Multiple sub-array beamspace CAATI algorithm for multi-beam bathymetry system

Transcription

1 Journal of arine Science and Application, Vol6, No, arch 007, pp 47-5 DOI: 0007/s x ultiple sub-array beamspace CAATI algorithm for multi-beam bathymetry system LI Zi-sheng, LI Hai-sen, ZHOU Tian, and YUAN Yan-yi College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 5000, China Abstract: This paper extends CAATI (Computed Angle-of-Arrival Transient Imaging) technique of ulti-angle Swath Bathymetry Sidescan Sonar (SBSS) into ulti-beam Bathymetry Sonar (BBS) and presents a new ultiple Sub-array Beamspace CAATI (SB-CAATI) algorithm The method not only can achieve high resolution seafloor mapping in the whole wide swath, but also can work well in complex acoustic environments or geometries Simulation results and processing results of sea-experiment data prove the validity and superiority of the algorithm Keywords: SB-CAATI; swath bathymetry; high resolution; multi-beam CLC number: TN97 Document code:a Article ID: (007) Introduction There are three sonar systems which can produce both bathymetric mapping and backscatter acoustic imaging: Swath Bathymetry Sidescan Sonar (SBSS), ulti-angle Swath Bathymetry Sidescan Sonar (SBSS) and ulti-beam Bathymetry Sonar (BBS) SBSS can provide high resolution seafloor imaging as well as associated bathymetric information based on assumption of flat seafloor [] SBSS is the extension of SBSS and it can solve difficulties of multiple concurrent arrivals [-3] while SBSS can not Compared with SBSS and SBSS, BBS has advantages such as wider coverage and longer range in complex seafloor terrain, since it utilizes larger aperture and stronger transmit power [4] Considering the methods of signal processing, SBSS uses CAATI (Computed Angle-of-Arrival Transient Imaging) technique [] which fits outputs of array elements according to extended Prony s method and directly solves the problems for both directions and amplitudes of multiple arrivals Theoretically, CAATI can achieve infinitely high resolution only using small aperture ( to 6 elements basically) Received date : Foundation item: Supported by the Foundation of the Chinese Doctoral Science Grant No , the Foundation of the Chinese Postdoctoral Science Grant No LRB005 and the Foundation of Underwater Acoustic Technology National Key Lab Grant No 940C C0 However, Prony s method requires high SNR [5-6], which practically constrains the application of SBSS In addition, SBSS faces accuracy difficulties in insonified areas of large grazing angles (close to nadir) [] On the other hand, most multi-beam systems use FT (Fourier Transform) beamforming technique which also affords high resolution DOA estimation at large grazing angles using large aperture However, spatial resolution of BBS decreases at increasingly shallow grazing angles due to decreasingly effective aperture This paper extends CAATI technique into multi-beam systems and presents a new algorithm: ultiple Sub-array Beamspace CAATI (SB-CAATI) The method subdivides an array into multiple overlapping sub-arrays and fits beam outputs with the same index from each sub-array using extended Prony s method and solves the problems for directions and amplitudes of multiple arrivals according to the spatial model SB-CAATI takes advantages of both FT and CAATI in such aspects that it not only maintains the robustness and high accuracy of FT at small cross-track distance but achieves high resolution of CAATI at shallow grazing angles oreover, the method has advantages of beamspace methods such as reduced computation load, lower SNR threshold and so on In this paper, principles of CAATI are firstly introduced, followed by theories of SB-CAATI

2 48 Journal of arine Science and Application, Vol6, No, arch 007 Simulation results and sea-experiment data processing results are given to prove the validity and superiority of the method finally Signal model and CAATI algorithm Discrete backscatter model is established on the assumptions that plane wave arrivals are received by N element array ( N > ) with equispaced interval d Transmit waveforms are narrowband and arrivals are in steady state The nth element output can be written as: j( n ) dum sn = ame, m= () u = ksin θ, m m whereθ m and a m are directions and amplitudes of the mth arrival, k = π / λ, λ is acoustic wavelength CAATI fits element outputs using Prony s method and forms the null steering equation: N ws n n= 0 () n= One can solve the equation and obtain the weights w n, then one can substitute equation () into () and derive the z transform representation: N p m p m m= p= 0 m= 0 = a w z = a W( z), z = e (3) One can find that zeros of polynomial W (z) jdu z m m = e contains the information of directions Hence, estimation of DOA is converted into finding zeros of W (z) Once u m am can be obtained using () at are obtained, amplitudes CAATI fits element outputs using Prony s method and it is able to solve for directions and amplitudes of arrivals accurately when noise perturbation is small enough Therefore, it has potentials for high resolution seafloor mapping This paper extends CAATI into multiple sub-array beamspace and improves its performance 3 SB-CAATI algorithm 3 Theories Signal model is the same as CAATI An N element array is subdivided into K overlapping sub-arrays each with P = N K + elements ( P K ) Structure of sub-arrays is shown in Fig P P P K Fig ultiple sub-array model Firstly, FT is performed in each sub-array and the beam output can be obtained with index i, ( i =,,, P) at the kth sub-array: k+ P j( n ) dum j( n k) dui (, ) = ame e = n= k m= P j( k ) dum j( n ) d( um ui) am n= m= yki e e, where u i is the compensation wave number at beam steering directionθ i N (4) Considering the fitting sub-array beam outputs with the same index using Prony s method, let c P j( n ) d ( um ui ) m, i = am e and substitute it into (4): n= j( k ) dum (, ) mi, m= yki = c e (5) Nulling the weighted sum of beam outputs at index i, one can obtain: K wyki k (, ) = 0 (6) k = Similar to (3), substitute (5) into (6) and derive the z transform representation as: K k mi, k mi, m= k= o m= (7) 0 = c w z = c W( z), z = e One can solve the problem for weights w and form polynomial W (z) as: ( ) ( ) W z = z + wz + wz + + w ( ) (8) Finding zeros at z = e, one can easily obtain directions u m and amplitudes a m 3 Solutions of w k This subsection discusses how to find unique nonzero solutions of nulling weights wk k from (6) under consideration of coherent arrivals The sub-array outputs are considered as element outputs and such elements are subdivided into overlapping element sub-arrays Let the first weight equal to and the

3 LI Zi-sheng, et al: ultiple sub-array beamspace CAATI algorithm for multi-beam bathymetry system 49 linearly independent instances of null steering equations can be obtained to avoid trivial solution In practice, the element outputs are attached with random noise and the coefficients w k have to be estimated using parameter estimation methods Least squares method is a direct method and it is appropriate for the matrix formyw = b : where T w = [ w w w ], Y = L,, K w = min Y, (9) w L,, K w y() l y() l y + () l y() l y3() l y () l + yk () l yk + () l yk() l y( l + ) y( l + ) y + ( l + ) y( l + ) y3( l + ) y + ( l + ) yk ( l + ) yk + ( l) yk( l + ) y( l + L ) y( l + L ) y + ( l + L ) y( l + L ) y3( l + L ) y + ( l + L ) yk ( l + L ) yk + ( l + L ) yk( l + L ) (0) wherey is the sampling matrix with L successive snapshots and sub-matrices of each snapshot are ( K ) ( + ) The minimum number of sub-arrays is K = and spatial covariance matrix with the same beam index is H R ˆ L,, K = YL,, K Y L,, K () The weight vector w can be estimated using total least squares method (TLS) [, 6] 33 Removal of correlated noise component Since multiple overlapping sub-arrays are introduced by SB-CAATI algorithm, correlated noise is also introduced Let en be the additive Gaussian white noise received by the nth element, noise output g k, i of the kth sub-array at beam index i can be written as: H T gki, = Ti ( ek ek+ ek+ P ), () jdui j( P ) dui T T = ( e e ) i It can be found that the noise correlated matrix Ê is no longer unitary but has the form as: Eˆ L,, K = P ( P ) ( P ) ( P ) P ( P ) + ( K ) L ( P ) ( P + ) P (3) Let σ be the variance of noise and the spatial covariance matrix ˆR becomes: Rˆ = ˆ (4) H YL,, K YL,, K + σ E L,, K In the environment of colored noise, distribution of eigenvalues of covariance matrix might deviate from the distribution in white noise environment, which might bring errors to the estimation of w [7] Fortunately, once the structure of noise covariance matrix is known, noise variance σ can be estimated and the correlated noise component can be removed [4] 34 Threshold method for estimation of source number For narrowband seafloor exploration systems, the sample number of signal pulse is practically small, which causes difficulties in source number estimation using statistics methods [8] In this paper, source number is not estimated Instead, degrees-of-freedom ~ ~ [] ( K ) is specified and ˆR becomes ˆR L ~ ~ beam outputs with larger response,, K of P beam steering directions are selected, then ~ solutions from each selected beam index are resolved ~ Therefore, totally solutions can be obtained and distorted solutions can be removed by plane wave screening [] The screening process is implemented by specifying a plane wave tolerance Δ, as an annulus in the z plane of width Δ and centered on the unit circle: Δ z ok + Δ, (5) where z ok are acceptable solution roots of polynomial W (z) Theoretically, zeros of W (z) at z = e are exactly on the unit circle, and solutions out of the annulus are removed

4 50 Journal of arine Science and Application, Vol6, No, arch 007 An empirical range of Δ is 0 05 Δ 0 5 [] Large Δ might retain erroneous solutions while small Δ might lead to removal of correct solutions 35 Summaries of SB-CAATI algorithm ) Form multiple sub-arrays and perform FFT according to Equation (4) ) Specify ~ and form covariance matrix ˆR ~ according to Equations (0), () 3) Estimate noise varianceσ and remove correlated noise component 4) Estimate weight vector w, form polynomial ~ W (z) and find zeros at z = e 5) Process plane wave screening using Equation (5) and obtain u m and a m using Equation () It should be noticed that the selection of sub-array number K ( K ~ ) is not arbitrary If K is too large, the element number of each sub-array might be too small to maintain accurate beam outputs; if K is too small, the equivalent array aperture of SB-CAATI might not be large enough to obtain high resolution estimation Simulation results show that when K is between N 4 and N 3, performance of SB-CAATI is optimal On the other hand, small K means reduced computation load comparing with conventional CAATI algorithm When SB-CAATI is applied to a practical system, the trade-off between computation load and performance should be considered 4 Simulations and processing of sea-experiment data 4 Simulations 4 Simulation Firstly, simulations are conducted to find the appropriate value of sub-array number K Two coherent sources are chosen and the parameters ~ are DOA =, 8, N = 3, L = 60, d = λ, = The plane wave tolerance is empirically set as Δ = 0 [] Experiments are conducted 00 times at different values of K and different SNR s n ( SNR = 0 log( σ / σ ), σ s and σ n are power of signal and additive Gaussian noise respectively), the mean values (degrees) of estimated DOAs and detection probability are given Successful detection is defined as that both of two sources are detected and the estimation error is less than half of beamwidth [9] Results are given in Table It can be seen that when K is 8 and 0, the performance of mean values and detection probability is optimal In other words, when K is between N 4 and N 3, SB-CAATI can achieve the best result Table Simulation results of SB-CAATI at different sub-array number SNR -5dB -0dB -5dB 0dB K DOA DOA Detection DOA DOA Detection DOA DOA Detection DOA DOA Detection % % % % % % % % % % % % % % % % % % % % % % % % Table Simulation results of CAATI and SB-CAATI Results 0dB 5dB 0dB 5dB 0dB 0dB 5 db 0 db Source CAATI Source Detection 0 % 0 % 0 % 0 % 0 % 0 % 00 % 00 % Source SB- Source CAATI Detection 8 5% 50 5% 00 % 00 % 00 % 00 % 00 % 00 % notes:- denotes that all solutions are removed by plane wave screening

5 LI Zi-sheng, et al: ultiple sub-array beamspace CAATI algorithm for multi-beam bathymetry system 5 4 Simulation Simulation parameters are the same as Simulation The sub-array number K is set as 0, and performance of CAATI and SB-CAATI at different SNR is tested Results are shown in Table From the simulation results it can be found that SB-CAATI has higher estimation accuracy and lower SNR threshold compared with CAATI 4 Process of sea-experiment data The raw data of a sea-experiment with a multi-beam system in a shallow sea area are used to test the performance of SB-CAATI in swath bathymetric imaging The experiment was conducted in South China Sea in good state and the depth of water was about 00 meters The transmitted signal was CW pulse and the frequency was 7 kilo hertz Parameters include N = 3, L = 3, K = 6 and Δ = 0 We choose K = 6 to reduce computation load while remaining acceptable performance Fig shows the processing results of conventional beamformer (to select beam output of the largest response at each sample time, also called maximum beam method [8] ), CAATI and SB-CAATI (b) CAATI (c) SB-CAATI Fig Processing results of sea-experiment data Results are given in grey level image plotting as TOA versus DOA, and pixel values in the images are determined by amplitudes estimated One can see that the resolution of CAATI and SB-CAATI is much better than that of conventional beamformer; the performance of CAATI degrades in areas close to nadir due to angular spread [3, 4] ; at shallow grazing angles, CAATI fails due to decreased SNR On the other hand, the processing results of SB-CAATI are better than those of CAATI at large grazing angles oreover, SB-CAATI remains valid in low SNR area and achieves high resolution swath bathymetric imaging in the whole wide swath 5 Conclusions The paper extends CAATI algorithm in SBSS into multi-beam systems and presents a new multiple sub-array beamspace CAATI algorithm The simulation results illustrate that SB-CAATI has higher estimation accuracy and lower SNR threshold compared with CAATI The processing results of sea-experiment data prove the robustness and high resolution ability of SB-CAATI The method can reduce the computation load for eigen decomposition and avoid the source number estimation oreover, the high resolution directions and amplitudes of multiple coherent arrivals can be obtained with only a small number of samples SB-CAATI takes advantages of both FT and CAATI and it can be applied in BBS systems to achieve high resolution swath bathymetric imaging in the whole wide swath Future research will focus on theoretical performance analysis and practical application in BBS of SB-CAATI algorithm (a) aximum beam method

6 5 Journal of arine Science and Application, Vol6, No, arch 007 References [] DENBIGH P N Swath bathymetry: Principles of operation and an analysis of errors [J] IEEE J Ocean Eng, 989, 4: [] KRAEUTNER P H Small aperture acoustic imaging using model based array signal processing [D] Burnaby: Simon Fraser University, 998 [3] KRAEUTNER P H, Charbonneau B ulti-angle swath bathymetry sidescan quantitative performance analysis [J] IEEE OCEANS, 00, 4: [4] ZHOU Tian, LI Haisen, LI Zisheng, et al ulti-beam bathymetry system using SB-USIC algorithm [A] WESPAC IX 006[C] Seoul, Korea, 006 [5] OUIBRAHI H Prony, Pisarenko, and the atrix Pencil: A unified presentation [J] IEEE Transactions on Acoustics, Speech, and Signal Processing, 989, 37: [6] RAO B D, ARUN K S odel based processing of signals: A state space approach [J] Proceedings of the IEEE, 99 80(): [7] FU Ji-hua, WANG Hongyang, HAO Bingbing DOA estimation for highly correlated signals under colored noise environment[j] odern Radar, 00(): (in Chinese) [8] ZHOU Tian A study on high resolution detection techniques for super wide seafloor bathymetry and physiognomy [D] Harbin: Harbin Engineering University, 005 (in Chinese) [9] RONHOVDE A, YANG L, TAXT T, et al High-resolution beamforming for multibeam echo sounders using raw E3000 data [A] Proc OCEANS 99 [C] Washington, USA, 999 LI Zi-sheng was born in Guangzhou, Guangdong Province, China in 98 He received the bachelor degree in Harbin in 004 He is currently a master student in the College of Underwater Acoustic Engineering, Harbin Engineering University His research interests are in array signal processing and swath bathymetry LI Hai-sen was born in Harbin, Heilongjiang Province, China in 96 He received the bachelor degree, master degree and doctor s degree in Harbin Engineering University in 984, 990 and 999 respectively From 984, he teaches in the College of Underwater Acoustic Engineering, Harbin Engineering University, China He is currently the professor in the College of Underwater Acoustic and postdoctoral of Instrument Science and Technology of Harbin Institute of Technology, China ZHOU Tian was born in Yancheng City, Jiangsu Province, China in 980 He received the bachelor degree, master degree and doctor s degree in Harbin Engineering University in 000, 00 and 005 respectively From 005, he teaches in the College of Underwater Acoustic Engineering, Harbin Engineering University, China His research interests are in the general area of underwater acoustic