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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. The Corporations. Government Agent. Randy Heuer. Consultant. Zachary Vogel. CheetahTrack.
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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
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,
Problem and Solution Problem: Noise Inaccuracies in measurement data Solution: Kalman Filter Account for noise to better predict Updates to better approximate noise
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
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.
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
Predict Step Predicts using transition matrix and current velocity value Advances state covariance matrix for update step
Update Step Updates position matrix based on weighting factor and residual Calculates Kalman Gain Matrix Recalculates state covariance matrix for predict step
Implementation Java - Efficient due to object-oriented nature Different class for filter and each matrix Modular - easy to modify
Implementation Java Libraries JAMA Matrix Library JAMA Matrix Library National Institute of Standards and Technology (NIST) Vector Class
Adaptations Adapted filter to different challenging environments: Polar Conversions Two Radars Collision Avoidance Maneuvering Targets Intercepting Targets
Polar Conversions Real life applications-Range and Bearing r Transformed coordinate system α θ
Updating the R Matrix Error of range and bearing not along the xy plane
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
Collision Avoidance Some Changes: Track two targets Within 12 mi, predict paths Within 1 mi, prompt for evasive action
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
Maneuvering Targets The Change: The Steps: • Detect • Count • Reset Target no longer follows one linear path and may maneuver
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
N Point of Interception B A β α Target γ τ D Interceptor Intercepting Targets
Further Applications Real Time Radar Tracking Variable Altitudes Acceleration
Conclusion • Exposure to and successful implementation of Kalman Filter • Many adaptations for our tracking system • Overall, successful and effective
THANK YOU! • Randy Heuer and Zachary Vogel • Dr. Miyamoto • Paul and Counselors • Course and Lab Teachers
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
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.