Multiple Sound Source Location in 3D Space with a Synchronized Neural System

Transcription

1 Multple Sound Source Locaton n D Space wth a Synchronzed Neural System Yum Takzawa and Atsush Fukasawa Insttute of Statstcal Mathematcs Research Organzaton of Informaton and Systems 0- Mdor-cho, Tachkawa, Tokyo JAPAN takzawa@sm.ac.jp Abstract: - Ths paper descrbes a synchronzed neural system to mnmze errors of predcton between observaton and estmaton. Ths scheme s dfferent to the prncple of conventonal learnng methods. The proposed scheme s appled to the problem of tme-space analyss of multple sound source locatons n D space. The number of sources s assumed 6 sounds wth a tme-frame of 5 sec, and number and sze of sensors are 6 and 0. meter cubc. The proposed scheme s confrmed wth well concdence of generaton tmes and locatons.. Key-Words: - Locaton estmaton, tme-space analyss, synchronzed neural system Locaton Estmaton A useful method s studed for sgnal processng of tme-space sequences based on novel neural networks. Ths algorthm was used for dscrmnaton of mpulse sgnals receved from spatally dstrbuted multple sound sources. Generaton of mpulse sgnals are at random temporally and spatally, vbraton sensors are set at each quarter of a square space. A system s consdered wth the followng confguraton. Impulse sound sgnals are receved from multple sound sources located at arbtrary ponts n space. Impulse sgnal s generated at arbtrary tme for each sound source. These receved data are treated as tme-space sequences. Sensor system s settled shown n Fg.. Multple Sources exst on arbtrary poston n a space. Four sensors are put n the corner of the cubc. Impulse sgnals from sources reached to sensors wth tme dfference. The locatons of the sources are calculated usng the tme dfference of reached mpulse sgnals. Ths paper descrbes a study on mechansm of locaton estmaton n bran based on sgnal processng bass va electrcal and bologcal approaches. The word locaton ncludes dstance and drecton whch are ponts n space coordnates. Locaton n D space has been reported already[]. Locaton for D space s taken up n ths paper. System Confguraton A useful method s studed for sgnal processng of tme-space sequences based on novel neural networks. Ths algorthm was used for dscrmnaton of mpulse sgnals receved from spatally dstrbuted multple sound sources. Generaton of mpulse sgnals are at random temporally and spatally, vbraton sensors are set at each quarter of a square space. A system s consdered wth the followng confguraton. Impulse sound sgnals are receved from multple sound sources located at arbtrary ponts n space. Impulse sgnal s generated at arbtrary tme for each sound source. These receved data are treated as tme-space sequences. Sensor system s settled shown n Fg.. Multple Sources exst on arbtrary poston n a plane. Four sensors are put n the corner of the plane. Impulse sgnals from sources reached to sensors wth tme dfference. The locatons of the sources are calculated usng the tme dfference of reached mpulse sgnals. When the mpulse ntervals are enough long, t s easy to decde the set of mpulse from same source and to estmate the poston of sound sources. ISBN:

2 However, actually a sensor receves the mpulse sgnals from dfferent sources mxed on tme axs. Tme-space data analyss for locaton of multple sources was not avalable wthout decson of combnaton of mpulse receved n sensors. But ths procedure requres huge number of calculaton to evaluate all combnatons of mpulses. 6 axes are used for D space n place of 4 axes for D space. The same neural system s used except number of axes to derve for D space data processng algorthm for separaton and dentfcaton of mpulse from multple sound sources. Z S6(0, 0, ) Y S4(0,, 0) S(-, 0, 0) S(, 0, 0) S(0, -, 0) S5(0, 0, -) : postons of sensors Fg. Settlement of sensors n D space. Sensor Sensor Arrvng mpulse from a source tme tme Scheme of Estmaton A calculaton flow of the proposed method s shown n Fg.. The procedure s as follows; () Detect mpulse tme Impulses are detected from sgnal waveforms n each sensor by a threshold. () Select sets of mpulse tme Excted neurons (Vxyzw th) are selected. One excted neuron assgns a set of mpulses for locaton calculaton of one source n Fg.. As ntal value, (xyzw) = (,,,), (,,,),, (N, N, N, N) are selected n ths study. () Estmate poston n space wth hyperbolc method Source locatons are calculated usng hyperbolc method appled to the tme dfference of the set of mpulses. (4) Estmate propagaton tmes Propagaton tmes n the sensors are estmated wth sphercal wave model from source locaton calculated n step (). (5) Calculate physcal concdence The concdences are calculated usng the estmated and observed tme of mpulse sgnals. (6) Convergence Decson Physcal concdence s the ndex of convergence. In the case of concdence < ε, go to end. Otherwse, go to the next step. (7) Calculate parameters of NN Neuron network parameters Wxyzw, pqrs, Txyzw are calculated usng physcal concdence. (8) Actvate neuron network Calculate the output Vxyzw of neuron networks. (9) Detect excted neurons. (0) go to step (). Sensor tme Sensor 4 Set of pulses belongng to a wave front from a source # tme Set of pulses belongng to a wave front from a source # Fg. Impulses arrve to each sensor. A lne shows a set of mpulse belong to a wave front from a same source. ISBN:

3 Evaluaton of Physcal Error for Estmaton Detect pulse tme Select sets of pulse tme Estmate poston n space wth hyperbolc method Estmate propagaton tmes The locaton of sngle objectve source s calculated by the followng equatons, whch exsts on ellptcal hyperbolod plane. Y a n n Y n Z Z = n Y Z = Y n Y Y Z + = n Z az d a ( d a ) + d a a ( d a ) d a ( d a ) () where, Calculate concdences D xyzw, Y, Z are space axes, Convergence Decson No Yes End dn s dstances of sensors. a, ay, az are dfference of dstance from sensor to objectve pont on each axs. Calculate W xyzw, pqrs and T xyzw Actvate Neuron Network Detect flashng neurons Fg. Calculaton Flow. 4 Computaton wth a Neural Network Acoustc emsson sources generated at arbtrary tmes and locatons, and these are receved as mpulse sgnals at each sensor. Locatons of multple sources are dstrbuted n arbtrary poston n a space. Ths study s to fnd each locaton wthout dependng on generaton tme of each mpulse sgnals. Totally four sensors are used for a system descrbed n Chap.4. NN s composed of a 4-D hyperspace wth 4 orthogonal axes. Ths theme s nduced nto solvng followng equaton whose solutons are gven by the operaton of convergence. E = AF + BF + CF, --- () ISBN:

4 F: Normalzed Error of observed and estmated mpulse arrval tmes [no dmenson], F: Degree of super-postons of wave-fronts from source locatons [no dmenson], F: Dfference of calculated and assumed number of effectve solutons [no dmenson]. 5 Result of Computer Smulaton The proposed scheme of tme space analyss s proved useful for the case of multple sound locaton dentfcaton. Multple sound pulse sources are randomly generated on tme and space. Evaluaton condton s as follows; A NN s composed to solve equaton (). Number of sound sources ~7, Transmsson tme of pulse E =, j W j V V j + U V V : output voltage of -th neuron [V], U : threshold current of -th neuron [A], W j : conductance of -th to j-th neuron [S]. --- () A physcal problem to fnd locatons for tme-space sequence data s expressed as a mathematcal problem to solve equaton (), whch corresponds to convergence problem of electrc energy wrtten by equaton (). The solutons of analyss by a novel confguraton of NN are shown n Fg. 5 as an example. It s suffcently shown that newly proposed scheme and NN modelng are twce useful and effectve to solve problems whch are mpossble to express by mathematcal equaton for software for Neumann computers. ~0 sec Tme wndow for analyss = 5 sec The sound locatons are shown for the correct and calculated locatons wth square and cross marks. The error of estmaton was proved small enough practcally. The computer smulaton n Fg. 4 shows followng ponts; The resoluton of locaton of ponts s 0(cm) for multple sounds located at 0(m) from sensors. The capablty of separaton s equal to dstance of two ears of anmals at the pont of 00 tmes of sensor dstance. The capablty of locaton by audtory sensng s found exceedng human capablty. Ths study suggests superor capablty of anmals except human knd. Fg. 4 Result of estmaton ponts group n space. ISBN:

5 6 Dscussons Acknowledgment: Ths paper s based on recent studes about tmespace sensng capablty of anmals, and our approach s also ntroduced about sensng executed by audtory sensaton. Weakly electrc fsh has not been analyzed about locaton capablty except jammng avodance response behavor based on dfferental values of zero-cross tme correlatng to frequences of electrcal feld. Barn owl has not been analyzed about dstance of source except drecton audtory sensng. Locaton fndng for sngle source s acheved by the methods of passve or actve sonars. Conventonal methods are not avalable for multple sources on space and tme wth random generaton. Our modelng s presented based on mathematcal and bologcal knowledge of central nerve systems. mpulse number n the second sensor ( = ) z-th 4 The authors express sncere grattude for Professor Tomoyuk Hguch, drector-general, and Professor Hroe Tsubak, vce drector-general, and Professor Noboru Sonehara, project leader of System of Human and Socety for ther leadershps and knd supports for ths research. The grater part of ths study s supported by the project of Functon and Inducton wth the Research Organzaton of Informaton and Systems. References: [] Takzawa Y., Fukasawa A., Novel Neural Network Scheme Composed of Predcton and Correlatons, Proceedngs of WSEAS Internatonal Conference on System, pp , 009. [] Takzawa Y., Rose G., Kawasak M., "Resolvng Competng Theores for Control of the Jammng Avodance Response: The Role of Ampltude Modulatons n Electrc Organ Dscharge Deceleratons," Journal of Expermental Bology 0, pp , [] Konsh M., Lstnng wth tow ears, Scentfc Amercan, 64 (4), pp. 66-7, 99.. [4] Konsh M., Audtory sensatonal nformaton processng wth tow ears n Barn Owl, Nkke Scence, Japanese edton, pp. 8-7, 007. [5] Yum Takzawa, Tme-Space Sensng Capabltes n Neural Systems and Its Applcatons, Proceedngs of Project Symposum of Transdscplnary research Integraton center. y-th ( = ) 4 5 x-th Fg. 5 Neural network confguraton. mpulse number n the frst sensor ( = ) ISBN: