1

Abstract—One of the principal cues believed to be used by

listeners to estimate the distance to a sound source is the ratio of energies along the direct and indirect paths to the receiver. In essence, this “direct-to-reverberant” energy ratio reveals the absolute distance component of the direct energy by normalising by what is assumed to be distance-independent reverberant energy. Earlier approaches to direct-to-reverberant energy ratio calculation made use of the estimated room impulse response, but these techniques are computationally expensive and inaccurate in practice. This paper proposes and evaluates an alternative approach which uses binaural signals to segregate energy arriving from the estimated direction of the direct source from that arriving from other directions, employing a novel binaural equalization-cancellation technique. The system is integrated with a probabilistic inference framework, particle filtering, to handle the nonstationarity of energy-based measurements. The algorithm is capable of using reverberation to estimate source distance in large rooms with errors of less than 1 m for static sources and 1.5-3.5 m for sources with varying degrees of motion complexity. Model performance can be accounted for largely in terms of a competition between auditory horizon and source energy fluctuation effects.

Index Terms—Acoustic distance measurement, direct-to- reverberant energy ratio, particle filtering, binaural sound source localization.

I. INTRODUCTION UDGEMENT of ego-centric distance to nearby objects is an important human sensory capability and is at times wholly -

and critically - dependent on auditory input. A cyclist uses engine noise from motor vehicles to estimate distance in order to pick up speed in time and prepare for evasive action. A runner listens to the footsteps and breathing of his or her opponents to evaluate whether their lead in the race is adequate enough. The approach of a mosquito person at night can be detected through the sound made by its vibrating wings.

A preliminary report of this work appeared at the International Workshop on

Acoustic Echo and Noise Control (Seattle, July 2008). This work was funded in part by EU Cognitive Systems STREP Project POP (Perception On Purpose), FP6-IST-2004-027268.

Yan-Chen Lu is with the Department of Computer Science, University of Sheffield, Regent Court, 211 Portobello Street, Sheffield, S1 4DP, U.K. (e-mail: yanchen@dcs.shef.ac.uk)

Martin Cooke is with the Language and Speech Laboratory, University of the Basque Country, Spain and IKERBASQUE (Basque Foundation for Science) (e-mail: m.cooke@ikerbasque.org).

Absolute sound energy at the receiver is a function of intrinsic source energy and source distance, both of which may be time-varying, precluding the use of energy alone as a cue to source-listener distance. However, the combination of energy received along the direct source-listener path with energy arriving following reflections has potential as a means of estimating source distance. The “direct-to-reverberant” energy ratio (DRR) has been suggested as part of the mechanism for source distance judgements in listeners [3-6]. Distance judgments are more accurate in a reverberant space than in an anechoic space, with small inter-test variation in judgements in the same environment [3]. Listeners may use reverberation as an absolute distance cue given that accurate distance judgments were obtained at first stimulus presentation [4]. Zahorik [7] suggested that the principal role of the DRR cue was to provide absolute distance information rather than support fine distance discriminations and was poor as a relative cue. Zahorik also suggested that DRR was perceptually more salient than an intensity cue, especially in a situation where prior knowledge of natural speech level could not be used due to other more variable and complex acoustic information in the surrounding environment [8].

Attempts have been made to exploit the DRR cue both monaurally and binaurally. Bronkhorst and Houtgast [9] proposed a computational model to predict human distance judgement in a controlled condition where the DRR cue is dominant. Their model demonstrated accurate prediction of subjects’ distance responses based on prior knowledge of certain acoustical properties of the environment (room volume, reverberation time and source directivity) using monaural data. Relying on blind identification of the room impulse response from the monaural signal, Larsen and colleagues [10] developed a technique to compute DRR based on certain assumed room acoustics parameters, such as the duration of direct sound. They found that source distance could also be determined as an intermediate output and arrived at underestimated judgments for sources at moderate and large distances (further away than 2 m), similar to the pattern found with human listeners. Other models based on binaural signals utilised either prior knowledge of the environment (e.g. room impulse responses [11]) or extensive spectral training data [12] to formulate source distance inference using the DRR concept. While these studies attempted to demonstrate that distance inference can be further improved with binaural input, neither study, surprisingly, emphasised the role of directional information.

Binaural Estimation of Sound Source Distance via the Direct-to-Reverberant Energy Ratio for

Static and Moving Sources Yan-Chen Lu and Martin Cooke

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IKELIHOOD FU

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V. SEQUENTIA

Previous secinaural signal

g. 9. DRR estima0 m space with TRRs, along with t

ndard deviatioer room descrse a constraint case up to 16 . 10 separatedintermediate

rther represente seen that, evis yielded forof Fig. 10) relakes it clear thaand azimuth, wnd distance foa natural lim

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M modelling. Asource distanaussian distribreduce Gausssian distributvarying azim

li, multiple GM algorithm

east three GMsf Fig. 8) were

nce performanons, ITD infoM for generamapping is nhe centre is re

AL MODELLINGDISTANC

ctions presents to produce

ates derived fromT60= 0.7 s. Grey the derived GM p

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d into three seand lateral),

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for lateral soumitation of EC

ution of the de

R does not cccuracy of dis

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muth. ConditiGMs, instead

associated ws (each formue found to sufnce in a pilot stformation helpating the likeneeded since equired.

G FOR TEMPORCE ESTIMATES

ted an algorithinstantaneous

m stimuli synthesiscircles are plotte

parameters.

. Again, as obon III, room

ective DRR ope data set in Fets of azimuth, using a grormation withal distances, sfront of the l sources (top aries as a func

respondence burces. This e

C-DRR owingelay-line from

correlate solelstance estimatl variable, the

vation associatmisjudged

way to minimthrough the

cribe equallyioned on theof one, are

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only the de

RAL INTEGRATS hm which prs estimates of

sed for a 18 m by ed for each of th

bserved volume

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ly with tion can e source ted with due to

mise the use of

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rated in ance the ceipt of

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TION OF

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disprasucinfexpstafiltappsyssimvado

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stance based actice, instantch as noisy obformation in plores the loca

atic virtual litering. Particproximate thestem state (hmulation [23]ariation and ominance of ob

ig. 10. Re-plottisplayed. The laterawn at the top pa0o:light grey). Th60o~30o) and (30o~

on the directaneous estim

bservations, anthe case of

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here, sound so. It allows ththe continu

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ting of Fig. 9 weral sources (at leanel with a grey che middle and bo~0o) from the me

ct-to-reverberamates can be nd fail to take f moving sousingle static ora rotating h

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with the associateast 60o offset frocolor representatiottom panel displedial plane respec

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7

sound localisation is described in [24, 25]. Details of the PF architecture used in the current study can be found in [19].

In essence, PF operates by iterating 3 steps: prediction, update and estimation. Each iteration alters the particles (i.e. independent hypotheses over the system state) and associated particle likelihood weights based on a predictive model of the sound source dynamics with the likelihood transformed by updated observations. Estimated source location is then calculated as the weighted mean across all particles. The implementation of these steps in the current study is described next.

A. PF prediction stage If available, a model of source dynamics can be used to

modify particle hypotheses at the PF prediction stage. Since no prior knowledge of source dynamics is assumed here, source motion is approximated by a zero-mean Gaussian noise term which is characterized by an adaptive standard deviation, itself a function of the corresponding particle likelihood weight. The observed dynamics in the current study is due to motion of the target source. Noise terms are applied to relocate source location hypotheses of all particles in both azimuth and distance in the PF prediction stage. Specifically, the state variable (i.e. hypothesised source location in distance n

trx ,and azimuth n

tx ,φ)

corresponding to particle n at time t is determined by

],[ ,,n

tn

trnt xxx φ= (14)

where the evolution of source azimuth location n

tx is formulated as an increment to the previous location n

tx 1− with

noise term ntμ As defined in (15), n

tμ is a zero mean Gaussian variable with a time-variant standard deviation n

tσ , which is a function of the particle likelihood weight n

t 1−ω and the constant maxσ .

max1

2 )12(],)(,0[ σωσσμ ⋅−⋅== −nt

nt

nt

nt N (15)

Since n

t 1−ω ranges between 0 and 1, maxσ specifies the maximum value of the standard deviation. The effect is that a weaker particle is more likely to possess a larger noise term, encouraging a wider range of exploration of the state space. The altered location hypotheses are subsequently evaluated with the observation model introduced next to update particle weights.

A fixed maximum standard deviation, empirically determined as 15o ( φσ max, ) and 2 m ( rmax,σ ) in azimuth and distance coordinates respectively, was applied across all particles. Note that the source azimuth is measured relative to the medial plane, as a function of head orientation. Particle hypotheses for source azimuth therefore need to be adjusted in accordance with head rotation.

B. PF update stage At the PF update stage, cues were fused by multiplying the

likelihood functions associated with the two different localisation cues, namely ITD and EC-DRR, for updating each particle’s likelihood weight. The derivation of the EC-DRR likelihood function according to the current observation and the pre-collected training data was demonstrated in Section IV. The

cross-correlation function, (2), computed from the input binaural signal can be directly used as the ITD likelihood function for source azimuth as in the pseudo-likelihood approach of Ward et al. [25]. The length of the delay line is M = 65 samples corresponding to 0.75 ms at the sampling frequency of 44.1 kHz used here. As illustrated in the lower plots of Fig. 3, the cross-correlation function acts as a weight for each time delays, which are further mapped into source azimuths through the transfer function described in Section II.A.

In parallel to PF, the peaks of the likelihood function produce instantaneous estimates of source azimuth and distance. Instantaneous azimuth information is also used to calculate EC-DRR and select the correct GM for generating the EC-DRR likelihood function for a given azimuth range, as outlined in Section IV.

C. PF estimation stage The mean of the 20% of particles with the highest likelihood

weight was used to generate source location estimates. This approach minimises the negative effect of weak particles and results in a degree of resistance to noisy observations. Since the instantaneous azimuth estimate is made without exploiting the head rotation cue, substantial localisation degradation is expected resulting from front-back reversals. This estimation error, which may be up to π , is principally on account of the use of the ITD cue rather than the detrimental effects of noisy environments. Therefore, the judgements suffering from front-back reversals occurring in the instantaneous estimation approach were rectified to the hemispheres used to generate the input stimuli. In this way, the advantage of sequential integration provided by PF can be properly assessed.

VI. EVALUATION

A. Stimuli

The “Roomsim” room simulator [26] was used to generate binaural stimuli for various listener-source configurations and reverberation conditions. Non-individual HRTFs recorded with a KEMAR dummy head [20] with inter-ear distance of 0.152 m were used to generate binaural room impulse responses based on the image method [27]. Stimuli were generated at a sampling rate of 44.1 kHz. Temperature and relative humidity were set at 20o C and 40% respectively during the simulations. The virtual room was an 18 m by 18 m by 10 m gym space. This was generated in two reverberant conditions with T60= 0.2 s and 0.7 s.

Training and test stimuli were generated by convolving a speech or pink noise source with the binaural room impulse responses. The simulated listener was static and placed in the south-west corner of the room in order to permit the use of quite large listener-source distances, all of which greater than 2 m, at no near-field distance cues are available [2], allowing a focus on the range where DRR cues are expected to dominate distance perception.

Variation of listener-source geometry at each time frame simulated motion of the sound source. The sound source was either static, moved linearly, or exhibited more complex motion which we refer to here as “zigzag motion”. Each simulation run

comofdi11

B.

EusoaneresinpethandeinfilByco

socoFithtoalesindire1)

Figgethezig onsisted of 60

moved towardsf 0.14 ms-1. irection but va1 shows the so

. Localisatio

Localisation puclidean distaource locationnd (iii) the unsrror refers to tstimate and thnitial conditionerformance mhe simulation.nalysis of thevelopment sen [19]. Evalualtering) was by contrast, tonstant betweeStatic auditor

ource distanceonsisting of twig. 12 presents

he sequential ao a large improll conditions. stimation erroncreased, wheistance estimeverberation. ) ComparisonHuman listen

g. 11. Syntheticenerated by a roome source. The posgzag motion are s

0 time steps os the SE cornerThe zigzag s

aried in velocitource trajector

n Performanc

performance wance (AED)

n; (ii) the unsisigned estimatthe absolute vhe ground trutns, since partic

measures are th. Frame 15 w

he convergenet using a framation in the sbased on arithmthe AED of en simulationsry cues, DRR e and azimuth wo reverberans results for th

algorithms (PFovement in loc

For static or increased ereas motionation for zig

n to human lisner localisatio

c sound source m simulator give

sition of the virtuashown.

of 0.75 s eacr of the room source movedty from stationry of each of t

ce

was measured between the

igned estimatition error in dialue of the di

th. To avoid ucle hypothesehe averages owas chosen bce of particl

me convergencequential casmetic means othe non-sequ

s. and ITD, werrespectively

nt spaces and the non-sequenF+DRR+ITD)calisation perfand linear m

as the levn complexity gzag moving

stener performon performan

dynamics. Virtuaen the spatial attral listener as well

h. The linear at a constant vd in a northenary to 0.42 mthe three cases

using (i) the atrue and es

ion error in azistance. The unfference betw

undue influences were set ranover frames 1based on an le hypothesece criterion dee (i.e. using p

over 100 simuuential algori

e used for estiacross six conthree source mntial (DRR+IT. Particle filterformance in v

moving sourcvel of reverb

resulted in sources wit

mance nce in azimu

al binaural stimuibutes of the listeas examples of lin

r source velocity easterly

ms-1. Fig. s.

average timated zimuth; nsigned

ween the ce from ndomly, 5-60 of offline

es in a escribed particle

ulations. ithm is

imating nditions motions. TD) and ring led

virtually ces, the beration

poorer th mild

uth and

discopelisrecfro

Wavlesdis

AprofunDe[2]Figavare

uli wereener andnear and

Fianmpaazshin

stance was tnfiguration asrformance intener is placectangular virtuom the model While listenererage Euclidess able to estistance. An alternativovided by Zahnction relatione and the true d] found a bestg. 14, althougherage across ae compatible w

ig. 12. Localisatind non-sequential

motions and reveranel), averaged uzimuth (bottom pahow averages ovntervals.

tested in [1]s in the curre

n localising aed in the centual space witfor the same s

rs and the modean distance imate azimuth

e measure ohorik [8], whnship, De=k·Ddistance Ds. Bt fit at a=0.54h it should nota large range owith the config

ion performance cl (DRR+ITD) algrberation levels. unsigned estimatianel) over 100 sim

ver the 6 conditi

] using a sient study. Figa static soundter of a 18 mh T60= 0.7 s, stimuli. del resulted inestimates, hu

h but outperfo

f human disho proposed a Ds

a, between thased on 84 dat

4 and k=1.32. t be taken too of conditions, guration used

comparison of segorithms as a funValues above baion error of distmulations of 45 sions. Error bars

imilar experig. 13 shows ld source wh

m by 18 m byalongside est

n very similar uman listenersformed the mo

tance estimatcompressive

he perceived dta sets, ZahoriThis fit is sholiterally since only some ofin the current

equential (PF+DRnction of differenars are mean AEance (middle pa

s each. The rightmdenote 95% co

8

imental listener

hen the y 10 m timates

overall s were odel in

tion is power

istance ik et al. own in it is an

f which t study.

RR+ITD)nt sourceEDs (topanel) andmost barsnfidence

GwECdimFrlaaure 2)

pechdepr

Figdisthride(D

FigPFcoan Given the distanwere fitted 0.65

C-DRR can istance beyond

multiple studierom the figure

arge as predicuditory horizoegion (see Fig.

) Effect of revA longer reveerception by haracterise theelays of earroperties of re

g. 14. Estimatestance. The stimuree different targeeal relationship. F

De=1.32·Ds0.54, squ

g. 13. PerformanF-based model of orresponds to azimnd average Euclid

nce estimates 5 and 2.02 (thonly functiond 2 m), while

es which usede, distance undcted by Zahoron effect of EC. 9).

verberation anerberation tail

enhancing e diffuse sounrly strong reflected surfac

d distance as a ulus-estimate relaet motions are preFitted power funuares) and in this

nce comparison bf source localizatiomuth errors whiledean distance.

obtained in ouhe dotted line in effectively Zahorik’s fun

d both near- aderestimation irik’s curve, p

C-DRR is pres

nd target motl is considerelater-arriving

d field. The roeflections, wes determine t

compressive powationship of outpesented. The blacknction curves are paper (De=2.02·D

etween human lison in azimuth ande the right y-axis

ur PF method, in Fig. 14). Nin far-field

nction is deriveand far-field in our model i

probably becasent at a rather

ion on EC-DRd helpful in d

g reflectionsoom size conthile the abstheir magnitud

wer function of sputs from PF runsk solid line (De=Dgenerated for daDs

0.65, diamonds)

steners (from [1])d distance. The les serves for both

a and k ote that (source ed from stimuli. is not as ause the r distant

RR distance

which trols the sorptive des. For

a fexDRaccspaacoHospa0.5whrev

TanRebelevintT60anzigtho0.2soumofinmo

Tof sho(9.upsoupothecoEC(0~to stiof in

Ffun

stimuluss for theDs) is theta in [2]

).

Fimdilin

) and theft y-axisdistance

fixed room sizistence of a diRR cue utilizcurate distancace, given timoustics. A simoutgast [9], whace with less 5 s). As a resuhen the room verberant caseThe distance

nalysed usingeverberation tween-group fvel and auditteraction of th0, was signifi

nalysis, using gzag moving ose for the oth2 s was betterurces (p < 0.0oving sourcesnding below aotions. The simulatedf stimulus distaown in Fig. 1.22 m) for the

p to 1.55 and urces and th

ossible EC-DRe region of thentains the oth

C-DRR is see~1.25 in the dthat of zigzagmuli for the T

f the boxes in FFig. 15.

Fig 16 displaynction in the

ig. 15. Listenemotions. The static

istances from 9.1near moving sour

ze, a longer reiffuse sound fzation. Mershce judgments wme to reach sumilar effect who discoveredreverberation ult, distance ureverberation

e. estimation re

g a two-waytime and sofactors so as ttory horizon he two betweeicant [F(2,594

Tukey’s HSDsources were

her two (p < 0r than T60= 0001), while ths (p < 0.001after examinin

d sources with ance variation15. The listenee static source

16.9 m werehe zigzag moRR distributione larger box inher two motionen in the stimdimensionlessg sources (-0.2T60= 0.7 s conFig. 16 are det

ys the GM prlow and high

r-source distancc sources were 9.29 to 10.74 m andrces and the zigza

everberation tafield, offering on et al. [5] were found foufficient familwas also foundd a closer “aud

(in their caseunderestimation was higher c

esults of the y repeated-mource motiono study the efon estimation

en-group facto4) = 231.4, p D, revealed te significantly0.001). The p

0.7 s for statiche reverse was). We return

ng the differen

zigzag motionn than the otheer-source distes. Stimulus de possible foroving sourcesn of zigzag soun Fig. 16, whens. Thus, a mmuli of statics horizontal ax25~1.5). The r

ndition is -1.25termined by c

riors for the h reverberatio

e variations for 22 m away from td from 5 to 18.69ag moving source

ail contributesbetter conditioreported that

r a more reveriarity with thed in Bronkhorditory horizone, with T60= 0.on was less frcompared to t

current studymeasures ANn were treatffect of reverbn performancors, source mo

< 0.001]. Pothat judgemeny less accuraterformance fo

c and linear ms true for the

n to this confnces between

n have a widerer source motiance was a coistance variatir the linear ms respectivelyurces is indica

ereas the smallmore limited ra

and linear sxis) when comrange of the tr5 to 1.5. The horresponding

EC-DRR likeon conditions.

three simulatedthe listener, while m were specifie

es respectively.

9

s to the ons for t more rberant e room rst and

n” for a .1 s vs. requent the less

y were NOVA. ted as eration e. The otion × ost hoc nts for te than or T60= moving zigzag

flicting source

r range ions, as onstant ions of moving y. The ated by ler box ange of sources mpared raining heights curves

elihood These

d sourcee varyingd for the

prsathECGasslith“alo17CdinuByawthre

Figas

Figsti

riors were learame gym spache T60= 0.7 s C-DRR. Cont

Gaussian means the source diight increase

he variance coauditory horizow reverberati7, indicating tonsequently, istance estimaumber of souny contrast, byway from the he static and everberation.

g. 17. Two Gaussociated with T60=

g. 16. The operatimuli correspondi

rned from the ce. As shown,condition leatinuously curvs. For T60= 0.7stance increasoccurs for di

ontinues to inzon” phenomeion condition the operating it may exp

ations in lownd sources fal

y operating in auditory horilinear sourceThis suggest

ssian mixtures fo= 0.2 s (grey) and

ting regions of ECing to the three si

training stimu, the greater rds to larger vves are forme7 s, log-inversses. However,stances beyon

ncrease. This enon. The audis indicated urange applie

lain the resuw reverberation

lling beyond tthe listener-soizon effect, des became mts that energ

r generating EC-d 0.7 s (black).

C-DRR likelihoodimulated source m

uli synthesisedreverberant envalues of log-ed by connectse EC-DRR in for T60= 0.2 snd 12 m alongmay result fr

ditory horizonunder the box ed to zigzag sulting less an for the incthe auditory hource distance

distance estimamore accurate

y fluctuation

DRR likelihood

d function (T60= 0motions.

d for the nergy in -inverse ting the ncreases s, only a g while rom the n of the

in Fig. sources. accurate creasing horizon. e region ates for in low

ns from

reveffmoloc 3)

APFnoantw(PF(nocoAEmimo

S0.2Figtheof theroucoThi.e

Cprenorel

function

Fifoovva

0.7 s) for

verberation arfect is absent. ore severely ication estimat

Benefit of seAs shown in thF can be reducot involve PF. nalysed using wo within-grou

F) algorithm won-PF) algorirrelated perfoED (the top piddle panel) exotion. Simulation res2 s for static sg. 18. Static soe effects of se

f source motioe non-PF apprughly from 1ntrary, PF dem

his decrease ste. 1 m error froConsidering tesent in the

on-PF azimuthlatively insen

ig. 18. The runnior the static sourcver 100 simulatioariation in estima

re more influThe measurem

in high reverbtes.

equential modhe top panel oed to about haThe effect of sa one-way r

up factors (souwas significanithm [F(1,198ormance distrpanel of Fig.xcept for the c

sults for both Pources are draources only arequential modon. From the uroach show lit1 to 9 m for monstrates a stops when it reom the figuresthe azimuth ITD likeliho

h localisation.sitive to distu

ing unsigned erroces with T60= 0.2ons for the PF mtes from frame to

ential when tments of EC-Dberation and

delling of Fig. 12, the alf of that for asequential morepeated-measurce motion × ntly superior t8) = 956.2, pributions are f 12) and thecondition of n

PF and non-Pawn as a functre presented h

delling indepenupper panel, thttle temporal c

9.22 m distmoothly decre

eaches the bests of non-PF. component,

ood function By contrast, urbance cause

or of distance (up2 s. Each symbol methods. The nono frame than the P

the auditory hDRR were disled to less ac

localisation eapproaches whodelling on AEsures ANOVAT60). The seq

to the non-seqp < 0.001]. Hfound for the distance erro

non-PF under

PF algorithms tion of time fr

here so as to exndently from he distance ercorrelation andant stimuli. Oeasing distanct EC-DRR can

spurious peawhich may the PF algori

ed by reverbe

pper) and azimuthrepresents an av

n-PF methods shoPF methods.

10

horizon srupted ccurate

error of hich do ED was A with quential quential Highly

e mean or (the zigzag

at T60= rame in xamine effects

rrors of d range On the ce error. n offer,

aks are disrupt ithm is eration.

h (lower)verage ofow more

11

PF particles close to the true source position are constantly supported by that part of the likelihood function, which may produce a lower weighing due to the existence of spurious peaks. This effect is depicted in the lower panel of Fig. 18. A rather smoother azimuth error is found for PF than non-PF despite the fact that the latter has been improved by correcting for front-back reversals. It seems likely that the sequential approach embodied in the PF framework provides some robustness to occasional observation errors, leading to more stable performance as a result of temporal cue integration.

It is generally found across conditions that the PF-based estimate for the azimuth component exhibits a faster convergence (sometimes showing convergence as early as the second frame, as exemplified in Fig. 18) than that for distance. This suggests that EC-DRR may be too sensitive to instantaneous energy fluctuations to be able to provide as precise a localisation estimate as ITD.

VII. DISCUSSION

The current study describes a system to extract useful information for determining sound source distance from reverberant binaural input. The direct-to-reverberant energy ratio was measured by assuming direct and reverberant signals can be separated with their differential incoming directions. A binaural equalization-cancellation (EC) technique was proposed to separate energy belonging to each lateral direction corresponding to a resolution of one delayed sample in a delay-line structure. The EC-based direct-to-reverberant energy ratio (EC-DRR) was calculated by dividing the energy aligned with the target location over the energy sum of the remaining directions. A cross-correlation based azimuth estimator was used to determine the target location.

During the evaluation of its potential as a distance cue for both simulated and real data, estimated EC-DRRs with substantially varying values even from a static sound source were commonly observed due to energy fluctuations of both target and background. Their correlation with source distance was only be observed in the longer term, i.e. under sequential examination over a few seconds.

An EC-DRR based likelihood function was developed in combination with interaural time differences to update estimates of sound source location in both distance and azimuth. The likelihood function was derived based on a given reverberation-related prior as a function of source azimuth, in the form of a set of Gaussian mixtures, uniquely determined for each room. Only the information of azimuth offset from the median plane is needed when integrating the reverberation-related prior. The latter can be derived as part of the process of learning the acoustics of the room. Our approach is hence insensitive to front-back reversals and consistent with Simpson and Stanton’s finding [28] on the irrelevancy of head movements to distance perception.

The framework of particle filtering (PF) integrates evidence over time to reduce the distorting effects of errors associated with instantaneous observations. The use of PF nearly halves the error in localisation compared to instantaneous estimates. Further, PF smoothes out the variation in reverberation effects

caused by the changing geometry between room surfaces and target source (or listener). PF also allows the learning of room acoustics (here, in terms of GM prior) independent from the positions of sound source and listener, and may offer a less complex alternative to the distance learning problem than presented in [12].

The auditory horizon effect was observed in both real and synthetic stimuli as a function of room reflection properties and probably led to the under-estimation of distance found over the upper part of the distance range (e.g. see Fig. 14). The auditory horizon is effectively an upper limit on perceived distance and may result from the mechanism that human listeners use to separate direct and reverberant energy components [9]. In the scheme used in the current study to separate direct energy from reverberation via a delay-line structure, an auditory horizon may be established if the direct signal is too weak (being sufficiently far away from the listener) to dominate the energy arriving from the target source azimuth.

The performance drop compared to real listeners suggests that the EC-DRR approach to distance estimation does not fully exploit the DRR cue. One weakness of the evaluated distance estimator is that EC-DRR was designed to operate principally in the non-near-field range i.e. for listener-source distances of greater than 2 m. It is known that other cues, such as interaural differences, are implicated in near-field distance estimation [2].

The evaluation used synthetic stimuli which reproduced the diffuse field with limited fidelity, perhaps resulting in a substantial amount of distance-dependent but non-direct energy. Further, the acoustic properties of synthetic stimuli were not completely unknown to the computational models during simulation: reverberation time served as a prior for configuring associated likelihood function parameters. Further work using both real stimuli and methods to learn reverberation time is required to overcome these limitations. The analytic function describing the relationship between DRR and listener-source distance can also be improved to reduce GM parameters by simplifying the learning of room reverberation.

A further development of the equalization-cancellation technique for identifying multiple source energies in the delay-line structure may be necessary to improve EC-DRR accuracy by removing strong early reverberation or interfering sources.

VIII. CONCLUSIONS The direct-to-reverberant energy ratio has long been

considered as an absolute auditory cue in human distance perception. Traditional methods for extracting this energy ratio are based on the post-processing of room impulse response, whose estimation is computationally expensive and inaccurate in practice. An alternative, which was employed here, is to estimate the energy arriving from the direction of the direct source, under the assumption that reverberant components result in a spatially-diffuse sound field. We proposed a binaural equalization-cancellation technique to calculate this energy ratio (EC-DRR) by locating the direct energy in a delay-line structure.

Simulations using synthetic stimuli indicated that the degrading effect of reverberation could be effectively mitigated

12

by sequential cue integration for both distance and azimuth estimations. The localisation error of the PF approach is in this way reduced to 47% of that for instantaneous estimation. The advantage of particle filtering was found to be mainly attributable to better localisation in distance, suggesting the importance of sequential integration for auditory cues based on energy measurements.

The performance of source distance estimation using DRR can be accounted for largely in terms of a competition between auditory horizon and energy fluctuation effects. As found for the sources with non-linear motions, better distance localisation performance for PF was obtained in the more reverberant space with a farther auditory horizon. Although energy fluctuations increased with the level of reverberation, their detrimental effect was smoothed by PF cue integration over time.

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Yan-Chen Lu received the B.Sc. and M.Sc. degrees in electronics engineering from National Chiao-Tung University, Hsinchu, Taiwan, in 1997 and 1999. He is currently pursuing the Ph.D. degree in the computer science department, University of Sheffield, UK. His research interests lie in spatial audio perception and computational audition. Martin Cooke received a B.Sc. in Computer Science and Mathematics from the University of Manchester in 1982 and a Ph.D. in Computer Science from the University of Sheffield in 1991. He has worked at the UK National Physical Laboratory, the University of Sheffield and is currently Ikerbasque Professor at the University of the Basque Country, Spain. His research interests include robust automatic speech recognition, speech perception, computational auditory scene analysis, active hearing, the effect of noise on speech production and second language acquisition of speech.