1. 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)

2. © Jacques du Toit 2007 Outline Jacques du Toit

3. 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

4. © Jacques du Toit 2007 Probabilistic Threat Evaluation Model Overview

5. 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

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

7. 7 of 44 Probabilistic Threat Evaluation Model Overview

8. © Jacques du Toit 2007 Flight path generation

9. 9 of 44 Data considerations Waypoint Flight path generation

10. 10 of 44 Flight path generation Dynamics Approach

11. 11 of 44 Flight path generation Path Planner

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

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

14. 14 of 44 Weighted and constrained least squares Flight path generation

15. 15 of 44 Flight path generation Weighted and constrained least squares

16. 16 of 44 Weighted and constrained least squares Flight path generation

17. 17 of 44 Incorporating time Flight path generation

18. 18 of 44 Multiple profiles Flight path generation

19. © Jacques du Toit 2007 Time to target probability

20. 20 of 44 Time to target probability

21. © Willa Lotz 2007 Outline Willa Lotz

22. 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

23. © Willa Lotz 2007 Probabilistic Threat Evaluation Model Overview

24. 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

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

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

27. 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)

28. 28 of 44 Model components: Component I (Probability of attack): Probabilistic Threat Evaluation Model Overview

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

30. © Willa Lotz 2007 Aircraft Attack Technique Analysis

31. 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)

32. 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.

33. 33 of 44 Aircraft Attack Technique Analysis

34. © Willa Lotz 2007 Aircraft Attribute Analysis

35. 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)

36. 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)

37. 37 of 44 Aircraft Attribute Analysis

38. © Willa Lotz 2007 Aircraft Membership Estimations

39. 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

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

41. 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

42. 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

43. 43 of 44 Example

44. 44 of 44 Example Example: X 6 X 2

45. 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%

46. 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