2010 Asia Pacific Conference on Circuits and Systems (APCCAS 2010)6 - 9 December 2010, Kuala Lumpur, Malaysia

Footstep Detection and Denoising using a SingleTriaxial Geophone

Vinod V. Reddy, V. Divya, Andy W. H. Khong and B. P. NgSchool of Electrical and Electronic EngineeringNanyang Technological University, Singapore

email: {e060001, divy0012, AndyKhong, ebpng}@ntu.edu.sg

AbstractIn this paper we propose a new footstep detectiontechnique for data acquired using a triaxial geophone. The ideaevolves from the investigation of geophone transduction principle.The technique exploits the randomness of neighbouring datavectors observed when the footstep is absent. We extend thesame principle for triaxial signal denoising. Effectiveness of theproposed technique for transient detection and denoising arepresented for real seismic data collected using a triaxial geophone.

I. INTRODUCTION

The problem of signal detection in noise has been studiedfor several decades. Conventionally, statistical hypothesis testsare formulated to detect sources embedded in noise. Veryefficient likelihood tests are devised for deterministic andrandom signal cases [1]. The problem is more challengingwhen it comes to the detection of intermittent sources withvery small pulse width, encountered in applications such asmachine fault [2] and footstep detection [3] for surveillenceamong others. Our focus on this topic is motivated to solvethe problem of detecting footsteps using a single three-axisgeophone. The use of triaxial geophones are becoming morepopular due to the ease of deployment as well as the additionalinformation obtained at almost the same cost as that of asingle-axis geophone.

Footsteps can be characterized as transient seismic eventspropagating through the ground. Some of the existing detectiontechniques for such transient signals include evaluating theeigenvalues of short-time segment autocorrelation matrices,kurtosis of short-time segments [3], cadence [3] and spectrumanalysis [4]. The first two metrics require a pre-defined thresh-old to declare the presence of the source while the latter twoare based on data specific conditions. The most common signalmodel used for sensor output is given by

x(k) =N1l=0

s(k l)h(l) + n(k), (1)

where x(k) is the channel sensor output at time index k, s(k) isthe source, n(k) is the additive noise, h(l) is the lth coefficientof the channel response between the source and the sensor,while N is the length of the channel response.

In practice, the sensor signals are subjected to some kindof preprocessing prior to detection. Signal denoising is acommon technique used to suppress the effect of n(k) in (1).Wavelet denoising is one of the most widely used technique

which transforms x(n) to the wavelet domain such that acompact representation is obtained unlike noise. The techniquepresented in [5] performs a wavelet packet transformation anduses kurtosis as a criterion to distinguish wavelets correspond-ing to signal from that of noise. The noise coefficients aresuppressed to obtain the signal with a higher SNR in timedomain.

In this paper, we first propose a new technique for footstepdetection using a triaxial geophone where three sensors are co-located orthogonally within a single casing. We achieve detec-tion by introducing two new metrics which exhibit distinctionbetween the signal and noise. This discrimination is basedon the geophone transduction principle and the independenceof the signals acquired in each of the co-located sensors.Furthermore, we adopt this principle for signal denoising priorto the succeeding stages in the footstep detection system.The advantage of the proposed algorithm for both footstepdetection and denoising is its effectiveness and reduced com-putational complexity.

II. PROPOSED METHODA. Geophone transduction principle

The geophone is a transducer which induces voltage pro-portional to the medium particle velocity using the principleof electromagnetic induction [6]. Any relative motion betweenthe suspended coil and the magnetic case generates a nonzerooutput voltage. When there are no seismic events, the in-duced voltages between the three orthogonal channels of thegeophone are uncorrelated. The background noise is due tothe random relative motion between the suspended mass andthe magnet, resulting in a nonzero voltage in each of thethree channels. Seismic waves, originated due to events suchas earthquake or footsteps, propagate through the ground inall directions and the coupling of the triaxial geophone withthe ground detects the velocity of the particle motion at thatlocation. The voltage acquired by each channel is thereforeproportional to the particle velocity being decomposed ontothe three orthogonal axes.

Defining x1(k), x2(k) and x3(k) as the received signalsfrom the two horizontal and one vertical axis, respectively, wedenote

x(k) = [x1(k) x2(k) x3(k)]T (2)

as the received signal vector at time instance k. In the absenceof footsteps, it is expected that consecutive instances of x(k)

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Fig. 1. Evolution of x(k) corresponding to (a) noise, (b) Footstep signal.

are uncorrelated with each other. In the presence of footsteps,however, the voltage induced in all the three axes due tothis seismic event is proportional to the particle velocity.Since the particle motion is well defined, the consecutive datavectors will be correlated. Due to the medium elasticity, theparticle velocity varies smoothly with time resulting in varyingvoltages at consecutive snapshots.

At a sampling frequency greater than Nyquist frequency thecorrelation between consecutive data samples can be observedexplicitly by normalizing each data vector with its 2-norm,

x(k) =x(k)

x(k)2 = [x1(k) x2(k) x3(k)]T . (3)

These normalized data vectors endure a more consistent andslow varying nature unlike x(k) in the presence of a footstep.In the absence of a seismic event however, vectors are expectedto be highly random.

Figures 1 (a) and (b) show an illustrative example of howx(k) varies with time for two separate instances of recordedbackground noise and footsteps, respectively. For each of theseplots, x(k) is plotted on a three dimensional vector space.For clarity, at each index k, the point x(k) is plotted asa line segment from the origin. From Fig. 1 (a), we notethat x(k) varies randomly with consecutive time instancesfor background noise while, Fig. 1 (b) shows x(k) varyingsmoothly forming a disc profile for a footstep signal. Thisfinding is consistent with the quaternion eigenaxis studiesdiscussed in [7] for elliptically polarized data. The distinctionbetween the noise and signal is apparently the slow variation ofconsecutive data vetors in the second case. Based on this newobservation, we proposed to use two distance metrics whichare subsequently used for the development of a detection rule.

B. Neighbourhood Euclidean Distance Metric

For multi-dimensional vectors, the most commonly useddistance metric is the Euclidean distance (ED), defined by

ed = x y2,where x,y RM . From Fig. 1, the ED between consecutivedata vectors is expected to approach zero when a footstep

is present, while a high ED is anticipated for noise onlydata snapshots. We therefore construct a time-domain Neigh-bourhood Euclidean Distance (NED) metric of all consecutivenormalized data vectors,

ex(k) = x(k + 1) x(k)2. (4)Figure 2 (a) illustrates the variation of ex(k) along with thescaled signal recorded from one of the triaxial geophonechannels resampled to 8 kHz. For this illustrative example,s(n) is generated using a hammer stroke at a distance of 18 mfrom the sensor. As expected, the variation of ex(k) is high inthe noise only time segments, whereas for the time segmentswhere the source is active, ex(k) varies less significantly.

Although a distinction between noise and signal can bemade using ex(k), the high temporal variation of ex(k) makessignal detection challenging especially if a threshold rule isapplied to ex(k). To address this, we process overlapping timeframes of ex(k), e(b) = [ex((b1)L+1) ex(bF )]T whereb, L and F are the frame index, frame shift length and framesize, respectively. The variance

e(b) =1

FeT (b)e(b), (5)

is plotted in Fig. 2 (b). An overlapping factor of 0.85 is used.As can be seen, although the high temporal variation of

ex(k) is reduced, e(b) does not show significant distinctionbetween the source signal and noise only segments. This leadsto difficulty in defining a detection rule. One of the reasonsfor this behaviour is that since unit norm data vectors x(k) areused, the maximum value ex(k) can take is 2. Therefore, e(b)is not significant for segregating the source and noise classes.Furthermore, for polarized particle motion, it is possible that

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Fig. 2. Euclidean distance in 3D space as a metric (a) recorded data withseismic event along with the corresponding NED, (b) variance of NED withF = 50 ms and L = 0.85 50 ms.

the signal is prolonged in one of the channels. Due to thebackground noise in other channels, e(b) is expected tobe high in those frames. Considering the above limitations,we further propose a simple metric based on ratio of theconsecutive samples.

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Fig. 3. Neighbourhood Ratio as a metric for a transient signal detection.Signals from (a) horizontal axis 1, (b) horizontal axis 2, (c) vertical axis.

C. Neighbourhood Ratio Metric

As noted in Section II-A, the consecutive time instancesof x(k) corresponding to the footstep time segments varyslowly if the sampling frequency is higher than the Nyquistrate. This implies that, for each channel the normalized signalxi(k), defined in (3) exhibits smooth variations for the footstepduration. With this understanding, we propose to employ theneigbourhood ratio (NR) metric for each channel given by

yi(k) =

{xi(k + 1)/xi(k) xi(k) > 1 otherwise, (6)

where is a small value which avoids data vectors correspond-ing to the zero crossings from consideration since under suchcircumstances, noise suppresses the transduced voltage. It isimportant to note that there are as many yi(k) as the sensorsunlike in the NED case.

When a footstep is present, yi(k) will be close to unity whilefor noise only segments this ratio varies randomly. Similar toex(k), the variance is computed for overlapping time framesof yi(b) for each channel using (5). This variance for each ofthe three axes are shown in Fig. 3 (a-c). A scaled version of thecorresponding sensor signals are shown for comparison. Forthe same data used to obtain Fig. 2 (b), we observe from Fig. 3that yi(b) reduces close to zero when the signal is active andincreases to a higher value for noise only segments. ComparingFigs. 2 (b) and 3, we note that yi(b) discriminates transientsignals better than e(b). This affirms that the NR metricprovides a better discretion of the signal from the backgroundnoise than the NED metric.

In order to define a detection rule, we propose to use afunction of the variance yi(b) given by,

zi(b) =1

(yi(b) + 1)P, (7)

where P > 1 is an integer. The value of zi(b) approachesunity in the presence of footstep and reduces to a low valueotherwise. The function that maps yi to zi is plotted inFig. 4 for varying values of P . We note that for higher values

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of P , zi(b) trails faster with increasing variance. Therefore,under noisy environments, a high P is required to reduce falsealarm. The complete procedure, including the detection rule isprovided in Table 1. We note that although zi(b) is computedfor detection in each channel , it is possible to combine thesedetection results to provide a unified robust solution.

TABLE ISTEPS FOR FOOTSTEP DETECTION USING TRIAXIAL GEOPHONE

1. Each vector of the multichannel data matrix X =[x(1)...x(K)], where K is the number of data snapshots,is normalized to have unit 2-norm.2. The matrix of NR metric is obtained as Y =[y(1)...y(K 1)], where y(k) = [y1(k) y2(k) y3(k)]Twith yk(k) as defined in (6).3. Variance for each channel data of Y is computed overoverlapped time frames using (5). A function of variancedefined in (7) is then evaluated.4. Signal detection rule: If zi(b) > , declare that thesignal is present in this frame.

D. Signal Denoising using the Proposed NR Metric

Based on the above discussion, we extend the same principlefor signal denoising. The variable zi(b) defined in (7) providesa value close to unity when the signal is present and a valueclose to zero otherwise. Weighing the sensor signal with zi(b)will therefore result in a denoised signal given by,

wi(k) = xi(k)zi(k), k, (8)where wi(k) is the denoised signal of the ith sensor.

III. EXPERIMENTAL RESULTS

We now present results of the proposed technique in thecontext of footstep detection and signal denoising. Sincethe technique exploits the transduction principle of the co-located geophones, the performance can be studied onlyon recorded seismic data. The setup consists of a triaxialgeophone (Geospace GS32-CT) whose output is preamplifiedprior to digitization using a multi-channel ADC. The geophoneis buried in an open grass field and human footsteps are usedto generate seismic events at desired distance from the sensor.The signal is downsampled to 8 kHz for processing.

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Fig. 5. Footstep detection performance (a) Footstep signal in horizontalaxis, (b) detection results using kurtosis, (c)detection results using proposedtechnique.

For validating the footstep detection technique, we usedata recorded when a person walks radially away from thegeophone starting from a distance of 5 m to 18 m. Forclarity of presentation, the recorded footsteps in one of theaxes is magnified and plotted in Fig. 5 (a). Figure 5 (b)shows the footsteps detected using the kurtosis measure aspresented in [3]. If the kurtosis, computed over 200 ms timeframes with an overlapping factor of 0.75, is greater than5, a footstep is adjudged. For the proposed NR technique,Fig. 5 (c) is obtained with the parameters , P and setto 0.05, 5 and 0.6 respectively. It can be observed that thedetection performance of the NR technique is more reliablewhen compared to that of the kurtosis technique. This is dueto the exploitation of the geophone transduction principle bythe proposed NR algorithm. Setting the thresholds based onthe real-time background noise profile ensures a highly reliabletransient detection.

The range of a footstep detection algorithm is dependenton the footstep intensity, medium composition and the pream-plification provided. Therefore, a fair comparison would beto compare the two methods for a given dataset. For theabove data, we observe that the proposed technique can detectfootsteps up to approximately 15 m while the kurtosis methodsucceeds in detecting footsteps only up to approximately 12 m.

We next present the denoising capability of the proposedtechnique. As described in Section II D, denoising is achievedby weighing the sensor output with the window defined in (7).The footsteps shown in Fig. 6 (a) refer to the data recordedfrom the horizontal component of the geophone buried at(0, 0) m and the person is walking from (5, 15) m to(5, 15) m. For comparison, denoising achieved by waveletpacket method proposed in [5] is shown in Fig. 6 (b) whileFig. 6 (c) shows the denoised signal wi(k) obtained by theproposed technique with and P set to 0.05 and 6, respec-

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tively. In order to quantify the noise suppression achieved, weevaluate average signal-to-noise ratio (SNR) over 11 footstepand noise segments. For each segment, the signal power iscomputed over a window of 250 ms containing a footstepwhile the noise power is evaluated for the remaining timesegment. The average SNR for the geophone signal shownin Fig. 6 (a), the denoised signals obtained by the method in[5] shown in Fig. 6 (b) and the proposed NR-based denoisingmethod shown in Fig. 6 (c) are found to be 10 dB, 23.7 dBand 28.8dB, respectively. This SNR improvement testifies thedenoising capability of the proposed technique.

IV. CONCLUSIONWe presented an effective footstep detection algorithm based

on the transduction principle of a triaxial geophone. Theproposed Neighbourhood Ratio metric is found to have an im-proved performance over the conventional Euclidean distance.Extending this principle for signal denoising is observed toprovide promising results over wavelet packet denoising.

REFERENCES[1] S. M. Kay, Fundamentals of Statistical Signal Processing, Volume 2:

Detection Theory. Pearson Education, 1998.[2] Z. K. Zhu, R. Yan, L. Luo, Z. H. Feng, and F. R. Kong, Detection

of signal transients based on wavelet and statistics for machine faultdiagnosis, Mechanical Systems and Signal Processing, vol. 23, no. 4,pp. 10761097, May 2009.

[3] R. G. G. Succi, D. Clapp and G. Prado, Footstep detection and tracking,vol. 4393, 2001, pp. 2229.

[4] K. M. Houston and D. P. McGaffigan, Spectrum analysis techniques forpersonnel detection using seismic sensors, in Proc SPIE Conf on UGSTechnologies and Applications V, vol. 5090, 2003, pp. 162173.

[5] P. Ravier and P.-O. Amblard, Wavelet packets and de-noising based onhigher-order-statistics for transient detection, Signal Processing, vol. 81,no. 9, pp. 1909 1926, 2001.

[6] W. Lowrie, Fundamentals of Geophysics, second edition ed. CambridgeUniversity Press, 2007.

[7] N. Le Bihan and J. Mars, Singular value decomposition of quaternionmatrices: a new tool for vector-sensor signal processing, Signal Process.,vol. 84, no. 7, pp. 11771199, 2004.

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