A moving ound ource localization method baed on TDOA Feng MIAO; Diange YANG ; Ruia WANG; Junie WEN; Ziteng WANG; Xiaomin LIAN Tinghua Univerity, China ABSTRACT The Time Difference of Arrival (TDOA) method ha been widely ued for ound ource localization. However, becaue of the Doppler-effect, the TDOA method cannot be directly ued for locating moving ound ource. Thi paper develop a moving ound ource localization method baed on TDOA, combining with Doppler-effect elimination and ource plane canning. Thi method i uitable for locating ound ource moving in a plane, with a meaurable velocity. In thi method, the ound ource plane i mehed into grid. Chooe one grid point a the aumed ound ource location, eliminate the Doppler-effect from the meaured ound preure ignal, and then locate the ound ource uing TDOA method. The deviation between the localization reult and the choen grid point i recorded. Do thi progre by canning all the grid on the plane. The grid point which minimize the deviation through the plane i taken a the ound ource location etimation. Simulation how that thi method can accurately locate high peed ound ource even with background noie, uing hort ection of ignal received by a four-microphone array. Keyword: Moving Sound Source Localization, Doppler-effect Elimination, Time Difference of Arrival I-INCE Claification of Subect Number(): 74.6. INTRODUCTION Sound ource localization i a practical reearch topic with many application. There are many method to olve thi problem including beam-forming (), acoutic holography (), and TDOA (3). The beam-forming method i uitable for locating moving ound ource (4, 5), but it patial reolution i limited to one wavelength. The near-field acoutic holography method ha high patial reolution (), but the meaurement ditance requirement greatly retrict it application. The far-field acoutic holography can locate ound ource in the far field, with high reolution (6, 7), but it need a relative long ection of ignal, and i not uitable for locating tranient or impule ound ource. The TDOA method can locate tatic ound ource, epecially the tranient one, with quite high accuracy (8). However, becaue of the Doppler-effect, the TDOA method cannot be directly ued for locating moving ound ource. A method called TDOA-FDOA can locate ingle-frequency moving emitting ource, for condition that the ound ource frequency and velocity are known (9, ). However, ingle-frequency ound ource i rarely een in practice. Therefore, none of the exiting method can locate moving ound ource with a hort ection of ignal and high reolution. Thi paper develop a moving ound ource localization method baed on TDOA, combining with Doppler-effect elimination and ource plane canning. Thi method i uitable for locating ound ource moving in a plane, with a meaurable velocity. Simulation have validated that thi method can locate high peed ound ource accurately with a hort ection of meaured ignal.. MATHEMATICAL MODEL. The TDOA Localization Model for Static Sound Source The TDOA ound ource localization method need an array with at leat four microphone. The microphone array ued in thi tudy i X-haped, a hown in Fig.. The center of the array i alo the origin of the Carteian coordinate. The microphone are numbered from to 4. The microphone m k (k =~4) i mounted at a fixed poition, with coordinate (x k, y k, ), and r k (k =~4) repreent the vector ydg@mail.tinghua.edu.cn Inter-noie 4 Page of 7
Page of 7 Inter-noie 4 from the origin O to microphone m k. The ound ource locate arbitrarily in the pace, with coordinate (x, y, z ), and r repreent the vector from the origin O to the ound ource. m (x,y,) r (x,y,z) r O r y m (x,y,) x z r 4 m3 (x3,y3,) r 3 m4 (x4,y4,) Figure The TDOA ound ource localization model Microphone m i the reference microphone. The geometry relationhip between the ound ource and microphone can be written a r r r r c t () k, k Where t (k =, 3, 4) i the TDOA between m,k k and m, which can be obtained uing the generalized cro-correlation (GCC) method (). A poitive t mean microphone m,k k i farther to the ound ource than m, while negative mean m k i nearer to the ound ource. c i the ound velocity, which i conidered a a contant of 34 m/. The ymbol repreent the length of a vector. Eq. () can be rewritten a k k, k x x y y z x x y y z c t () Eq. (3) can be obtained deriving from Eq. (): Where a b b b a b a b x, y a a a a z x x x y y y c x x y y ct, x x t x x t x x t x x t, a 3,,3 4,,4 y y t,3 y y3 t, y y t,4 y y4 t, c t c t c t c t, b 3,,3 4,,4 y y t,3 y y3 t, y y t,4 y y4 t, c x y x y c t, The localization of the ound ource i preented in Eq. (3). A the z-coordinate i the quare root of a function, it ha two olution, one poitive and the other negative. In a practical application, the ign of z-coordinate i predefined, o that the z-coordinate can be determined.. The Moving Sound Source Localization Model The moving ound ource localization method i baed on the traditional TDOA method, combining with Doppler-effect elimination and ource plane canning. The localization ytem i hown in Fig.. The microphone array i the ame a that in ection.. The ound ource move in a plane P, and the microphone array plane P m i parallel to P. The ditance between P and P m i z. The ound ource ha a contant velocity of v, and the velocity direction i parallel to the x-axi. The plane P, the ditance z, and the velocity v can be meaured by other mean and are conidered known (3) (4) Page of 7 Inter-noie 4
Inter-noie 4 Page 3 of 7 in thi method. P Pm v y z m x m m4 O m3 z Figure The moving ound ource localization ytem To locate a moving ound ource, firtly, the frequency hift caued by the Doppler-effect hould be eliminated from the meaured ignal. After that, the TDOA method can be applied to locate the ound ource, uing the Doppler-effect eliminated ignal. The Doppler-effect model of a moving ound ource i hown in Fig. 3. m R R θ x v Figure 3 The Doppler-effect model Figure 3 how that, at the moment of t, the moving ound ource i at, with R ditance from the microphone m. However, the ound wave reaching m at thi moment i emitted when the ound ource wa at, with R ditance from the microphone. The microphone ignal can be written a Eq. (5) according to More (). q' t R / c q co v / c v pt () 4 R v co / c 4 R v co / c Where p(t) i the ound preure ignal received by the microphone, q(t) i the ound ource intenity, i the angle between the ound ource velocity direction and the line which connect the microphone and the ound ource at. The Doppler-effect elimination method (3) i hown in Eq. (6). Where v v pt co v ptdt R co pt R c c (6) pt i the Doppler-effect eliminated ignal, and R i the ditance between the ound ource and the microphone, auming the ound ource wa tatic. Equation (6) how that, to eliminate the Doppler-effect, the ound ource location and the velocity mut be predefined. Thi become a problem when the ound ource i to be located. To olve thi problem, the ound ource plane P i mehed into M N grid. Chooe one grid a the aumed ound ource location, eliminate the Doppler-effect uing Eq.(6), and then locate the ound (5) Inter-noie 4 Page 3 of 7
Page 4 of 7 Inter-noie 4 ource uing TDOA method mentioned in ection.. The deviation value between the calculated location and the choen grid point i recorded. Do thi progre by canning all the grid. If the grid i exactly where the ound ource locate, the Doppler-effect elimination and TDOA localization would be trictly correct, and the deviation would be zero, if there i no background noie and the calculation i precie. Therefore, the grid which minimize the deviation can be taken a the ound ource location etimation. The deviation at the grid ( ) (i=~m, =~N) i defined in Eq. (7). d ri, rl % (7) r Where d i the deviation between the calculated ound ource location and the grid ( ), r i, i the vector from the origin to the grid ( ), and r l i the vector from the origin to the correponding calculated ound ource location. The deviation of all the grid contitute the matrix: D d (8) MN The grid which minimize the deviation i taken a the ound ource location etimation e. The coordinate i written a (x e, y e, z e). The localization error i defined in Eq. (9). e r r = x x y y z z (9) e e e e Where r repreent the vector from the origin O to the ound ource, and O to the calculated ource location etimation e. The whole proce i hown in Fig. 4. re i the vector from Moving Sound Source r MN Mehed Source Plane Sound Source Velocity v Doppler-effect Elimination Sound Preure Signal, ~ 4 pk t k TDOA Localization, ~ 4 pk t k Deviation Matrix rl MN D Localization Reult d MN x, y, z e e e e Figure 4 Schematic of TDOA-baed moving ound ource localization method Page 4 of 7 Inter-noie 4
Inter-noie 4 Page 5 of 7 3. SIMULATION 3. Numerical Simulation The moving ound ource localization method i validated by imulation. The microphone array i X-haped. The array center i the origin of the Carteian coordinate. The four microphone are located at (.5,.5, ) m, (-.38,.38, ) m, (-.5, -.5, ) m, and (.38, -.38, ) m. The ound ource move in a contant velocity of m/ along the poitive direction of the x ax in the plane m away from the microphone array. The plane P i 4 m 4 m, and i mehed into grid of. m. m. The ound ource i at the point of (,, ) m at t= moment. The ound preure ignal i a mixture of Hz, 4 Hz, 6 Hz, 8 Hz, and Hz coine ignal. The ignal to noie ratio (SNR) i db. Signal with length of m are received by the microphone with the ampling frequency of khz. The whole proce wa programmed, and the reult were olved numerically in MATLAB. The localization reult i hown in Fig. 5..5 Deviation / % 6 5.5 4 y / m 3 -.5 - -.5 - - -.5 - -.5.5.5 x / m Figure 5 The deviation matrix (%) with the ource at (,, ) m The real ound ource i hown a the white circle in the center of Fig. 5. The grid which minimize the deviation i the point (,, ) m, which i exactly where the ound ource locate. The localization error e=. The region near to the real ource i blue, which mean the deviation d at thee grid are maller than %. When the ditance between the grid and the real ource get farther, the deviation become bigger. Thi method can alo locate the ound ource when it i not at any grid. Figure 6 how that, when the real ound ource i at (-.5,.5, ) m, the localization reult i (-.,., ) m. The localization error e=.7 m, which i quite mall. The localization error can be controlled even maller by adding grid..5 Deviation / % 6 5.5 4 y / m 3 -.5 - -.5 - - -.5 - -.5.5.5 x / m Figure 6 The deviation matrix (%) with the ource at (-.5,.55, ) m Inter-noie 4 Page 5 of 7
Page 6 of 7 Inter-noie 4 3. Parameter Study To undertand how variou parameter affect the accuracy of the localization, imulation are conducted by varying one parameter with other parameter held contant. The parameter tudy reult i how in Figure 7. () SNR The SNR i changed from db to db, and the other parameter are the ame a in ection 3.. Figure 7(a) how that, a the SNR become larger, the localization error become maller. The localization i acceptable when the SNR i above 5 db with the error below. m, and i precie when the SNR i above db, where the error i below. m. Thi mean that the localization reult will be better if the environment i not too noiy or reverberant. () Meauring ditance The meauring ditance z between the ound ource plane P and the microphone array plane P m i changed from m to 3 m, and the other parameter are the ame a in ection 3.. Figure 7(b) how that the localization error will become larger when the meauring ditance i farther. There are mainly two reaon. Firtly, when the ource get farther, the TDOA between microphone are maller, and the GCC calculation error will be more evident, o that the localization reult will be le accurate. Secondly, when the ource get farther, the change rate of TDOA along with the ound ource movement i maller, o the deviation at grid far to the real ource may get maller, and it i more difficult to find the correct location. The localization i atifactory when the meauring ditance i below m..5.4.3.. 3 4 (a) SNR (db).5.4.3.. 3 (b) z (m).5.4.3.. 5 (c) v (m/).5.4.3.. 4 6 8 (d) Signal length (m) Figure 7 Effect of parameter on the localization error (3) Sound ource velocity The velocity of the moving ound ource i changed from to m/, and the other parameter are the ame a in ection 3.. Figure 7(c) how that, a the ound ource move fater, the localization error lightly become lager. Thi i becaue that the calculation error of the Doppler-effect elimination would become bigger when the velocity become larger. However, the localization error i only about. m even when the velocity i a high a m/, which mean that thi method can be ued for locating ound ource on high peed car and train. Page 6 of 7 Inter-noie 4
Inter-noie 4 Page 7 of 7 (4) Signal length The ignal length i changed from m ( data point) to m ( data point), and the other parameter are the ame a in ection 3.. Figure 7(d) how that, a the ignal become longer, the localization error become maller. The localization reult i acceptable when the ignal length i over 4 m, and i accurate when the ignal length i over 8 m, which mean thi method can be ued for locating a tranient or impule ound ource in hort time. The parameter tudy how that, the meauring ditance ha the bigget effect on the localization error, following by the ignal length. The SNR ha little effect on the localization error a long a it i above db. The ound ource velocity ha mall effect on the localization error. 4. CONCLUSIONS Thi paper developed a moving ound ource localization method baed on TDOA, combining with Doppler-effect elimination and ource plane canning. Thi method i uitable for locating ound ource moving in a plane, with a meaurable contant velocity. Thi method ha been validated by imulation. The parameter involved in thi method were tudied, including the SNR, the meauring ditance, the ound ource velocity, and the ignal length. Simulation how that thi method can locate the ound ource a long a the SNR i above 5 db, the meauring ditance i below m, and the ignal length i longer than 4 m. The ound ource velocity ha little influence on the localization accuracy. Thi method i uitable for locating ound ource in high peed car or train that move in a traight line. REFERENCES. Johnon DH, Dudgeon DE. Array ignal proceing: concept and technique. Simon & Schuter; 99.. Maynard JD, William EG. Nearfield holography, a new technique for noie radiation meaurement. INTER-NOISE and NOISE-CON Congre and Conference Proceeding. Intitute of Noie Control Engineering; 98. 3. Wu SF, Zhu N. Locating arbitrarily time-dependent ound ource in three dimenional pace in real time. J Acout Soc Am. ; 8():78-39. 4. Mellet C, Letourneaux F, Poion F, Talotte C. High peed train noie emiion: Latet invetigation of the aerodynamic/rolling noie contribution. J Sound Vib. 6; 93 (3):535-46. 5. Nagakura K. Localization of aerodynamic noie ource of Shinkanen train. J Sound Vib. 6; 93 (3):547-56. 6. Park S, Kim Y. Viualization of pa-by noie by mean of moving frame acoutic holography. J Acout Soc Am. ; (5):36-39. 7. Yang D, Wang Z, Li B, Luo Y, Lian X. Quantitative meaurement of pa-by noie radiated by vehicle running at high peed. J Sound Vib. ; 33 (7):35-64. 8. Zhu N, Wu SF. Sound ource localization in three-dimenional pace in real time with redundancy check. J Comput Acout. ; (). 9. Ulman RJ, Gerantioti E. Motion detection uing TDOA and FDOA meaurement. Aeropace and Electronic Sytem, IEEE Tranaction on. ; 37 ():759-64.. Lee SC, Lee WR, You KH. TDOA/FDOA Baed Aircraft Localization Uing Adaptive Fading Extended Kalman Filter Algorithm. Power control and optimization: Proceeding of the 3rd Global Conference on Power Control and Optimization. AIP Publihing;.. Knapp C, Carter GC. The generalized correlation method for etimation of time delay. Acoutic, Speech and Signal Proceing, IEEE Tranaction on. 976; 4(4):3-7.. More PM, Ingard KU. Theoretical Acoutic. Yang X, Lv R, Dai G, tran. Beiing: Science Pre; 986. 3. Yang D, He C, Wang Z. Quantitative meaurement method for a moving ound ource baed on an non-implified time domain model. J Tinghua Univ (Sci & Tech). 3; 53(4): 56-566. Inter-noie 4 Page 7 of 7