AIM9X: A Modeling

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AIM-9XA Modeling Simulation Success Story

• A. Rex Rivolo

25 June 2002
Institute for Defense Analyses 4850 Mark Center
Drive Alexandria, VA 22311-1882
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AIM-9X System Description
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AIM-9X Launch Envelope
Range
OBA
AIM-9X
AIM-9X
AIM-9M
AA-11
AA-11
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Prototype for Simulation Based Acquisition
The primary method for evaluating Pk is with the
use of MS AIM-9X Test
Evaluation Master Plan, 1998

• Why Simulation?
• Save time
• Save money
• Not practical/possible to test

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What We Expect From a Simulation?
The Correct Answer to the Appropriate Question !

• For a guided missile simulation we expect answers
  to three questions
• Can the missile reach its intended target under
  the proposed scenario? (kinematic performance)
• What is the probability the missile will
  successfully guide to the target under the
  proposed scenario? (Guide Probability, PG)
• What is the probability the missile will destroy
  the target under the proposed scenario? (Kill
  Probability, PK)

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What Do We Gain From Credible Simulation?

• Ability to explore improvements to missile
  performance without the need to shoot
• Tracker algorithm development
• Assess new component design
• Reduced need for live fire in OTE
• Live fire used to validate simulation
• Simulation used to assess performance
• Tactics development
• Baseline for future development

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Anatomy of a Missile Simulation
Pk Determination
Region
Intercept Plane
A simulation MUST reproduce everything in green!
Targets Trajectory
Targets CM
Aim-point Bias
LAR Determination
Intercept Window
Region
Aim-point Dispersion
Fraction of Guide Failures
Family of all Possible Trajectories (Ensemble)
Launch Point
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The Hard Part
Validation of PK and PG

• Miss distance is everything
• Quantify agreement between each test shot and
  simulation prediction
• Sample over whole parameter space
• Aggregate agreement measure across all test shots

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Miss Distance is Everything
10
2 m
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Proper Missile Simulation Architecture
Target Dynamics
Radiation Field at a Point in Space and Time
Missile Dynamics
Tracking Loop
Tracking Error
Tracking Algorithms
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Simulation Architecture Before AIM-9X
Missile Dynamics
Open Loop Process
Tracking Error
Stochastic Rules Based on Expected Average
Outcome
Stochastic Rules Based on Locally Measured
Behavior
Tracking Algorithms
OR
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Averages Mask What We Want To Know
Simulated World 2
Simulated World 1
Real World
lt PK gt 0.5
lt PK gt 0.5
lt PK gt 0.5
Frequency
Frequency
Frequency
0
0
0
1.0
PK
1.0
1.0
PK
PK
A simulation must reproduce the correct
ensemble distribution
The prediction of mean values is no
prediction at all!
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Method of Locally Measured Behavior
Characterize AVERAGE behavior through captive
flight testing HERE

P1
PK 0.33
Characterize AVERAGE behavior through captive
flight testing HERE
PK 0.66

PK 0
Characterize AVERAGE behavior through captive
flight testing HERE

P2
If parameter space is large, then
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Proper Sampling of the Intercept Parameter Space
Is Seldom Done
Mean PK 0.61
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Measure of Agreement
Plane of Closest Approach
Definition Pi (Tail Probability). Fraction of
prediction points outside the tangent point
contour.
LIVE-FIRE MISS POINT
Pi 0.16
MISS DISTANCE PROBABILITY DENSITY CONTOURS
SIMULATION PREDICTED MISS POINTS
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Test Ensemble Data
Flight 1
Flight 2
Flight N
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Combined Probability Test
Fishers Statistic
N
1
S
F
loge
(Pi)

N
i 1
Single Shot Tail Probabilities
Pi is uniformly distributed in the interval 0 -
1.0
Implies
F is ?2 distributed with 2N Degrees of Freedom
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Real Data
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AIM-9X in Action
t 0.300
t 0
t 1.635
t 1.835
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AIM-9X Parameter Space Sampling
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AIM-9X Kinematic Validation
Angle of Attack
Mach Number
Simulation
Simulation
Actual
Actual
18 Flights, 84 Hz sampling, 25 Monte-Carlos
(Approx. 500,000 data points)
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AIM-9X PK Validation (Fishers Test)
Test Result (Point Estimate)
Perfect Agreement
Uncertainty Distribution
80 Confidence Interval
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SECRET SLIDES(Not Available for This
Presentation)
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Conclusions

• Based on 15 (of 19) live missile firings,
  Fishers Combined Probability Test indicates the
  Integrated Flight Simulation (IFS) is accurately
  predicting missile effectiveness with respect to
  guide and kill probability within uncertainty.
• AIM-9X Operational Test and Evaluation (OPEVAL)
  will add 22 live missile firings to the
  validation data set, further reducing
  uncertainty.
• If at conclusion of OPEVAL IFS remains in
  agreement with live fire events, the IFS alone
  will be used to assess AIM-9X performance against
  the ORD requirements and to satisfy SPEC
  compliance.