Satellite Conjunction Analysis Dr. Salvatore Alfano

Overview Introduction Review of assumptions Maximum probability Q Introduction Review of assumptions Maximum probability SOCRATES demo Collision Avoidance Maneuver Planning Upcoming Improvements

Introduction Q 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

Debris producing events Q 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/

Review of linear assumptions Q All calculation data taken at TCA Rel velocity ^ to rel distance Combined positional uncertainties Constant covariance – rapid encounter Zero-mean Gaussian Physical objects modeled as spheres Attitude info not required (or known?) Linear relative motion Straight collision tube (permits simple projection & reduction)

Reorient Q Rotate so that relative velocity is into screen

Uncertainty ellipses Mean Miss Distance Vector Q B A Mean Miss Distance Vector Apply individual uncertainties Relative velocity vector is now into page

Combine uncertainties 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

Define collision region size Q By definition B could be anywhere B B B B A B B B Map out all possibilities of B touching A This defines locus of contact (footprint)

Now ready to compute probability Q Combined covariance ellipse B A Combined object footprint Mean Miss Distance Vector

Gaussian probability density Q Overlay probability density contours + + Integrate over combined object’s footprint to get probability of collision

Review Find the minimum miss distance vector Q 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

Putting it all together Q 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

Doing the right thing improperly Desired outcome Grill some burgers at pool party Chosen Approach Could lead to unintended consequence

Doing the right thing improperly Desired outcome Conjunction Probability Chosen Approach May not give decision maker sufficient information

Maximum Probability & Dilution Q Mathematically both are correct, but with different association STK AdvCAT also computes these Low Risk Poor Data Quality

Another benefit of max probability Q For TLEs covariance not given Choose this one

SOCRATES Q 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

SOCRATES Demonstration Q 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

CELESTRAK Homepage Demo Q Click Here

Demonstration -Introduction -Methodology -Tech papers -Enhancements Q -Introduction -Methodology -Tech papers -Enhancements -Resources -Service Provider

Demonstration ANALYZE IRIDIUM VS. COSMOS (APR 20 REPORT) ACCURACY Q IRIDIUM VS. COSMOS (APR 20 REPORT) ASSUMES SAME SIGMA FOR ALL AXES ACCURACY (SIGMA) REQUIRED 5 KM ANALYZE

Analysis Button Demonstration Q TLEs provided Cut & paste as you wish STK Button Sequence Can obtain STK/CAT trial license

Automated STK/CAT Scenario Builder Q SOCRATES Button Sequence Launch STK Build Scenario Pick viewing time(s) Enter, TCA, Exit

STK/CAT Alteration (if desired) Q Replace TLEs with better Pos/Vel Data Change Covariance Change Physical Object Size

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)

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

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

Test Case: Intelsat Owner ephemerides Public orbital data IS-6B IS-3R IS-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

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

Collision Avoidance Maneuver Planning Run initial warning tool (SOCRATES) Build STK/AdvCAT Scenario Perform Parametric D-V Analysis One-on-one with simplified orbital dynamics We use a MATLAB program that interfaces with STK Test proposed D-V – Feed into STK Scenario for One-on-all conjunction analysis Mission impact Recovery to nominal orbit

MATLAB & STK Connect Single-Axis Parametric Analysis Auto read from STK or XLS (user can modify) Topography created Velocity Normal Co-Normal User input Press button

MATLAB with STK CONNECT Double-Axes Parametric Analysis Choose maneuver time (-2500s) Topography created V - N N - C C - V User input Press button

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?

Addressing nonlinear motion Q Treat each small segment as linear Must reintroduce 3rd dimension along each length of tube

Upcoming Improvements Q Test for linearity Assessing nonlinear motion Adjoining right cylinders Gap elimination Handling non-spherical shapes

Eliminating gaps & overlaps Q Re-introduce long axis into linear method Use ERF method (pixelation) for 3D gaps/overlap Piece-wise integration of bundled, rectangular parallelepipeds (elongated voxels)

All data rotated to align new z axis with axis12r Eliminating gaps & overlaps Q All data rotated to align new z axis with axis12r axis12r = [0 0 1] axis13r axis12r & axis23r are unit vectors axis13r = axis12r + axis23r Compound miter ┴ to axis13r

Eliminating gaps & overlaps Q Object cross section (axis into screen) Compute 2D probability of each pixel Compute 1D probability of each parallelepiped’s Mahalanobis length based on dz

Bundles easily address complex shapes Q Just light up different pixels Concave, Spiral Hollow, Convex In theory, satellite could fly thru

Where can I get shapes? From image files Iridium silhouette Q From image files Iridium silhouette from STK Area Tool Oriented along relative velocity vector

Combined object footprint Q Raster sweep for combined object footprint No need to alter integrand Only compute red pixels Footprint can be dynamic (tumbling)

Raster sweep example Q

MATLAB image merging tool Q

Chan’s approach to complex objects Q 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 Q Inherently accounts for proper solar panel orientation relative velocity orientation, offsets, eclipsing/exclusions

Elimination of linear assumptions Q 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 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)

Uses many different STK features Q 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

Wrap up Assumptions Maximum probability & dilution SOCRATES demo Q Assumptions Maximum probability & dilution SOCRATES demo Collision Avoidance Maneuver Planning Upcoming Improvements

Q Need help? Just call I would love to change the world, but they won't give me the source code - Unknown