1. Principles of Radar Target Tracking Jay Bhalodi, Jeff Cao, Lily Healey, Wendy Lin, Tuling Ma, Zara Mannan, Brandon Millman, Zachary Purdy, Divya Sharma, Mimi Xu

2. The Corporations CheetahTrack Jay Bhalodi, Lily Healey, Wendy Lin, Tuling Ma, Mimi Xu TRAC Jeffrey Cao, Zara Mannan, Brandon Millman, Zachary Purdy, Divya Sharma, Government Agent Consultant Randy Heuer Zachary Vogel

3. Problem and Solution Solution: Kalman Filter Updates to better approximate noise Problem: Noise Inaccuracies in measurement data Account for noise to better predict

4. Kalman Filter: Background Derived by R.E. Kalman Published A New Approach to Linear Filtering and Prediction Problems in the Journal of Basic Engineering in 1960 Kalman Filter used extensively in fields of navigation and tracking

5. Kalman Filter Model = The foundation of the Kalman filter lies in its model of both the target’s movement and the actual measurement of the position.

6. Kalman Theory The Kalman Filter is a two-step algorithm : First the algorithm “predicts” the target’s next expected location Then update predictions based on new measurements PREDICTUPDATE

7. Predict Step Predicts using transition matrix and current velocity value Advances state covariance matrix for update step

8. Update Step Calculates Kalman Gain Matrix Updates position matrix based on weighting factor and residual Recalculates state covariance matrix for predict step

9. Implementation Modular - easy to modify Different class for filter and each matrix Java - Efficient due to object-oriented nature

10. Implementation JAMA Matrix Library Java Libraries JAMA Matrix Library Vector Class National Institute of Standards and Technology (NIST)

12. Residuals- difference between our results and real data

13. Adaptations Adapted filter to different challenging environments: Polar Conversions Two Radars Collision Avoidance Maneuvering Targets Intercepting Targets

14. r α θ Polar Conversions Real life applications-Range and Bearing Transformed coordinate system

15. Updating the R Matrix Error of range and bearing not along the xy plane

17. Multiple Radars Added update method to recalculate state transition (Φ) matrix Two changes: multiple data-input sources variable time Implementation: Tagged data to later reconcile to single reference frame

19. Collision Avoidance Some Changes: Track two targets Within 12 mi, predict paths Within 1 mi, prompt for evasive action

20. Collision Avoidance (cont.) Sequence of Steps: Run filter for each target Check distance each iteration If less than 12 miles: Solve for time Predict if they will come within 1 mi of each other (40)

22. Maneuvering Targets The Change: Target no longer follows one linear path and may maneuver The Steps: Detect Count Reset

25. Residuals

26. Intercepting Targets β Target Point of Interception Interceptor τ α N D B A γ E Use Law of Sines to find α and β can be found using

27. Intercepting Targets β Target Point of Interception Interceptor τ α N D B A γ

29. Further Applications Real Time Radar Tracking Variable Altitudes Acceleration

30. Conclusion Exposure to and successful implementation of Kalman Filter Many adaptations for our tracking system Overall, successful and effective

31. THANK YOU!  Randy Heuer and Zachary Vogel  Dr. Miyamoto  Paul and Counselors  Course and Lab Teachers

32. Thank you Jewish Communal Fund John and Laura Overdeck NJGSS Alumnae and Parents, 1984 - 2008 Novartis Schering-Plough Foundation The Dorr Foundation The Edward W. and Stella C. Van Houten Memorial Fund The Jennifer A. Chalsty Foundation

33. Any Questions?

34. References [1] Blackman SS. 1986. Multiple-Target Tracking with Radar Applications. Artech House, Inc. [2] Atwood B. 2003. Covariance and GLAST.. Accessed 2008 July 21. [3] [IEEE] Institute of Electrical and Electronics Engineers. 2003 Jan 23. Rudolf E. Kalman, 1930-. IEEE History Center.. Accessed 2008 July 21. [4] Kalman, R. E. 1960. A New Approach to Linear Filtering and Prediction Problems. ASME Journal of Basic Engineering 1960 March.