BIOSONAR-INSPIRED SOURCE LOCALIZATION IN LOW SNR

Sasha Apartsin

1

, Leon N. Cooper

2

and Nathan Intrator

1

1

Blavatnik School of Computer Science, Tel-Aviv University, Tel-Aviv, Israel

2

Institute For Brain and Neural Systems and Physics Department, Brown Univeristy, Providence, U.S.A.

Keywords: Biosonar, Underground exploration, Threshold effect, Source localization, Time of arrival.

Abstract: Some mammals use sound signals for communications and navigation in the air (bats) or underwater

(dolphins). Recent biological discovery shows that blind mole rat is capable of detecting and avoiding

underground obstacles using reflection from seismic signals. Such a remarkable capacity relies on the ability

to localize the source of the reflection with high accuracy and in very low Signal to Noise Ratio (SNR)

conditions. The standard methods for source localization are usually based on Time of Arrival (ToA)

estimation obtained by the correlation of received signal with a matched filter. This approach suffers from

rapid deterioration in the accuracy as SNR level falls below certain threshold value: the phenomenon known

in the Radar Theory as a “threshold effect”. In this paper we describe biosonar-inspired method for ToA

estimation and 2D source localization based on the fusion of the measurements from biased estimators

which are obtained using a family of unmatched filters. Suboptimal but not perfectly correlated estimators

are combined together to produce a robust estimator for ToA and 2D source position which outperforms

standard matched filter-based estimator in high noise. The proposed method can be applied for mapping of

underground instalments using low power infrasound pulses.

1 INTRODUCTION

Echolocation, also called Biosonar, is the biological

sonar used by several mammals such as bats,

dolphins and whales. Echolocating animals emit

calls out to the environment, and listen to the echoes

of those calls that return from various objects in the

environment. They use these echoes to locate, range,

and identify the objects. Echolocation is used for

navigation and for foraging (or hunting) in various

environments.

It has been recently discovered (Kimchi et al.,

2005) that the blind mole rat uses sonar-like

exploration of the underground. This rat, which lives

underground and has no functioning eyes, generates

ground stimulation by banging its head on the wall

of its tunnels.

Mole rat can dig a tunnel 300ft long in one night

while detecting and avoiding voids and obstacles

(e.g. stones) that are several feet ahead.

The tunnels of mole rats can reach a length of

two miles and a mole rat runs inside the tunnel at a

thus indicating that it can “see” quite well, although

This work was supported in part by the U.S. Army Research

Office

its eyes are not functioning. From behavioural

studies, we learn that a mole rat finds out if some

intruder got into its tunnel very quickly (as they

become very aggressive).

It thus follows; that the mole rat can utilize its

infrasound exploration device to a long range of

over a mile. How are the ping returns being

transformed into an image, we do not quite know,

but one can expect that the mechanism is similar to

the one employed by Bats, Dolphins and other

biosonar animal. However, in the case of blind mole

rat, the transmitted seismic pulse has low central

frequency or otherwise it will be quickly absorbed

by the soil.

Analysis of signals from returned pings is used

extensively in seismic underground exploration. The

method requires a controlled seismic source of

energy, such as dynamite, a specialized air gun or

vibrators, commonly known by their trademark

name Vibroseis. These seismic sources produce high

energy pulses to ensure high Signal to Noise Ratio at

receivers. Obviously, the energy of the explosion is

nowhere comparable to the power of pulses

generated by blind mole rat.

399

Apartsin S., Cooper L. and Intrator N..

BIOSONAR-INSPIRED SOURCE LOCALIZATION IN LOW SNR.

DOI: 10.5220/0003126803990404

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2011), pages 399-404

ISBN: 978-989-8425-35-5

Copyright

c

2011 SCITEPRESS (Science and Technology Publications, Lda.)

The typical analysis of returned signal involves

correlation of the returned signal with a matched

filter. The matched filter approach suffers from

rapid deterioration in the sensing accuracy as SNR

level falls below certain threshold value; the

phenomenon known in the Radar Theory as a

“threshold effect”(Woodward, 1953).

Figure 1: Gaussian modulated sinusoidal pulse (top) and

its autocorrelation function y(t).

According to Woodward who studied the

threshold effect back in 1953, it is “one of the most

interesting features of radar theory”. It appears that

when SNR at a receiver falls below certain threshold

value, the mean square error of the estimation

rapidly increases, causing dramatic drop in sensing

accuracy. A receiver operating with SNR above this

threshold value is said to be in a coherent state. The

matched filter-based estimator is usually used for the

coherent receiver. For the SNR levels substantially

below the threshold value, a receiver said to be

noncoherent with the assumption that most of the

information about the pulse carrier phase is lost due

to the noise. For in-between levels of SNR, a

receiver is said to be a semi-coherent receiver,

balancing between coherent and noncoherent states.

The threshold effect is intensified (i.e. occurs at

higher SNR levels) as pulse central frequency is

reduced. Therefore the conventional matched filter

approach might not be the best choice for the

processing of responses from low-power low-

frequency pulses.

In this paper, we describe a robust single pulse

ToA estimation method for semi-coherent receiver.

We show how to construct a family of suboptimal

and biased estimators, using phase-shifted versions

of source waveform as unmatched filters. The

outcomes of estimators are fused together into a

single ToA estimator, which outperforms

conventional Matched Filter (MF) based estimator

for a range of low SNR levels.

The same idea can be applied to the problem of

2D source localization, provided matched features

have complex reflection cross-section. In 2D case, a

family of unmatched filters can be generated from

the feature’s template using phase shift in several

directions. The increased number of degrees of

freedom (phase shift directions) results in even

larger improvement in the accuracy.

One of the possible applications for the described

method involves detection and mapping of the

underground installments by low-power infrasound

pulses. Using a family of unmatched filters, the

accuracy of the localization can be significantly

improved without increasing the power of source

pulses. Limiting pulse power has great importance

when exploration is performed by autonomous

robots (Morris et al., 2006) with limited energy

source or usage of higher energy pulses is not

desirable (e.g. in order to stay undetected in hostile

environment).

2 MAXIMUM LIKELIHOOD

MATCHED FILTER

ESTIMATOR

In remote sensing applications such as radar or

sonar, the common scenario starts by a transmitter

sending out a pulse waveform

(

)

. The pulse is

reflected from a target and it is picked up by a

receiver at time

. The estimated two-way travel

time (lag) can be used to calculate distance to the

target assuming the speed of the pulse propagation

in the medium is known.

The signal recorded at the receiver might be

represented as

(

)

=∗

(

−

)

+()

where

(

)

is Additive White Gaussian Noise

(AWGN) which corrupts the signal. The < 1

factor is used to account for all non-free space

propagation losses (e.g. attenuation of the signal in

the medium). We are interested in estimating the

Time of Arrival (ToA) parameter

under the

assumption that noise is large relative to c*s(t).

The standard method for ToA estimation

employs Matched Filter (MF) applied to the received

signal. The Matched Filter maximizes peak signal to

mean noise ratio (Whalen, 1995), making its output

suitable for the Maximum Likelihood (ML)

estimator of the ToA. The Matched Filter Maximum

Likelihood (MFML) estimator of ToA is obtained by

taking the position of the global maximum in the

BIOSIGNALS 2011 - International Conference on Bio-inspired Systems and Signal Processing

400

output of the Matched Filter (MF). The output of the

Matched Filter can be expressed as a correlation of

the signal with the pulse waveform:

(

)

=

(

)

∘

(

)

=

(

)

+()

Where

(

)

is scaled and shifted version of the

pulse’s autocorrelation function and

(

)

is filtered

noise. A typical Gaussian-modulated sinusoidal

pulse and its autocorrelation function are shown in

Figure 1.

Figure 2: The MFML estimator threshold effect. The error

increases rapidly as SNR falls below a threshold.

In the absence of noise, the maximum value of

(

)

is achieved at =

. As the level of noise

increases, the filtered noise

(

)

may cause a slight

shift in the location of the peak of

(

)

. However, at

the high noise levels, a location around one of the

side lobes of

(

)

may occasionally become the

global maximum of

(

)

.

A side lobe of autocorrelation function

mistakenly taken as its global maximum is a major

reason behind deterioration in accuracy of MFML

estimator known as threshold effect (Woodward,

1953). The threshold effect manifests itself in rapid

increase in the Root Mean Square Error (RMSE) of

the MFML estimator as shown in the Figure 2. In

semi-coherent state, the posterior distribution of the

possible lag locations becomes multimodal (Figure

3) because of the significant height of

autocorrelation function’s side lobes.

The height of the side lobes of the

autocorrelation function is affected by the pulse

bandwidth. Therefore, the threshold effect is

considerable for low-frequency narrowband pulses.

The analysis of the performance of different time-of-

arrival estimation methods is essential for Radar,

Sonar and other remote sensing applications. Rather

than compute the exact error of a specific estimator,

it is often more convenient to lower-bound the error

of any estimators for a given problem.

Figure 3: The probability density function for MFML

estimator error. There are significant local maxima under

low SNR.

The conventional Matched Filter Maximum

Likelihood (MFML) estimator is considered

efficient as it asymptotically attains the Cramer-Rao

Bound (CRB) under sufficiently high SNR

conditions (Van Treese,

1968). However, under

lower SNR levels, the Cramer-Rao Bound appears to

be over-optimistic and a more tight forms of bound

are required if the level of noise is high. The

Barankin Bound (Barankin, 1949) and associated

Barankin Theory provide tools for constructing

useful bounds for mean error of an estimator under

low SNR. Although in its general form the Barankin

bound depends on the estimated parameter and

therefore can’t be easily computed, it is able to

account for the threshold phenomena in the

estimation of the time-of-arrival parameter.

3 UNMATCHED FILTER

MAXIMUM LIKELIHOOD

ESTIMATOR

Given an arbitrary pulse waveform

(

)

, we

construct a pair of Phase Shifted Unmatched (PSU)

filters

(

)

and

(

)

by shifting the phase of

each pulse by + and − respectively. A

Gaussian-modulated sinusoidal pulse and its PSU

filter pair generated using =/ are shown in

Figure 4.

The cross correlation of the signal

(

)

and a

PSU pair’s filter can be expressed as:

±

(

)

=

(

)

∘

±

(

)

=

±

(

)

+

±

(

)

BIOSONAR-INSPIRED SOURCE LOCALIZATION IN LOW SNR

401

Figure 4: Phase shifted pulses (top) and their cross

correlation functions (bottom). Note asymmetric shape of

side lobes.

The Unmatched Filter Maximum Likelihood

(UFML) estimators

and

corresponding to a

PSU pair can be defined as:

±

=

±

(

)

= (

(

)

∘

±

(

)

)

The side lobes of the cross-correlation function

±

(

)

=

(

)

∘

±

(

)

have unequal heights, making

the UFML estimators biased toward the higher side

lobe as shown in Figure 5.

Figure 5: Bias of UFML estimator pair. Unmatched filter

pair produces biased estimator pair with bias of the same

value but opposite sign.

The bias of the two UFML estimators has equal

absolute value but opposite sign due to symmetry in

the heights and position of the cross-correlation side

lobes. As SNR is increased, the bias decreases since

the position of the cross-correlation maximum is less

affected by the noise. Note that autocorrelation and

PSU filter cross-correlation produce signals of the

same power, however application of unmatched

filter produces lower peak signal-to-mean-noise ratio

as compared to matched filter.

The Root Mean Square Error (RMSE) of a single

UFML estimator is higher as compared to the RMSE

of MFML. However, the UFML estimators

corresponding to a PSU filter pair are not perfectly

correlated.

Figure 6: RMSE improvement by fixed and adaptive phase

AoUFML estimators. For each SNR there is the best

performing value of a phase shift (color lines). The black

line shows error for adaptive selection of phase-shift

value.

Therefore we can define a new estimator by

averaging results from a pair of UFML:

=

+

At low SNR levels, the resulting Average of UFML

(AoUFML) estimator has lower RMSE as compared

to MFML (Figure 6).

The AoUFML estimator outperforms MFML

estimator at SNR levels corresponding to semi-

coherent receiver state. At higher SNR levels, the

effect of side lobes is insignificant, therefore, the

shape of the main peak of cross-correlation function

have critical impact on the estimator’s RMSE. Since

an unmatched filter produces smaller peak signal-to-

mean-noise ratio and the UFML pair is almost

perfectly correlated at higher SNR levels, the MFML

estimator outperform the AoUFML estimator

at

coherent receiver state.

The crossover points between AoUFML and

MFML RMSE curves can be controlled by choosing

appropriate phase shift parameter as described in

(Apartsin et al., 2010). Finally, we note that many of

the commonly used source waveforms have side

lobes in their autocorrelation function (e.g. Ryan,

1994). Therefore, although the effectiveness of the

proposed method is demonstrated using Gaussian-

modulated sinusoidal pulse, the method can be

applied to other source waveforms as well.

4 2D SOURCE LOCALIZATION

The described method can be used for the

localization of reflection source in 2D or 3D

seismic/acoustic maps. Using sensor arrays, a 2D or

BIOSIGNALS 2011 - International Conference on Bio-inspired Systems and Signal Processing

402

3D image of the underground can be computed. On

the computed map we might want to pinpoint the

location of specific features and voids like a “box”

feature shown at Figure 7(left).

Figure 7: Left: Density map of a “box” feature (void),

Right: 2D autocorrelation function, lighter points

corresponds to larger values. There are 4 local peaks in

autocorrelation function corresponding to 4 edges of the

box.

If underground exploration is performed using

low power low frequency seismic pulses, the

resulting image would be heavily corrupted by noise.

As in one-dimensional case, the estimation of a

feature position using conventional matched filters

or 2D template would suffer from the threshold

effect due to existence of 4 local peaks in the

feature’s 2D autocorrelation function (Figure 7

right). Again, instead of relying on a correlation with

a single matched filter, the family of 2D unmatched

filters using a phase shift can be generated.

Unlike the one-dimensional case, in 2D we have

greater choice of phase directions. It seems

reasonable to choose phase shift values in the

direction of local peaks of the autocorrelation

functions. For “box” feature it translates into the

vertical and horizontal directions of phase shift. This

choice of directions corresponds to the family of 4

unmatched filters (two members of this family are

shown at Figure 8). Estimators corresponding to

each unmatched filter are biased toward one of the

two local maxima in the direction of the phase shift.

However, the estimators are not completely

correlated as in one dimensional case.

Therefore, by averaging the position of the peaks

obtained by cross-correlating noisy map image with

filters from the constructed filter family, the

accuracy of the position estimation (localization) of

the feature is significantly improved (Figure 9). For

features with more complex configuration the

number of filters can be increased even further to

account for all of local maxima in autocorrelation

function.

Figure 8: Phase-shifted 2D filters (left column) and their

cross-correlation with “box” feature (right column) for

horizontal (top row) and vertical (bottom) phase shift

directions.

5 CONCLUSIONS

Inspired by the capability of blind mole rat to cope

with the threshold effect while exploring

underground using low-power low-frequency pulses,

we suggest a method for robust time of arrival

estimation and 2D source localization and template

matching.

We showed that using Phase Shifted Unmatched

(PSU) filters, a pair of Unmatched Filter Maximum

Likelihood (UFML) estimators can be computed to

obtain biased Time of Arrival estimators. In semi-

coherent receiver state, the UFML estimators are not

perfectly correlated and, therefore, can be combined

together into estimator that outperforms

conventional Matched Filter Maximum Likelihood

estimator.

The described method can be applied for 2D

source localization using a family of Unmatched

Filters generated by phase shifting original template

in multiple directions. The method can be applied

for underground exploration and mapping using low

power low frequency seismic signals.

BIOSONAR-INSPIRED SOURCE LOCALIZATION IN LOW SNR

403

Figure 9: RMSE as function of SNR Using fusing from 4

estimators (2 horizontal phase shift and 2 vertical phase

shift) gives higher accuracy than conventional matched-

filter approach.

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