Principles of Radar Target Tracking

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

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

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. PREDICT UPDATE 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

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

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

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

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

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

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

17. Multiple Radars Two changes: multiple data-input sources variable time Implementation: Added update method to recalculate state transition (Φ) matrix 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 (40) If less than 12 miles: Predict if they will come within 1 mi of each other Solve for time

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

25. Residuals

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

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

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 John and Laura Overdeck Jewish Communal Fund NJGSS Alumnae and Parents, 1984 - 2008 Schering-Plough Foundation Novartis 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. <http://www-glast.slac.stanford.edu/software/AnaGroup/WBA072003-Covariance.pdf>. Accessed 2008 July 21. [3] [IEEE] Institute of Electrical and Electronics Engineers. 2003 Jan 23. Rudolf E. Kalman, 1930-. IEEE History Center. <http://www.ieee.org/web/aboutus/history_center/biography/kalman.html>. 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.