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Interception Planning System

Interception Planning System. Omer Cohen Shilo Abramovicz With the guidance of: Eliran Abutbul and Sharon Rabinovich. Project Definition. Designing an algorithm for intercepting ballistic missiles with a ballistic interceptor, based on target and interceptor model. Problem Definition.

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Interception Planning System

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  1. Interception Planning System Omer Cohen ShiloAbramovicz With the guidance of: EliranAbutbuland Sharon Rabinovich

  2. Project Definition Designing an algorithm for intercepting ballistic missiles with a ballistic interceptor, based on target and interceptor model.

  3. Problem Definition Finding an interception plan (a launch yaw and pitch) Which satisfies the following constraints: 1.The launch does not occur in the past 2.The maximum height of the interceptor doesn’t cross a certain height. 3. The interceptor’s velocity at the interception point must be larger then the user’s demand. 4. The aspect of the interception must be close enough to .

  4. Problem Definition From the feasible solutions we choose the one that maximize the following objective function: (w1, w2, w3)- user’s input. w1*IcpVel+w2*RelativeVel+w3*IcpAccel

  5. Development Steps • Building a model of ballistic missile trajectory. • Finding all the feasible interception plans under • the given constraints • Choosing the optimal plan according the objective • function.

  6. Model Design- Forces - Drag Force A force that oppose the relative motion of an object through a fluid (a liquid or gas). -Velocity Vector -Drag Coeff -Cross-sectional area -Material Density -Gravitation

  7. Motion Equations Ballistic Coefficient

  8. Atmosisa Function [T a P rho]=atmosisa(height) The function gets the height above sea level And returns: -Temparture -Pressure -Air Density -Speed of sound

  9. Atmosisa Function Uses the International Standard Atmosphere model This function uses another function, “atmosplase”, with constants, such as: and are calculated using the Ideal Gas Model.

  10. Calculating β(ballistic coeff) We calculate βusing a linear interpolation

  11. Euler’s Approximation Method A second order approximation method, used here to solve the motion equations. For a certain and the initial conditions :

  12. RK4 - Approximation Method A second order approximation method, used here to solve the motion equations. For a certain and the initial conditions :

  13. RK4 - Approximation Method Using this method for propagating the location requires the calculation of the velocity at half the time, such as: Which complex the calculation difficulty. Therefore, we used the following approximation :

  14. Comparing the Methods

  15. Comparing the Methods

  16. Tolerances-Temperature

  17. Creating The Table We’ll Us two tables- one for the lower impact angle and the other for the larger.

  18. Solution Demonstration of the relation between the angle and the range and height paremeters:

  19. Finding Optimal Solution • Developing the target’s trajectory • Projecting each point to a 2D plane – z axis stays the same xy transform to • Range. • Performing the “best” interpolation from table data. • Checking if the constraints are being satisfied. • Calculating the target function and replacing the current solution if • necessary.

  20. Finding Optimal Solution

  21. Other Possible Solutions Each point in the space can be achieved with two different launch pitches Suggestions: • fit every relevant paremeter (pitch angle, impact angle, • impact velocity, etc.) to a fifth degree polynomial. • fitting using ANN.

  22. Surface Fitting surface fitting was performed for each table parameter resulting a Two variable, five degree polynomial. The fitting is based on MMSE. Instead of performing the interpolation, the height and range will be Inserted into to polynomial and that will give us the wanted parameter.

  23. Surface Fitting

  24. Surface Fitting

  25. Artificial Neural Network Using Matlab's Neural Network Fitting Tool it is possible to create a neural network that is a close fit to the table. The table cells are given to the tool and it trains a suitable Neural network. In order to achieve better results this method will consume to much time and memory.

  26. Artificial Neural Network

  27. Graphic User Interface

  28. Refernces • http://en.wikipedia.org/wiki/Drag_%28physics%29 • http://en.wikipedia.org/wiki/Drag_coefficient • http://en.wikipedia.org/wiki/Drag_equation • The International Standard Atmosphere (ISA) • http://www.learnartificialneuralnetworks.com/ a tutorial about ANN • http://mathworld.wolfram.com/Runge-KuttaMethod.html-RK4 method • http://www3.ee.technion.ac.il/labs/eelabs/Upload/Projects/Enrichment • /winter2011/Graphics%20and%20GUI%20using%20Matlab.pdf

  29. THE END!

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