dr. douglas hope research scientist u.s. air force academy distribution a. approved for public...
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The problem of non-resolved space object identification from an information theoretic perspective
Dr. Douglas HopeResearch Scientist
U.S. Air Force Academy
Distribution A. Approved for public release, distribution unlimited
Problem of non-resolved space object identification
Imaging SOI spatial information on object from resolved imagery
Non-resolved SOI Infer physical information about object, i.e. materials, orbital
parameters, shape and morphology from observed light curves
NRSOI for a geosynchronous satellite Nadir-pointing attitude is fixed The pose of the satellite essentially does not change
Information in a GEO light curve depends on Object shape Surface materials The illumination geometry between the Sun, object and observer
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NRSOI from an information perspective
NRSOI is an estimation problem Ill-posed problem Extraction of information about the object depends on both
measurements and a priori information on the object
Statistical information as a priori information on an object Estimate symbol value from the channel output (in the presence of
noise) Characterize any a priori information on the symbol by a probability
distribution A measure of information (entropy) is assigned to this symbol
probability distribution Example: Let X denote the symbol for the FA abundance of solar cell material on a GEO
Gaussian distribution with
mean value = 0.70
5.01 bits
6.04 bitsSymbol distribution on
the right has a greater potential to convey
information about the FA
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NRSOI from an information perspective
Mutual information Measures information between the symbol distribution and measurement
distribution Marginal measurement probability function
Computed via Bayes Theorem Evaluate integral using Metropolis-Hastings Monte-Carlo algorithm and compute MI
NRSOI Task: Measure and Estimate the abundance of surface materials on a GEO satellite
Objective #1 Assess an observation strategy for completing the NROSI taskCompute the MI in data obtained using different FTN observation modalities• Use this metric to compare the information on materials
obtained using different observational/measurement scenarios
• Consider Broadband ( Johnson B,V and R filters) vs. spectroscopic measurements Distribution A. Approved for public release, distribution unlimited
Objective #1 Assess an observation strategy for estimating the fractional abundance of materials on a GEO
Single site vs. simultaneous observations from multiple sites in the Northern and Southern hemispheres (Spring Equinox 2014)
Scenario #1: Single site in La Junta (southwest) Colorado
Scenario #2: observations from Chile
and Colorado
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Objective #1 Assess an observation strategy for estimating the fractional abundance of materials on a GEO
Model the GEO as a single rectangular facet with appropriate dimensions
GEO model(5) Surface materials
Area is equivalent to the fractional abundance of
the material
Material
Material DescriptionFractional
AbundanceMean value
1 TASAT BRDF# MB 0023 Solar Cell, Silicon, Sun Side
0.80
2 TASAT BRDF# MB 0001 Aluminum Alloy, 2024-T3, Polished
0.07 +/- 0.007
3 TASAT BRDF# MB 0026 Kapton, Aluminized 1 Mil 0.05 +/- 0.005
4 TASAT BRDF# MB 0029 Mylar, Aluminized, Mylar Side
0.05 +/- 0.005
5 TASAT BRDF# MB 0061 Paint, Chemglaze Z202, White
0.05 +/- 0.005
Assess MI on the fractional abundances of materials from broadband measurements and spectroscopic measurements
a priori statistical information
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Mutual Information on materials for GEO observations
Increasing spectral resolution
MI = 3.8 bits broadband
measurements from Colorado
Distribution A. Approved for public release, distribution unlimited
Maximum MI possible is
9 bits
Mutual Information on materials for GEO observations
MI in spectroscopic
measurements from
La Junta, CO
Increasing spectral resolution
MI = 3.8 bits broadband
measurements from Colorado
Distribution A. Approved for public release, distribution unlimited
Maximum MI possible is
9 bits
Mutual Information on materials for GEO observations
Increasing spectral resolution
MI in spectroscopic measurements from Colorado and Chile
MI = 3.8 bits broadband
measurements from Colorado
MI=4.8 bitsbroadband
measurements from Colorado and Chile
MI in spectroscopic
measurements from
La Junta, CO
Δλ = 80 nm
Distribution A. Approved for public release, distribution unlimited
Maximum MI possible is
9 bits
Conclusions and Future work
Applied mutual information to an NRSOI task (abundances of materials)
Use the MI to assess the performance of the FTN when acquiring information on the surface materials of a GEO using broadband and spectroscopic measurement modes from multiple sites (Colorado and Chile)
Next, evaluate MI in the estimated fractional abundances
Compare different mutual information quantities to assess the performance of algorithm when extracting information from the data
Information in the data
Information in the estimates
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Estimation of material abundances
• Fractional abundances estimated using non-negative least squares algorithm ( Lawson, 1974)
• Solves
• This approach requires the probability distribution be computed empirically
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Estimation of material abundances
• Distribution of estimated solar cell abundances for single object
Truth FA
Distribution A. Approved for public release, distribution unlimited
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