Maximum power dynamic acoustic source direction-of-arrival tracking algorithm based on acoustic vector sensor

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1 DOI: /CTA Control Theory & Applications Vol. 31 No. 2 Feb. 2014,, (, ) :, (DOA).,, DOA.,, Kalman.. : ; ; ; : TP391 : A Maximum power dynamic acoustic source direction-of-arrival tracing algorithm based on acoustic vector sensor HU Zhen-tao, LI Song, JIN Yong (Institute of Image Processing and Pattern Recognition, Henan University, Kaifeng Henan , China) Abstract: To effectively locate and trac the target in spatially non-uniform noise, we propose the maximum power dynamic acoustic source direction-of-arrival (DOA) algorithm based on the acoustic vector sensor. In this algorithm, according to the estimated noise covariance, the measurement of acoustic vector sensor is pre-whitened and the weight parameter is determined. Thus, a maximum power algorithm based on fixed weight parameter (WPF--MP) is formed. The accuracy of DOA estimation is improved when the power ratio of the sound pressure to the noise power in the velocity domain is unnown. Moreover, the output of the maximum power DOA estimator is employed to build the measurement equation of the dynamic source in the system of polar coordinates; and the cubature Kalman filtering algorithm is introduced to realize the state-tracing of the dynamic sound source. Theoretical analysis and experimental results show the feasibility and efficiency of the proposed algorithm. Key words: direction of arrival estimation; target tracing; acoustic vector sensor; dynamic acoustic source 1 (Introduction) (direction of arrival, DOA),.,.,., ( ), ( ) ( ). DOA., DOA. Nehorai DOA (CRLB) [1], Hawes [2], DOA., DOA [3]., [4], : ; : hzt@henu.edu.cn. : ( , U ); (13IRTSTHN021); ( ); (13A413066, 2008A510001); (HDXJJG ).

2 ,, (MUSIC) [5] (ESPRIT) [6]., Suresh, MUSIC DOA [7],., DOA (MUSIC ESPRIT ),., Levin, DOA [8],, DOA, CRLB., DOA., DOA,,,,,.,, [9 10].,. Zhong Capon, 2-D [11],., [8],,, DOA ;, Kalman,. 2 (Observation modeling of acoustic vector sensor) 3 1,. f S, u : u x cos θ cos ϕ u = u y = cos θ sin ϕ. (1) sin θ u z θ [ π/2, π/2] ϕ ( π, π]. p, v = (v x, v y, vz ) T, v = p u /(ρ 0 c), (2) : ρ 0, c.,, DOA. N, S R 1 N, ε R 4 N ε p εv = [ε vx ε vy εvz ] T, Y R 4 N Y v, : = ap S + ε p, (3) Y v = a v S + ε v. (4) [ ] a R 4 1, a = =e (j2πfτ ) a v [ ] 1, τ S. u /ρ 0 c S ε p, εv, σ 2 s,, σ2 p, σ2 v,. 3 DOA (Maximum power dynamic acoustic source DOA tracing algorithm based on acoustic vector sensor) 3.1 DOA (Maximum power DOA estimation algorithm based on weight parameter fixed), q T q = 1, û = arg max{ 1 N [α p q N,n + αv q T Y,n] v 2 }, (5) n=1 : α p,n, αq v T Y,n v. N Θ = Θ vp [ Θ pp Θpv Θ vp Θvv ] = 1 N N n=1 a p [ ] [ ] T,n,n. (6) Y,n v Y,n v = (Θpv )T ; Θ pp Θvv. (maximum power, MP) [8], (5) T (q ) = 1 N N [α p,n + αv q T Y,n] v 2 q n=1

3 2 : 211, q T (q ) = α p Θvp + (1 αp )Θvv q. (7) α p MP, [8], α p, αv, α p + α v = 1. α p = σ2 v,/(σp, 2 + σv,), 2 α p /αv, DOA CRLB.,, MP, DOA.,, 1, 0.5., (WPF--MP). : N, S ε p εv, (3) (4) (6), : Θ = a σ 2 s,a T + ˆQ, (8) : ˆQ N, N, ˆQ [ ] σp, σv,i [12], ˆQ, [ ] ] Ŷ,n = ˆQ 1 p 2,n [Ŷ,n =, n = 1,, N. (9) Y,n v Ŷ,n v, [ ] ˆΘ ˆΘpp ˆΘ pv = = 1 p N [Ŷ,n N n=1 Ŷ,n v ˆΘ vp ˆΘ vv ] [Ŷ p,n Ŷ v,n ] T. (10), (8) (9), ˆΘ = ˆQ 1 2 (a σs,a 2 T + ˆQ )( ˆQ 1 2 )T.,,., (7) α p = σ2 v, /(σ2 p, + σv,) ˆα 2 = 0.5, MP, [8], q t ( q t+1 q ε), t, DOA CRLB. WPF--MP : 1) : t = 0, t, L, µ, ε. 2) ˆQ. 3) (9) Ŷ,n, n = 1, 2,, N. 4) (10) q 0 = û 0 vp = ˆΘ / ˆΘ vp. 5) for t 1 to L q t+1 if q t+1 end = q t + µ[ˆα 6) : û = q t. ˆΘ vp q t < ε, brea vv + ˆα ˆΘ vp vv ˆΘ ˆΘ, q t ], ˆα = WPF MP DOA (Dynamic acoustic source DOA tracing algorithm based on WPF--MP) DOA,,,.,, DOA,. DOA,, (cubature Kalman filter, CKF) DOA,. X = Φ 1 X 1 + Γ 1 W 1, (11) : X = (x, ẋ, y, ẏ, z, ż ) T, x, y z X, Y, Z, ẋ, ẏ ż ; Φ 1, Γ 1, W 1. WPF--MP û = (û x, û y, û z ) T CKF, û : V Z = (ˆθ, ˆϕ ) T, (12) R = E{[Z h(x )][Z h(x )] T }, (13) h(x )., X, (13) R. ε p, εv σ2 p,, σ2 v,, WPF--MP DOA, Monte Carlo, DOA, Z R = [ N (Z l N Z m/n)/n] l=1 m=1 [ N (Z l N Z m/n)/n]t. (14) l=1 m=1

4 212 31, (WPF--MPT), DOA [13],. WPF--MPT, WPF--MPT : 1). 1 P 1 1, P 1 1 = S 1 1 (S 1 1 ) T. (15) X i, 1 1 = S 1 1 ξ i + x 1 1, (16) : ξ i = m/2[ ] i, i = 1, 2,, m, [ ] i R n 1 [I n n I n n ] R n m i, I n n n, m = 2n. X i, 1 = Φ 1X i, 1 1. (17) : ˆx 1 = 1 m X i, 1 m, (18) P 1 = 1 m m 2). X i, 1 X T i, 1 ˆx 1 ˆx T 1 + Γ 1 Q 1 Γ T 1. (19) WPF--MP û. û ˆθ ˆϕ, Z = ( ˆθ, ˆϕ ) T. P 1 : P 1 = S 1 (S 1 ) T. (20) X i, 1 = S 1 ξ i + x 1. (21) : Z i, 1 = h(x i, 1 ). (22) ẑ 1 = 1 m m Z i, 1. (23) : P zz, 1 = 1 m Z m i, 1 Z T i, 1 ẑ 1 ẑ T 1 + R, (24) P xz, 1 = 1 m X m i, 1 Z T i, 1 : ˆx 1 ẑ T 1. (25) K = P xz, 1 P 1 zz, 1. (26) : ˆx = ˆx 1 + K (Z ẑ 1 ), (27) P = P 1 K P zz, 1 K T. (28) ˆx,. 4 (Simulation results and analysis) 4.1 WPF--MP DOA (DOA estimation based on WPF--MP) (MSAE) [1] DOA, N 8000, MP WPF--MP DOA, θ =30, ϕ = 30, σ 2 s, = 10, σ 2 p, = 1.5, σ 2 v, = 0.5. WPF--MP µ ε DOA. [8] MP, q t 20.,, WPF--MP MP, L = 50, µ = 1, ε = ,, MP, α p DOA, 0.01; WPF--MP ˆα = 0.5 DOA. MC = 10000,, MP WPF-- MP MSAE CRLB, MP DOA, 1. 1 MP WPF--MP Fig. 1 The comparision of estimation precision for MP and WPF--MP

5 2 : 213 1,, WPF--MP DOA MSAE MP α p MSAE, CRLB. MP α p, MP DOA. WPF-- MP,, Capon [14] DOA, (RMSE) MP WPF--MP. Capon DOA, 0.1, 0 60., MP α p = σ2 v,/ (σp, 2 + σv,), 2, MP α p RMSE Table 1 The comparision of RMSE and time-consuming for three algorithms RMSE/( ) RMSE/( ) /( ) MP Capon WPF--MP , T = 1 s. CKF Z R (14). = 120 DOA, 2 3 WPF--MPT WPF--MP DOA RMSE. 2 RMSE Fig. 2 The comparision of RMSE for elevation 1,, MP WPF--MP DOA Capon. MP, α p DOA ; WPF--MP DOA, RMSE, WPF--MP Capon MP. 1 1, WPF--MP,. 4.2 WPF--MPT DOA (Dynamic acoustic source DOA tracing based on WPF--MPT) WPF--MP, DOA., d = 1000 m, θ 0 = 30 ϕ 0 = 30, X, Y, Z 20 m/s, 10 m/s, 20 m/s, σ 2 s, = 10, σ 2 p, = 1.5, σ 2 v, = 0.5, (11), WPF--MP DOA, Z =(ˆθ, ˆϕ ) T. Q 1 =diag{10 2, 10 2, 10 2 } 3 RMSE Fig. 3 The comparision of RMSE for azimuth 2 3, WPF--MPT DOA RMSE WPF--MP. CKF,, RMSE. 4.1 WPF--MP, 2 3, WPF--MPT.,, WPF--MP WPF--MPT DOA RMSE. 2 WPF--MP RMSE Table 2 The mean of RMSE for WPF--MP under different signal-to-noise ratio σ 2 s, σ 2 p, σ 2 v, /( ) /( )

6 WPF--MPT RMSE Table 3 The mean of RMSE for WPF--MPT under different signal-to-noise ratio σ 2 s, σ 2 p, σ 2 v, /( ) /( ) , WPF--MPT, DOA WPF--MP.,, 4 σ 2 s, = 10, σ 2 p, = 1.5, σ 2 v, = 0.5 WPF--MPT MSAE MSAE CRLB,,, WPF--MPT DOA MSAE CRLB, WPF--MPT. 4 WPF--MPT MSAE CRLB Fig. 4 The comparision of CRLB for WPF--MPF and static MSAE 5 (Conclusions), DOA., DOA, DOA, Kalman DOA,. DOA, WPF--MPT :, DOA (MUSIC ESPRIT ), WPF--MPT, DOA,, ;, Kalman,, DOA, DOA, ;, DOA,. (References): [1] NEHORAI A, PALDI E. Acoustic vector sensor array processing [J]. IEEE Transations on Signal Processing, 1994, 42(9): [2] HAWKES M, NEHORAI A. Effects of sensor placement on acoustic vector sensor array performance [J]. IEEE Journal of Oceanic Engineering, 1999, 24(1): [3],,,. DOA [J]., 2010, 38(10): (GU Chen, HE Jin, ZHU Xiaohua, et al. Extended-aperture twodimensional DOA estimation with acoustic vector sensor array using the propagator method [J]. Acta Electronica Sinica, 2010, 38(10): ) [4],. [J]., 2005, 30(1): (CHEN Huawei, ZHAO Junwei. Coherent signal subspace wideband optimal beamforming for acoustic vector-sensor array [J]. Acta Electronica Sinica, 2005, 30(1): ) [5] WONG K T, ZOLTOWSKI M D. Self-initiating MUSIC-based direction finding in underwater acoustic particle velocity-field beamspace [J]. IEEE Journal of Oceanic Engineering, 2000, 25(2): [6] CHEN H, ZHAO J. Coherent signal-subspace processing of acoustic vector sensor array for doa estimation of wideband sources [J]. Signal Process, 2005, 85(4): [7] SURESH K N, DIBU J P, BHATTACHARYA C. DOA estimation using compressive beamforming in shallow ocean using acoustic vector sensors [C] //Annual IEEE India Conference. India: IEEE, 2012: [8] LEVIN D, GANNOT S, HABET S. Direction-of-arrival estimation using acoustic vector sensors in the presence of noise [C] //IEEE International Conference Acoustics, Speech and Signal Processing. Prague: IEEE, 2011: [9],,,. MIMO DOA [J]., 2012, 30(3): (LIU Nan, ZHANG Juan, ZHANG Linrang, et al. A low complexity 2-D estimation method for MIMO rader [J]. Acta Electronica Sinica, 2012, 30(3): ) [10] HU D X, ZHAO Y J, LI D H.Joint source number detection and DOA trac using particle filter [C] //International Conference on Measuring Technology and Mechatronics Automation. Changsha: IEEE, 2010: [11] ZHONG X H, PREMKUMAR A B, MADHUKUMAR A S. Particle filtering and posterior cramer-rao bound for 2-D direction of arrival tracing using an acoustic vector sensor [J]. IEEE Sensor Journal, 2012, 12(2): [12] WU Y T, HOU C H. Direction-of-arrival estimation in the presence of unnown non-uniform noise fields [J]. IEEE Journal of Oceanic Engineering, 2006, 31(2): [13] ARASARATNAM I, HAYKIN S. Cubature Kalman filters [J]. IEEE Transactions on Automatic Control, 2009, 54(6): [14] HAWKES M, NEHORAI A. Acoustic vector-sensor beamforming and Capon direction estimation [J]. IEEE Transactions on Automatic Control, 1998, 46(9): : (1979 ),,,,, hzt@henu.edu.cn; (1988 ),,,, lisonghenu@163.com; (1972 ),,,,, jy@henu.edu.cn.

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