time evolution of risk cola
DESCRIPTION
Time Evolution of Risk COLA. Vaš Majer Integral Systems, Inc AIAA Space Operations Workshop 15-16 April 2008 9/26/2014 12:01 PM. Introduction. Hello. Agenda. OASYS COLA Risk Analysis Drift-By Scenario On-Station [Home] Drifting[Visitor] Time Evolution of Separation Risk. COLA. - PowerPoint PPT PresentationTRANSCRIPT
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Time Evolution of Risk COLA
Vaš MajerIntegral Systems, Inc
AIAA Space Operations Workshop15-16 April 2008
04/21/23 03:45
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Introduction
Hello
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Agenda OASYS COLA Risk Analysis
Drift-By Scenario On-Station [Home] Drifting [Visitor]
Time Evolution of Separation Risk
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COLA
OASYS Collision Risk Assessment
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Given
t → u(t) = y(t) – x(t) 3D Separation Vector Ephemeris Vehicle Y with Respect to Vehicle X u=0: Vehicle Y @ Vehicle X Center of
Mass
t → R(t) 3D Joint Uncertainty Covariance
Ephemeris
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The Scenario
0
0
Collision Avoidance Scenario
x
y
separation,u
sphere,S
covariance,R a
b
d
u Separation EstimateR Covariance of Estimator
d Radius of Hard Body Stay-Out Sphere, S
z = (x,y) Any Trial Vector
TRUTH, z=Z, is, As Always, Nowhere to be Seen, FixedBut Unknown
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The Definition
Collision TRUTH, Z, is Inside Stay-Out Sphere S
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The Objective
Quantify Risk of Collision For Estimators, t → u(t), t T In View of Uncertainty, R(t) In View of Stay-Out Sphere, S With a Scalar Function, t → r(t)
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Attributes of Risk Statistic, r
0 < r ≤ 1 r = 0 Lowest Possible Risk r = 1 Highest Possible Risk r is Conservative r is Robust
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Conservative Because Estimator, u...
Is Biased Relative to Truth, Z Bias u-Z is Unknown
And Because Estimator Covariance, R... Should be Centered on Truth, Z, which is Unknown Is Notoriously Optimistic [Small] Under-States Variance/Uncertainty
We Want Risk Statistic, r, Such That... r is Upper Bound on Risk r Threshold Levels Have Meaning
Independent of Scenario Geometry r > 0; Risk Never Sleeps r = 1 OK; Extreme Risk Deserves Notice
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Robust r Conforms to Intuitive Notion of
Risk r increases as |u| decreases r increases as |R| increases r increases as d increases
r is Sensible for Limiting Scenarios u in S implies r = 1 u near S implies r ~ 1 r makes sense even for d=0
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Risk of Collision, rC
OASYS™ COLA Statistic
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Risk of Collision, rC if (0 ≤ |u| ≤ d)
rC = 1; else
v = d (u/|u|);V = {z | J(z; v,R) < J(u; v,R)}
q = ∫V dp(z; v,R)
rC = 1 – q;
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Risk of Collision Heuristic Make the NULL Hypothesis:
u is a Trial Estimator of Truth Z=v, where v = d (u/|u|); d = radius of S; and Trial Estimators are z ~ Gauss(v,R)
v is the Point in S which is Closest to Estimator u
V is the (v,R) Metric Sphere of Radius |R-1/2(u-v)| Centered at v
Estimator u is on the Boundary of V
q is the Probability Measure of the (v,R)-Sphere, V the Probability that a Random Trial Estimator of Z=v Lies in V
rC = 1-q is the Probability Measure of the Complement of V an Upper Bound on the Probability that the NULL Hypothesis is TRUE
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Drift-By Scenario
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GEO Drift-By
SatX [HEX] on GEO Station COV Epoch @ t=0
SatY [WHY] in GEO Drift-By COV Epoch @ t = 0 Close Approach to HEX @ t ~ 10
hours
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COLA Analysis Controls Hard-Body Sphere Around HEX
100 m
Alarm Levels
Alarm Risk Separation
RED 1x10-3 1 km
YELLOW 1x10-6 10 km
GREEN 1x10-9 100 km
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Common Risks
Event Risk
Winning Lottery 1/100M= 1e-8
Car Crash KSI 6/1000 = 6e-3
Ace of Hearts 2/104 = 2e-2KSI: Killed or Seriously Injured
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Common GEO Separations
Description Separation
1 deg/day Relocation 89 km
50 mdeg Slot Half-Width 37 km
100 Eccentricity 08 km
: micros, 1e-6
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Time Evolution COLA
10 Day Span Centered on COV Epoch @
t=0
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Time Evolution of Separation
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Discussion of Separation
Near Linear Approach and Departure Clear Point of CAP @ t ~ 10 hours Alarm Level sepYEL=100 km Active Alarm Level sepRED= 10 km InActive
sepMIN=10.023 km > sepRED = 10 km
Looks Safe Enough...
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Time Evolution of Risk
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Discussion of Risk log10(1) = 0
Periodic rskMAX ~= 1 12 hour Period
Risk Alarms Triggered Well Before and Well After CAP Risk Alarm Level Transitions Closely Spaced
High Risk Levels Despite Large Separations COV Epochs @ t=0 Uncertainty Grows Forward/Backward in Time
In Real Life... COV Epochs are Many Revs Prior to CAP Growth of Uncertainty is Significant
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Time Evolution of J,H Metrics
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Discussion of Metrics The Whole Story Encapsulated
H ~ Squared Separation [cyan] J ~ ChiSquared Separation [blue]
Minima of H ~ Minima of Separation Apparently Benign Alarm Levels
Minima of J ~ Maxima of Risk Alarm Levels Triggered Well in Advance Risk Maxima Identified
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Summary Useful
COL Risk Analysis CAP Separation Analysis Complementary Views of Close Encounter
Essential Time Evolution Study of Risk/Separation Acknowledge Growth of Uncertainty with Time
Myopic and Even Dangerous Restrict COLA to Times of CAP Restrict COLA to 2D Relative Velocity
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The End