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Dr. Salvatore Alfano Satellite Conjunction Analysis

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Pg 2 of 50 www.centerforspace.com CSSI Introduction Review of assumptions Maximum probability SOCRATES demo Collision Avoidance Maneuver Planning Upcoming Improvements Q Overview

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Pg 3 of 50 www.centerforspace.com CSSI 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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Pg 4 of 50 www.centerforspace.com CSSI 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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Pg 5 of 50 www.centerforspace.com CSSI Review of linear assumptions Attitude info not required (or known?) Combined positional uncertainties Constant covariance – rapid encounter Zero-mean Gaussian Linear relative motion Straight 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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Pg 6 of 50 www.centerforspace.com CSSI Reorient Rotate so that relative velocity is into screen Q

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Pg 7 of 50 www.centerforspace.com CSSI Uncertainty ellipses Apply individual uncertainties Relative velocity vector is now into page Mean Miss Distance Vector A B Q

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Pg 8 of 50 www.centerforspace.com CSSI Combine uncertainties A B Combine uncertainties & center at B 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 Q

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Pg 9 of 50 www.centerforspace.com CSSI A B B B B B B Define collision region size B Map out all possibilities of B touching A This defines locus of contact (footprint) By definition B could be anywhere Q

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Pg 10 of 50 www.centerforspace.com CSSI A B Mean Miss Distance Vector Combined object footprint Combined covariance ellipse Now ready to compute probability Q

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Pg 11 of 50 www.centerforspace.com CSSI Gaussian probability density Overlay probability density contours Integrate over combined objects footprint to get probability of collision + Q +

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Pg 12 of 50 www.centerforspace.com CSSI 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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Pg 13 of 50 www.centerforspace.com CSSI 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 tubes footprint using projected probability density Q

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Pg 14 of 50 www.centerforspace.com CSSI Desired outcome Grill some burgers at pool party Doing the right thing improperly Chosen Approach Could lead to unintended consequence

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Pg 15 of 50 www.centerforspace.com CSSI Desired outcome Conjunction Probability Doing the right thing improperly Chosen Approach May not give decision maker sufficient information

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Pg 16 of 50 www.centerforspace.com CSSI Maximum Probability & Dilution STK AdvCAT also computes these Q Mathematically both are correct, but with different association Low Risk Poor Data Quality

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Pg 17 of 50 www.centerforspace.com CSSI Another benefit of max probability Choose this one Q For TLEs covariance not given

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Pg 18 of 50 www.centerforspace.com CSSI 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 Q

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Pg 19 of 50 www.centerforspace.com CSSI SOCRATES Demonstration Easy to find from CelesTrak home pageCelesTrak –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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Pg 20 of 50 www.centerforspace.com CSSI CELESTRAK Homepage Demo Click Here Q

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Pg 21 of 50 www.centerforspace.com CSSI Demonstration -Introduction -Methodology -Tech papers -Enhancements -Resources -Service Provider Q

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Pg 22 of 50 www.centerforspace.com CSSI Demonstration IRIDIUM VS. COSMOS (APR 20 REPORT) ASSUMES SAME SIGMA FOR ALL AXES ACCURACY (SIGMA) REQUIRED 5 KM ANALYZE Q

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Pg 23 of 50 www.centerforspace.com CSSI Analysis Button Demonstration TLEs provided Cut & paste as you wish Can obtain STK/CAT trial license STK Button Sequence Q

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Pg 24 of 50 www.centerforspace.com CSSI 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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Pg 25 of 50 www.centerforspace.com CSSI STK/CAT Alteration (if desired) Change Covariance Replace TLEs with better Pos/Vel Data Change Physical Object Size Q

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Pg 26 of 50 www.centerforspace.com CSSI 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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Pg 27 of 50 www.centerforspace.com CSSI 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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Pg 28 of 50 www.centerforspace.com CSSI 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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Pg 29 of 50 www.centerforspace.com CSSI IS-6BIS-3RIS-11 IS-6BIS-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

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Pg 30 of 50 www.centerforspace.com CSSI 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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Pg 31 of 50 www.centerforspace.com CSSI 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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Pg 32 of 50 www.centerforspace.com CSSI MATLAB & STK Connect Single-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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Pg 33 of 50 www.centerforspace.com CSSI 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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Pg 34 of 50 www.centerforspace.com CSSI 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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Pg 35 of 50 www.centerforspace.com CSSI Addressing nonlinear motion Treat each small segment as linear Must reintroduce 3 rd dimension along each length of tube Q

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Pg 36 of 50 www.centerforspace.com CSSI Upcoming Improvements Test for linearity Assessing nonlinear motion –Adjoining right cylinders –Gap elimination Handling non-spherical shapes Q

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Pg 37 of 50 www.centerforspace.com CSSI 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) Q

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Pg 38 of 50 www.centerforspace.com CSSI Eliminating gaps & overlaps 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 Q

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Pg 39 of 50 www.centerforspace.com CSSI Eliminating gaps & overlaps Compute 2D probability of each pixel Compute 1D probability of each parallelepipeds Mahalanobis length based on dz Object cross section (axis into screen) Q

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Pg 40 of 50 www.centerforspace.com CSSI Bundles easily address complex shapes Concave, Spiral Hollow, Convex In theory, satellite could fly thru Just light up different pixels Q

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Pg 41 of 50 www.centerforspace.com CSSI Iridium silhouette from STK Area Tool Where can I get shapes? Oriented along relative velocity vector From image files Q

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Pg 42 of 50 www.centerforspace.com CSSI 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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Pg 43 of 50 www.centerforspace.com CSSI Raster sweep example Q

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Pg 44 of 50 www.centerforspace.com CSSI MATLAB image merging tool Q

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Pg 45 of 50 www.centerforspace.com CSSI Chans approach to complex objects Q 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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Pg 46 of 50 www.centerforspace.com CSSI Inherently accounts for proper solar panel orientation relative velocity orientation, offsets, eclipsing/exclusions Q Our approach – just let STK do it

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Pg 47 of 50 www.centerforspace.com CSSI 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 Bundled Parallelepipeds Q

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Pg 48 of 50 www.centerforspace.com CSSI 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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Pg 49 of 50 www.centerforspace.com CSSI Assumptions Maximum probability & dilution SOCRATES demo Collision Avoidance Maneuver Planning Upcoming Improvements Q Wrap up

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Pg 50 of 50 www.centerforspace.com CSSI I would love to change the world, but they won't give me the source code - Unknown Need help? Just call Q

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