Satellite Conjunction Analysis. Dr. Salvatore Alfano. Overview. Q. Introduction Review of assumptions Maximum probability SOCRATES demo Collision Avoidance Maneuver Planning Upcoming Improvements. Introduction. Q.
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Satellite Conjunction Analysis
Dr. Salvatore Alfano
Overview
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Q
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Attitude info not required
(or known?)
All calculation data taken at TCA
Rel velocity ^ to rel distance
Linear relative motion
Straight collision tube (permits simple projection & reduction)
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Combined positional uncertainties
Constant covariance – rapid encounter
Zero-mean Gaussian
Physical objects modeled
as spheres
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Rotate so that relative velocity is into screen
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B
Mean Miss
Distance Vector
A
Apply individual uncertainties
Relative velocity vector is now into page
Q
Combine
uncertainties
& center at B
B
A
In effect, I have
transferred all the
uncertainty to Object B
Choice is arbitray
I could have just as easily
done this by centering on A
A
B
B
B
B
B
B
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By definition
B could be
anywhere
B
Map out all possibilities
of B touching A
This defines locus
of contact (footprint)
A
Now ready to compute probability
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Combined
covariance
ellipse
B
Combined object
footprint
Mean Miss
Distance Vector
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Overlay
probability
density
contours
+
+
Integrate over combined object’s
footprint to get probability of collision
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Relative motion creates path (collision tube) through combined uncertainty ellipsoid
Rotate ellipsoid & Project to reduce to 2D
Define footprint
Integrate over tube’s footprint
using projected probability density
Desired outcome
Grill some burgers at pool party
Chosen Approach
Could lead to unintended consequence
Desired outcome
Conjunction Probability
Chosen Approach
May not give decision maker sufficient information
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Mathematically both
are correct, but with
different association
STK
AdvCAT
also
computes
these
Low Risk
Poor Data
Quality
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Choose this one
For TLEs covariance not given
Satellite Orbital Conjunction Reports Assessing Threatening Encounters in Space
Center for Space Standards & Innovation (CSSI) offers SOCRATES conjunction advisory service starting May 2004
Each day, CSSI runs all payloads (active and inactive) against all objects on orbit (as of 2008 April 10)
2,864 payloads vs. 11,406 objects (10.763 Conjunctions within 5KM)
Provides daily, searchable reports via CelesTrak
Reports are freely provided
No registration -- no e-mail solicitation
http://celestrak.com/SOCRATES/
Associated orbital data freely available
http://www.space-track.org
http://celestrak.com
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Click Here
CELESTRAK Homepage Demo
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-Introduction
-Methodology
-Tech papers
-Enhancements
-Resources
-Service Provider
ASSUMES
SAME SIGMA
FOR ALL AXES
ACCURACY
(SIGMA)
REQUIRED
ANALYZE
5 KM
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IRIDIUM VS. COSMOS (APR 20 REPORT)
TLEs provided
Cut & paste
as you wish
STK
Button
Sequence
Can obtain
STK/CAT
trial license
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SOCRATES Button Sequence
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Replace TLEs with better Pos/Vel Data
Change Covariance
Change Physical Object Size
Data preparation
Data sources
Owner ephemeris
Convert to standard format
Run SOCRATES-GEO
Select GEO data
Public orbital data
Generate ephemerides
TLE data
Produce enhanced TLEs
Generate/Upload reports
Send notifications
Owner ephemerides
Public orbital data
Supplemental TLEs
AFSPC TLEs
IS-11
IS-6B
IS-3R
43.00° W
43.25° W
42.75° W
IS-6B
IS-3R
IS-11
183.98 km
Auto read
from STK or XLS
(user can modify)
User input
Press button
Velocity
Co-Normal
Topography
created
Normal
Choose
maneuver
time (-2500s)
User input
Press button
V - N
C - V
N - C
Topography
created
Treat each small
segment as linear
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Must reintroduce
3rd dimension along
each length of tube
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Eliminating gaps & overlaps
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Re-introduce long axis into linear method
Use ERF method (pixelation) for 3D gaps/overlap
Piece-wise integration of bundled, rectangular
parallelepipeds (elongated voxels)
axis13r
Eliminating gaps & overlaps
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All data rotated to align new z axis with axis12r
axis12r = [0 0 1]
axis12r & axis23r are unit vectors
axis13r = axis12r + axis23r
Compound miter ┴ to axis13r
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Object cross section (axis into screen)
Compute 2D probability of each pixel
Compute 1D probability of each parallelepiped’s Mahalanobis length based on dz
Concave, Spiral
Hollow, Convex
In theory, satellite could fly thru
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Just light up different pixels
Where can I get shapes?
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From image files
Iridium silhouette
from STK Area Tool
Oriented along
relative velocity
vector
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Raster sweep for combined object footprint
No need to alter integrand
Only compute red pixels
Footprint can be dynamic (tumbling)
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Q
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Model components as spheres, cylinders, cones +
circular, rectangular, & triangular plates . . .
Approximate individual probabilities
Sum all the pieces
Account for sun angle for proper solar panel orientation
relative velocity orientation, offsets, eclipsing/exclusions
Determine approximate equivalent cross sectional areas
Our approach
– just let STK do it
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Inherently accounts for proper solar panel orientation
relative velocity orientation, offsets, eclipsing/exclusions
Physical Objects Modeled as Spheres
Attitude information not required (not known?)
Linear Relative Motion
Straight collision tube (permits simple projection & reduction)
Positional Uncertainties
Zero-mean Gaussian
Uncorrelated (permits simple summing for combination)
Constant (over encounter time)
All Calculation Data Taken at Time of Closest Approach
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Precise shape &
orientation with time
Adjoining Right Cylinders
Bundled
Parallelepipeds
Cov Propagation required
Gaps (faster) or no gaps (slower) in abutting cylinders
New linearity tests (coarse & fine)
AdvCAT
Determine TCA
Test for linearity
Compute appropriate probability
HPOP or ODTK for 6x6 covariance propagation
Vector Geometry Tool for proper viewing alignment
Area Tool for image extraction
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Wrap up
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Need help? Just call