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Sniper Localization Using Acoustic SensorsAllison DorenAnne KitzmillerAllie Lockhart

Under the Direction of Dr. Arye NehoraiDecember 11, 2013

[6]OutlineBackgroundMuzzle Blast ModelSniper LocalizationMaximum LikelihoodCramr-Rao BoundMean Square ErrorResultsDetectionConclusions

BackgroundExisting Work:Shooter Localization in Wireless Microphone Networks, comparing muzzle blast and shock wave models and using Cramr-Rao lower bound analysis[1]Analysis of Sniper Localization for Mobile, Asynchronous Sensors, relying on time difference of arrival measurements, and providing a Cramr-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 vehiclesCivilian Environments: can detect gunfire to alert local authorities

Example of a sensor network[2]= sensor= shooter

Types of ModelsShockwave Model (SW)Exploits the shockwave of a gun shot, which comes about as a result of the supersonic bulletsMuzzle Blast Model (MB)Exploits the bang of a gun shotCombined Model (Shockwave and Muzzle Blast)

The shockwave from the supersonic bullet reaches the microphone before the muzzle blast [1]Muzzle Blast Model: First StepMuzzle Blast Model: Second StepeMuzzle Blast Model: Second StepCramr-Rao BoundThe Cramr-Rao Bound (CRB) is a lower bound on the variance of an unbiased estimatorWe use a Multivariate Normal Distribution, because TDOA vector has a length equal to N-1Cramr-Rao BoundCRB for Multivariate CaseThe Fisher Information Matrix (FIM) for N-variate multivariate normal distribution

Cramr-Rao BoundCramr-Rao BoundMean Square ErrorSignal-to-Noise Ratio (SNR)Results

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

Comparison of localization performance on various six sensor geometriesSensor Network GeometryShooter surrounded by sensors is ideal, but not practicalLine of sensors does not provide sufficient information

Comparison of localization performance on various random sensor geometriesSensor Network GeometryIncreased number of sensors increases accuracy, but not realistic to have this many sensors in close range

MSE of sniper position (x, y) vs. SNRAs the signal-to-noise ratio increases, error decreasesThus as noise increases, error increases

MSE of position vs. SNR

rMSE converges to the CRB as SNR increases

Detection - generalDetection of a shotDetection of a shot

ROC CurveROC Curve generated from detection applied in the scalar case (2 sensors)PDConclusionsWe used the Maximum Likelihood Method, Cramr-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 increasesMSE converges to the CRB as SNR increasesWe studied the concept of detection and applied it to the scalar case of detecting a sniper with two sensorsWe would have liked to compare our results to actual data obtained from sensorsFurther Research Adding walls or other obstacles to sensor modelUsing different types of sensors, ie. optical, infraredExplore shockwave or combined MB-SW modelCompare results to real dataReferencesD. Lindgren, O. Wilsson, F. Gustafsson, and H. Habberstad, Shooter localization in wireless sensor networks, Information Fusion, 2009, FUSION 09, 12th International Conference on, pp. 404-411, 2009.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.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.Stephen, Tan Kok Sin. (2006). Source localization using wireless sensor networks (Masters thesis). Naval Postgraduate School, 2006. Web. Sept 2013.Berkowitz, Bonnie, Emily Chow, Dan Keating and James Smallwood. Shots heard around the District. The Washington Post 2 Nov. 2013. Investigations Web. Nov. 2013.Photograph of Sniper.Photograph. n.d. Shooter Localization Mobile App Pinpoints Enemy Snipers.Vanderbilt School of Engineering.Web. 11 Nov 2013.Hogg, Robert V., and Allen T. Craig.Introduction to Mathematical Statistics. New York: Macmillan, 1978. 90-98. Print.

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.Questions?