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Probability of Attack of Fixed Wing Aircraft in a Ground 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)

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© Jacques du Toit 2007 Outline Jacques du Toit

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3 of 44 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 Outline Jacques du Toit

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© Jacques du Toit 2007 Probabilistic Threat Evaluation Model Overview

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5 of 44 Aircraft attack techniques (flight profiles) Probabilistic Threat Evaluation Model Overview Combat Hump Dive Combat Turn Dive Toss-Bombing High Level Dive Low Level Attack I Low Level Attack II Low Level Attack III Low Level Attack IV

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6 of 44 Model components Component I (probability of attack) Probabilistic Threat Evaluation Model Overview

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7 of 44 Probabilistic Threat Evaluation Model Overview

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© Jacques du Toit 2007 Flight path generation

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9 of 44 Data considerations Waypoint Flight path generation

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10 of 44 Flight path generation Dynamics Approach

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11 of 44 Flight path generation Path Planner

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12 of 44 Curve scheme (B-splines) Flight path generation

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13 of 44 Weighted and constrained least squares Interpolated Approximated Flight path generation

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14 of 44 Weighted and constrained least squares Flight path generation

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15 of 44 Flight path generation Weighted and constrained least squares

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16 of 44 Weighted and constrained least squares Flight path generation

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17 of 44 Incorporating time Flight path generation

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18 of 44 Multiple profiles Flight path generation

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© Jacques du Toit 2007 Time to target probability

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20 of 44 Time to target probability

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© Willa Lotz 2007 Outline Willa Lotz

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22 of 44 Outline Willa 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

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© Willa Lotz 2007 Probabilistic Threat Evaluation Model Overview

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24 of 44 Aircraft attack techniques (flight profiles) Probabilistic Threat Evaluation Model Overview Combat Hump Dive Combat Turn Dive Toss-Bombing High Level Dive Low Level Attack I Low Level Attack II Low Level Attack III Low Level Attack IV

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25 of 44 Aircraft type Formative Element Combinations Aircraft attack technique Weapon type } C2=C2= {,, }, C1=C1= {, Cn=Cn= { },, Probabilistic Threat Evaluation Model Overview

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26 of 44 Model components: Component I (Probability of attack): Probabilistic Threat Evaluation Model Overview

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27 of 44 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-Bombing Combat 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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28 of 44 Model components: Component I (Probability of attack): Probabilistic Threat Evaluation Model Overview

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29 of 44 Model components: Component I (Probability of attack): Probabilistic Threat Evaluation Model Overview

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© Willa Lotz 2007 Aircraft Attack Technique Analysis

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31 of 44 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 (3D)

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32 of 44 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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33 of 44 Aircraft Attack Technique Analysis

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© Willa Lotz 2007 Aircraft Attribute Analysis

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35 of 44 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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36 of 44 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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37 of 44 Aircraft Attribute Analysis

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© Willa Lotz 2007 Aircraft Membership Estimations

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39 of 44 Techniques applied Density estimation 1.Kernel estimation 2.Maximum Likelihood Estimation (MLE) Model components: Component I (Probability of attack): Aircraft membership Estimations

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40 of 44 Estimating the probability that an observed aircraft are embodied in a specific formative element combination Aircraft Membership Estimations

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41 of 44 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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42 of 44 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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43 of 44 Example

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44 of 44 Example Example: X 6 X 2

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45 of 44 Example System time Product S388%0% S293%19%18% S117%88%15% S012%100%12% = 45% System time Product S489%0% S341%0% S220%4%1% S119%47%9% S03%100%3% = 13% = (0.13 X 0.75) + (0.45 X 0.25) = 21%

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46 of 44 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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