The problem of non-resolved space object identification from an information theoretic perspective

Dr. Douglas HopeResearch Scientist

U.S. Air Force Academy

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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

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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

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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

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