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A Comparative Study of Sound Localization Algorithms for Energy Aware Sensor Network Nodes

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640 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 51, NO. 4, APRIL 2004
A Comparative Study of Sound LocalizationAlgorithms for Energy AwareSensor Network Nodes
Pedro Julián
, Member, IEEE
, Andreas G. Andreou, Larry Riddle, Shihab Shamma, David H. Goldberg, andGert Cauwenberghs
, Member, IEEE
Abstract—
Sound localization using energy-aware hardwarefor sensor networks nodes is a problem with many applicationsin surveillance and security. In this paper, we evaluate fouralgorithms for sound localization using signals recorded in anatural environment with an array of commercial off-the-shelf microelectromechanical systems microphones and a speciallydesigned compact acoustic enclosure. We evaluate performanceof the algorithms and their hardware complexity which relatesdirectly to energy consumption.
IndexTerms—
Directionofarrivalestimation,intelligentsensors,networks.
I. I
NTRODUCTION
S
OUND localization using compact sensor nodes deployedin networks [1] has applications in security, surveillance,and law enforcement [2]. Several groups have reported on co-herent [3] and noncoherent [4] methods for sound localization,
detection, classification, and tracking in sensor networks [5].Coherent methods are based on the arrival time differencesof the acoustic signal to the sensors [6]. In standard systems,microphones are separated to maximize accuracy, therefore,the nodes need to achieve synchronization to produce a validestimate [4]. The need of synchronization implies a frequentcommunication which is expensive in terms of power con-sumption. Noncoherent methods like closest point of approach(CPA) [4] are not critical with respect to synchronization,but are sensitive to sensor mismatch and differences in thechannels between the sound source and the sensors. Themethods discussed in this paper are all coherent approaches at
Manuscript received March 25, 2003; revised December 2, 2003. This workwas supported in part by the Defense Advanced Research Projects Agency/Of-fice of Naval Research under Contract N00014-00-C-0315 and in part byIntelligent and Noise-Robust Interfaces for Microelectromechanical SystemsAcoustic Sensors. The work of P. Julián, A. G. Andreou, and D. H. Goldbergwas supported by the National Science Foundation under Grant EIA-0130812.P. Julián is with the Electrical and Computer Engineering Department, TheJohns Hopkins University, Baltimore, MD 21210 USA and also with ConsejoNacional de Investigaciones Cientificas y Técnicas (CONICET), Capital Fed-eral CP1033,Argentina,onleavefrom theDipartimentode IngenieriaEléctricay Computadoras, Universidad Nacional del Sur, 8000 Bahía Blanca, Argentina(e-mail: pjulian@ieee.org).A. G. Andreou, D. H. Goldberg,and G. Cauwenberghsare with the Electricaland Computer Engineering Department, The Johns Hopkins University, Balti-more, MD 21210 USA.L. Riddle is with the Signal Systems Corporation, Annapolis, MD 21146USA.S. Shamma is with the Department of Electrical Engineering, University of Maryland, College Park, MD 20742 USA.Digital Object Identifier 10.1109/TCSI.2004.826205Fig. 1. Photograph of ASU enclosure.
the node level, therefore eliminating the need for synchroniza-tion. Indeed, one of the presented methods, the gradient flowalgorithm, is capable of bearing estimation with subwavelengthdistances among sensors.In the above-mentioned references, low-power commercialoff-the-shelf (COTS) hardware are employed. However, evenwith low-power state-of-the-art hardware, COTS devices con-sume power at the milliwatt level. While in some applications,this is adequate, in truly autonomous nodes that harvest energyfrom the environment (sun) the power dissipation must be re-duced many orders of magnitude to the microwatt level. Thiscanonlybeattainedbyco-designingthealgorithmswithcustommixed analog–digital hardware [7]–[9].
Inthispaper,weevaluatefourdifferentalgorithmsforbearingestimation using signals recorded in a natural environment withan array of four microelectromechanical systems (MEMS) mi-crophones, embedded in a custom designed acoustic enclosure(see Fig. 1). The algorithms are aimed towards a custom mixedanalog–digital integrated circuit implementations and the com-plexity of the algorithm is related to the power dissipation in thefinal system.II. S
TATEMENT OF
P
ROBLEM
A general array of four microphones as illustrated in Fig. 2,pairwise separated by a distance , will be considered. The ob- jective pursued is the estimation of the bearing angle, i.e., theangle of the sound source with respect to either coordinate axis.
1057-7122/04$20.00 © 2004 IEEE
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: COMPARATIVE STUDY OF SOUND LOCALIZATION ALGORITHMS 641
Fig. 2. Microphones array to measure the bearing angle.
For example, referring to Fig. 2, if we are using the pair of mi-crophones M1 and M3, then, the bearing angle will be given by, whereas if the pair of microphones is M2 and M4, then thebearing angle will be given by .The study is based on a particular application that employsan acoustic surveillance unit (ASU) enclosure (shown in Fig. 1)with an array of four Knowles SiSonic MEMS microphones.The distance between microphones is 6 cm; however, theacousticenclosureproducesaneffectiveseparationbetweenmi-crophones 15.9 cm. In all cases, we are assuming that thesound source is far away from the microphones . TheASUenclosurealsoincludesasignalconditioningcircuitrycon-sisting ofa low-passfilter and a gainstage. Thesrcinal motiva-tion for the study was to develop an algorithm able to localize abroad-band signal in the frequency range 20 Hz 300 Hz withan accuracy of one degree, using an estimation period of 1 s. Inorder to evaluate different algorithms, signals were recorded ina natural environment using a digital audio acquisition board at2048 samples/s. In Section III, the different algorithms are in-troduced while in Section IV, the details of the experiment andthe obtained results are described.III. B
EARING
E
STIMATION
A
LGORITHMS
In this section, we summarize the four algorithms employedto estimate the bearing of the sound source with respect to thefour microphones in the ASU. The algorithms are: 1) cross-cor-relation algorithm (CA) [6] ; 2) cross-correlation derivativealgorithm (CDA); 3) spatial-gradient algorithm (SGA) [10];4) stereausis algorithm (SA)[11].All methods employ time-domain signal processing based oncoherent localization, with the particular feature that nodes arespaced at subwavelength spacing. All methods are inspired bybiological information processing structures.
A. Cross-Correlation Algorithm (CA)
Bearing estimation using time-domain CAs has been exten-sively studied in the literature (see [6] and [12]
–
[14]). A time-domain CA is also used by many animals such as the barn owltoprovideazimuthinformation[15].Ananalog very-largescaleintegration (VLSI) implementation of the barn owl azimuth lo-calization system was reported by Lazzaro and Mead [16].Consider one pair of microphones with signals andarriving at the two microphones given by(1)where is the signal emitted by the source, andareuncorrelatednoisesignals,and isthetimedelaybetweenmicrophones. Under the assumption that the source is far away,the signal arriving at the two microphones can be approximatedby a plane wave, and the following relation holds:(2)where 345 m/s is the speed of sound in air at ambient tem-perature and is the maximum delay. The corre-lation between signals and is given by(3)After replacing (1) into (3), and considering that andare uncorrelated, (3) can be rewritten as(4)This function will exhibit a maximum at . Therefore,onewaytoestimatethetimedelayistogenerate(3)numericallyand calculate the time where the maximum is achieved.In practice, the signal is sampled at a certain frequencyand the correlation is approximated using a discrete timeversion(5)where is such that is the time window under con-sideration. From now on, we will discard in the notation,and instead we will use discrete instants indexed with an in-teger.Operation(5)canbeimplementedinadigitalfashionafterquantization of the signals. Using experimental data, we foundthat a 1-bit quantization was sufficient to obtain accurate esti-mations, as will be shown later. From a hardware perspective,coding the signal with just 1 bit produces a dramatic reductionin complexity. The resulting architecture consists of a numberof stages in the form of (6)where is an index to the stage number (see Fig. 3).At this point, some practical considerations are in order. Asampling frequency of 200 kHz is required (see Appendix) toestimate the angle with an accuracy of one degree for angles inthe range . As the test signals weresampled at 2048 Hz, for this particular case, it was necessaryto interpolate and resample the signals at 200 kHz. This choiceof sampling frequency implies that every discrete time delay iss. As the maximum possible delay, that corresponds toan angle is s, 92 stages arenecessary. Accordingly, index in (6) ranges from 0 to 91.
642 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS
—
I: REGULAR PAPERS, VOL. 51, NO. 4, APRIL 2004
Fig. 3. Estimation architecture for CA.
Froma hardware viewpoint, thedigital implementationof (6)requires shift registers to generate the delayed versions of , acounterimplementingthecorrelationoperationandoneblocktodetermine where the maximum has occurred. Once the signal isquantized with 1 bit, the information corresponding to the timedelay between both signals is encoded in the relative changesof state from zero to one and one to zero. Accordingly, no in-formation is contained in those parts of the signal where thereare no state changes. However, every stage (6) counts all thetime at the speed set by the clock, regardless of input values. Asthe frequency of the clock is much higher than the frequency of the signal, this architecture will dissipate more power than whatis actually necessary. This observation motivated the approachpresented in Sections III-B
–
D. Another point that must be con-sidered in this approach is the need to calculate the occurrenceof the maximum of (6), which requires the implementation of additional circuitry (a winner-takes-all circuit or an equivalentdigital circuit).
B. Cross-Correlation Derivative Algorithm (CDA)
As we said, the maximum of the correlation occurs when thedelay producedbytheshift registerchain coincides withtherel-ativedelaybetweensignals. Mathematically,detectingthemax-imum of the correlation function is equivalent to detecting thezerocrossingofitsderivativewhenthesecondderivativeisneg-ative. This has several advantages as we will show.If we consider (6) and calculate the discrete difference be-tween adjacent elements for every stage, we get(7)A careful observation of (7) reveals that it is in fact anup/down (
UP/DN
) counter. The counter counts up whenand the other signal satisfies and; it counts down when and theother signal satisfies and .Accordingly, the signals
UP
and
DN
commanding the countercan be written as(8)
Fig. 4. Estimation architecture for CDA.
Inthiscase,thecountisonlyupdatedwhenoneofthetwosig-nalschangesitsstate,anditisidletherestofthetime.Thismodeof operation reduces the activity of the circuit and consequentlyimpliesareducedpowerconsumptionandalsosmallercounters.Inaddition,toobtainthevalueofthedelay,itisjustnecessarytoread the position of the stage where the zero crossing occurred.Relatedtothis,noticethatallcountersabovethestagewherethecoincidence occurs will have a count of a given sign, whereasall counters below will have a count of the opposite sign. There-fore, the zero crossing can be detected by connecting the signbit of every pair of adjacent blocks (7) to an
XOR
gate, in sucha way that it will become active when two adjacent cells havea count of different sign (see Fig. 4). Then, if the
XOR
gates areconnected to encoders the position of the zero crossing is con-verted to a binary number that gives the reading. Notice herethat the use of the derivative in the calculation of the correlationeliminates the need to search for the maximum of the outputs,and instead provides a straightforward architecture to read thevalue of the delay.A final observation regarding the number of maxima occur-ring. In this application, we are relying on the fact that the min-imum period of the signal 3.3 ms is larger thanthe maximum delay, so that only one maximum will be notice-able in the range of times considered, given by 460 s . An-other assumption for this observation to be true is that only onesource of sound is present. The introduction of multiple sourceswould give rise to several maxima (and minima).
C. Stereausis Approach (SA)
This approach is inspired in the stereausis network describedin [11] that uses two cochlea channels to preprocess the inputsignals. In this case, every channel only reproduces the transferfunction of the basilar membrane (The model presented in [17]also models the outer ear and fluid-cilia coupling stages). Fol-lowing the work in [17] and [11], the output of every section of
basilar membrane is modeled with an infinite impulse response(IIR) (bandpass) digital filter. The frequency responses (magni-tude) of the 32 filters used are shown in Fig. 5. Analog VLSIimplementations of the basilar membrane as bank filters havealso been described in the literature [18].
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: COMPARATIVE STUDY OF SOUND LOCALIZATION ALGORITHMS 643
Fig. 5. Frequency response (in magnitude) of the stereausis network bandpass filters.
In the stereausis network, the sound from the left and rightmicrophonesarefedtotheipsi-lateralandcontra-lateralcochleachannels, respectively. Then, all outputs are quantized to onebit and the outputs of every stage of one channel are digitallycorrelated with the outputs of the other channel. In this way, aspatialarrangementofelementsresults,whichcanbeassociatedto an image, namely , whose element is thecorrelation between the output of the th element of the ipsi-lateral channel and the output of the th element of the contra-lateral channel (see Fig. 6). When the left and right signals areequal, the resulting image will have a significant density of nonzero elements along the main diagonal. However, if there isa delay in one of the signals, the image will show a shift of the main diagonal toward one of the sides. This is illustrated inFig. 7, which shows the response of the network to a set of realdata where one of the inputs is delayed. The simulated network consists of a 32-stage cochlea with cutoff frequencies between252 and 618 Hz. Notice that as a delay of s is equivalent to aphase shift of , the higher the frequency the morenoticeable the unbalance of the image with respect to the maindiagonal.Actually,thefrequencyrangeofthefilterwasadjustedto maximize the detection sensitivity through simulations.
1
The indication of time delay is calculated by measuring theunbalance of image with respect to the main diagonal. Thisis done by computing the difference between the sum of upperdiagonal elements and lower diagonal elements, i.e.,(9)
1
At first sight, it might seem surprising that the cutoff frequencies of the fil-ters are higher than the signal bandwith. Regarding this, the reader should notethat everycochleafilter sectionisabandpassfilter withaverylongtail.Accord-ingly, the filter with the highest cutoff frequency (e.g., 618 Hz) still amplifiesthe contribution of lower frequency signals.Fig. 6. Estimation architecture for stereausis algorithm.Fig. 7. Response of the stereausis network to two signals with a relative delay.
D. Spatial Gradients Approach (SPGA)
In this approach, the signals recorded by the microphonesare interpreted as samples of a field sound wave and the
644 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS
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I: REGULAR PAPERS, VOL. 51, NO. 4, APRIL 2004
bearingangleisestimatedusingfirst-orderderivatives[10].Thisalgorithm, as opposed to the previous ones, takes full advantageof the four microphones for the time delay estimation. For thepresent situation let us consider the position of the microphoneswith respect to the center of the array. We will assume that forany given location in the plane, where , the magni-tude represents the time delay between the wavefront of the sound wave at and the wavefront of the sound wave at thecenter of the array. Using this convention, we can express thefield , in a Taylor series around aneighborhood of the srcin(10)Tofirstorder,andaftergeometricconsiderations,itcaneasilybe seen that(11)where , arethe delays with respect to the coordinate axes. Then, a simplemanipulation of the variables leads to(12)If we sample the signals with a sampling time ,and assume that can be adequately measured by fil-tering ,then,(12)isastandardleastmeans-square(LMS)problem and , can be obtained independently after col-lecting samples as
2
(13)where(14)and .This approach heavily relies on the accuracy of the signalsmeasurement, especially due to the need of an estimate of thederivative. For this reason, even though in this case the signal issampled in time, its amplitude cannot be quantized. In practice,the srcinal signal was used with the srcinal sampling rate of 2048 samples/s, and the derivative was calculated using finite
2
Similar results can be obtained using adaptive algorithms.Fig. 8. Testing setup showing location of ASU, speaker, and measured angles.
differences. The derivative is obtained using a one-step differ-ence equation . As is well known,this scheme might produce noise amplification at high frequen-cies. In this particular case, high frequencies are filtered by theanti-alias filter and by a high-order low-pass filter with cutoff frequencyat300Hz.
3
AscanbeseenfromFig.13(shownlater),the amplitude of the signal is higher than the amplitude of thenoise in most of the spectrum of interest 0 Hz 800 Hz .In the remaining part of the spectrum, both signal and noise arenegligible. Integration of signal and noise power in the full fre-quencyrange 0 Hz 1024 Hz indicatesthatthesignal-to-noiseratio and . This observa-tion agrees with the experimental results presented in [7]. Nev-ertheless, it must be pointed out that this scheme could producenoise amplification, for example, if noise conditions were dif-ferent, or the signals were narrowband instead of broad-band,or the sampling rate were higher (producing a greater band-width). In these cases, more elaborate calculation schemes forthe derivative should be chosen [19].IV. E
XPERIMENTS AND
N
UMERICAL
R
ESULTS
In order to design and test the different algorithms, experi-mental data were collected in a field test in a public park in Sev-erna Park, MD. The ASU was located in the center of a field,and one 30.5-cm (12 in) subwoofer was placed 18.3 m away.A Gaussian white noise signal was played through the speakerand the signals received at the four microphones were recordedusing a sampling time of 2048 samples/s. For every angle, weplayed 30 s of data and obtained 30 different readings of timedelay, corresponding to different estimations during a 1-s timewindow. Two different sets of data were collected. One set of
3
This is the result of a second-order low-pass filter plus the low-pass filteraction of the microphone itself.

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