Dr. Salvatore Alfano Satellite Conjunction Analysis.

Dr. Salvatore Alfano

Satellite Conjunction Analysis

Pg 2 of 50 www.centerforspace.comCSSI

• Introduction• Review of assumptions• Maximum probability• SOCRATES demo• Collision Avoidance Maneuver

Planning• Upcoming Improvements

Overview

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

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/

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

Reorient

Rotate so that relative velocity is into screen

Uncertainty ellipses

Apply individual uncertainties

Relative velocity vector is now into page

Mean Miss Distance Vector

Combine uncertainties

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

Define collision region size

Map out all possibilitiesof B touching A

This defines locusof contact (footprint)

By definitionB could be anywhere

Mean Miss Distance Vector

Combined objectfootprint

Combined covariance ellipse

Now ready to compute probabilityQ

Gaussian probability density

Overlay probability densitycontours

Integrate over combined object’s footprint to get probability of collision

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

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

Doing the right thing improperly

Chosen Approach

Could lead to unintended consequence

Desired outcome

Conjunction Probability

Doing the right thing improperly

Chosen Approach

May not give decision maker sufficient information

Maximum Probability & Dilution

STKAdvCAT

alsocomputes

Mathematically both are correct, but with different association

Low Risk Poor Data

Quality

Another benefit of max probability

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 providedNo registration -- no e-mail solicitation

http://celestrak.com/SOCRATES/– Associated orbital data freely available

http://www.space-track.org

http://celestrak.com

SOCRATESQ

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

CELESTRAK Homepage Demo

Click Here

Demonstration

-Introduction

-Methodology

-Tech papers

-Enhancements

-Resources

-Service Provider

Demonstration

IRIDIUM VS. COSMOS (APR 20 REPORT)

ASSUMES

SAME SIGMA

FOR ALL AXES

ACCURACY

(SIGMA)

REQUIRED

ANALYZE

Analysis Button Demonstration

TLEs provided

Cut & paste

as you wish

Can obtain

STK/CAT

trial license

Button

Sequence

Automated STK/CAT Scenario Builder

1. Launch STK

2. Build Scenario

3. Pick viewing time(s)

Enter, TCA, Exit

SOCRATES Button Sequence

STK/CAT Alteration (if desired)

Change Covariance

Replace TLEs with better Pos/Vel Data

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

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

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 -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

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

MATLAB with STK CONNECT Double-Axes Parametric Analysis

Choose

maneuver

time (-2500s)

User input

Press button

Topography

created

N - C C - V

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

Treat each small

segment as linear

Must reintroduce

3rd dimension along

each length of tube

Upcoming Improvements

• Test for linearity

• Assessing nonlinear motion– Adjoining right cylinders– Gap elimination

• Handling non-spherical shapes

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

x y z( ) xa ya za( )

compound miterr1r

x y z( ) xa ya za( )

compound miterr1r

dzdx axis13r

x dy axis13r

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

Long axis (P1d)

z directionParallelepiped face (P2d)

Long axis (P1d)

z direction

objx objy objz( )

Compute 2D probability of each pixel

Compute 1D probability of each parallelepiped’s Mahalanobis

length based on dz

Object cross section (axis into screen)

Long axis (P1d)

z direction Parallelepiped face (P2d)

Long axis (P1d)

z direction

Bundles easily address complex shapes

Concave, Spiral

Hollow, Convex

In theory, satellite could fly thru

objx objy objz( )

Just light up different pixels

Iridium silhouette

from STK Area Tool

Where can I get shapes?

Oriented along

relative velocity

vector

From image files

Combined object footprint

Raster sweep for combined object

footprint

No need to alter integrand

Only compute red pixels

Footprint can be dynamic

(tumbling)

Raster sweep exampleQ

MATLAB image merging toolQ

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

Inherently accounts for proper solar panel orientation

relative velocity orientation, offsets, eclipsing/exclusions

QOur approach – just let STK do it

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

• 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

• Assumptions• Maximum probability & dilution• SOCRATES demo• Collision Avoidance Maneuver

Planning• Upcoming Improvements

Wrap up

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

Dr. Salvatore Alfano Satellite Conjunction Analysis.

b q slide

probability q slide

b b b b b b

socrates q slide

screen q slide

cssi debris

cssi demonstration

rel distance q slide

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