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. Ng

School of Electrical and Electronic Engineering

Nanyang Technological University, Singapore

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

Abstract—In 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 studied

for several decades. Conventionally, statistical hypothesis tests

are formulated to detect sources embedded in noise. Very

efficient likelihood tests are devised for deterministic and

random signal cases [1]. The problem is more challenging

when it comes to the detection of intermittent sources with

very small pulse width, encountered in applications such as

machine fault [2] and footstep detection [3] for surveillence

among others. Our focus on this topic is motivated to solve

the problem of detecting footsteps using a single three-axis

geophone. The use of triaxial geophones are becoming more

popular due to the ease of deployment as well as the additional

information obtained at almost the same cost as that of a

single-axis geophone.

Footsteps can be characterized as transient seismic events

propagating through the ground. Some of the existing detection

techniques for such transient signals include evaluating the

eigenvalues of short-time segment autocorrelation matrices,

kurtosis of short-time segments [3], cadence [3] and spectrum

analysis [4]. The first two metrics require a pre-defined thresh-

old to declare the presence of the source while the latter two

are based on data specific conditions. The most common signal

model used for sensor output is given by

x(k) =N−1∑l=0

s(k − l)h(l) + n(k), (1)

where x(k) is the channel sensor output at time index k, s(k) is

the source, n(k) is the additive noise, h(l) is the lth coefficient

of 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 kind

of preprocessing prior to detection. Signal denoising is a

common 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 a

compact representation is obtained unlike noise. The technique

presented in [5] performs a wavelet packet transformation and

uses kurtosis as a criterion to distinguish wavelets correspond-

ing to signal from that of noise. The noise coefficients are

suppressed to obtain the signal with a higher SNR in time

domain.

In this paper, we first propose a new technique for footstep

detection 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 distinction

between the signal and noise. This discrimination is based

on the geophone transduction principle and the independence

of the signals acquired in each of the co-located sensors.

Furthermore, we adopt this principle for signal denoising prior

to the succeeding stages in the footstep detection system.

The advantage of the proposed algorithm for both footstep

detection and denoising is its effectiveness and reduced com-

putational complexity.

II. PROPOSED METHOD

A. Geophone transduction principle

The geophone is a transducer which induces voltage pro-

portional to the medium particle velocity using the principle

of electromagnetic induction [6]. Any relative motion between

the suspended coil and the magnetic case generates a nonzero

output voltage. When there are no seismic events, the in-

duced voltages between the three orthogonal channels of the

geophone are uncorrelated. The background noise is due to

the random relative motion between the suspended mass and

the magnet, resulting in a nonzero voltage in each of the

three channels. Seismic waves, originated due to events such

as earthquake or footsteps, propagate through the ground in

all directions and the coupling of the triaxial geophone with

the ground detects the velocity of the particle motion at that

location. The voltage acquired by each channel is therefore

proportional to the particle velocity being decomposed onto

the three orthogonal axes.

Defining x1(k), x2(k) and x3(k) as the received signals

from the two horizontal and one vertical axis, respectively, we

denote

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

as the received signal vector at time instance k. In the absence

of footsteps, it is expected that consecutive instances of x(k)

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2010 Asia Pacific Conference on Circuits and Systems (APCCAS 2010)

6 - 9 December 2010, Kuala Lumpur, Malaysia

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Fig. 1. Evolution of x̄(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 to

this seismic event is proportional to the particle velocity.

Since the particle motion is well defined, the consecutive data

vectors will be correlated. Due to the medium elasticity, the

particle velocity varies smoothly with time resulting in varying

voltages at consecutive snapshots.

At a sampling frequency greater than Nyquist frequency the

correlation between consecutive data samples can be observed

explicitly by normalizing each data vector with its �2-norm,

x̄(k) =x(k)

‖x(k)‖2 = [x̄1(k) x̄2(k) x̄3(k)]T . (3)

These normalized data vectors endure a more consistent and

slow varying nature unlike x(k) in the presence of a footstep.

In the absence of a seismic event however, vectors are expected

to be highly random.

Figures 1 (a) and (b) show an illustrative example of how

x̄(k) varies with time for two separate instances of recorded

background noise and footsteps, respectively. For each of these

plots, x̄(k) is plotted on a three dimensional vector space.

For clarity, at each index k, the point x̄(k) is plotted as

a line segment from the origin. From Fig. 1 (a), we note

that x̄(k) varies randomly with consecutive time instances

for background noise while, Fig. 1 (b) shows x̄(k) varying

smoothly forming a disc profile for a footstep signal. This

finding is consistent with the quaternion eigenaxis studies

discussed in [7] for elliptically polarized data. The distinction

between the noise and signal is apparently the slow variation of

consecutive data vetors in the second case. Based on this new

observation, we proposed to use two distance metrics which

are subsequently used for the development of a detection rule.

B. Neighbourhood Euclidean Distance Metric

For multi-dimensional vectors, the most commonly used

distance metric is the Euclidean distance (ED), defined by

ed = ‖x− y‖2,where x,y ∈ R

M . From Fig. 1, the ED between consecutive

data vectors is expected to approach zero when a footstep

is present, while a high ED is anticipated for noise only

data snapshots. We therefore construct a time-domain Neigh-

bourhood Euclidean Distance (NED) metric of all consecutive

normalized data vectors,

ex(k) = ‖x̄(k + 1)− x̄(k)‖2. (4)

Figure 2 (a) illustrates the variation of ex(k) along with the

scaled signal recorded from one of the triaxial geophone

channels resampled to 8 kHz. For this illustrative example,

s(n) is generated using a hammer stroke at a distance of 18 m

from the sensor. As expected, the variation of ex(k) is high in

the noise only time segments, whereas for the time segments

where the source is active, ex(k) varies less significantly.

Although a distinction between noise and signal can be

made using ex(k), the high temporal variation of ex(k) makes

signal detection challenging especially if a threshold rule is

applied to ex(k). To address this, we process overlapping time

frames of ex(k), e(b) = [ex((b−1)L+1) · · · ex(bF )]T where

b, L and F are the frame index, frame shift length and frame

size, respectively. The variance

σe(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, σe(b) does not show significant distinction

between the source signal and noise only segments. This leads

to difficulty in defining a detection rule. One of the reasons

for this behaviour is that since unit norm data vectors x̄(k) are

used, the maximum value ex(k) can take is 2. Therefore, σe(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 the

background noise in other channels, σe(b) is expected to

be high in those frames. Considering the above limitations,

we further propose a simple metric based on ratio of the

consecutive samples.

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y1

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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 instances

of x̄(k) corresponding to the footstep time segments vary

slowly if the sampling frequency is higher than the Nyquist

rate. This implies that, for each channel the normalized signal

x̄i(k), defined in (3) exhibits smooth variations for the footstep

duration. With this understanding, we propose to employ the

neigbourhood ratio (NR) metric for each channel given by

yi(k) =

{x̄i(k + 1)/x̄i(k) x̄i(k) > δ1 otherwise,

(6)

where δ is a small value which avoids data vectors correspond-

ing to the zero crossings from consideration since under such

circumstances, noise suppresses the transduced voltage. It is

important to note that there are as many yi(k) as the sensors

unlike in the NED case.

When a footstep is present, yi(k) will be close to unity while

for noise only segments this ratio varies randomly. Similar to

ex(k), the variance is computed for overlapping time frames

of σyi(b) for each channel using (5). This variance for each of

the three axes are shown in Fig. 3 (a-c). A scaled version of the

corresponding sensor signals are shown for comparison. For

the same data used to obtain Fig. 2 (b), we observe from Fig. 3

that σyi(b) reduces close to zero when the signal is active and

increases to a higher value for noise only segments. Comparing

Figs. 2 (b) and 3, we note that σyi(b) discriminates transient

signals better than σe(b). This affirms that the NR metric

provides a better discretion of the signal from the background

noise than the NED metric.

In order to define a detection rule, we propose to use a

function of the variance σyi(b) given by,

zi(b) =1

(σyi(b) + 1)P, (7)

where P > 1 is an integer. The value of zi(b) approaches

unity in the presence of footstep and reduces to a low value

otherwise. The function that maps σyi to zi is plotted in

Fig. 4 for varying values of P . We note that for higher values

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Fig. 4. Function mapping σyi to zi.

of P , zi(b) trails faster with increasing variance. Therefore,

under noisy environments, a high P is required to reduce false

alarm. The complete procedure, including the detection rule is

provided in Table 1. We note that although zi(b) is computed

for detection in each channel , it is possible to combine these

detection 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)]

T

with yk(k) as defined in (6).

3. Variance for each channel data of Y is computed over

overlapped time frames using (5). A function of variance

defined in (7) is then evaluated.

4. Signal detection rule: If zi(b) > γ, declare that the

signal is present in this frame.

D. Signal Denoising using the Proposed NR Metric

Based on the above discussion, we extend the same principle

for signal denoising. The variable zi(b) defined in (7) provides

a value close to unity when the signal is present and a value

close 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 the

context of footstep detection and signal denoising. Since

the technique exploits the transduction principle of the co-

located geophones, the performance can be studied only

on recorded seismic data. The setup consists of a triaxial

geophone (Geospace GS32-CT) whose output is preamplified

prior to digitization using a multi-channel ADC. The geophone

is buried in an open grass field and human footsteps are used

to generate seismic events at desired distance from the sensor.

The signal is downsampled to 8 kHz for processing.

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15m from sensor

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sensor

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 use

data recorded when a person walks radially away from the

geophone starting from a distance of 5 m to 18 m. For

clarity of presentation, the recorded footsteps in one of the

axes is magnified and plotted in Fig. 5 (a). Figure 5 (b)

shows the footsteps detected using the kurtosis measure as

presented in [3]. If the kurtosis, computed over 200 ms time

frames with an overlapping factor of 0.75, is greater than

5, a footstep is adjudged. For the proposed NR technique,

Fig. 5 (c) is obtained with the parameters δ, P and γ set

to 0.05, 5 and 0.6 respectively. It can be observed that the

detection performance of the NR technique is more reliable

when compared to that of the kurtosis technique. This is due

to the exploitation of the geophone transduction principle by

the proposed NR algorithm. Setting the thresholds based on

the real-time background noise profile ensures a highly reliable

transient detection.

The range of a footstep detection algorithm is dependent

on the footstep intensity, medium composition and the pream-

plification provided. Therefore, a fair comparison would be

to compare the two methods for a given dataset. For the

above data, we observe that the proposed technique can detect

footsteps up to approximately 15 m while the kurtosis method

succeeds in detecting footsteps only up to approximately 12 m.

We next present the denoising capability of the proposed

technique. As described in Section II D, denoising is achieved

by weighing the sensor output with the window defined in (7).

The footsteps shown in Fig. 6 (a) refer to the data recorded

from 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 wavelet

packet method proposed in [5] is shown in Fig. 6 (b) while

Fig. 6 (c) shows the denoised signal wi(k) obtained by the

proposed technique with δ and P set to 0.05 and 6, respec-

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Fig. 6. Signal denoising (a) recorded data, (b) wavelet packet denoising, (c)proposed technique with NR time window.

tively. In order to quantify the noise suppression achieved, we

evaluate average signal-to-noise ratio (SNR) over 11 footstep

and noise segments. For each segment, the signal power is

computed over a window of 250 ms containing a footstep

while the noise power is evaluated for the remaining time

segment. The average SNR for the geophone signal shown

in Fig. 6 (a), the denoised signals obtained by the method in

[5] shown in Fig. 6 (b) and the proposed NR-based denoising

method shown in Fig. 6 (c) are found to be 10 dB, 23.7 dB

and 28.8dB, respectively. This SNR improvement testifies the

denoising capability of the proposed technique.

IV. CONCLUSION

We presented an effective footstep detection algorithm based

on the transduction principle of a triaxial geophone. The

proposed Neighbourhood Ratio metric is found to have an im-

proved performance over the conventional Euclidean distance.

Extending this principle for signal denoising is observed to

provide 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, “Detectionof signal transients based on wavelet and statistics for machine faultdiagnosis,” Mechanical Systems and Signal Processing, vol. 23, no. 4,pp. 1076–1097, May 2009.

[3] R. G. G. Succi, D. Clapp and G. Prado, “Footstep detection and tracking,”vol. 4393, 2001, pp. 22–29.

[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. 162–173.

[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. 1177–1199, 2004.

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