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Satellite Conjunction Analysis

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### Satellite Conjunction Analysis

Dr. Salvatore Alfano

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

- December 1991

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

- Chinese ASAT Test (Jan 2007)
- 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?)

All calculation data taken at TCA

Rel velocity ^ to rel distance

Linear relative motion

Straight collision tube (permits simple projection & reduction)

Q

Combined positional uncertainties

Constant covariance – rapid encounter

Zero-mean Gaussian

Physical objects modeled

as spheres

Uncertainty ellipses

Q

B

Mean Miss

Distance Vector

A

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

A

B

B

B

B

B

B

Q

By definition

B could be

anywhere

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

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
- 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

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

SOCRATESQ

SOCRATES Demonstration Encounters in Space

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

Demonstration Encounters in Space

Q

-Introduction

-Methodology

-Tech papers

-Enhancements

-Resources

-Service Provider

ASSUMES Encounters in Space

SAME SIGMA

FOR ALL AXES

ACCURACY

(SIGMA)

REQUIRED

ANALYZE

5 KM

DemonstrationQ

IRIDIUM VS. COSMOS (APR 20 REPORT)

TLEs provided Encounters in Space

Cut & paste

as you wish

STK

Button

Sequence

Can obtain

STK/CAT

trial license

Analysis Button DemonstrationQ

Automated STK/CAT Scenario Builder Encounters in Space

Q

SOCRATES Button Sequence

- Launch STK
- Build Scenario
- Pick viewing time(s)
- Enter, TCA, Exit

STK/CAT Alteration (if desired) Encounters in Space

Q

Replace TLEs with better Pos/Vel Data

Change Covariance

Change Physical Object Size

SOCRATES-GEO Encounters in Space

- 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 Encounters in Space

- 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

Data preparation Encounters in Space

Data sources

Owner ephemeris

Convert to standard format

Run SOCRATES-GEO

Select GEO data

Public orbital data

Generate ephemerides

TLE data

Produce enhanced TLEs

Generate/Upload reports

Send notifications

SOCRATES-GEO Process FlowOwner ephemerides Encounters in Space

Public orbital data

Supplemental TLEs

AFSPC TLEs

IS-11

IS-6B

IS-3R

43.00° W

43.25° W

42.75° W

IS-6B

IS-3R

IS-11

183.98 km

Test Case: IntelsatSOCRATES-GEO Encounters in Space

- 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 Encounters in Space

- 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

Auto read Encounters in Space

from STK or XLS

(user can modify)

User input

Press button

Velocity

Co-Normal

Topography

created

Normal

MATLAB & STK ConnectSingle-Axis Parametric AnalysisChoose Encounters in Space

maneuver

time (-2500s)

User input

Press button

V - N

C - V

N - C

Topography

created

MATLAB with STK CONNECT Double-Axes Parametric AnalysisTest candidate maneuver Encounters in Space

- 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?

- Mission Impact

Addressing nonlinear motion Encounters in Space

Treat each small

segment as linear

Q

Must reintroduce

3rd dimension along

each length of tube

Upcoming Improvements Encounters in Space

Q

- Test for linearity
- Assessing nonlinear motion
- Adjoining right cylinders
- Gap elimination

- Handling non-spherical shapes

Eliminating gaps & overlaps Encounters in Space

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)

axis13r Encounters in Space

Eliminating gaps & overlaps

Q

All data rotated to align new z axis with axis12r

axis12r = [0 0 1]

axis12r & axis23r are unit vectors

axis13r = axis12r + axis23r

Compound miter ┴ to axis13r

Eliminating gaps & overlaps Encounters in Space

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 Encounters in Space easily address complex shapes

Concave, Spiral

Hollow, Convex

In theory, satellite could fly thru

Q

Just light up different pixels

Where can I get shapes? Encounters in Space

Q

From image files

Iridium silhouette

from STK Area Tool

Oriented along

relative velocity

vector

Combined object footprint Encounters in Space

Q

Raster sweep for combined object footprint

No need to alter integrand

Only compute red pixels

Footprint can be dynamic (tumbling)

Raster sweep example Encounters in Space

Q

MATLAB image merging tool Encounters in Space

Q

Chan’s approach to complex objects Encounters in Space

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 Encounters in Space

– just let STK do it

Q

Inherently accounts for proper solar panel orientation

relative velocity orientation, offsets, eclipsing/exclusions

Elimination of linear assumptions Encounters in Space

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

Q

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)

AdvCAT Encounters in Space

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 featuresQ

Wrap up Encounters in Space

Q

- Assumptions
- Maximum probability & dilution
- SOCRATES demo
- Collision Avoidance Maneuver Planning
- Upcoming Improvements

I would love to change the world, but they won't give me the source code - Unknown

Q

Need help? Just call

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