Spatial Interpolation Between
Satellites: Development of a Data Fusion Implementation for MultiSpacecraft
Missions, 159306
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Principal Investigators
JörgMicha Jahn
Sandee Jeffers
Martin Wüest
Inclusive Dates: 04/01/02  09/30/03
Background  Satellite constellation missions
give for the first time full access to the true threedimensionality of the
space environment. They allow the detection and measurement of vector and scalar
field gradients and discontinuities. Determining spatial gradients is a
challenging endeavor, since spacecraft constellations not only move with respect
to the region of interest, but the constellation members themselves move
constantly with respect to each other. Recent literature has provided a
theoretical framework for this analysis and the errors affecting the gradient
calculation. In this project we implemented a data fusion system based on the
barycentric coordinate and the least squares minimization formalisms, allowing
us to calculate spatial gradients for constellations of four or more spacecraft.
For development we were primarily using data from the Cluster Plasma Electron
And Current Experiment (PEACE), which is part of the joint EuropeanUS Cluster
mission launched in 2000.
Approach  In order to address the objectives
formulated above, we built a software package which, based on a set of input
data, calculates spatial gradients of desired quantities. The following main
procedures are implemented in the package:
 Timealignment of
input data. All data need to be brought to a common timeline using time
series resampling methods before any kind of meaningful analysis or fusion can
be performed.
 Evaluation of the
tetrahedron geometry. By calculating the "volumetric tensor" we quantify
and classify the geometry of a tetrahedron at any given time step.
 Calculation of
spatial gradients and curls. Spatial gradients of all physical quantities
are calculated under inclusion of the satellite orbital positions at each
measurement instance. In addition, the curl of vectors is calculated, if
appropriate.
Accomplishments  We produced an operational
software package that represents an implementation of two different algorithms
to calculate spatial gradients and spacecraft tetrahedron geometrical quantities
and quality factors. The package is written in objectoriented C++, it is highly
modular, generic, portable, and adaptable. A User's and Programmer's Guide is
available for this software package.
The software reads ASCII or Southwest Research Institute® IDFS™ (Instrument
Data File System™) input data, then it performs (1) a multisatellite orbit
interpolation to calculate the exact tetrahedron shape at the time of science
measurements, (2) the gradient calculation, (3) a calculation of the tetrahedron
characteristic quantities (size, elongation, planarity), and (4) data output
into ASCII files for easy postprocessing analysis. The system is capable of
processing arbitrarily long data sets. It is also capable of calculating the
curl of a vector and the divergence of a quantity. The software package has been
extensively tested with synthetic ASCII data and data in IDFS™ format from
the Cluster PEACE instrument. Without changes, the software can be applied to
any constellation of four or more spacecraft, as was demonstrated when we
analyzed data form four spacecraft located in the solar wind.

Figure 1. Example Cluster pass through the
Cusp from 1215 to 1250 UT. The bottom three panels show the total pressure
for two spacecraft each, clearly showing differences in pressure from
spacecraft to spacecraft. These differences are larger than the instrument
error bar and thus represent an ideal test case for calculating the pressure
gradient. 

Figure 2. Pressure gradient for example
Cluster pass through the Cusp. Red lines indicate orbits of individual
Cluster spacecraft, the green line indicates the orbital trace of the mesocenter
of the spacecraft constellation. Blue dots indicate the positions of the
four cluster spacecraft at the start of the time interval which is 1215 UT
to 1250 UT. Blue lines emanating from the mesocenter trace indicate the
value (= length) and direction of the calculated pressure gradient (using
the total scalar pressure as input). 

Figure 3. Solar wind speed gradient for a
twoday time period in May 1998. Displayed are, from the top, the three GSE
components of the pressure gradient and its absolute value. Data from SOHO,
Wind, ACE and IMP8 were used for this plot. At approximately 21 UT a CME
with associated shock passes through the spacecraft cluster. Note the
increased spatial gradients in solar wind speed after this event. (Data
courtesy Dr. R. Goldstein, Space Science and Engineering Division). 
2003 Program
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