satellite conjunction analysis
DESCRIPTION
Satellite Conjunction Analysis. Dr. Salvatore Alfano. Overview. Q. Introduction Review of assumptions Maximum probability SOCRATES demo Collision Avoidance Maneuver Planning Upcoming Improvements. Introduction. Q. - PowerPoint PPT PresentationTRANSCRIPT
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Dr. Salvatore Alfano
Satellite Conjunction Analysis
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• Introduction• Review of assumptions• Maximum probability• SOCRATES demo• Collision Avoidance Maneuver
Planning• Upcoming Improvements
Q
Overview
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Introduction
• Many operators are aware of the possibility of a collision between their satellite and another object– December 1991
• COSMOS 1934 & COSMOS 926 debris• 980 km mean altitude, 83° inclination
– July 1996• CERISE & ARIANE 1 (third stage)• 700 km polar orbit
– January 2005• CZ-4 launch vehicle (third stage) & DMSP Rocket Body• 885 km altitude above south polar region
Q
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Debris producing events
• Deliberate debris generation– Chinese ASAT Test (Jan 2007)
• Generated 2,300+ cataloged pieces– USA 193 intercept (Feb 2008)
• Generated 130+ reported pieces• Within 5KM of SPOT 5, QUICKBIRD 2,
IRIDIUM 46, IRIDIUM 86, OFEQ 7, LANDSAT 5, SAR-LUPE 3, & ISS
• Other 2007 events– SL-12 Rocket Body Explosion (Feb)– BREEZE-M Rocket Body Explosion (Feb)
• More info at http://celestrak.com/
Q
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Review of linear assumptions
Attitude info not required (or known?)
Combined positional uncertaintiesConstant covariance – rapid encounterZero-mean Gaussian
Linear relative motionStraight collision tube (permits simple projection & reduction)
Physical objects modeled
as spheres
All calculation data taken at TCA
Rel velocity to rel distance
Q
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Reorient
Rotate so that relative velocity is into screen
Q
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Uncertainty ellipses
Apply individual uncertainties
Relative velocity vector is now into page
Mean Miss Distance Vector
A
B
Q
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Combine uncertainties
A
B
Combineuncertainties& center at B
In effect, I have transferred all theuncertainty to Object B
Choice is arbitrayI could have just as easily
done this by centering on A
Q
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AB
BB
BBB
Define collision region size
B
Map out all possibilitiesof B touching A
This defines locusof contact (footprint)
By definitionB could be anywhere
Q
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A
B
Mean Miss Distance Vector
Combined objectfootprint
Combined covariance ellipse
Now ready to compute probabilityQ
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Gaussian probability density
Overlay probability densitycontours
Integrate over combined object’s footprint to get probability of collision
+
Q
P1
2 x y
OBJ
OBJ
x
OBJ2
x( )2
OBJ2
x( )2
yexp1
2
x xm
x
2y ym
y
2
d
d
+
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Review
• Find the minimum miss distance vector– This is the point of closest approach
• Rotate so that relative velocity is into screen
• Combine the individual uncertainty (ellipses) and center them at B– This defines the probability density
• Combine the object sizes and center them at A
• Use the miss distance, size, and density from two ellipses to compute probability
Q
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Putting it all together
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
Q
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Desired outcome
Grill some burgers at pool party
Doing the right thing improperly
Chosen Approach
Could lead to unintended consequence
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Desired outcome
Conjunction Probability
Doing the right thing improperly
Chosen Approach
May not give decision maker sufficient information
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Maximum Probability & Dilution
STKAdvCAT
alsocomputes
these
Q
Mathematically both are correct, but with different association
Low Risk Poor Data
Quality
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Another benefit of max probability
Choose this one
Q
For TLEs covariance not given
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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 providedNo registration -- no e-mail solicitation
http://celestrak.com/SOCRATES/– Associated orbital data freely available
http://www.space-track.org
http://celestrak.com
SOCRATESQ
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SOCRATES Demonstration
• Easy to find from CelesTrak home page– Click on link for SOCRATES
– Provides basic information along with:• Top 10 Conjunctions by Maximum Probability• Top 10 Conjunctions by Minimum Range• Search Capability
– No subscription or sign-up required– No solicitation of user information
Q
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CELESTRAK Homepage Demo
Click Here
Q
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Demonstration
-Introduction
-Methodology
-Tech papers
-Enhancements
-Resources
-Service Provider
Q
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Demonstration
IRIDIUM VS. COSMOS (APR 20 REPORT)
ASSUMES
SAME SIGMA
FOR ALL AXES
ACCURACY
(SIGMA)
REQUIRED
5 KM
ANALYZE
Q
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Analysis Button Demonstration
TLEs provided
Cut & paste
as you wish
Can obtain
STK/CAT
trial license
STK
Button
Sequence
Q
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Automated STK/CAT Scenario Builder
1. Launch STK
2. Build Scenario
3. Pick viewing time(s)
Enter, TCA, Exit
SOCRATES Button Sequence
Q
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STK/CAT Alteration (if desired)
Change Covariance
Replace TLEs with better Pos/Vel Data
Change Physical Object Size
Q
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SOCRATES-GEO
• Extend SOCRATES system on CelesTrak– Limit to GEO conjunctions (for now)– Replace TLEs, where possible
• Owner/operator ephemeris (including maneuvers)• Public owner/operator data
– 11-parameter data– Keplerian/Cartesian state vectors
• Enhanced TLEs for non-cooperative objects (debris)
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SOCRATES-GEO Implementation
• New SOCRATES-GEO system on CelesTrak– Looks for all objects which pass within 250 km of GEO– Uses improved data sources, when available– Generates standard reports, including orbital data– Allows user-defined notification criteria– Automatically sends notification– Web access via secure system– Privacy protected – CSSI acts as trusted data broker
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SOCRATES-GEO Process Flow
Data sources
Owner ephemeris
Public orbital data
TLE data
Convert to standard format
Generate ephemerides
Produce enhanced TLEs
Select GEO data
Data preparation
Run SOCRATES-GEO
Generate/Upload reports
Send notifications
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IS-6B IS-3R IS-11
IS-6B IS-3RIS-11
43.25° W 43.00° W 42.75° W
183.98 km
Owner ephemerides
Public orbital data
Supplemental TLEs
AFSPC TLEs
Test Case: Intelsat
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SOCRATES-GEO
• Collaborative effort addresses current limitations– Improves orbital accuracy through cooperation– Reduces search volumes– Reduces false-alarm rate– Provides more than public catalog
• Already operating – subscription required– Need orbital data in your format– Need definition of data format, coordinate & time
systems
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Collision Avoidance Maneuver Planning
• Run initial warning tool (SOCRATES)
• Build STK/AdvCAT Scenario
• Perform Parametric -V Analysis– One-on-one with simplified orbital dynamics– We use a MATLAB program that interfaces with STK
• Test proposed -V – Feed into STK Scenario for– One-on-all conjunction analysis– Mission impact– Recovery to nominal orbit
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MATLAB & STK ConnectSingle-Axis Parametric Analysis
Auto read
from STK or XLS
(user can modify)
User input
Press button
Topography
created
Velocity
Normal
Co-Normal
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MATLAB with STK CONNECT Double-Axes Parametric Analysis
Choose
maneuver
time (-2500s)
User input
Press button
Topography
created
V - N
N - C C - V
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Test candidate maneuver
• Feed maneuver back into STK scenario• Determine
– Mission Impact• Temporarily degraded capability?• Maneuver to return to nominal orbit?• How long to task sensors and recover ephemeris?
– Fuel usage • Shortened lifespan?• Recovery to nominal orbit?• Reschedule routine station-keeping (saves fuel)
– Future conjunctions• Did I increase the possibility of a future conjunction
with a different satellite?
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Addressing nonlinear motion
Treat each small
segment as linear
Must reintroduce
3rd dimension along
each length of tube
Q
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Upcoming Improvements
• Test for linearity
• Assessing nonlinear motion– Adjoining right cylinders– Gap elimination
• Handling non-spherical shapes
Q
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Eliminating gaps & overlaps
Re-introduce long axis into linear method
Use ERF method (pixelation) for 3D gaps/overlap
Piece-wise integration of bundled, rectangular
parallelepipeds (elongated voxels)
Parallelepiped face (P2d)
Long axis (P1d)
z direction Parallelepiped face (P2d)
Long axis (P1d)
z direction
Q
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Eliminating gaps & overlaps
x y z( ) xa ya za( )
compound miterr1r
r3r
r2r
x y z( ) xa ya za( )
compound miterr1r
r3r
r2r
dzdx axis13r
x dy axis13r
y
axis13rz
axis12r & axis23r are unit vectors
axis13r = axis12r + axis23r
Compound miter ┴ to axis13r
All data rotated to align new z
axis with axis12r
axis12r = [0 0 1]
axis13r
Parallelepiped face (P2d)
Long axis (P1d)
z directionParallelepiped face (P2d)
Long axis (P1d)
z direction
Q
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Eliminating gaps & overlaps
objx objy objz( )
Compute 2D probability of each pixel
P1d
1
2erf
Mf
2
erfM
i
2
Compute 1D probability of each parallelepiped’s Mahalanobis
length based on dz
Object cross section (axis into screen)
Parallelepiped face (P2d)
Long axis (P1d)
z direction Parallelepiped face (P2d)
Long axis (P1d)
z direction
Q
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Bundles easily address complex shapes
Concave, Spiral
Hollow, Convex
In theory, satellite could fly thru
objx objy objz( )
Just light up different pixels
Q
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Iridium silhouette
from STK Area Tool
Where can I get shapes?
Oriented along
relative velocity
vector
From image files
Q
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Combined object footprint
Raster sweep for combined object
footprint
No need to alter integrand
Only compute red pixels
Footprint can be dynamic
(tumbling)
Q
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Raster sweep exampleQ
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MATLAB image merging toolQ
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Chan’s approach to complex objectsQ
Model components as spheres, cylinders, cones +
circular, rectangular, & triangular plates . . .
Account for sun angle for proper solar panel orientation
relative velocity orientation, offsets, eclipsing/exclusions
Determine approximate equivalent cross sectional areas
Approximate individual probabilities
Sum all the pieces
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Inherently accounts for proper solar panel orientation
relative velocity orientation, offsets, eclipsing/exclusions
QOur approach – just let STK do it
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Elimination of linear assumptions
• 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
New linearity tests (coarse & fine)
Gaps (faster) or no gaps (slower) in abutting cylinders
Precise shape &orientation with time
Adjoining Right Cylinders
Cov Propagation required
BundledParallelepipeds
Q
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• 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
Uses many different STK features Q
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• Assumptions• Maximum probability & dilution• SOCRATES demo• Collision Avoidance Maneuver
Planning• Upcoming Improvements
Q
Wrap up
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I would love to change the I would love to change the
world, but they won't give world, but they won't give
me the source code me the source code
- Unknown- Unknown
Need help? Just call
Q