Satellite Conjunction Analysis Dr Salvatore Alfano Overview

Satellite Conjunction Analysis Dr. Salvatore Alfano

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

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 CSSI Pg 3 of 50 www. centerforspace. com

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 5 KM 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/ CSSI Pg 4 of 50 www. centerforspace. 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) CSSI Pg 5 of 50 www. centerforspace. com

Reorient Q Rotate so that relative velocity is into screen CSSI Pg 6 of 50 www. centerforspace. com

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

Combine uncertainties Q Combine uncertainties & center at B B A In effect, I have transferred all the uncertainty to Object B CSSI Pg 8 of 50 Choice is arbitray I could have just as easily done this by centering on A www. centerforspace. com

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

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

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

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 CSSI Pg 12 of 50 www. centerforspace. com

Putting it all together Q Relative motion creates path (collision tube) through combined uncertainty ellipsoid Rotate ellipsoid & Project to reduce to 2 D Define footprint Integrate over tube’s footprint using projected probability density CSSI Pg 13 of 50 www. centerforspace. com

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

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

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

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

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 5 KM) • Provides daily, searchable reports via Celes. Trak – 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 CSSI Pg 18 of 50 www. centerforspace. com

SOCRATES Demonstration Q • Easy to find from Celes. Trak 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 CSSI Pg 19 of 50 www. centerforspace. com

CELESTRAK Homepage Demo Q Click Here CSSI Pg 20 of 50 www. centerforspace. com

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

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

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

Automated STK/CAT Scenario Builder Q SOCRATES Button Sequence 1. Launch STK 2. Build Scenario 3. Pick viewing time(s) Enter, TCA, Exit CSSI Pg 24 of 50 www. centerforspace. com

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

SOCRATES-GEO • Extend SOCRATES system on Celes. Trak – 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) CSSI Pg 26 of 50 www. centerforspace. com

SOCRATES-GEO Implementation • New SOCRATES-GEO system on Celes. Trak – – – – CSSI 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 Pg 27 of 50 www. centerforspace. com

SOCRATES-GEO Process Flow Data sources Data preparation Owner ephemeris Convert to standard format Public orbital data Generate ephemerides TLE data Produce enhanced TLEs Select GEO data Run SOCRATES-GEO Generate/Upload reports Send notifications CSSI Pg 28 of 50 www. centerforspace. com

Owner ephemerides Test Case: Intelsat IS-6 B IS-11 Public orbital data IS-3 R Supplemental TLEs AFSPC TLEs 43. 25° W 43. 00° W 42. 75° W IS-6 B IS-3 R IS-11 183. 98 km CSSI Pg 29 of 50 www. centerforspace. com

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 CSSI Pg 30 of 50 www. centerforspace. com

Collision Avoidance Maneuver Planning • Run initial warning tool (SOCRATES) • Build STK/Adv. CAT 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 CSSI Pg 31 of 50 www. centerforspace. com

MATLAB & STK Connect Single-Axis Parametric Analysis Velocity Auto read from STK or XLS (user can modify) User input Press button Co-Normal Topography created CSSI Normal Pg 32 of 50 www. centerforspace. com

MATLAB with STK CONNECT Double-Axes Parametric Analysis Choose maneuver time (-2500 s) V-N User input Press button N-C C-V Topography created CSSI Pg 33 of 50 www. centerforspace. com

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? CSSI Pg 34 of 50 www. centerforspace. com

Addressing nonlinear motion Q Treat each small segment as linear Must reintroduce 3 rd dimension along each length of tube CSSI Pg 35 of 50 www. centerforspace. com

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

Eliminating gaps & overlaps Q Re-introduce long axis into linear method Use ERF method (pixelation) for 3 D gaps/overlap Piece-wise integration of bundled, rectangular parallelepipeds (elongated voxels) CSSI Pg 37 of 50 www. centerforspace. com

Eliminating gaps & overlaps Q axis 13 r All data rotated to align new z axis with axis 12 r = [0 0 1] axis 12 r & axis 23 r are unit vectors axis 13 r = axis 12 r + axis 23 r Compound miter ┴ to axis 13 r CSSI Pg 38 of 50 www. centerforspace. com

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

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

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

Combined object footprint Q Raster sweep for combined object footprint No need to alter integrand Only compute red pixels Footprint can be dynamic (tumbling) CSSI Pg 42 of 50 www. centerforspace. com

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

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

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 CSSI Pg 45 of 50 www. centerforspace. com

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

Elimination of linear assumptions Q • Physical Objects Modeled as Spheres Precise shape & – Attitude information not required (not known? ) orientation with time • Linear Relative Motion – Straight collision tube (permits simple projection & reduction) • Positional Uncertainties Adjoining Right Cylinders – Zero-mean Gaussian Bundled Parallelepipeds – Uncorrelated (permits simple summing for combination) – Constant (over encounter time) Cov Propagation required • All Calculation Data Taken at Time of Closest Approach Gaps (faster) or no gaps (slower) in abutting cylinders New linearity tests (coarse & fine) Pg 47 of 50 CSSI www. centerforspace. com

Uses many different STK features Q • Adv. CAT – Determine TCA – Test for linearity – Compute appropriate probability • HPOP or ODTK for 6 x 6 covariance propagation • Vector Geometry Tool for proper viewing alignment • Area Tool for image extraction CSSI Pg 48 of 50 www. centerforspace. com

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

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