folkner, et al. [22] seek to determine the polar mo-
ment of inertia for the planet Mars. They proffer that this
value will improve the accuracy of internal composition
models of the planet (constraining the solution set of
possible models) and help to ascertain the amount of
mass that is transferred between the polar ice caps and
the atmosphere. Data from surface-based measurement as
well as Doppler shift data from the Mars Pathfinder and
Viking missions has been utilized to determine a set of
projected values, which are presented by Folkner, et al.
Subsequent work has further refined these numbers.
Zuber, et al. [23] utilize the same gravitational and la-
ser altimeter data collected by the Mars Global Surveyor
spacecraft as [21] to characterize the internal structure of
Mars and project its early history. By comparing the al-
timeter data with the altimeter data, Bouguer gravity
anomalies are identified. These anomalies indicate dif-
ferences in crust thickness and density and the presence
of various features (e.g., volcanos). Based on this analy-
sis, Zuber, et al. proffer that the crust of Mars has an av-
erage thickness of 50 km and a maximum and minimum
thickness of 92 km and 3 km, respectively. They also
note that the density is projected to be 2900 kg/m3. In
addition to generating this basic statistical data about
Mars, the fusion of the two data sources allows a project-
tion about water flows on Mars earlier in the planet’s
history. Underground channels, projected to be about 200
km in width with lengths of thousands of kilometers, are
Copyright © 2013 SciRes. JDAIP
projected to have transported water (in significant quan-
tity) and sediment to northern areas. This sediment is
predicted to have had a role in the northern lowland re-
2.4.3. Data Product Utilized for Testing
The work described herein utilizes the EGM2008 Global
Gravitational Model dataset [24] created by the National
Geospatial-Intelligence Agency. This data product [25]
contains 233,301,600 geoid undulations covering the Earth
as a 1-meter by 1-meter grid (equi-angularly spaced) in
10,801 rows and 21,600 columns. The data values range
from 106.910 to 85.840. For display purposes, these
have been normalized on a 0 to 255 range to produce a
greyscale image. Figure 1 shows a visual depiction of a
partial area (5000 m × 5000 m) of the Earth’s gravita-
tional model. Figure 2 depicts the gravitational model
for the entire Earth. Note that this display is based on the
EGM2008 grid, which skews the actual orientation of the
Earth somewhat (note the fact that most continents ap-
pear at an unnatural angle, for example).
3. Model Based Data Transmission of
Gravitational Model Data
MBDT of gravitational data builds from previous work
[9,11] on reducing data transmission requirements for
image data through the comparison of source data to a
pre-shared or co-transmitted model. The highest level of
reduction is possible with a pre-shared model. For plane-
tary science work (e.g., a mission for data collection to
another planet) this model could be generated from
Earth-based or Earth-orbiting (e.g., a satellite) observa-
Figure 1. Earth’s gravitational model, 5000 × 5000 meter
area, produced from [24].
Figure 2. Earth gravitational model, produced from [24].
tions. This allows the base model, which may be resolu-
tion-limited by the sensitivity of the instrumentation, to
be transmitted over high speed data links. Updates,
which should (presuming accuracy of the initial model,
subject to resolution limitations) be smaller can then be
transmitted over the lower-bandwidth, higher-cost data
link between the spacecraft in orbit of the remote planet.
Some gravity model data is collected via monitoring
spacecraft telemetry from Earth. The projected orbit is
compared to the actual orbit and discrepancies are util-
ized to identify gravitational features of the planet. In this
instance, the gravity model is assembled on Earth, and no
transmission (and thus transmission bandwidth reduction
technique) is applicable. To attain the highest possible
data, however, multiple orbital craft have been deployed.
GRACE [14] demonstrated this technique in Earth orbit;
GRAIL [26] demonstrated this same approach for gravity
mapping of the moon.
For Earth observation purposes, the data link is not as
large of an issue for pristine-class spacecraft (e.g., typical
large missions like GRACE); it may still be for small
spacecraft (such as those utilizing SmallSat and CubeSat
form factors). The MBTR technique can be used, for
these missions, to prioritize data for transmission, based
on the size of the discrepancy from the model and to cre-
ate a data product with a known maximum level of error,
without having to incur the costs to transmit and store a
high resolution model. This may be particularly impor-
tant for ad hoc users of the data (e.g., users in the field).
A basic algorithm implements the process of deter-
mining what the most effective way to transmit the data
is. Figure 3 depicts this MBDT decision-making algo-
rithm for gravitational data. It makes the decision as to
whether to transmit no data, model-updates, the model
combined with updates or the raw data based on the tar-
get resolution, the correlation of the higher-resolution
data with the model and the communications bandwidth
3.1. Transmission with Pre-Existing Model
MBDT update messages are utilized to make minor cor-
rections to a model. If the model is pre-shared (e.g., col-
Copyright © 2013 SciRes. JDAIP
Copyright © 2013 SciRes. JDAIP
Targ etRes olution
Th reshol d
NoDa taInExcessof
Minimu mDifferenc e
Proje ctedorLow
Tr ansmissionCostof
La rge rthanData
Ev a luateData
Correlati onwith
CreateMo del
Val idati onMessage,
Tr ansmission
Message,Tra nsmi t
CreateMo del
SufficientCapabili ty
Prioritiz eData
fo rTr ansmi ssion
Figure 3. MBDT decision model for gravitational data processing.
lected on Earth and pre-loaded onto the spacecraft before
launch), then only updates are required to be sent. Model
updates, conceptually, can be either single-value or re-
gion-based. The work described herein only utilizes sin-
gle-value updates, as the model is well-aligned (due to
being derived from the high-resolution source data that it
will be compared to). Region-based updates are used to
correct a large area of data that is significantly different
than the model to allow this to be performed as one large
bounded update that can be overridden by one or more
single-value updates.
3.2. Co-Transmission with Model
If a model is not available to be pre-shared or the model
turns out to be highly inaccurate, an alternate (but not as
efficient) MBDT process can be utilized to minimize
transmission requirements. In this instance, a low-reso-
lution model is created based on the target-resolution
data and is transmitted with the update messages. The
updates are then applied to the model at the destination.
In some cases, this will require less data transmission
than transmitting the raw data. Both the low-resolution
model and the update messages can, generally, benefit
from similar compression techniques as could be applied
directly to the raw data, and thus outperform the ap-
proach of simply compressing the model. As shown in
Figure 3, the efficacy of using this approach to reduce
transmission requirements is validated before transmis-
sion (to ensure that transmitting the raw data wouldn’t be
more efficient).
3.3. Maximum Error Thresholds
In many cases, small errors in data are unimportant to a
given application. For example, a small deviation in a
graphic file may not create a perceptible (or applica-
tion-relevant) difference to the image. A small deviation
in a topographic data file will, in many cases, have no
impact on the routing of an aircraft. While these small
errors may have no relevance to a particular application,
they can create a significant number of update messages.
A maximum error threshold approach ignores error levels
below the threshold by not transmitting update messages
for them. This work implements a maximum grid-loca-
tion-difference approach. However, thresholds can be
implemented on a regional as well as local basis (corre-
sponding to the triggering or suppression of regional and
local updates).
4. Data Format
The data format, for gravitational data, is derived from
the format used for image data in [9,11]. As with this
prior work, the update message includes a message
header, a section header and section data. The same data
segmentation method is utilized; this avoids requiring
several bytes of location information for each grid loca-
tion change (which would be required if all changes were
defined in a global-to-image context). Due to the utiliza-
tion of the same format, interoperability between differ-
ent data types is possible. This is important for higher
levels of MBTR which require the analysis of multiple
data types in order to derive and validate high-value con-
4.1. Header
The header format is exactly the same as used in [9,11].
The header consists of five fields: craft identification,
transmission identification, sequence number, time/date
stamp and validation.
The craft identification field is a locally unique value
that identifies the source craft. This field is utilized for
identifying the collecting (or processing) craft when one
craft relays for another. Data products produced via
processing and analysis of data from other craft stamp
the message with their own ID. Validation data (allowing
ground controllers to verify correct functionality of the
processing routines) retains the craft identifier of its col-
lecting craft.
The transmission identification field has two key pur-
poses: it identifies the transmission (uniquely to an im-
plementation) and it identifies the data type and target of
the data. The format of this field is not strongly defined,
allowing it to be utilized in the most effective manner for
each implementation (based on the number of expected
targets, transmissions and data types).
The sequence number field is used to identify the order
of messages that relate to a given target (based on a
common transmission identification field value). This
field is particularly important if area-level changes are
made, as the order of application (e.g., the area is applied
first and then the individual values) is important.
The time/date stamp field is utilized to store the date
and time that data is collected at or a processed data
product is produced. The validation field, which is op-
tional, stores a checksum or hash value that can be util-
ized to ensure that no changes (e.g., due to transmission
errors or otherwise) have affected the message. Many
lower-level protocols will provide this service, rendering
this field unneeded in those instances.
4.2. Section Header
The section header identifies the location of the section
within the data set. Each section is 256 × 256 grid coor-
dinates. This allows single-byte (28 × 28 = 65,536 grid
locations) to be used for each of the X and Y coordinates
within the section, decreasing file size. The section
header includes its own X and Y location, within the lar-
ger data set. These values are stored in 5-byte fields. A
2-byte field is used to identify the length of the section.
4.3. Section Data
The section data format is data type-specific; however,
the format used for gravitational data is structurally
similar to the format utilized for image data in [9,11].
Like with image data, two prospective addressing
schemes can be utilized. The first includes a coordinate
set (x and y) for each correction. The alternate, which is
preferable if it is believed that lines will have an average
of one or more corrections, includes an entry for each
line in the data set. Lines are delimited with a set of all
zeros (an x-coordinate of 0, correction value = all zeros).
4.4. Encapsulation into Lower-Level Data
Neither MBTR or its MBDT component defines low-
level transmission procedures. In terms of the OSI Model
(see [27]), the entire MBTR process (including the
MBDT work described herein) operates at the application
layer (layer 1). However, it must make use of lower-level
services (layers 2 - 7) to transmit data, as required. The
protocol utilized will vary by application. For space ap-
plications, protocols such as the Space Data Link Proto-
col (CCSDS 132.0-B-1) [28] and the Space Packet Pro-
tocol (CCSDS 133.0-B-1) [29] are recommended stan-
dards. MBTR and MBDT are also useful for aerial and
surface robotics applications; applications in these me-
diums will (particularly if not communicating with space
assets, as discussed in [10]) generally utilize alternate
communications protocols.
5. Experimental Design
A five-phase experiment has been conducted to validate
the efficacy of MBDT approach for use with gravita-
tional model data. These phases include 1) measuring the
transmission requirements for a selection of the raw data;
2) measuring the transmission requirements when ZIP
(DEFLATE/RFC 1951 [30]) compression is utilized; 3)
applying and measuring transmission requirements when
the MBTR approach is utilized; 4) applying and measur-
ing transmission requirements when the MBTR approach
Copyright © 2013 SciRes. JDAIP
incorporating a maximum-error threshold is utilized; and
5) applying and measuring transmission requirements
when the maximum-error threshold MBTR approach is
combined with ZIP compression.
5.1. Transmission Requirements for a Selection
of Raw Data
The first phase of the experiment, the control condition,
will involve characterizing the data transmission re-
quirements for the raw data. A 5000 × 5000 grid location
section of data will be selected from the global model,
shown in Figure 2. The size of this file is compared to
the data generated in phases two through five.
5.2. Transmission Requirements with ZIP
The second phase of the experiment tests a simple ap-
proach to reducing transmission requirements: compres-
sion. In this instance, the common ZIP format is utilized
with DEFLATE/RFC 1951 [30] compression. Numerous
compression techniques, which do not require or rely on
knowledge of the underlying data, exist. Their compari-
son is beyond the scope of this work. It is important to
note, however, that any compression technique will in-
volve a trade-off between onboard resources required for
compression and decreased transmission requirements.
Thus, the selection of a particular compression technique
requires a knowledge of the computer system (e.g., the
onboard computing system of a spacecraft or UAV) that
it will be running on. Comparing computational require-
ments for MBDT versus conventional compression tech-
niques represents a potential focus for future work.
5.3. Implementing the MBDT Approach
Phase three tests the MBDT approach to reducing gravi-
tational data transmission requirements. In this phase, the
pre-shared model and model-plus-updates approaches
(described in Sections 3.1 and 3.2) are compared, with
multiple model resolution levels (of 5%, 10%, 25% and
50% of the high-resolution version). These eight experi-
mental conditions are compared with each other in terms
of the resulting size of the data to be transmitted. Note
that all of these approaches will result, when the updates
are integrated back into the model, with the same
high-resolution data as the original.
5.4. The MBTR Minimum-Error Threshold
As discussed in Section 3.3, in many cases limited error
is acceptable. Phase four tests the value of accepting dif-
ferent levels of error in further reducing transmission
requirements. Maximum acceptable error (MAE) thresh-
olds, the maximum amount of difference allowable (rep-
resented as a percentage of the total range of possible
data) between the high-resolution imagery and the result
of combining the model with a set of updates are thus
incorporated. MAE levels of 5%, 10% and 25% are
tested in conjunction with model resolutions of 5%, 10%,
25% and 50% of the high-resolution data. Data is col-
lected for both pre-shared and co-transmitted model ap-
Comparing the resulting transmission requirements
across these 24 experimental conditions is, however, not
valid, as the data products are of substantially different
levels of quality. In [11] a metric for combining quality
and file size, image quality as a function of file size
(IQFFS), was utilized. A similar metric will be utilized
for gravitational data: data accuracy as a function of file
size (DAFFS). This metric is defined and named in such
a way as to be applicable to numerous other applications.
IQFFS is, thus, now a special image-data-only case of
DAFFS. The DAFFS metric is derived by dividing the
one minus the average grid location difference value
(AGLDV) by the file size. In the image MBDT work
presented in [11], the file size was represented in 1/10
MB units, so as to keep the numbers within a convenient
range. It is expected that DAFFS metric value units will
vary from application to application and experiment to
experiment, based on the type and size of data that is
being processed.
6. Results
This section presents the results of the experiments de-
scribed in Section 5. This begins with documenting the
size of the base data and the reduction possible with
ZIP-style file compression. Then the MBDT approach is
implemented initially without and subsequently with the
incorporation of a MAE threshold.
6.1. Transmission Requirements for a Selection
of Raw Data
The base data used in this experiment consumes 65,536
bytes of data. This data is depicted in Figure 4.
6.2. ZIP Compression Data
Application of ZIP compression to the entire Earth-cov-
ering gravitational model provides a 3% decrease in file
6.3. MBDT Approach Data
Low-resolution models were created at four different
sizes, comparative to the resolution of the base data: 5%,
10%, 25% and 50%. Note that the model resolution lev-
els are percentages of the height and width (e.g., 5%
means 5% of the base height and 5% of the base width),
not of the total area. Table 1 presents the sizes of these
Copyright © 2013 SciRes. JDAIP
models. Table 2 presents the model size as a percentage
of the base data, for comparison purposes. Note, from
Table 2, that the models are larger than the comparative
surface area, due to file format constraints. Figures 5(a)-
(d) display the models for comparison.
The models that were created (and for which size data
was presented in Tables 1 and 2) were then processed,
comparative to the original, to generate a set of MBDT
updates that, when applied, would make the model ex-
actly the same as the original. Table 3 presents the size
of the models (repeated from Table 1, for ease of com-
parison) and updates. It also presents the combined size
of the model plus the applicable updates. Table 4 pre-
sents this data as a percentage of the base data size.
6.4. MBDT Minimum-Error Threshold
Approach Data
MBDT was next applied with MAE thresholds which
specified a level of error that was acceptable (meaning
Figure 4. Visual depiction of raw data file used for experi-
(a) (b) (c) (d)
Figure 5. (a) 5% model, left; (b) 10% model, middle left; (c)
25% model; middle right; (d) 50% model, right.
that for error at this level or below, no update would be
generated). Table 5 presents the size of the MBDT up-
dates for each model resolution level. Table 6 presents
this data as a percentage of the base data.
In some cases, the model may be of insufficient qual-
ity to facilitate effective updating (e.g., the updates
would be bigger than transmitting the raw data), in others
no a priori shared model may exist. In this case, the
model is transmitted with the updates. Table 7 presents
the size of the base model combined with the updates
required to correct it to the MAE threshold. Note that
when a location is corrected, it is corrected to the exact
value, not to a value that is within the MAE range (as
there is no performance benefit for inexactness). Table 8
presents these values as a percentage of the base data.
The data with updates to MAE specifications, while
not being of the same quality as the original, is of
known-bounded error. This data may be usable for many
Table 1. Model size.
Model Resolution Levels
5% 10% 25% 50%
Model 574 2134 12,342 49,206
Table 2. Model size as a percent of base data.
Model Resolution Levels
5% 10% 25% 50%
Model 0.88% 3.26% 18.83% 75.08%
Table 3. Updates without MAE threshold.
Model Resolution Levels
5% 10% 25% 50%
Model 574 2134 12,34249,206
Updates 72,314 49,392 25,80015,250
Combined 72,888 51,526 38,14264,456
Table 4. Model size and updates plus model as a percent of
base data size.
Model Resolution Levels
5% 10% 25% 50%
Updates 110.34%75.37% 39.37% 23.27%
Combined 111.22%78.62% 58.20% 98.35%
Table 5. Updates with MAE threshold.
Model Resolution Levels
5% 10% 25% 50%
5% 1842 10,204 4320 2304
10% 1278 1440 4320 2296
25% 1278 1278 1296 2296
Copyright © 2013 SciRes. JDAIP
Table 6. Updates as percent of base.
Model Resolution Levels
5% 10% 25% 50%
5% 2.81% 15.57% 6.59% 3.52%
10% 1.95% 2.20% 6.59% 3.50%
25% 1.95% 1.95% 1.98% 3.50%
Table 7. Updates plus model.
Model Resolution Levels
5% 10% 25% 50%
5% 2416 12,338 16,662 51,510
10% 1852 3574 16,662 51,502
25% 1852 3412 13,638 51,502
Table 8. Updates plus model as percent of base.
Model Resolution Levels
5% 10% 25% 50%
5% 3.69% 18.83% 25.42% 78.60%
10% 2.83% 5.45% 25.42% 78.59%
25% 2.83% 5.21% 20.81% 78.59%
applications that can benefit from lower transmission
requirements while suffering the applicable reduction in
data quality. Figures 6-9 present data for the 5% MAE
threshold and the 25% MAE threshold with model sizes
of 5%, 10%, 25% and 50%.
7. Analysis of Results
The data presented in Section 6 demonstrates that ZIP
compression is not an effective solution for compressing
this format of gravitational data. While it is likely that
additional compression (above 3%) is possible with con-
ventional compression techniques, this does not approach
the level of transmission reduction possible with a for-
mat-aware reduction technique, such as MBDT.
MBDT results, without incorporating a MAE threshold,
were able to reduce the data to 58.20% of its original size.
This is a 31.8% reduction in file size, or about ten times
the level of compression possible with the ZIP format.
Incorporating the MAE threshold, MBDT was able to get
the transmission to 2.83% of the base file or a 97.17%
reduction in file size (allowing a MAE of up to 25%,
which may be too large to be suitable for many applica-
tions). With a MAE of 5% (which would likely be suit-
able for most applications), the file size was reduced to
3.69% of base, or a 96.31% reduction.
It is notable, when looking at the update sizes in Ta-
bles 5 and 6 that the update sizes do not increase consis-
tently with a smaller model. This is likely a characteristic
of the data being relatively close in value. The data was
(a) (b)
Figure 6. (a) 5% model with 5% MAE threshold, left; (b)
10% model with 5% MAE threshold, right.
(a) (b)
Figure 7. (a) 25% model with 5% MAE threshold, left; (b)
50% model with 5% MAE threshold, right.
(a) (b)
Figure 8. (a) 5% model with 25% MAE threshold, left; (b)
10% model with 25% MAE threshold, right.
intentionally selected to incorporate a noticeable varia-
tion (many areas, to a human viewer of its rendering ap-
pear simply to be a solid color or minor gradient). How-
ever, even with this variation, the difference is not dra-
matic across the image. This allows minor fluctuations to
be dramatized by some size-reduction magnitudes, but
not by others.
8. Conclusion & Future Work
This work has demonstrated the viability of using the
MBDT technique to reduce transmission requirements
for gravitational model data. A pre-existing data set for
the Earth has been utilized to demonstrate the approach’s
Copyright © 2013 SciRes. JDAIP
(a) (b)
Figure 9. (a) 25% model with 25% MAE threshold, left; (b)
50% model with 25% MAE threshold, right.
efficacy; however, the techniques should be applicable to
gravity models for other planets and space objects (e.g.,
asteroids, etc.). Future work will focus on applying MBDT
to other gravitational data sets, applying MBDT to other
data types and combining multiple data sources to gener-
ate higher-value data products as part of higher levels of
the MBTR paradigm.
9. Acknowledgements
Small spacecraft development work at the University of
North Dakota is or has been supported by the North Da-
kota Space Grant Consortium, the University of North
Dakota Faculty Research Seed Money Committee, North
Dakota NASA EPSCoR and the National Aeronautics
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