IMPROVING EFFICIENCY AND RELIABILITY OF GUNSHOT DETECTIONSYSTEMS

Talal Ahmed, Momin Uppal and Abubakr Muhammad

Dept of Electrical Engineering, LUMS School of Science and Engineering, Lahore, Pakistan

ABSTRACT

In this paper, we focus on setting up a gunshot detec-tion system with high detection performance, robustnessto noise and low computational complexity. To achievethese objectives, we formulate a two-stage approach witha less costly impulsive event detection framework fol-lowed by a relatively more complex gunshot recognitionstage. To improve detection performance of the gun-shot recognition stage, we propose a template matchingmeasure in conjunction with the eighth order linear pre-dictive coding coefficients to train a support vector ma-chine classifier. Using an extensive audio database, wewere able to achieve a better gunshot recognition perfor-mance than with the well-known existing features usedfor gunshot detection.

Index Terms— Gunshot detection systems, Acous-tic signal processing, Event detection, Support vectormachines, Template matching

1. INTRODUCTION

Acoustic gunshot detection systems have been proposedas a tool for the law-enforcement agencies to detect andreport gunfire. In addition, such systems also have mili-tary applications where they could allow soldiers on thebattlefield to not only detect, but also localize enemy fire.Different characteristics of a gunshot audio signal can beexploited for detection of a gunshot acoustic. A gunshotacoustic consists of a muzzle blast that lasts for aboutthree milliseconds, sound of mechanical action associatedwith operation of a firearm and possibly a shockwavewhen the bullet is travelling at supersonic speed [1].

A field employable gunshot detection system shouldhave a high detection rate, minimal false alarm rate, ro-bustness to background noise, and low processing time.Unlike some of the past work that is focused on maxi-mization of gunshot detection performance [2][3][4], thefocus of our work is on the system-level design of a fieldemployable gunshot detection system that exhibits allthe aforementioned qualities. To decrease computationalcomplexity, we propose a multi-level system architectureconsisting of an impulsive event detection block followedby a gunshot detection block. The event detection block

ensures that the more complex gunshot detection blockis activated only in the case of an acoustic event. Thus,because of the high complexity of feature extraction al-gorithms in the gunshot recognition stage, the objectiveof the event detection block is to minimize computa-tional load on the succeeding stage. But, the decreasein computational complexity comes at a cost: lower thesensitivity of the event detection stage, lower the com-putational load on the succeeding gunshot recognitionstage but higher the missed event detection rate and viceversa. Thus, a trade-off between computational complex-ity of the system and missed event detection rate has tobe made in the event detection stage. Three impulsiveevent detection schemes are proposed in [5] that dependon evolution of power sequence obtained from incomingaudio signal segments. One of these methods, that uses anoise-adaptive threshold on the power sequence for pulsedetection, provides a nice compromise between detectionperformance and system response delay [5]. Though thismethod allows tuning of the threshold with sensitivity ofthe scheme, there is no way to set the threshold to meetany particular missed event detection rate requirement.Modeling the energy of a signal segment as either chi-square or non-central chi-square distributed, we build ananalytical framework on top of this impulsive event de-tection method such that the event detection thresholdcan be set to precisely meet any missed detection rate re-quirement while minimizing computational load on themore complex feature extraction stage.

When a particular audio segment is flagged by theevent detection block, it is passed to the gunshot recog-nition stage. The problem of gunshot recognition is par-ticularly difficult due to the countless possibilities of non-gunshot impulsive audio events in the operating environ-ment. The recognition system should be able to distin-guish a gunshot from sounds such as that of a clap, doorslam, fire-cracker etc. It is important to have the falsepositive rate as low as possible, since a high false posi-tive rate may lead to lower productivity and lack of confi-dence for law enforcement personnel in gunshot detectionsystems [6]. In recent work, an audio event detection sys-tem using two parallel Gaussian mixture model (GMM)classifiers has been proposed for the detection of screams

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and gunshots [2]. The gunshot detection problem hasalso been pursued as a maximization task employing adynamic programming solution to the detection problem[3]. More recently, the use of correlation against a gun-shot template has been proposed by Freire and Apoli-nario [7]. The superior performance of this detectionfeature was then reported under noisy environments incomparison with other known methods of gunshot de-tection [4]. However, we have found in our experimentsthat even though the correlation method of [7] gives ahigh true positive rate (TPR), it yields an undesirablyhigh false positive rate (FPR). As a means of reducingthis FPR, we propose using cross-correlation maximumagainst a gunshot template in conjunction with eighthorder linear predictive coding (LPC) coefficients [8] asfeatures with a gaussian radial basis function (RBF) Ker-nel for a support vector machine (SVM) classifier [9].Using an extensive audio database consisting of gunshotrecordings, door slams, ticks, and human voice for aneight-fold cross validation experiment, we were able toachieve a 97.62% true positive rate and a negligible falsepositive rate on our audio database.

Thus, our contributions towards building a field de-ployable gunshot detection system are two-fold: First,we provide an analytical framework for a segment powerbased event detection framework that allows us to meetthe missed detection rate requirements of the event de-tection stage while minimizing computational load on thegunshot detection system. Second, we propose the use ofSVMs with template correlation maximum, LPC coeffi-cients and the kernel trick to get high gunshot detectionrate while minimizing the FPR.

2. ACOUSTIC EVENT DETECTION

The event detection task over an audio segment canbe formulated as a binary hypothesis testing problem:

H0: segment contains noise onlyH1: segment contains an acoustic event

The audio signal segment at time t can be written as

r(t) = hs(t) + n(t) (1)

where h = 0 under hypothesis H0 and h = 1 underhypothesis H1, s(t) represents the acoustic event andn(t) represents zero-mean additive white gaussian noiseprocess with power spectral density N0

2 .Over a sampling period T , we use the normalized

received signal energy given by

Z =2

N0

∫ T

0

r2(t) dt (2)

as a decision statistic. According to [10], Z follows a chi-square distribution with 2WT degrees of freedom underhypothesis H0, where W is the positive bandwidth of

the received signal. Alternatively, under hypothesis H1,Z follows non-central chi-square distribution with 2WTdegrees of freedom and a non-centrality parameter 2γ,where γ is the signal-to-noise (SNR) ratio of the receivedsignal [10]. Defining a = TW , the probability densityfunction of the decision statistic Z can be given as

fZ(z) =

{1

2aΓ(a)za−1e−

z2 H0,

12 ( z

2γ )u−12 e−

2γ+z2 Iu−1(

√2γz) H1.

(3)

where Γ(.) is the gamma function and In is the nth or-der modified Bessel function of the first kind [11]. Theprobability of missed detection and false alarm are

Pm = Pr(Z < λ|H1), (4)

Pfa = Pr(Z > λ|H0), (5)

respectively, where λ is the decision threshold on theenergy statistic Z. Using (3), we obtain

Pm = 1−Qa(√

2γ,√λ ), (6)

Pfa = 1−γ(a, λ2 )

Γ(a)=

Γ(a, λ2 )

Γ(a), (7)

where Qa is the generalized Marcum Q-function [12],γ(., .) is the lower incomplete gamma function and Γ(., .)is the upper incomplete gamma function [11].

The performance of the event detection block can becharacterized by Pfa; the lower the Pfa, the lower thenumber of false events reported to the gunshot recogni-tion block and lower is the computational load on themore complex feature extraction stage. However, a morecritical parameter associated with event detection is themissed detection rate (Pm). Events missed in the eventdetection stage are lost, whereas falsely reported eventscan still be removed in the gunshot recognition stage.Our design philosophy for the event detection scheme isto set the decision threshold λ to meet a constant misseddetection rate (CMDR) requirement, so that the optimaltrade-off between Pm and Pfa can be achieved under sys-tem constraints on Pm. From (6), it can be observed thatλ can be set so that the CMDR requirement is alwaysmet, given that the SNR can be estimated (as describednext). We design our event detection scheme such thatonly the events with segment signal energy above a fixedminimum value of Esmin are detected. This value Esmin

would depend on the coverage radius of the detectionsystem, minimum sound pressure level at the gunshotsource, and gain of the microphone. Noise energy Encan be estimated using a long-term median filter on en-ergy values of the previous audio signal segments [5]. Thelength of the median filter can be decreased so that thedetection scheme responds to impulsive events only.

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Given an En estimate, the SNR is estimated on thebasis of worst case segment power Esmin under hypoth-esis H1. Thus, the decision threshold λ can be set on

the basis of a CMDR and SNRmin =Esmin

Enby finding

numerical solution for λ from (6). Our scheme ensuresthat a CMDR requirement for the event detection stageis always met, given that segment power remains aboveEsmin under hypothesis H1.

3. SVM-BASED GUNSHOT RECOGNITION

Audio segments flagged by the event detection stage arepassed onto the gunshot recognition block. In this sec-tion, we describe the audio features, the classificationmethod, and the experimental setup we’ve used to eval-uate performance variation of the gunshot recognitionsystem with different feature combinations and kerneltypes.

Let the flagged segment comprise of N samples, witheach sample denoted by xf [n], n = 0, . . . , N − 1. Lett[n] denote the samples of the template, where the tem-plate segment is zero-padded to make sure that it alsocomprises of N samples. The flagged segment, as wellas the template are normalized between 1 and -1 beforecalculating the cross-correlation as

R(m) =

{∑N−m−1n=0 xf [n+m]t[n] m ≥ 0,∑N+m−1n=0 xf [n]t[n−m] m < 0.

(8)

The cross-correlation maximum for the flagged segmentis found by picking the maximum R(m). Other featuresextracted from the flagged segment for comparison arethe eighth order Linear Predictive Coding (LPC) coef-ficients and the first 13 Mel-Frequency Cepstral Coeffi-cients (MFCC) [8]. LPC coefficients are calculated usingMATLABs Signal Processing Toolbox, and MFCC coeffi-cients are calculated using the auditory toolbox by Inter-net Research Corporation [13]. The aforementioned fea-tures were extracted from our audio database to evaluategunshot detection performance of the different featuretypes. Once a database of relevant feature sets corre-sponding to both gunshot and outsider signals was built,eight-fold cross-validation [14] was used to train and testSVMs. More details about the experimental setup arementioned in Section 4.

4. EXPERIMENTAL EVALUATIONS

In this section, we describe the specifics of our audiodatabase, the computational gain of the even detectionscheme, and the detection performance of the differentfeature sets introduced in Section 3.

4.1. Data AcquisitionWe acquired an audio database of gunshots by makingrecordings at a local firing range using a standard PC

sound card. An extensive database of G3 and MP5 gun-shots was acquired for different shooter distances of 100meters (m), 200 m, and 300 m. All audio signals weresampled at 44.1 kHz with 8-bit quantization. Moreover,sounds like claps, door slams, ticks, and random peopletalking were recorded to be used as outsider signals forthe gunshot recognition system. In all, our acquired au-dio database amounted to 434 audio clips consisting of332 gunshot and 102 outsider signals1.

4.2. Evaluating Event Detection StageIn this section, we use the analytical results derived inSection 2 to evaluate performance of the event detectionstage. The event detection stage is designed such thatgiven a value for Esmin , the detection threshold adaptswith the noise power estimate via SNRmin such that aconstant missed detection rate is maintained. However,the computational gain of this stage is directly linkedwith the false alarm rate; the lower the false alarm rate,the lesser the load on the more complex gunshot recog-nition stage. Using numerical solutions to (7), we plotin Figure 1 the false alarm rate variation of the eventdetection stage with the system parameter SNRmin for agiven missed detection rate of 5% and an audio segmentsize of 1300 samples. The figure shows that the falsealarm rate drops to about 67% at a SNRmin of 15 dB,and about 2% at a SNRmin of 20 dB, which is not anuncommon SNR value in gunshot detection systems.

10 15 20 2510

−15

10−10

10−5

100

SNRmin

Pro

babi

lity

of F

alse

Ala

rm

Fig. 1. Performance evaluation of event detection stagewith SNRmin.

4.3. Evaluating Gunshot Recognition Stage

We devised separate experiments to evaluate perfor-mance of cross-correlation maximum, LPC coefficientsand MFCC features for gunshot recognition. Once adatabase of relevant feature sets corresponding to both

1The audio database we used to run our experiments is availableat http://adcom.lums.edu.pk/gunshotdatabase.html

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gunshot and outsider signals was built, eight-fold cross-validation [14] was used to train and test SVMs. Inparticular, a separate eight-fold cross-validation exper-iment was devised for LPC coefficients and MFCCs.Each dataset was divided into eight subsets. In turn,seven subsets were used to train the SVM classifier andthe remaining one was used to test it. However, for faircomparison with [4], the cross-correlation feature wastested with a threshold only.

0 20 40 60 80 100 1200

10

20

30

40

50

60

Cross−correlation maximum

Fre

quen

cy

Gunshot SignalsOutsider Signals

Fig. 2. Histogram of cross-correlation maxima of 434audio clips with a gunshot template.

To compare the performance of the different featuresets, we used the average TPR and FPR as measuresof classification accuracy. Average TPR is defined asthe percentage of gunshots classified as gunshots in thetesting subset as an average over the eight turns of thecross-validation test. Similarly, average FPR is the per-centage of outsider signals classified as gunshots in thetesting subset as an average over the eight turns of thecross-validation test. The results of the aforementionedthree experiments are shown in Table 1. Though corre-lation based template matching has been proposed as ahigh performance gunshot detection algorithm in [7] [4],it gives a high FPR with our database. Moreover, Fig-ure 2 shows the inseparable overlap in cross-correlationmaxima of gunshots and outsider signals with a gun-shot template. Thus, we need to use more feature(s)along with cross-correlation maximum to separate gun-shots and outsider signals in the feature space. From Ta-ble 1, it can be seen that LPC coefficients give a relativelyhigher average TPR while correlation-based feature givesa relatively lower average FPR. The two features arethen used together with SVMs to get a better averageTPR and FPR simultaneously. The results indicate thateven though we improve the TPR, the false alarm rate of8.33% is still too high for practical purposes. So, we tryout the kernel trick with our combinative feature set. InTable 2, we show that LPC coefficients, cross-correlation

maximum and RBF kernel can be used together withSVMs to obtain a 97.6% TPR and a negligible averageFPR 2. For comparison, we display results for the otherfeatures too when used with the RBF kernel. For theseexperiments involving use of the RBF kernel, the ker-nel parameter and the penalty parameter were optimizedusing the grid-searching algorithm [15]; different pairs ofkernel parameter and penalty parameter were tested andthe one which gave the best detection performance in theeight-fold cross-validation was used to generate results.The use of cross-validation ensured that the classifier didnot over-fit to the training data.

FeatureSet

Classifier TPR FPR

Cross-correlationmaximum [7]

Threshold 94.580 8.824

MFCC SVM 97.321 50.000LPC SVM 99.702 11.458LPC + Cross-correlation

SVM 99.702 8.333

Table 1. Classification accuracy (as percentages) fordifferent feature sets with linear kernel and SVMs

FeatureSet

TPR FPR

MFCC 92.497 15.625LPC 96.429 1.042Cross-correlationmaximum

97.917 10.417

LPC + Cross-correlation

97.619 ∼ 0

Table 2. Classification accuracy (as percentages) fordifferent feature sets with RBF kernel and SVMs.

5. CONCLUSION

In this paper, we have proposed a gunshot detection sys-tem with high gunshot detection performance, robust-ness to noise and low computational complexity. Ourproposed analytical framework for event detection en-ables minimization of computational complexity of thesystem without escalating the chances of missing outon acoustic events. Moreover, we showed that templatematching cannot be used alone for gunshot classificationbecause of the high FPR. Instead, we propose to use thetemplate matching feature in conjunction with eighth or-der LPC coefficients and gaussian RBF kernel to trainSVMs for gunshot detection.

2Of the 102 outsider signals we tested with LPC + Cross-correlation, we did not get any false positive.

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