Obtaining 3D High-Resolution Underwater Acoustic Images by Synthesizing Virtual Aperture on the 2D Transducer Array of Multibeam Echo Sounder

remote sensing

Article Obtaining 3D High-Resolution Underwater Acoustic Images by Synthesizing Virtual Aperture on the 2D Transducer Array of Multibeam Echo Sounder

Bo Wei 1,2,3 , Haisen Li 1,2,3, Tian Zhou 1,2,3,* and Siyu Xing 1,2,3 1 Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China; [email protected] (B.W.); [email protected] (H.L.); [email protected] (S.X.) 2 Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology, Harbin 150001, China 3 College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China * Correspondence: [email protected]; Tel.: +86-0451-82589147

Received: 1 September 2019; Accepted: 7 November 2019; Published: 8 November 2019

Abstract: In recent decades, imaging sonar has been the most widely employed remote sensing instruments in the field of underwater detection. The multibeam echo sounder (MBES) plays an important role in obtaining high-accuracy seabed topography. However, the resolution of the MBES substantially decreases with the increasing distance. Synthetic aperture sonar (SAS) achieves constant resolution on the along-track, improving the fineness of the image. However, conventional side-scan SAS usually only achieves 2D images, and gaps always exist. In this modeling and experimental research paper, we propose a novel underwater acoustic imaging scheme to improve the imaging performance of MBES, based on the complementarity of MBES and SAS systems. We design a 2D transducer array to increase the detection efficiency and obtain spatial gain. Moreover, the processing scheme is analyzed to design the working parameters in actual engineering applications. We exploit a target echo simulation approach to establish the research basics of the imaging algorithms, which also reflects the shapes and shadows of targets to match actual situations as realistically as possible. The proposed imaging algorithm synthesizes a virtual aperture receiving array on the along-track and reserves the multi-element manifold on the across-track. This helps to improve the imaging quality of the MBES and achieves high-resolution 3D detection with no gaps. Simulation and tank experimental results demonstrate that the proposed scheme can significantly improve the detection ability of the MBES, especially for small 3D target detection, thus making it suitable for 3D high-resolution underwater detection applications.

Keywords: multibeam echo sounder; underwater acoustic imaging; 2D transducer array; 3D high- resolution detection

1. Introduction Imaging sonar systems are major remote sensing instruments that require a high resolution to guarantee detection accuracy that has many technology branches [1]. The multibeam echo sounder (MBES) has been widely used in recent decades as an effective underwater acoustic detection instrument. The MBES achieves full-scan 3D detection in the whole detecting area through carrier movement and imaging mosaic methods. Water column and snippet side scan imaging are also practical technology of MBES to detect fish schools or bottom targets in detail [2–4]. However, the resolution of the MBES on the along-track and across-track both decreases substantially with an increasing beam width and distance. Synthetic aperture sonar (SAS) is used as a kind of imaging sonar that can provide a constant high resolution on the along-track, independent of the echo frequency and distance [5,6]. SAS can

Remote Sens. 2019, 11, 2615; doi:10.3390/rs11222615 www.mdpi.com/journal/remotesensing Remote Sens. 2019, 11, 2615 2 of 22 provide a detailed backscattered acoustic image that is widely employed, e.g., for cables and unexploded ordnance detection. In most recent research, SAS systems are usually based on the echo model of side-scan sonar (SSS), which also introduces disadvantages such as the gap problem and have to employ an additional MBES as the gap filler [7,8]. Furthermore, conventional SAS usually achieve 2D images that just indicate the azimuth and range direction. Accurate depth information of the targets cannot be obtained directly from SAS images [9,10]. Although some interferometric synthetic aperture sonar (InSAS) or multi-receiver SAS can estimate depth information through phase differences between the multiple elements on the along-track, the depth accuracy of InSAS is much lower than that of MBES, which is usually employed as an assistant reference. Multi-receiver SASs usually employ only several elements on the along-track, which is much less than the dozens or even hundreds of receivers placed by the MBES [11]. The scale of the transducer array limits the depth estimation accuracy of InSAS. Multibeam synthetic aperture sonar (MBSAS) is proposed as a novel imaging sonar technology that effectively overcomes the disadvantages of MBES and SAS but has been rarely researched. MBSAS achieves a 3D full-scan detecting with no gaps problem and more accurate height detection, compared with SAS. Higher resolution can also be obtained through the synthesizing virtual aperture on the along-track, compared with MBES. MBSAS could be achieved through the MBES scheme or other 2D transducer arrays and is suitable to be employed in the field of detailed underwater surveys. Some basic research of MBSAS has been carried out, such as the basic echo model of a single-line MBSAS system [12]. The feasibility of single-line MBSAS is verified preliminarily through a tank experiment [13]. Motion error and its influence on the imaging and estimation algorithm of the 2D transducer array have also been proposed [14]. However, the complete theoretical system of MBSAS has not been fully discussed. The target simulation, processing scheme, and working conditions of MBSAS are also research domains where the system could be shown to be efficient and valuable. In this paper, we propose a novel underwater acoustic imaging scheme to improve the imaging performance of MBES, based on the complementarity of MBES and SAS systems. The transducer array and signal processing scheme are analyzed to design the working parameters for engineering applications. For targets with shadow, a simulation approach is introduced to generate MBSAS echoes. We propose an imaging algorithm that integrates the theories of MBES and SAS to provide high-resolution detection in 3D space. A principle prototype of MBSAS is also designed to verify the proposed theory. The performance of the novel instrument is demonstrated through simulations and tank experiments. We also discuss the working conditions and prospect of the novel device.

2. Echo Model and Processing Scheme of MBSAS

2.1. Basic Echo Model of MBSAS MBSAS combines the technical characteristics of MBES and SAS so that the array manifold is specially designed. The 2D MBSAS system employs a uniform linear array (ULA) with a number of receiving elements on the across-track, as in the conventional MBES. There are also several linear receiving arrays located on the along-track that form a planar transducer array. The proposed 2D transducer array model is shown in Figure1a. The MBSAS system needs a larger beam angle width on the along-track than MBES to illuminate the target more times on the trajectory. Therefore, we designed a transmitter located on the edge of the receiving array, which is different from the behind side as in the conventional MBES. The sampling interval on the along-track is limited by the principle of SAS imaging, which requires the carrier to move slowly to ensure signal synthesis [15]. The element on the along-track is first processed by the synthetic aperture, and then a virtual line receiving array is obtained on the across-track. Beamforming processing is carried out on the virtual array to divide the across-track into beam-space. A planar transducer array can increase the detection efficiency because echoes can also be received by the elements on the along-track. The sampling interval on the along-track limits the quality of the synthesizing algorithm. A high carrier moving speed will introduce a grating lobe problem, which is also synthesized in the imaging Remote Sens. 2019, 11, 2615 3 of 22 processing.Remote Sens. Thus, 2019, 11 the, x FOR carrier PEER REVIEW speed is limited in order to guarantee the effectiveness of the3 of imaging23 algorithm, which reduces the sonar detection efficiency. The multiple elements on the along-track can algorithm, which reduces the sonar detection efficiency. The multiple elements on the along-track managecan manage this problem this problem by receiving by receiving more more echoes echoes atat didifferentfferent detected detected angles angles in a insingle a single synthesized synthesized apertureaperture period period so so that that the the carrier carrier speed speed cancan bebe increased.increased. A A wideband wideband signal signal can can also also be managed be managed to solveto thesolve grating the grating lobeproblem. lobe problem. MBSAS MBSAS employs employs linear linear frequency frequency modulated modulated (LFM) (LFM) signals signal tos to provide a largeprovide time-bandwidth a large time-bandwidth product andproduct high and distance high distance resolution, resolution, which which is widely is widely used used in SSS in SSS and SAS systemsand SAS [16 ,systems17]. The [16 synthetic,17]. The synthetic processing processing occurs occurs through through the motion the motion of the of the carrier carrier so so that that a a virtual aperturevirtual array aperture is generated array is generated on the along-track. on the along- Thetrack. 2D The transducer 2D transducer array array still still keeps keeps the the multi-element multi- transducerelement arraytransducer manifold array on manifold the across-track. on the across Finally,-track. as Finally, shown inas Figureshown1 a, in theFigure 2D transducer1a, the 2D array transducer array is converted to a virtual ULA which has a large aperture on the along-track and is converted to a virtual ULA which has a large aperture on the along-track and keeps the manifold as keeps the manifold as MBES on the across-track. The processing scheme is discussed in detail in MBES on the across-track. The processing scheme is discussed in detail in Section 2.2. Section 2.2. In actualIn actual applications, applications, the the elementselements and and the the bandwidth bandwidth cannot cannot be increased be increased bound boundlessly,lessly, but are but are inevitablyinevitably limited limited by by the the transducertransducer array array manufacturing manufacturing process process and the and cost. the We cost. compromised We compromised by by applyingapplying the the echo echo synthesis synthesis algorithm algorithm in a in very a very narrow narrow space space just below just below the carrier the carrier to avoid to avoidthe the gratinggrating lobe lobe problem. problem. An An image image of of the the whole whole detected detected area area can can also also be be obtained obtained by by moving moving the the carrier. Wecarrier. designed We adesigned 2D array a 2D structure array structure that has that 4 ULAs,has 4 ULAs and, eachand e ULAach ULA has has 32 32 receiving receiving elements. elements. Thus, we canThus, research we can research some imaging some imaging algorithms algorithm baseds based on on the the subarray subarray structurestructure with with the the beam beam width width of of   3 . 0 on the across-track. Then, the four ULAs on the along-track can also introduce the θ 3dB 3.03dB ◦ on the across-track. Then, the four ULAs on the along-track can also introduce the array − ≈ gainarray and gain the 2Dand imaging the 2D imaging algorithm algorithm can be taken.can be taken Furthermore,. Furthermore, the total the total number number of receiving of receiving elements is 128elements which is is 128 acceptable which is andacceptable economical and economical in the field in the of engineeringfield of engineering application. application The. echo The echo just below the carrierjust below can the also carrier be received can also whichbe received is diff whicherent is from different the SAS from directivity, the SAS directivity so that the, so gapthat problemthe gap does problem does not exist. The transducer array is designed and produced following the parameters not exist. The transducer array is designed and produced following the parameters shown in Figure1b, shown in Figure 1b, which meets the requirement of high-resolution detection and also considers which meets the requirement of high-resolution detection and also considers engineering applications engineering applications and cost. Through the moving of the carrier, we can synthesize a virtual andarray cost. with Through the aperture the moving size L. of The the imaging carrier, wealgorithm can synthesize we proposed a virtual is base arrayd on withthe point the apertureby point size L. Thescanning imaging thatalgorithm the actual we proposedpositions is of based the elements on the point should by pointbe calculated scanning through that the the actual motion positions of theparameters elements from should the sensors. be calculated The carrier’s through trajectory the motion is compensated parameters so fromthat the the actual sensors. time The delay carrier’s trajectorybetween is the compensated target and element so that is the obtained. actual time delay between the target and element is obtained.

Depth Transmitter z v Receiver （） x0, y0, 0 Sonar receiving array Along track L Virtual Array Across track

Trajectory

R1 R2

Imaging area Received beam y

Transmit beam x Target (x , y , z ) T T T (a)

(b)

Figure 1. (a) Basic echo model of multibeam synthetic aperture sonar (MBSAS). (b) Designed 2D MBSAS transducer array. Remote Sens. 2019, 11, 2615 4 of 22

Normally, the SAS transmitter and receiver are regarded as located at the equivalent phase center (EPC) [18]. However, the 2D MBSAS transducer array locates the transmitter beside the receiving array. Therefore, the range between the transmit position and the scanned area R1 should be accurately calculated based on the geometric relationships as represented by q 2 2 2 R = (xT x ) + (yT y ) + zT (1) 1 − 0 − 0

The transmitter’s initial position is (x0, y0, 0) and the scanned target is located at (xT, yT, zT). The distance between the receiving element and the scanned area is depicted as R2 when the carrier moves at the speed of v q 2 2 2 R = (xT x (n)) + (yT y (n) vτ (n)) + zT (2) 2 − k − k − k th th where (xk(n), yk(n), 0) is the initial position of the n element on the k linear receiving transducer array. Therefore, the carrier’s moving time can be indicated as τk(n), which is also the echo time-delay. The acoustic range can be expressed as Equation (3), and the solution expressed in Equation (4) is employed as the time-delay of the back projection (BP) imaging algorithm; c is the acoustic speed.

R1 + R2 = cτk(n) (3)

q 2 2 2 2 2 vyk(n) vyT+c x 2x0xT+x +y 2y0 yT+y +z (n) = − 0− T 0− T T τk (c2 v2) uv − u 2 2 2 2 2 2 u 4 c v x x (n) 2x0xT + 2xk(n)xT + y y (n) 2y0 yT + 2yk(n)yT tu 0 k 0 k (4) − − − − q − − 2 + ( ) + 2 + 2 + 2 + 2 + 2 2vyk n 2vyT 2c x0 2x0xT xT y0 2y0 yT yT zT + − − − − 2(c2 v2) − The initial element coordinates on the across-track and along-track indicate the transducer array manifold, which is considered in the imaging algorithm of MBSAS. The echoes should be subjected to the preprocessing before the imaging algorithm, including orthogonal transformation to get the analytical signal and pulse compression processing to increase the range resolution. Equation (4) is the analytic solution of the time delay of the transducer array at different synthesized positions, which is a complex process. In actual situations, the transducer array manifold is given and the initial positions can be user-defined so that Equation (4) can be simplified effectively. The transmitting signal is the LFM, which can be expressed as Equation (5) when travel time is t ( t t 1, t 1 T s (t) = rect( ) exp[j(2π f t + πut2)], rect( ) = | | ≤ 2 (5) t T 0 T 0, others where f0 is the initial frequency of the LFM, which lasts for pulse length T. B is the bandwidth of LFM and µ = B/T represents the chirp rate. The received echo of the selected element after target reflection through travelling time τk(n) can be expressed as Equation (6)

t τk(n) 2 sr(t) = rect( − ) exp[j(2π f (t τ (n)) + πu(t τ (n)) )] (6) T 0 − k − k

2.2. Processing Scheme of the MBSAS Imaging System The processing scheme is divided into four steps: orthogonal transformation, pulse compression, synthetic processing on the along-track, and beamforming processing on the across-track, and the Remotefirst two Sens. steps2019, 11 are, 2615 taken as preprocessing. The echo received by the receiver is converted 5to of an 22 analytical signal through orthogonal transformation. The LFM signal is compressed through the matched filter which obtains the processing gain. The main limit condition of the SAS processing on isthe that along the-track target is should that the be target illuminated should be at leastilluminated on the at edge least of on each the footprint edge of each as shown footprint in Figure as shown1a. Thein Figure echo coherence 1a. The echo must coherence be guaranteed mustthat be guaranteed we should take that the we SAS should processing take the in SAS a single processing synthesized in a aperturesingle synthesized period. The aperture receivers period. of the The designed receivers 2D of transducer the designed array 2D are transducer separated array into are 32 subarrays,separated andinto each32 subarrays, subarray and has 4each elements subarray on the has along-track. 4 elements on Synthetic the along processing-track. Synthetic on the along-track processing is on done the inalong each-track subarray, is done generating in each subarray, a virtual 1Dgenerating ULA that a hasvirtual 32 elements 1D ULA onthat the has across-track. 32 elements The on processingthe across- schemetrack. The of MBSASprocessing imaging scheme system of MBSAS is shown imaging in Figure system2. is shown in Figure 2.

FigureFigure 2.2. Processing scheme of MBSASMBSAS imagingimaging system.system.

AsAs shownshown inin FigureFigure2 2,, a a complex complex weighting weighting process process is is conducted conducted on on the the analytical analytical signal, signal, which which isis similarsimilar toto DFTDFT processing.processing. An integralintegral operation is takentaken inin thethe wholewhole syntheticsynthetic apertureaperture periodperiod n and each element achieves a 2D SAS image. The weight W (yn, r) is calculated through the time delay and each element achieves a 2D SAS image. The weight kWk (,) y r is calculated through the time between the transmitter and the receiver considering the position of the elements, the moving speed delay between the transmitter and the receiver considering the position of the elements, the moving and the scanned points, as Equation (4). A weighted summation is taken by each subarray and a speed and the scanned points, as Equation (4). A weighted summation is taken by each subarray and virtual element is obtained. Therefore, a ULA similar to an MBES is generated so that the beamforming a virtual element is obtained. Therefore, a ULA similar to an MBES is generated so that the process can be conducted. Phase shift beamforming then takes place, which employs the near-field beamforming process can be conducted. Phase shift beamforming then takes place, which employs model that considers spherical wave propagation. The weight is calculated through the preset beam the near-field model that considers spherical wave propagation. The weight is calculated through the angle and the range. A weighted summation of the phase shifted data is performed on the 32 elements, preset beam angle and the range. A weighted summation of the phase shifted data is performed on and a 3D MBSAS image is obtained which indicates the coordinate system of y r θ. The 3D image the 32 elements, and a 3D MBSAS image is obtained which indicates the −coordinate− system of can also be transmitted to the Cartesian coordinate system through the relationship between distance andyr beam angle.. The 3D image can also be transmitted to the Cartesian coordinate system through the relationship between distance and beam angle. 2.3. Grating Lobe Problem of MBSAS 2.3. GMovingrating Lobe speed Problem of the of carrier MBSAS is an important working parameter of SAS that limits the surveying efficiencyMoving of thespeed carrier. of the In carrier the theory is an important of SAS, the working max range parameter determines of SAS the that moving limits the speed surveying as the detectedefficiency target of the has carrier. to be illuminatedIn the theory on of the SAS, edge the of themax footprint range determines at least. That the means moving we takespeed the as SAS the processingdetected tar inget a singlehas to synthesizedbe illuminated aperture on the period. edge of More the footprint times the at echo least. synthesizes That means in we a single take the period, SAS the better the imaging performance which can be obtained, but this lowers the carrier moving speed limit at the same time. The sampling interval, which also limits the moving speed of the carrier, is an important working parameter in engineering applications. According to the sampling theory in 3D space, when the sampling interval exceeds half the size of the transmitter, the grating lobe appears. The grating lobe introduces false targets, decreases the SNR, and is harmful to target recognition. Therefore, the grating lobe problem limits the moving speed and the detection efficiency. As shown in Remote Sens. 2019, 11, x FOR PEER REVIEW 6 of 23

processing in a single synthesized aperture period. More times the echo synthesizes in a single period, the better the imaging performance which can be obtained, but this lowers the carrier moving speed limit at the same time. The sampling interval, which also limits the moving speed of the carrier, is an important working parameter in engineering applications. According to the sampling theory in 3D Remotespace, Sens. when2019 ,the11, 2615sampling interval exceeds half the size of the transmitter, the grating lobe appears.6 of 22 The grating lobe introduces false targets, decreases the SNR, and is harmful to target recognition. Therefore, the grating lobe problem limits the moving speed and the detection efficiency. As shown Figure3a, the single-element SAS system has no grating lobe problem and indicates the single point in Figure 3a, the single-element SAS system has no grating lobe problem and indicates the single target accurately at a sampling interval of 0.5D, where D is the real transmitter aperture size. When point target accurately at a sampling interval of 0.5D, where D is the real transmitter aperture size. the sampling interval reaches 2.0D, false peaks appear and the actual target cannot be recognized. When the sampling interval reaches 2.0D, false peaks appear and the actual target cannot be Therefore, we need to analyze the grating lobe problem of MBSAS and provide a method to improve recognized. Therefore, we need to analyze the grating lobe problem of MBSAS and provide a method the moving speed of the carrier that meet the actual engineering applications. to improve the moving speed of the carrier that meet the actual engineering applications.

(a) (b)

Figure 3. Grating lobe comparison between sampling intervals: (a) grating lobe of single element at Figure 3. Grating lobe comparison between sampling intervals: (a) grating lobe of single element at sampling interval of 0.5D; (b) grating lobe of single element at sampling interval of 2.0D; (c) grating sampling interval of 0.5D; (b) grating lobe of single element at sampling interval of 2.0D; (c) grating lobe lobe of MBSAS at sampling interval of 0.5D; (d) grating lobe of MBSAS at sampling interval of of MBSAS at sampling interval of 0.5D; (d) grating lobe of MBSAS at sampling interval of equivalent equivalent value 5.0D. value 5.0D.

TheThe restrictiverestrictive conditioncondition ofof thethe samplingsampling intervalinterval limitslimits thethe movingmoving speedspeed ofof thethe carrier,carrier, which which alsoalsoreduces reduces thethe detectiondetection eefficiencyfficiency.. ForFor example,example, whenwhen thethe transmittertransmitter apertureaperture sizesize isis 1616 cm,cm, thethe movingmoving speed speed that that guarantees guarantees a a strict strict sampling sampling interval interval of of 0.5D 0.5D is is just just 8 8 cm cm/s/s.. The The lowlow moving moving speed speed isis not not acceptable acceptable in in actual actual applications. applications. TheThe multiplemultiple receiversreceivers onon thethe across-trackacross-track cancan alleviatealleviate thethe gratinggrating lobe lobe problem problem to to some some extent extent by by coherent coherent accumulation. accumulation. ThreeThree methods methods cancan be be employed employed to to overcome overcome such such a a situation. situation. TheThe firstfirstis isto toimprove improvethe thepulse pulse repetitionrepetition frequencyfrequency (PRF),(PRF), alsoalso called the p pinging r rateate in in the the field field of of MBES. MBES. When When the the moving moving speed speed is islimited, limited, the the higher higher the the ping ping rate rate,, the the less less equivalent the samplingsampling interval.interval. ManyMany kindskinds ofof maturemature MBESsMBESs cancan achieve a a ping ping rate rate up up to to 50 50 Hz, Hz, such such as the as theSeaBat SeaBat 7125, 7125, EM 2040 EM 2040,, and SeaBat and SeaBat T50P. T50P.High Highping pingrate ratedetection detection reduces reduces the thesampling sampling interval interval equivalently equivalently so so that that we we can can increase thethe movingmoving speedspeed ofof thethe carrier.carrier. AsAs shownshown inin FigureFigure3 d,3d, we we simulated simulated carrier carrier moves moves at at a a speed speed of of 1.6 1.6 m m/s/s andanda a ping rate of 2 Hz, which indicates that the equivalent sampling interval is 5.0 D. The imaging result in the whole space is acceptable and the grating lobe level increases slightly compared with Figure3c. However, the high ping rate limits the maximum detection distance, because echoes must be received and coherently accumulated at each synthesized position. Remote Sens. 2019, 11, x FOR PEER REVIEW 7 of 23 ping rate of 2 Hz, which indicates that the equivalent sampling interval is 5.0 D. The imaging result inRemote the Sens.whole2019 space, 11, 2615 is acceptable and the grating lobe level increases slightly compared with Figure7 of 22 3c. However, the high ping rate limits the maximum detection distance, because echoes must be received and coherently accumulated at each synthesized position. TheThe second wayway toto manage manage the the grating grating lobe lobe problem problem is tois placeto place multiple multi elementsple elements on the on along-track. the along- track.MBSAS MBSAS is designed is designed based based on the on structure the structure of MBES, of MBES for which, for which we designed we designed a 2D transducera 2D transducer array arrayto increase to increase the sampling the sampling interval. interval. Multiple Multi elementsple elements on the on along-track the along-track can managecan manage the grating the grating lobe lobeproblem problem as each as each individual individual ULA canULA receive can receive an echo an in echo a narrow in a narrow scope belowscope thebelow array, the which array, equates which equateto increasings to increasing the spatial the spatial sampling sampling density density on the on along-track. the along-track Multiple. Multiple elements elements on the on along-track the along- trackalso introduce also introduce array gain,array somegain, 2Dsome beamforming 2D beamforming and subarray and subarray processing processing algorithms algorithms can also can be taken also beto improvetaken to improve the imaging the imaging performance performance of MBSAS of system.MBSAS system. SideSidelobelobe and and grating grating lobe lobe are are suppressed suppressed according according to the to coherent the coherent accumulation, accumulation which, which is similar is similarto spatial to gain.spatial We gain. compared We compare the syntheticd the synthetic aperture aperture processing processing output betweenoutput between the single-line the single and- linemulti-line and multi ULA,-line which ULA,are which sliced are onsliced the on along-track the along- (Figuretrack (Figure4). It is4) obvious. It is obvious in Figure in Figure4a that 4a thethat thesidelobe sidelobe and and grating grating lobe lobe levels level seriouslys seriously increase, increase, together together with with the the sampling sampling interval.interval. When the the samplingsampling interval interval reaches reaches 10 10 times times the the real real transmitter transmitter aperture aperture size, size, a a serious serious false false peak probl problemem appears.appears. T Thehe multi multipleple elements elements set set in in Figure Figure 4 bb improveimprove thethe situationsituation soso thatthat thethe falsefalse peakspeaks cancan bebe managedmanaged effectively. effectively. However However,, the problem cannot be thoroughly solved just by adding adding elements elements on on thethe along along-track-track considering considering the the system system complexity.

(a) (b)

FigureFigure 4. SideSide lobe lobe comparison between between single single-line-line and and multi multi-line-line receiving array systems systems.. ( (aa)) Side Side lobelobe of of single single-line-line array array;; and and ( (bb)) multi multi-line-line array array at at different diﬀerent sampling intervals.intervals.

TheThe third third choice to manage thethe gratinggrating lobelobe problemproblem is is to to increase increase the the signal signal bandwidth, bandwidth, which which is isalso also called called the the low-quality low-quality factor factor method. method. LFM LFM signal signal is employedis employed in thein the MBSAS MBSAS system system so thatso that the theSNR SNR and and detecting detecting distance distance can be can improved be improved eﬀectively. effectively. Figure5 a–cFigure compares 5a–c compare the imagings the output imaging of outputthe 2D of transducer the 2D transducer array designed array asdesigned above withas above a single with point a single target, point where target the, qualitywhere the factors quality are factorQ = 15,s are 5, Q=15, and 3.75. 5, and The 3.75. 3D The image 3D image is sliced is sliced on the on same the same depth depth plane plane which which not onlynot only indicates indicate thes thegrating grating lobe lobe on on the the along-track along-track but but also also shows show thes the sidelobe sidelobe level level on on the the across-track. across-track. It is obvious fromfrom the the comparison comparison that that increasing increasing Q Q can can help help to to manag managee the the grating grating lobe lobe and and side side lobe lobe problem. problem. HoweverHowever,, with Q increasing increasing as as sliced sliced,, shown shown in in Figure Figure 5d,d, the main lobe level reaches the limit value value.. MoreoverMoreover,, ininengineering engineering applications, applications, the the wideband wideband transducer transducer array array is diﬃ iscult difficult to design to and design produce and produceat low cost. at low cost.

Remote Sens. 2019, 11, 2615 8 of 22

Remote Sens. 2019, 11, x FOR PEER REVIEW 8 of 23

(a) (b)

FigureFigure 5. Side5. Side lobe lobe comparison comparison between between signal signal bandwidthbandwidth situations:situations: ( (aa)) MBSAS MBSAS output output 2D 2D sliced sliced when Q = 15; (b) when Q = 5; (c) when Q = 3.75; (d) MBSAS output sliced on the along-track. when Q = 15; (b) when Q = 5; (c) when Q = 3.75; (d) MBSAS output sliced on the along-track.

TheThe grating grating lobe lobe problem problem is is not not solved solved thoroughly,thoroughly, limitedlimited by the the system system complexity complexity and and cost, cost, especiallyespecially in in actual actual engineering engineering applications.applications. Therefore, Therefore, we we have have to tocompromise compromise in this in thissituation situation to meet the actual requirements. As the grating lobe appears at a certain distance and beam angle from to meet the actual requirements. As the grating lobe appears at a certain distance and beam angle the transducer array center, we can only take the MBSAS processing in a narrow area just below the from the transducer array center, we can only take the MBSAS processing in a narrow area just below array to avoid the problem. A whole detecting image can be achieved by moving the carrier so that the array to avoid the problem. A whole detecting image can be achieved by moving the carrier the image can be stitched together, which is a common method in the MBES imaging field. In so that the image can be stitched together, which is a common method in the MBES imaging field. summary, we designed the processing scheme of the MBSAS which employs the wideband signal In summary,and the 2D we transducer designed array the processingto manage the scheme grating of lobe the MBSASproblem. which The mult employsi-ping themethod wideband and image signal andmosaic the 2D also transducer help to improv arraye to the manage sampling the interval grating and lobe detection problem. efficiency The multi-ping to meet actual method engineering and image mosaicapplication also help requirements. to improve the sampling interval and detection efficiency to meet actual engineering application requirements. 3. Target Simulation and Imaging Algorithm 3. Target Simulation and Imaging Algorithm Target simulation is the basic and necessary work of MBSAS modeling. To provide a detailed echoTarget signal simulation to the imaging is the algorithm, basic and not necessary only the worktarget ofmain MBSAS body modeling.but also the Toshadows provide at different a detailed echosynthetic signal topositions the imaging should algorithm, be simulated not in only detail. the targetAn acoustic main highlight body buts alsomodel the is shadows employed at to di carryfferent syntheticthe complex positions target should echo simulation. be simulated Furthermore in detail. An, an acousticimaging highlightsalgorithm is model proposed is employed to demonstrate to carry thethe complex feasibility target of the echo 2D simulation. MBSAS model. Furthermore, an imaging algorithm is proposed to demonstrate the feasibility of the 2D MBSAS model. 3.1. Target with Shadow Simulation Approach 3.1. Target with Shadow Simulation Approach The basic unit of target simulation is the single highlight, which is widely employed to evaluate theThe performance basic unit of a target detection simulation algorithm, is the such single as received highlight, beam which angle is width widely and employed sidelobe level to evaluate [19]. theThus, performance the solid of target a detection is divided algorithm, into dozens such of as highligh receivedts through beam angle the tangents width and, as sidelobeshown in level Figure [19 ]. Thus,6a. the Highlights solid target on theis divided surface into contribute dozens toof highlights the echo accumulated through the ontangents, the elements as shown, ignor in Figureing the6 a.

Remote Sens. 2019, 11, 2615 9 of 22

RemoteHighlights Sens. 2019 on, the 11, surfacex FOR PEER contribute REVIEW to the echo accumulated on the elements, ignoring the penetration9 of 23 of the echo. Movement of the 2D transducer array is more complex than the SAS which has single-element penetration of the echo. Movement of the 2D transducer array is more complex than the SAS which or multiple receivers on the along-track. The carrier should move as a uniform rectilinear motion in has single-element or multiple receivers on the along-track. The carrier should move as a uniform theory, but an ideal trajectory cannot always be maintained that the motion error must be estimated rectilinear motion in theory, but an ideal trajectory cannot always be maintained that the motion error and compensated. The MBSAS can be equipped by surface vessel or AUV that the high accuracy must be estimated and compensated. The MBSAS can be equipped by surface vessel or AUV that the motion sensors (USBL, DVL, and compass) or motion estimation algorithms based on the echo (DPC high accuracy motion sensors (USBL, DVL, and compass) or motion estimation algorithms based on and PGA) are employed to calculate the position of each element, considering diﬀerent application the echo (DPC and PGA) are employed to calculate the position of each element, considering different scenarios [20]. application scenarios [20]. The carrier has six dimensional motion parameters, which can be separated by position (sway, The carrier has six dimensional motion parameters, which can be separated by position (sway, surge, and heave) and motion (yaw, roll, and pitch), as shown in Figure6b. Assuming that the 2D surge, and heave) and motion (yaw, roll, and pitch), as shown in Figure 6b. Assuming that the 2D array has M ULAs on the along-track and each ULA has N elements on the across-track, the array we array has M ULAs on the along-track and each ULA has N elements on the across-track, the array we designed has a 4 32 manifold. designed has a 4× 32 manifold.

(a) (b)

FigureFigure 6. TargetTarget segmentation segmentation and and moving moving trajectory trajectory of carrier: of carrier (a) highlights: (a) highlights segmented segmented on the surface;on the surface(b) moving; (b) moving trajectory trajectory of the carrier. of the carrier.

TheThe coordinatescoordinates ofof each each element element should should be calculated be calculated accurately accurately according according to position to position and motion and motionparameters parameters to guarantee to guarantee the validity the validity of the imaging of the imaging algorithm. algorithm. We deﬁne We the define rotation the anglerotation along angle the x-axis, y-axis, and z-axis as [α, β, γ], respectively, then the rotation matrix Mα, N , Q can be expressed along the x-axis, y-axis, and z-axis as [ , , ]  , respectively, then the rotation matrixβ γ M , N ,Q can as Equation (7) be expressed as Equation (7)        1100 0 0  coscosβ 00 sin sin β  cossin0cosϕ  sin ϕ 0       −  Mα =  0 cos α sin α Nβ = 0 1 0 Qϕ = sin ϕ cos ϕ 0  (7) M  0cossin−  N  0 1 0  Q   sincos0  (7)   0 sin α cos α   sin β 0 cos β   0 0 1  − 0sincos sin 0 cos 001 Assuming the carrier’s translation along the x-axis, y-axis, and z-axis is ∆x, ∆y, ∆z, respectively, the translationAssuming matrixthe carrier’s can be deﬁned translation as P along= [∆ x the; ∆ yx; -∆axis,z], where y-axis∆, ( and) is the z-axis spanned is x1 , MNy , vector.z , ∆ · × The positions of the receiving elements Pr1 can be calculated through the rotation matrix and() translation respectively, the translation matrix can be defined as P [;;]  x  y  z , where is the matrix from the initial position Pr0 as Equation (8) spanned 1 MN vector. The positions of the receiving elements Pr1 can be calculated through the P = M N Q P + P (8) rotation matrix and translation matrix fromr1 theα initialβ ϕ positionr0 ∆ Pr0 as Equation (8)

Similarly, the transmitter’s positionPMrr10 can N be Q calculated PP through Equation (9). (8)

Similarly, the transmitter’s positionPT 1can= Mbeα calculatedNβQϕPT0 + throughP∆ Equation (9). (9)

In the simulation of the target, the shadows area is an important factor that also indicates the PMTT10 N Q PP  (9) characteristics of the target. We employ the normal vector of the surface to calculate the shadow area of

In the simulation of the target, the shadows area is an important factor that also indicates the characteristics of the target. We employ the normal vector of the surface to calculate the shadow area of the target. Any plane in the 3D space can be described by the point normal equation. The surface

Remote Sens. 2019, 11, x FOR PEER REVIEW 10 of 23 Remote Sens. 2019, 11, 2615 10 of 22 of the target contributes to the signal when it is illuminated by the transmitted echo. When the includedthe target. angle Any planebetween in the the 3D normal space vector can be and described the connection by the point fro normalm the transmitter equation. The to the surface surface of the is antarget obtuse contributes angle, this to the surface signal contri whenbutes it is illuminated to the received by the signal. transmitted The normal echo. Whenvector the Figure included 7a shows angle thatbetween each thesur normalface has vectorits own and normal the connection vector and from the bottom the transmitter is never toilluminated the surface. The is an normal obtuse vector angle, ofthis the surface surface contributes can be expressed to the received as n  signal.( ,ABC , ) The, which normal is vector vertical Figure to the7a plane shows. Given that each a certain surface point has its own normal vector and the bottom is never illuminated. The normal vector of the surface can be Mx0000 ( ,y ,z ) on the surface, any point on the surface Mx ( ,y ,z ) has the limit as n  MM 0 , expressed as →n = (A, B, C), which is vertical to the plane. Given a certain point M = (x , y , z ) on which is also calculated as Equation (10). 0 0 0 0 the surface, any point on the surface M = (x, y, z) has the limit as →n MM→ , which is also calculated as ⊥ 0 Equation (10). nMMAxxByyCzz0000 ()()()0 (10) → →n MM0 = A(x x0) + B(y y0) + C(z z0) = 0 (10) The included angle between· the target− surface and− the coordinate− system plane can be expressed as EquationThe included (11) angle between the target surface and the coordinate system plane can be expressed as Equation (11)

mn→  → co s  m n cos θ = · (11(11)) mn  m→ →n · wwherehere m→m is is the the normal normal vector vector of of each each coordinate coordinate plane, plane, such such as asm→ mx,yxy,= ((0,0,1)0, 0, 1), ,m→ my,zyz, = ((1,0,0)1, 0, 0),, → mmxx,z,z = (0 (0, ,1 1, ,0 0 )..

(a) (b)

Figure 7. TargetTarget simulation modelmodel:: ( (aa)) normal normal vector vector of of target target surface surface;; ( (bb)) s shadowhadow area area of target calculated from the carrier position.position.

The target echo echo shadow shadow area area is is delineated delineated through through the the line line connecting connecting the the transmit transmit position position OO and the seabed as shown in Figure7 7b.b. TheThe pointspoints UU1––UU44 areare the the top top vertices vertices of of the the target and points L1––LL44 areare the bottom bottom vertices.vertices. Points Points A–D A–D are are subpoints subpoints of O ofthat connectthat connect the top the vertices top vertices and seabed. and seabed.The shadow The shadow area is definedarea is defined by the by linear the linear function functionl( ), which l() connects, which connects the transmit the transmit position positionO and · the and vertices, the vertices together, together with the with seabed. the seabed. Furthermore, Furthermore, when when the target the target is located is located on the on seabed,the seabed, the thebottom bottom side side also cannotalso cannot contribute contribute to the returnedto the returned echo. The echo. shadow The shadow area can area be analytically can be analytically described describedaccording according to the connection to the connection between the between sampling the positionsampling and position the vertices and the of vertices the target. of the We target. define the plane equation of side U4L4L3U3 as y = y1 and that of side U1L1L2U2 as y = y2, where y1 and y2 We define the plane equation of side U4L4L3U3 as yy and that of side U1L1L2U2 as yy , are constant to indicate the location of the target. The connection1 between the vertices and the origin2 wherevaries withy1 and diff erenty2 are synthetic constant positions to indicate and the forms location different of the shadow target. areas,The connection described between by Equation the vertices(12). The and synthetic the origin shadow varie areas with after different imaging synthetic is the intersection positions ofand the form shadows different areas formedshadow at areas each, describedsampling position,by Equation which (12). is The smaller synthetic than ashadow single-position area after shadow imaging is the intersection of the shadow areas formed at each sampling position, which is smaller than a single-position shadow   lL A < 0&lAB < 0&lBC < 0&lCL < 0&lL L < 0&lL L < 0, vt < y1  1 3 3 4 4 1  l < 0&l < 0&l < 0&l < 0&l < 0&l < 0, y < vt < y (12)  L1A AB BC CD DL4 L4L1 1 2  lL1L2 < 0&lL2B < 0&lBC < 0&lCD < 0&lDL4 < 0&lL4L1 < 0, vt > y2

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3.2. Imaging Algorithm for 2D MBSAS SAS imaging theory separates the detection area into diﬀerent pixel points. The time delay between the pixel points and the elements is compensated and the echoes accumulate coherently according to the array manifold. The 2D SAS image of the detection area, which only indicates the azimuth and range direction, can be obtained intuitively [21]. Single-element SAS processing is ﬁrst performed on the along-track. After that, the multi-element SAS signals are coherently accumulated to convert the multiple elements to a virtual single element. SAS processing of the received echo in the element space is undertaken to obtain the 2D SAS image according to Equation (13), where the center of the virtual array is the origin coordinates

Γ/2 −Z * 1 * * I( r ) = sr(t (t; r )), t) exp(j2π f t (t; r ))dt (13) Γ d 0 d Γ/2

* * * where td(t, r T) = 2 r (t) r T /c is the time-delay of the SAS echo, which is the vector expression of * − * τk(n); and r (t) is the vector of the carrier and r T is the vector of the target, which is processed in the * synthetic aperture period Γ. r (t) is the analytic vector in the 3D space and performs scalar in the range and time delay as r. The center frequency of the echo is expressed as f0, and B is the bandwidth of the LFM echo. The single-element imaging output of SAS processing is shown in Equation (14), which has been solved analytically [22]

2 f0 (y yT)vΓ 2B 4π f0 I(y, r) = sin c( q − ) sin c( (r rT)) exp(j (r rT)) (14) c 2 2 · c − · c − (y yT) + r − After traversing all the elements, the 2D transducer array is converted to a virtual ULA on the across-track, which is similar to a conventional MBES system. On the across-track, beamforming is conducted to estimate the echo direction of arrival (DOA). The full-scan 3D imaging result is achieved as Equation (15), and the Taylor expansion is employed to simplify the formula

N 1 ( 2Nπdx ( )) P 2 f0 (y yT )vΓ B sin λ sin θ sin θT ( ) = − ( + ( ) ) ( − ) ( 2 ( )) − II y, r, θ I y, r cτ n , n sin c c q sin c c r rT 2πdx 2 2 sin( (sin θ sin θT )) n=0 ≈ (y yT ) +r · − · λ (15) − − (N 1)πdx(sin θ sin θT ) exp(j( 4π (r r ) + − − )) · λ − T λ th where τ(n) = sin θ nd/c is the n time delay of the element. The average element spacing dx and the · number of elements N indicates the manifold of the designed transducer array; λ is the wavelength of the echo, and d = λ/2 as designed; and θ is the preset beam angle and θT is the beam angle of the target. In the theory of sonar imaging, when the scanned point matches the target position, the echoes superpose most effectively. It is also shown in Equation (15) that the imaging output II(y, r, θ) is maximum when y = yT, r = rT, θ = θT. The output is the 3D image under the coordinates of y r θ, − − which is not obvious for detection. The image should be transmitted to the coordinates of x y z to − − produce the echo image on the across-track and along-track, and the depth direction. The image points are transmitted uniformly according to x = r sin θ, z = r cos θ. MBSAS images show the energy output in 3D space, while in actual situations, we pay more attention to detecting of the time of arrival (TOA) of the preformed angles. Accurate TOA estimated from noised echoes is also the thinning of the detailed sonar image. Target detection plays a more important role in the field of engineering [23]. The output of MBSAS beamforming contains phase information that could be employed for TOA estimation. General energy-based detection methods such as weighted mean time (WMT) and phase difference methods such as the split beam and multi-subarray (MSA) algorithms can also be introduced in MBSAS detection theory, which is similar to the MBES detection system [24,25]. Remote Sens. 2019, 11, x FOR PEER REVIEW 12 of 22 subarray (MSA) algorithms can also be introduced in MBSAS detection theory, which is similar to Remote Sens. 2019, 11, 2615 12 of 22 the MBES detection system [24,25].

3.3. Simulation Simulation To evaluateevaluate thethe performanceperformance of of the the MBSAS MBSAS modeling modeling and and the the imaging imaging algorithm, algorithm, simulations simulations are areundertaken undertaken according according to the to echo the modelecho model we designed we de insigned Figure in1 .Figure First, plane 1. First, targets plane are targets simulated. are Wesimulated. locate dozens We locate of independent dozens of independent highlights on high the samelights depth on the plane, same which depth can plane, more which directly can indicate more directlythe performance indicate ofthe the performance MBSAS imaging of the algorithm, MBSAS im especiallyaging algorithm, on the along-track. especially The on mainthe along-track. parameters Theare shownmain parameters in Table1. Aare virtual shown receiving in Table array1. A virtual with an receiving aperture array of 4 m with is generated an aperture through of 4 m the is processing.generated through The across-track the processing. is defined The as across-track the direction is ofdefined x and theas the along-track direction as of y. x and the along- track as y. Table 1. Transducer array and target parameters Table 1. Transducer array and target parameters Parameter Value Parameter Value Echo frequency 150 kHz SignalEcho bandwidth frequency 150 20 kHz kHz SignalPulse bandwidth width 20 10kHz ms PulseDepth width 10 10ms m HighlightDepth spacing 10 15 m cm Highlight spacing 15 cm Figure8 8 compares compares di differentfferent imaging imaging results. results. The Th trajectorye trajectory and positionand position of the of element the element are shown are shownin Figure in 8Figurea, showing 8a, showing that we that locate we locate 25 highlights 25 highlights on theon the same same depth depth plane plane with with 15 15 cm cm spacing.spacing. DifferentDifferent imagingimaging algorithms algorithms are are used used to to compare compar thee the results. results. Figure Figure8b shows 8b shows the SAS the imaging SAS imaging result, withresult, the with same the number same number of elements, of elements, which can which separate can separate the target the location targeton location the along-track. on the along-track. However, However,the SAS theory the SAS can theory only obtain can only the 2Dobtain image, the so2D thatimage, the so actual that locationthe actual on location the across-track on the across-track is replaced withis replaced range. with Moreover, range. theMoreover, size of thethe targetsize of on the the target along-track on the along-track is seriously is distorted seriously with distorted a reduced with aenergy reduced focusing energy ability.focusing Figure ability.8c Figure indicates 8c indicates that the aliasingthat the aliasing problem problem damaged damaged the validity the validity of the ofimaging the imaging result obtainedresult obtained via MBES, via which MBES, was whic defocusedh was defocused seriously onseriously the along-track. on the along-track. Moreover, Moreover,the energy the leaking energy to leaking the side to lobethe side also lobe affected also affected the beamforming the beamforming processing processing on the on across-track. the across- Althoughtrack. Although the targets the targets can be separated,can be separated, false peaks false appear peaks and appear the energyand the focusing energy abilityfocusing decreases ability decreasesseriously. Theseriously. number The of number targets andof targets locations and of lo highlightscations of are highlights mixed. Forare comparison,mixed. For comparison, the imaging theresult imaging obtained result via obtained MBSAS isvia shown MBSAS in Figureis shown8d. in The Figure targets 8d.can The be targets separated can be on separated the along-track on the withalong-track constant with resolution. constant resolution. Beamforming Beamforming on the across-track on the across-track achieves the achieves same resolutionthe same resolution as MBES, whichas MBES, also which recognizes also therecognizes targets. MBSASthe targets. also MBSA achievesS also higher achieves energy higher focusing energy ability, focusing owing toability, more owingecho superposition. to more echo superposition.

(a) (b)

Figure 8. Cont.

Remote Sens. 2019, 11, 2615 13 of 22 Remote Sens. 2019, 11, x FOR PEER REVIEW 13 of 22

Figure 8. ComparisonComparison between between imaging algorithms: ( (aa)) target target set set and and position position of of carrier; carrier; ( (b)) imaging imaging result viavia SAS SAS algorithm; algorithm; (c) ( imagingc) imaging result result via MBES via MBES algorithm; algorithm; (d) imaging (d) imaging result via result MBSAS via algorithm. MBSAS algorithm. The image above is also sliced and shown on the across-track and along-track to observe the resolution.The image The above beamforming is also sliced on the and along-track shown on of the MBSAS across-track is similar and to along-track that of MBES, to observe so we canthe resolution.evaluate the The results beamforming under one angleon the coordinate. along-track The of SAS MBSAS image is is similar under theto coordinatesthat of MBES, of y so rwe, which can − cannot be compared with the MBES and MBSAS system on the across-track. Figure9a indicatesy that− r evaluate the results under one angle coordinate. The SAS image is under the coordinates of , whicheven if cannot the targets be compared can be separated with the by MBES MBES and on MBSAS the across-track, system on some the across-track. false peaks appear. Figure The9a indicates sidelobe thatlevels even were if damagedthe targets by can the be mixed separated echo from by MBES the along-track. on the across-track, MBSAS imaging some false reveals peaks the appear. beam width The of the array and separates the multiple targets by θ 3dB, which has the same target resolution on the sidelobe levels were damaged by the mixed echo from− the along-track. MBSAS imaging reveals the across-track as conventional MBES. The resolution on the along-track of MBSAS does not vary with beam width of the array and separates the multiple targets by θ− , which has the same target the beam angle, and we focus more on the constant resolution in engineering3dB situations. Therefore, the resolutionimaging resolution on the across-track on the along-track as conventional is sliced underMBES. Cartesian The resolution coordinates. on the Italong-track is shown in of Figure MBSAS9b doesthat thenot resolutionvary with ofthe MBES beam decreases angle, and substantially we focus more with on increasing the constant beam resolution angle and in cannot engineering easily situations.separate the Therefore, multiple targets.the imaging SAS imagingresolution has on constant the along-track resolution is sliced on the under along-track Cartesian that coordinates. can separate Itthe is targets.shown in However, Figure 9b the that SAS the has resolution a low ability of MBES to estimate decreases the DOA substantially on the across-track, with increasing so that beam the anglemixed and echo cannot reduces easily the separate sidelobe the level multiple of the image.targets. TheSAS MBSAS imaging imaging has constant is slice resolution performed on with the along-trackconstant high that resolution, can separate which the hastargets. the sameHowever, ability the as SAS SAS. has The a low multiple ability targets to estimate can bethe separated DOA on theclearly across-track, with high so energy that the focusing mixed ability,echo reduces given thethe narrowsidelobe main level lobe of the width image. and The low MBSAS sidelobe imaging level. isRemote slice Sens. performed 2019, 11, x FORwith PEER constant REVIEW high resolution, which has the same ability as SAS. The multiple14 of 23 targets can be separated clearly with high energy focusing ability, given the narrow main lobe width and low sidelobe level.

(a) (b) (a) (b) Figure 9.9. Comparison ofof sliced sliced imaging imaging output: output: resolution resolution on on (a) the(a) the across-track across-track and (andb) the (b along-track.) the along- Figuretrack. 9. Comparison of sliced imaging output: resolution on (a) the across-track and (b) the along- track.After that, a solid target is simulated to evaluate the performance of diﬀerent imaging algorithms in theAfter 3D space. that, a Assuming solid target that is simulated there is a solidto evaluate target locatedthe performance in a detection of different area divided imaging into algorithms hundreds inof the highlights,After 3D space that, and .a Assum solid the targeting distance that is simulated there between is a solid to the evaluate target highlights locatedthe performance is in 0.3 a mdetection on of the different area across-track, divided imaging into 0.1 algorithms hundreds m on the inof thehighlights 3D space., and Assuming the distance that betweenthere is a the solid highlights target located is 0.3 min oan detection the across area-track, divided 0.1 m into on thehundreds along- oftrack highlights,, and 0.2 andm in the the distance depth direction between, therethe highlights are 125 echo is 0.3 highlights m on the across-track,located in the 0.1 detection m on the area. along- To evaluate the validity of the model, the target is first briefly simulated while ignoring the shadows and seabed, according to the designed 2D MBSAS model and the referred imaging theory. The imaging result is the full 3D detection of the scanned area. Therefore, the sonar image is prospectively sliced to evaluate the performance of the MBSAS imaging algorithm. The simulation parameters are listed in Table 2.

Table 2. Transducer array and cube target parameters

Parameter Value Echo frequency 150 kHz Signal bandwidth 20 kHz Pulse width 10 ms Target size (x, y, z) 1.2 m0.4 m0.8 m Target separation distance (x, y, z) 30 cm10 cm20 cm Figure 10a shows the image achieved by the MBES imaging algorithm. The positions and number of targets on the along-track cannot be identified, as such detection is limited by the beam footprint. Moreover, due to echo aliasing throughout the whole space, the sliced perspective image is severely defocused, which introduces false targets. Figure 10b indicates the image achieved by the MBSAS imaging algorithm. The targets can be effectively recognized with high contrast. The image slices show that the targets can also be identified in detail in 3D space, as shown. Targets located at the vertical bottom area can still be detected, rather than detecting gaps as in the SAS image. Moreover, the MBSAS image has a better echo energy focusing ability than MBES, owing to the array gain of the 2D planar transducer array. The simulation results indicate that the model and the imaging algorithm of MBSAS can effectively improve the resolution of MBES without gaps.

Remote Sens. 2019, 11, 2615 14 of 22 along-track, and 0.2 m in the depth direction, there are 125 echo highlights located in the detection area. To evaluate the validity of the model, the target is ﬁrst brieﬂy simulated while ignoring the shadows and seabed, according to the designed 2D MBSAS model and the referred imaging theory. The imaging result is the full 3D detection of the scanned area. Therefore, the sonar image is prospectively sliced to evaluate the performance of the MBSAS imaging algorithm. The simulation parameters are listed in Table2.

Table 2. Transducer array and cube target parameters.

Parameter Value Echo frequency 150 kHz Signal bandwidth 20 kHz Pulse width 10 ms Target size (x, y, z) 1.2 m 0.4 m 0.8 m × × Target separation distance (x, y, z) 30 cm 10 cm 20 cm × ×

Figure 10a shows the image achieved by the MBES imaging algorithm. The positions and number of targets on the along-track cannot be identified, as such detection is limited by the beam footprint. Moreover, due to echo aliasing throughout the whole space, the sliced perspective image is severely defocused, which introduces false targets. Figure 10b indicates the image achieved by the MBSAS imaging algorithm. The targets can be effectively recognized with high contrast. The image slices show that the targets can also be identified in detail in 3D space, as shown. Targets located at the vertical bottom area can still be detected, rather than detecting gaps as in the SAS image. Moreover, the MBSAS image has a better echo energy focusing ability than MBES, owing to the array gain of the 2D planar transducer array. The simulation results indicate that the model and the imaging algorithm of MBSAS can effectively improve the resolution of MBES without gaps. Remote Sens. 2019, 11, x FOR PEER REVIEW 15 of 23

(a) (b)

Figure 10.10. ComparisonComparison of of 3D 3D imaging imaging algorithms: algorithms: sliced sliced view view of (a of) MBES (a) MBES image image and (b and) MBSAS (b) MBSAS image. image. To evaluate the performance of the modeling of targets with shadows, a detailed simulation is conductedTo evaluate under the the performance parameters shownof the modeling in Table3 of. Atargets cube targetwith shadows, is located a ondetailed the seabed simulation with ais shadowconducted area. under The the echo parameters signal is accumulated shown in Table in the 3. 2DA cube transducer target arrayis located according on the to seabed the designed with a arrayshadow manifold area. The and echo the syntheticsignal is accumulated position. MBSAS in the imaging 2D transducer and target array detection according based to the on thedesigned phase diarrayﬀerence manifold method and are the undertaken. synthetic position. MBSAS imaging and target detection based on the phase difference method are undertaken.

Table 3. Simulation parameters for target with shadows

Parameter Value Target size (x, y, z) 2 m0.8 m2 m Target separation distance (x, y, z) 0.1 m0.1 m0.1 m Seabed separation distance (x, y) 0.2 m0.4 m Cube center location (x, y, z) (5, 2, –9) Synthetic aperture size 4 m The target highlights and shadow area are simulated, where the shadows vary as the transducer array sails along the trajectory. The target obstructs the echo and forms the shadows area on the designed seabed. The shadow area forms according to the line connecting the transmit position and the seabed at different view positions, as shown in Figure 11a–c. The shadow area has center symmetry on the whole moving trajectory. The synthetic shadows area is the intersection of the shadows formed at each sampling position and is smaller than a single-position shadow. The synthetic shadow area is constant and does not change with the sampling position, which can effectively demonstrate the location of the target. The synthetic shadow shown in Figure 11d is smaller than a single-position shadow area. The carrier moving trajectory and the location of the receiving elements at different sampling moments are also shown in the figure. The center of the array is regarded as the origin, which limits the line connecting the transducer array and the seabed.

Remote Sens. 2019, 11, 2615 15 of 22

Table 3. Simulation parameters for target with shadows.

Parameter Value Target size (x, y, z) 2 m 0.8 m 2 m × × Target separation distance (x, y, z) 0.1 m 0.1 m 0.1 m × × Seabed separation distance (x, y) 0.2 m 0.4 m × Cube center location (x, y, z) (5, 2, –9) Synthetic aperture size 4 m

The target highlights and shadow area are simulated, where the shadows vary as the transducer array sails along the trajectory. The target obstructs the echo and forms the shadows area on the designed seabed. The shadow area forms according to the line connecting the transmit position and the seabed at different view positions, as shown in Figure 11a–c. The shadow area has center symmetry on the whole moving trajectory. The synthetic shadows area is the intersection of the shadows formed at each sampling position and is smaller than a single-position shadow. The synthetic shadow area is constant and does not change with the sampling position, which can effectively demonstrate the location of the target. The synthetic shadow shown in Figure 11d is smaller than a single-position shadow area. The carrier moving trajectory and the location of the receiving elements at different sampling moments are also shown in the figure. The center of the array is regarded as the origin, which limits the line connecting the transducer array and the seabed. Remote Sens. 2019, 11, x FOR PEER REVIEW 16 of 23

(a) (b)

FigureFigure 11. Target 11. Target and and shadow shadow areas areas at at di differentfferent viewingviewing positions: positions: shadows shadows at the at the(a) start (a) start viewing viewing position; (b) middle viewing position; (c) end viewing position; and (d) final synthetic shadow area. position; (b) middle viewing position; (c) end viewing position; and (d) final synthetic shadow area. Three cube targets are also simulated to evaluate the performance of distinguishing adjusted Three cube targets are also simulated to evaluate the performance of distinguishing adjusted targets. We locate the cube targets on both sides and the right bottom of the trajectory. The targets targets.and Wethe locateshadow the area cube are targetsconsidered on in both the sidesmodel and to reveal the right their bottommutual influences. of the trajectory. The targets The are targets and theindependent shadow areaof each are other, considered and their in position the models are to parallel reveal and their progressive. mutual influences. The image Theis sliced targets as are independentshown in ofFigure each 12 other,, where and the theirtargets positions and the shadows are parallel are marked. and progressive. The image is sliced as shown in Figure 12, where the targets and the shadows are marked.

(a) (b)

Figure 12. Simulation of three adjusted targets: (a) imaging output of the targets; (b) perspective- sliced image from the bottom view.

The sliced image is shown in Figure 12a. The adjusted targets can be separated after MBSAS image processing as marked. Then, the 3D image is sliced in the bottom view, which can indicate the shadows and the seabed in more detail. The targets in Figure 12b match the MBSAS imaging result. The seabed and shadows are the same as calculated in Equation (12). The cube bottom on the seabed

Remote Sens. 2019, 11, x FOR PEER REVIEW 16 of 23

(a) (b)

Figure 11. Target and shadow areas at different viewing positions: shadows at the (a) start viewing position; (b) middle viewing position; (c) end viewing position; and (d) final synthetic shadow area.

Three cube targets are also simulated to evaluate the performance of distinguishing adjusted targets. We locate the cube targets on both sides and the right bottom of the trajectory. The targets and the shadow area are considered in the model to reveal their mutual influences. The targets are independentRemote Sens. 2019 of, 11 each, 2615 other, and their positions are parallel and progressive. The image is sliced16 of as 22 shown in Figure 12, where the targets and the shadows are marked.

(a) (b)

FigureFigure 12. Simulation ofof threethree adjusted adjusted targets: targets (a: )(a imaging) imaging output output of theof targets;the targets (b); perspective-sliced (b) perspective- slicedimage image from thefrom bottom the bottom view. view.

TheThe sliced sliced image is shown in Figure 12a. The The adjusted adjusted targets targets can can be be separated after after MBSAS imageimage processing processing as as marked. marked. Then, Then, the the 3D 3D image image is is sliced sliced in in the the bottom bottom view, view, which which can can indicate indicate the the shadowsshadows and and the the sea seabedbed in in more more detail. detail. The The targets targets in in Figure Figure 1212bb match match the the MBSAS MBSAS imaging imaging result. result. TheThe seabed and shadows areare thethe samesame asas calculatedcalculated in in Equation Equation (12). (12). The The cube cube bottom bottom on on the the seabed seabed is not highlighted because the bottom is not illuminated by echoes. Furthermore, the targets directly below the trajectory do not generate shadows, as they are vertically irradiated. The adjusted targets can be recognized eﬀectively with high resolution according to MBSAS theory. It is important to note that, limited by the beam width, the imaging resolution on the across-track inevitably decreases with increasing distance. Therefore, some high-resolution beamforming algorithms used on the across-track, such as minimum variance distortionless response (MVDR) and deconvolved beamforming, should be researched further but are not the focus of this paper [26,27].

4. Instrument Design and Experimental Results The MBSAS principle prototype was designed and produced to verify the novel theory proposed. The instrument is designed according to the 2D transducer array manifold with 128 sampling channels. Dozens of high-speed operational ampliﬁers (OAs) and analog to digital converter (ADCs) are employed by FPGA to acquire the echo signal. The total amount of data uploaded to the processing unit is up to 1.15 Gbit/s, owing to the hundreds of elements and a high sampling rate. The data transmission rate is a bottleneck of system application that downsampling and reducing sample length methods are employed to coordinate with the processing unit. The MBSAS prototype system is shown in Figure 13a, and a control unit is also designed to manage the data and supply the power. The performance of the proposed modeling and imaging algorithm was evaluated through a designed tank experiment. An anechoic tank was employed to undertake the experimental research. The accurate trajectory of the MBSAS transducer array should also be strictly guaranteed. Therefore, a four degree of freedom (DOF) automatic rotation device was employed to move the transducer array to the designed sampling position. The experiment site, MBSAS transducer array, and targets to be detected are shown in Figure 13b. In this tank experiment, we designed the 2D array to move from 70 cm to 70 cm to synthesize a − virtual receiving transducer array whose aperture is equal to 140 cm. The echo in eight sampling positions was synthesized with a step of 20 cm. The main parameters of the echo signal are shown in Table4. First, we located a single 13 cm diameter solid ball in the experimental tank. To compare with the resolution of the MBES imaging algorithm, we should locate the target from a long distance. Therefore, the range between the targets and the transducer array was approximately 13 m. Thus, the footprint of the beam on the along-track was approximately 40 cm, which is much larger than the actual size that Remote Sens. 2019, 11, x FOR PEER REVIEW 17 of 23

is not highlighted because the bottom is not illuminated by echoes. Furthermore, the targets directly below the trajectory do not generate shadows, as they are vertically irradiated. The adjusted targets can be recognized effectively with high resolution according to MBSAS theory. It is important to note that, limited by the beam width, the imaging resolution on the across-track inevitably decreases with increasing distance. Therefore, some high-resolution beamforming algorithms used on the across- track, such as minimum variance distortionless response (MVDR) and deconvolved beamforming, should be researched further but are not the focus of this paper [26,27].

4. Instrument Design and Experimental Results The MBSAS principle prototype was designed and produced to verify the novel theory proposed. The instrument is designed according to the 2D transducer array manifold with 128 sampling channels. Dozens of high-speed operational amplifiers (OAs) and analog to digital converter (ADCs) are employed by FPGA to acquire the echo signal. The total amount of data uploaded to the processing unit is up to 1.15 Gbit/s, owing to the hundreds of elements and a high sampling rate. The data transmission rate is a bottleneck of system application that downsampling and reducing sample length methods are employed to coordinate with the processing unit. The MBSAS prototype system is shown in Figure 13a, and a control unit is also designed to manage the data and supply the power. The performance of the proposed modeling and imaging Remotealgorithm Sens. 2019 ,was11, 2615 evaluated through a designed tank experiment. An anechoic tank was employed to17 of 22 undertake the experimental research. The accurate trajectory of the MBSAS transducer array should also be strictly guaranteed. Therefore, a four degree of freedom (DOF) automatic rotation device was the actualemployed target to size move cannot the transducer be recognized. array to The the constant designed resolution sampling on position. the along-track The experiment of MBSAS site, was approximatelyMBSAS transducer 8 cm, limited array, and by thetargets actual to be aperture detected ofare the shown transmitter. in Figure 13b.

(a) (b)

Figure 13. Experimental site and targets to be detected: (a) MBSAS principle prototype used in the Figure 13. Experimental site and targets to be detected: (a) MBSAS principle prototype used in the experiment; (b) experimental site and targets. experiment; (b) experimental site and targets.

In this tank experiment,Table we 4. designedMain parameters the 2D array for MBSASto move experiment. from –70 cm to 70 cm to synthesize a virtual receiving transducer array whose aperture is equal to 140 cm. The echo in eight sampling positions was synthesized with a stepParameter of 20 cm. The main parameters of Valuethe echo signal are shown in RemoteTable Sens. 4. 2019, 11, x FOR PEER REVIEWEcho frequency 150 kHz 18 of 23 Signal bandwidth 20 kHz TableSampling 4. Main parameters rate for MBSAS experiment 600 kHz SyntheticPulse width aperture size 101.4 ms m First, we located a single 13Transmitter cm diameterParameter size solid ball in the experimental 16Value cm tank. To compare with the resolution of theReceiver MBES aperture imaging onEcho algorithm along-track frequency/,across-track we should locate 44the150 cm target/ 16kHz cm from a long distance. DetectionSignal distance bandwidth 20 13 kHz m Therefore, the range between Syntheticthe targets aperture and the size transducer array was ap 1.4proximately m 13 m. Thus, the footprint of the beam on the along-trackSampling was rate approximately 40 cm, which600 kHz is much larger than the actual size that the actual target size cannotPulse width be recognized . The constant10 resolution ms on the along-track of MBSASThe imaging was approximately output in Figure 8 cm, 14Transmitter limited shows by that sizethe the actual target aperture is located of the16 only transmitter.cm in the center beam on the across-track,The imaging which output is similarlyReceiver in Figure aperture limited 14 showson by along the that beam-track the footprint./ targetacross -istrack located Therefore, 44 onlycm /16 wein cm the display center the beam image on underthe theacross coordinate-track, which system is ofsimilarlyy r. Figure limitedDetecti 14 byaon the shows distance beam the footprint. MBES image Therefore, where13 we m the display actual the size image of the under target − isthe magniﬁed. coordinate The system actual of position yr . Figure of the 14 preseta shows target the MBES is also image falsely where indicated. the actual The size resolution of the target on the along-trackis magnified. decreases The actual substantially position of with the increasingpreset target range. is also Furthermore, falsely indicated. echo energyThe resolution aliasing on disturbs the thealong beamforming-track decreases on the substanti across-trackally with where increasing the false range. target Furthermore, occurs in echo the image.energy aliasing As a comparison, disturbs Figurethe beamforming 14b shows the on MBSAS the across image-track indicating where the the false actual target size occurs and location in the image. of thetarget. As a comparison, Moreover,the noiseFigure is suppressed 14b shows the well, MBSAS which image clears indicating the background the actual of size the image.and location MBSAS of the also target. increases Moreover, the echo energythe noise focusing is suppressed ability, which well, iswhich a great clears beneﬁt the background to high-resolution of the image. sonar. MBSAS also increases the echo energy focusing ability, which is a great benefit to high-resolution sonar.

(a) (b)

FigureFigure 14. 14.Imaging Imaging output output andand targettarget sizesize comparison: imaging imaging results results from from (a) ( aMBES) MBES of ofthe the middle middle beam,beam, and and (b ()b MBSAS) MBSAS of of the the middle middle beam.beam.

Second, we located a cube target with a side length of 30 cm in the tank experiment. The imaging result of the conventional side scan sonar system is shown in Figure 15a. Limited by the footprint on the along-track, the actual size of the target cannot be effectively recognized where the echo mixed seriously. The SAS processing is taken as a comparison to identify the actual size of the target on the along-track. In Figure 15b we can see that a peak highlight is obvious in the position where we located the target. The effective echo lasted for a long period on the along-track and some suspected sidelobe peaks appear with a low energy contrast. The imaging result on the along-track can indicate the size of the target through the width of the main lobe. However, the imaging of the side scan sonar and the SAS can only achieve the 2D result, which just indicate the position of the target on the along- track and range direction. The imaging algorithms are also disturbed by the echo from the across- track as the cube target also has an actual size on the across-track. Therefore, we should employ the 3D view image to identify the position and size in the whole space.

Remote Sens. 2019, 11, 2615 18 of 22

Second, we located a cube target with a side length of 30 cm in the tank experiment. The imaging result of the conventional side scan sonar system is shown in Figure 15a. Limited by the footprint on the along-track, the actual size of the target cannot be eﬀectively recognized where the echo mixed seriously. The SAS processing is taken as a comparison to identify the actual size of the target on the along-track. In Figure 15b we can see that a peak highlight is obvious in the position where we located the target. The eﬀective echo lasted for a long period on the along-track and some suspected sidelobe peaks appear with a low energy contrast. The imaging result on the along-track can indicate the size of the target through the width of the main lobe. However, the imaging of the side scan sonar and the SAS can only achieve the 2D result, which just indicate the position of the target on the along-track and range direction. The imaging algorithms are also disturbed by the echo from the across-track as the cube target also has an actual size on the across-track. Therefore, we should employ the 3D view imageRemote to Sens. identify 2019, 11 the, x FOR position PEER REVIEW and size in the whole space. 19 of 23

(a) (b)

Figure 15. Comparison of imaging algorithms: cube target imaging results via (a) side-scan sonar; (b) Figure 15. Comparison of imaging algorithms: cube target imaging results via (a) side-scan sonar; SAS; (c) MBES; and (d) MBSAS. (b) SAS; (c) MBES; and (d) MBSAS. The MBES imaging algorithm generates 3D detection in the whole space, as shown in Figure 15c. The MBES imaging algorithm generates 3D detection in the whole space, as shown in Figure 15c. The 3D image is also sliced in the depth direction to show the resolution on the across-track and The 3D image is also sliced in the depth direction to show the resolution on the across-track and along-track. It is obvious that the position is recognized effectively, and the size of the target on the along-track. It is obvious that the position is recognized eﬀectively, and the size of the target on the along-track and across-track is larger than the actual one, which is limited by the footprint in the two along-trackdirections. andThe across-trackbeamforming isprocessing larger than can the increase actual the one, resolution which ison limited the along by-track, the footprint but it is not in the twounlimited. directions. We Thealso beamformingemploy MBSAS processing imaging processing can increase to achieve the resolution a more detailed on the along-track,result as shown but it isin not Figure unlimited. 15d. Synthetic We also aperture employ MBSASprocessing imaging is taken processing on the along to achieve-track and a morebeamforming detailed on result the as shownacross in-track Figure that 15 obtaind. Synthetic a 3D detection aperture processingresult. Three is highlights taken on the appear along-track on the andalong beamforming-track, which on theindicate across-track not only that the obtain position a 3D, but detection also the result.size of Threethe target highlights with a appearhigh energy on the focusing along-track, ability which, as indicatethe size not designed only the. position,The echo but is separatedalso the size by of the the beamforming target with a onhigh the energy across focusing-track, so ability, that theas the sizehighlights designed. on Thethe along echo is-track separated are independent. by the beamforming on the across-track, so that the highlights on the along-trackTo evaluate are the independent. ability of MBSAS imaging to separate adjusted targets, dual solid ball targets are located to test the resolution of the imaging algorithm. The diameter of a single ball is 13 cm, and the distance between the sphere centers is 20 cm. The imaging output of MBSAS indicates the positions of the targets in the 3D space. The image is sliced on the top of the target plane to show the detailed resolution of MBSAS. Figure 16a shows the result of MBES imaging, which cannot separate the dual balls, owing to the limit of the beam footprint. Echo aliasing occurs in the beam-space and is difficult to observe in the image. The beam width and sidelobe of the MBES algorithm also disturb the actual shape imaging in the detection area. Figure 16b shows the imaging result of the MBSAS algorithm. Dual balls are separated effectively by actual size with a constant resolution that ignores the beam width and range. Furthermore, the echo energy focusing ability is clearly enhanced.

Remote Sens. 2019, 11, 2615 19 of 22

To evaluate the ability of MBSAS imaging to separate adjusted targets, dual solid ball targets are located to test the resolution of the imaging algorithm. The diameter of a single ball is 13 cm, and the distance between the sphere centers is 20 cm. The imaging output of MBSAS indicates the positions of the targets in the 3D space. The image is sliced on the top of the target plane to show the detailed resolution of MBSAS. Figure 16a shows the result of MBES imaging, which cannot separate the dual balls, owing to the limit of the beam footprint. Echo aliasing occurs in the beam-space and is diﬃcult to observe in the image. The beam width and sidelobe of the MBES algorithm also disturb the actual shape imaging in the detection area. Figure 16b shows the imaging result of the MBSAS algorithm. Dual balls are separated eﬀectively by actual size with a constant resolution that ignores the beam Remotewidth Sens. and 2019 range., 11, x Furthermore,FOR PEER REVIEW the echo energy focusing ability is clearly enhanced. 20 of 23

(a) (b)

FigureFigure 16. 16. ComparisonComparison of of imaging imaging algorithms: algorithms: dual dual ball ball imaging imaging slice slice of of ( (aa)) MBES MBES and and ( (bb)) MBSAS. MBSAS.

5.5. Discussion Discussion

5.1.5.1. Advantages Advantages of of MBSAS MBSAS as as an an Imaging Imaging System System MBESMBES and and SAS SAS are are widely widely employed employed as as the the major major imaging imaging sonar sonar systems systems in in the the application application of of cables,cables, unexploded unexploded ordnance, ordnance, seabed seabed mapping, mapping, harbor harbor security security,, and and gas detecting. Many Many mature mature productsproducts have have been been provided provided to to users, users, such such as as Kongsberg Kongsberg EM EM 2040, 2040, RESON RESON SeaBat SeaBat 7125 7125 (MBES) (MBES),, KongsbergKongsberg HISASHISAS 1030, 1030, and and Kraken Kraken AQUAPIX AQUAPIX (SAS). (SAS). Practical Practical technologies technologies have also ha beenve also proposed been proposedto improve to theimprove performance the performance of SAS, such of SAS, as the such multi-subarray as the multi-subarray SAS or interferometric SAS or interferometric synthetic syntheticaperture sonaraperture (InSAS). sonarNevertheless, (InSAS). Nevertheless, limited by limited the detection by the principle, detection shortcomings principle, shortcoming of the systemss of theare systems also obvious. are also SAS obvious. systems SAS obtain systems a constant obtain along-track a constant resolutionalong-track but resolution have to equip but have an additional to equip anMBES additional as a gap MBES filler as to a detectgap filler the to area detect just the below area thejust carrier, below whichthe carrier, is limited which by is thelimited transducer by the transducerdirectivity. directivity. The accuracy The of accuracy the height of the information height information is lower than is lower MBES, tha throughn MBES, thethrough fewer the elements fewer elementsphase di ffphaseerence difference or the inversion or the inversion algorithms. algorithm MBESs. technology MBES technology is also greatly is also developedgreatly developed that the thatdetailed the detailed images imag performes perform a benefit a benefit for target for target surveying, surveying, such assuch the as function the function of water of water column, column, dual dualswath, swath, and and snippet snippet side side scan. scan. Although Although MBES MBES can can achieve achieve a a full-scan full-scan image image withwith a high accuracy accuracy heightheight estimation, estimation, the the along along-track-track resolution resolution decreases decreases seriously seriously with with the increasing distance distance.. MBSASMBSAS is a a novelnovel MBES MBES technology technology attempting attempting to combineto combine the benefits the benefit of MBESs of MBESand SAS. and MBSAS SAS. MBSAScan achieve can achieve a 3D full-scan a 3D full detection-scan detection without with extraout gap extra filler. gap Dozens filler. orDozens even hundredsor even hundreds of elements of elementson the across-track on the across guarantees-track guarantees high-resolution high-resolution beamforming beamf andorming supply and thesupply detailed the detailed water column water columnimage, together image, together with an accuratewith an target accurate depth target estimation. depth Syntheticestimation. aperture Synthetic algorithm aperture processing algorithm on processingthe along-track on the off ersalong a constant-track offers resolution a constant as SAS resolution and the 2D as transducerSAS and the array 2D also transducer introduces array obvious also introducesarray gain. obvious Therefore, array MBSAS gain. Therefore, performs aMBSAS potential performs device thata potential achieves device a 3D that full-scan achieve imagings a 3D full with- scana high-resolution. imaging with a high-resolution.

5.2. Foresight and Limiting Condictons of the Application of MBSAS MBSAS system combines the benefits of MBES and SAS but also partly limited by the theory of them. Especially for the SAS theory, the moving speed of the carrier and the motion estimation and compensation problem inevitably affect the imaging performance. Usually, the moving speed is limited by the max range of the sonar and the target should be illuminated at least on the edge of each footprint. The echo coherence must be guaranteed that we take the SAS processing in a single synthesized aperture period. In the actual applications, we do not need to guarantee no grating lobe at the whole area that we just take the imaging at the narrow area just below the array. The bandwidth of the LFM can also increase the sampling interval on the along-track that the moving speed of the carrier can be improved to meet the engineering applications. Owing to the design of the transducer array and the processing scheme of our MBSAS, we can achieve a 1.6 m/s moving speed of the carrier that meets most applications.

Remote Sens. 2019, 11, 2615 20 of 22

5.2. Foresight and Limiting Condictons of the Application of MBSAS MBSAS system combines the benefits of MBES and SAS but also partly limited by the theory of them. Especially for the SAS theory, the moving speed of the carrier and the motion estimation and compensation problem inevitably affect the imaging performance. Usually, the moving speed is limited by the max range of the sonar and the target should be illuminated at least on the edge of each footprint. The echo coherence must be guaranteed that we take the SAS processing in a single synthesized aperture period. In the actual applications, we do not need to guarantee no grating lobe at the whole area that we just take the imaging at the narrow area just below the array. The bandwidth of the LFM can also increase the sampling interval on the along-track that the moving speed of the carrier can be improved to meet the engineering applications. Owing to the design of the transducer array and the processing scheme of our MBSAS, we can achieve a 1.6 m/s moving speed of the carrier that meets most applications. Current MBES can usually be mounted on the surface vessel but can also be carried by AUV with the water-pressure resistance transducer array, such as the SeaBat 7125. MBSAS system can also be equipped by the surface vessel and the AUV system. An ideal moving trajectory cannot always be maintained which is inevitably influenced by wind and waves. Carrier’s motion error must be estimated and compensated to manage the image defocusing problem. The surface vessel can supply accurate motion information through the high precision sensors, such as the compass and the aided GPS, also help to improve the correctness of the motion parameters. The accuracy of the sensors is enough to the MBSAS imaging proposed above, especially for the structure of point by point imaging algorithm that we can calculate each element’s actual position. AUVs surveying in the deep water have a more stable working condition than the surface vessel. Although the application of GPS is limited underwater, USBL, DVL, INS, and compass are also optional sensors that can supply the motion parameters, which are widely equipped by AUVs such as HUGIN 1000. Compensation algorithms based on target echo or images, such as phase gradient autofocus (PGA) and displaced phase center (DPC) algorithms are also useful methods to manage the motion mismatch problem. They use the correlation of the echo overlapping phase center or focused iterative method to estimate the motion error of the carrier. Therefore, the moving trajectory of the carrier can be compensated that the practical application of MBSAS is possible. MBSAS performs as a novel MBES with a higher along-track resolution that the application scenarios contain not only the traditional functions and purpose as water column, fish school, seabed surveying, but also the detailed imaging such as pipeline detecting, bottom target, and even the gas detecting. The flexible carriers including the surface vessel and the AUVs also expanded the application areas of MBSAS that it may become a new trend of imaging sonar. We have finished the modeling, target simulation, and imaging algorithm study as above and working for the motion estimation and field experiment in further research.

6. Conclusions In this paper, we propose a novel underwater acoustic imaging scheme to improve the imaging performance of MBES, based on the complementarity of MBES and SAS systems. The MBSAS system is designed to enhance the performance of conventional underwater imaging instruments. The main research focuses on the complete theory of MBSAS, including the modeling, processing scheme, prototype design, target simulation, imaging algorithms, and experiment. The basic echo model of MBSAS and the processing scheme of the imaging system are analyzed and designed to meet engineering applications. A target with shadow area simulation approach is introduced according to the designed 2D array manifold. We also propose an imaging algorithm integrating the theories of MBES and SAS that provides high 3D full-scan resolution. The simulation results indicate that MBSAS can achieve higher resolution on the along-track than MBES. In addition, MBSAS overcomes the disadvantages of SAS and obtains 3D images with no gap problems. We can achieve more detailed Remote Sens. 2019, 11, 2615 21 of 22 acoustic images by this approach than via the MBES system. A principle prototype of MBSAS is designed and produced to verify the novel theory proposed. The feasibility and performance of the MBSAS modeling method and proposed imaging algorithm are demonstrated through a tank experiment. The experimental results indicate that MBSAS imaging can obtain constant resolution on the along-track. The MBSAS imaging method effectively separates adjusted targets with higher energy focusing ability, which is a great benefit to high-resolution sonar imaging systems. The MBSAS system will become a new trend in imaging sonar that can be widely employed in the field of underwater observation and detection. High resolution imaging algorithms and fast imaging schemes should be researched further to obtain more detailed 3D underwater acoustic images. Increasing the surveying efficiency through transducer array design and processing algorithms is a precondition of the wide extension of MBSAS. Designing and producing a practical detection instrument with powerful real-time processing ability is also an important foundation for engineering applications and large scene detection of MBSAS, based on the theoretical research above.

Author Contributions: Conceptualization, B.W. and T.Z.; Methodology, B.W. and H.L.; Software, B.W. and S.X.; Investigation, B.W. and T.Z.; Resources, H.L.; Writing—original draft preparation, B.W.; Writing—review and editing, B.W., H.L., T.Z., and S.X.; Visualization, B.Z. and S.X.; Supervision, T.Z. and H.L.; Project administration, T.Z.; Funding acquisition, H.L. Funding: This work was funded by the National Natural Science Foundation of China under grant No. U1709203, 41606115, and 41376103; the National Key Research and Development Program of China under grant No. 2017YFC0306000; and the China State Shipbuilding Corporation Joint Foundation for Equipment Pre-Research under grant No. 6141B04060802. Acknowledgments: The authors would like to thank the anonymous reviewers and editors for their constructive comments and suggestions. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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