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Probability of Attack Probability of Attack
of Fixed Wing Aircraft in a of Fixed Wing Aircraft in a
Ground Based Air Defence EnvironmentGround Based Air Defence Environment
Presentation by Jacques du Toit and Willa Lotz
Division of Applied Mathematics
Department of Mathematical Sciences
University of Stellenbosch
November 2007
Supervisors:J.H. van Vuuren (Department of Logistics)J.N. Roux (Reutech Radar Systems)
© Jacques du Toit 2007
OutlineJacques du Toit
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Part A
Probabilistic threat evaluation model overview
Flight path generation
Time to target probability
Part B (Willa Lotz)
Probabilistic threat evaluation model overview
Aircraft attack technique analysis
Aircraft attribute analysis
Aircraft membership estimations
OutlineJacques du Toit
© Jacques du Toit 2007
Probabilistic Threat Evaluation Model Overview
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Aircraft attack techniques(flight profiles)
Probabilistic Threat Evaluation Model Overview
Combat Hump Dive
Combat Turn Dive
Toss-Bombing
High Level DiveLow Level Attack I
Low Level Attack II
Low Level Attack III
Low Level Attack IV
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Model components
Component I (probability of attack)
Probabilistic Threat Evaluation Model Overview
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Probabilistic Threat Evaluation Model Overview
© Jacques du Toit 2007
Flight path generation
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Data considerations
Waypoint
Flight path generation
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Flight path generation
Dynamics Approach
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Flight path generation
Path Planner
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Curve scheme(B-splines)
Flight path generation
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Weighted and constrained least squares
Interpolated
Approximated
Flight path generation
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Weighted and constrained least squares
Flight path generation
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Flight path generation
Weighted and constrained least squares
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Weighted and constrained least squares
Flight path generation
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Incorporating time
Flight path generation
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Multiple profiles
Flight path generation
© Jacques du Toit 2007
Time to target probability
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Time to target probability
© Willa Lotz 2007
OutlineWilla Lotz
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OutlineWilla Lotz
Part A (Jacques du Toit)
Probabilistic threat evaluation model overview
Flight path generation
Time to target probability
Part B
Probabilistic threat evaluation model overview
Aircraft attack technique analysis
Aircraft attribute analysis
Aircraft membership estimations
© Willa Lotz 2007
Probabilistic Threat Evaluation Model Overview
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Aircraft attack techniques(flight profiles)
Probabilistic Threat Evaluation Model Overview
Combat Hump Dive
Combat Turn Dive
Toss-Bombing
High Level DiveLow Level Attack I
Low Level Attack II
Low Level Attack III
Low Level Attack IV
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Aircraft type
FormativeElement
Combinations
Aircraft attack techniqueWeapon type
}C2= { ,,},C1={ ,
Cn= { },,
Probabilistic Threat Evaluation Model Overview
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Model components:
Component I (Probability of attack):
Probabilistic Threat Evaluation Model Overview
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Low Level Attack I
Low Level Attack II
Combat Turn Dive
High Level Dive
Low Level Attack III
Low Level Attack IV
Probabilistic Threat Evaluation Model Overview
Aircraft attack techniques(flight profiles)
Combat Hump Dive Toss-BombingCombat Hump Dive Toss-Bombing
Toss-Bombing (2D)
Combat Hump Dive (2D)
Aircraft attack technique stages
Combat Hump Dive (3D)
Toss-Bombing (3D)
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Model components:
Component I (Probability of attack):
Probabilistic Threat Evaluation Model Overview
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Model components:
Component I (Probability of attack):
Probabilistic Threat Evaluation Model Overview
© Willa Lotz 2007
Aircraft Attack Technique Analysis
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Aircraft Attack Technique Analysis
Each aircraft attack technique associated with a formative element combination is subdivided into a number of smaller segments known as stages.
Combat Hump Dive (2D)
Combat Hump Dive (2D)
Combat Hump Dive (3D)
Combat Hump Dive (3D)
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Technique applied
Data mining (Cluster analysis)
Aircraft Attack Technique Analysis
Each aircraft attack technique associated with a formative element combination is subdivided into a number of smaller segments known as stages.
Reduce data requirements
Reduce real-time computations
The total number of formative elements combinations considered are reduced.
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Aircraft Attack Technique Analysis
© Willa Lotz 2007
Aircraft Attribute Analysis
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Aircraft Attribute Analysis
The minimum number of aircraft attributes, necessary to describe each stage of an aircraft attack technique associated with a given formative element combination, are identified.
Combat Hump Dive (2D)Combat Hump Dive (3D)
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Aircraft Attribute Analysis
The minimum number of aircraft attributes, necessary to describe each stage of an aircraft attack technique associated with a given formative element combination, are identified.
Reduce data requirements
Reduce real-time computations
Technique applied
Data mining (Regression analysis)
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Aircraft Attribute Analysis
© Willa Lotz 2007
Aircraft Membership Estimations
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Techniques applied
Density estimation1. Kernel estimation2. Maximum Likelihood Estimation (MLE)
Model components:
Component I (Probability of attack):
Aircraft membership Estimations
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Estimating the probability that an observed aircraft are embodied
in a specific formative element combination
Aircraft Membership Estimations
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Estimating the probability that an observed aircraft finds itself in any one of the stages of an aircraft attack technique associated with a
specific formative element combination
Aircraft Membership Estimations
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Questions
Jacques du Toit
Division of Applied Mathematics
Department of Mathematical Sciences
University of Stellenbosch
jacques@dip.sun.ac.za
Willa Lotz
Division of Applied Mathematics
Department of Mathematical Sciences
University of Stellenbosch
willa@dip.sun.ac.za
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Example
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Example
Example:
X 6
X 2
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Example
System time
Product
S3 88% 0% 0%
S2 93% 19% 18%
S1 17% 88% 15%
S0 12% 100% 12%
= 45%
System time
Product
S4 89% 0% 0%
S3 41% 0% 0%
S2 20% 4% 1%
S1 19% 47% 9%
S0 3% 100% 3%
= 13%
= (0.13 X 0.75) + (0.45 X 0.25)
= 21%
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Questions
Jacques du Toit
Division of Applied Mathematics
Department of Mathematical Sciences
University of Stellenbosch
jacques@dip.sun.ac.za
Willa Lotz
Division of Applied Mathematics
Department of Mathematical Sciences
University of Stellenbosch
willa@dip.sun.ac.za
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