1. Sniper Localization Using Acoustic Sensors Allison Doren Anne Kitzmiller Allie Lockhart Under the Direction of Dr. Arye Nehorai December 11, 2013 [6]

2. Outline  Background  Muzzle Blast Model  Sniper Localization  Maximum Likelihood  Cramér-Rao Bound  Mean Square Error  Results  Detection  Conclusions

3. Background  Existing Work:  “Shooter Localization in Wireless Microphone Networks,” comparing muzzle blast and shock wave models and using Cramér-Rao lower bound analysis [1]  “Analysis of Sniper Localization for Mobile, Asynchronous Sensors”, relying on time difference of arrival measurements, and providing a Cramér-Rao bound for the models [2]  “ShotSpotter” uses acoustic sensors to detect outside gunshot incidents in the D.C. area [5]  Applications:  Military Operations: can be worn by soldiers or placed in vehicles  Civilian Environments: can detect gunfire to alert local authorities Example of a sensor network [2] = sensor = shooter

4. Types of Models 1.Shockwave Model (SW)  Exploits the shockwave of a gun shot, which comes about as a result of the supersonic bullets 2.Muzzle Blast Model (MB)  Exploits the “bang” of a gun shot 3.Combined Model (Shockwave and Muzzle Blast) The shockwave from the supersonic bullet reaches the microphone before the muzzle blast [1]

5. Muzzle Blast Model: First Step

6. Muzzle Blast Model: Second Step e

8. Cramér-Rao Bound  The Cramér-Rao Bound (CRB) is a lower bound on the variance of an unbiased estimator  We use a Multivariate Normal Distribution, because TDOA vector has a length equal to N-1

9. Cramér-Rao Bound  CRB for Multivariate Case  The Fisher Information Matrix (FIM) for N-variate multivariate normal distribution

10. Cramér-Rao Bound

12. Mean Square Error

13. Signal-to-Noise Ratio (SNR)

14. Results

15. (a) Sensor network and shooter position(b) Localization error of position Placement of sensors in Matlab model and localization error  Variance = 0.01  Minimum values of error at (0,0), our true sniper location

16. Comparison of localization performance on various six sensor geometries Sensor Network Geometry  Shooter surrounded by sensors is ideal, but not practical  Line of sensors does not provide sufficient information

17. Comparison of localization performance on various random sensor geometries Sensor Network Geometry  Increased number of sensors increases accuracy, but not realistic to have this many sensors in close range

18. MSE of sniper position (x, y) vs. SNR  As the signal-to-noise ratio increases, error decreases  Thus as noise increases, error increases MSE of position vs. SNR

19. r  MSE converges to the CRB as SNR increases

20. Detection - general

21. Detection of a shot

23. ROC Curve ROC Curve generated from detection applied in the scalar case (2 sensors) PDPD

24. Conclusions  We used the Maximum Likelihood Method, Cramér-Rao Bound, and Mean Square Error in the Muzzle Blast Model to analyze our simulated shooter data, with different values of variance (noise)  As predicted, MSE increases as noise increases  MSE converges to the CRB as SNR increases  We studied the concept of detection and applied it to the scalar case of detecting a sniper with two sensors  We would have liked to compare our results to actual data obtained from sensors  Further Research  Adding walls or other obstacles to sensor model  Using different types of sensors, ie. optical, infrared  Explore shockwave or combined MB-SW model  Compare results to real data

25. References 1.D. Lindgren, O. Wilsson, F. Gustafsson, and H. Habberstad, “Shooter localization in wireless sensor networks,” Information Fusion, 2009, FUSION ’09, 12 th International Conference on, pp. 404-411, 2009. 2.G. T. Whipps, L. M. Kaplan, and R. Damarla, “Analysis of sniper localization for mobile, asynchronous sensors,” Signal Processing, Sensor Fusion, and Target Recognition XVIII, vol. 7336, 2009. 3.P. Bestagini, M. Compagnoni, F. Antonacci, A. Sarti, and S. Tubaro, “TDOA-based acoustic source localization in the space-range reference frame,” Multidimensional Systems and Signal Processing, Vol. March, 2013. 4.Stephen, Tan Kok Sin. (2006). Source localization using wireless sensor networks (Master’s thesis). Naval Postgraduate School, 2006. Web. Sept 2013. 5.Berkowitz, Bonnie, Emily Chow, Dan Keating and James Smallwood. “Shots heard around the District.” The Washington Post 2 Nov. 2013. Investigations Web. Nov. 2013. 6.Photograph of Sniper. Photograph. n.d. Shooter Localization Mobile App Pinpoints Enemy Snipers. Vanderbilt School of Engineering. Web. 11 Nov 2013. 7.Hogg, Robert V., and Allen T. Craig. Introduction to Mathematical Statistics. New York: Macmillan, 1978. 90-98. Print.

26. Thank You!  Thank you to Keyong Han, the PhD student who has been guiding us throughout this project.  Thank you to Dr. Arye Nehorai for all of his help in overseeing our work and our progress.

27. Questions?