CIRCULAR SYNTHETIC APERTURE SONAR WITHOUT A BEACON

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1 CIRCULAR SYNTHETIC APERTURE SONAR WITHOUT A BEACON Hayden J Callow a, Roy E Hanen a, Stig A Synne a, Tortein O Sæbø a a Norwegian Defence Reearch Etablihment, P O Box 25, NO-2027 Kjeller, Norway Contact author: Hayden Callow, Norwegian Defence Reearch Etablihment, P O Box 25, NO-2027 Kjeller, Norway, fax: , Hayden-John.Callow@ffi.no Abtract: Collection of ynthetic aperture onar (SAS) data along a circular track and forming a circular SAS (CSAS) image ha everal benefit over traditional tripmap SAS: the area of interet i oberved from all apect angle giving a better perception; the reolution in the image increae and hadow zone are avoided. Navigation requirement however, become even more tringent than for rectilinear SAS. Previouly, CSAS image have been formed through ue of an underwater beacon to alleviate the navigation problem. We preent a cheme whereby CSAS may be achieved without ue of a beacon. In thi paper, we calculate the required accuracy in navigation, bathymetry and ound velocity for ucceful circular SAS. We preent a new proceing chain for CSAS with modification to micronavigation and autofocu. Modification to micronavigation and autofocu have not previouly been dicued in the literature. Finally, we how the reult from the new proceing chain with circular SAS image of mall target. Thee data have been collected over an arbitrary eafloor by the HUGIN autonomou underwater vehicle carrying the Kongberg HISAS A a reult of thee invetigation we conclude that CSAS without beacon ue i feaible for benign imaging geometrie. Image interpretation however become more challenging. In addition we found that relative height wa of coniderable importance, with challenging topographic feature cauing degradation. To combat thi we propoe a hybrid autofocu / interferometry ytem to treat the height etimation problem in an iterative framework. Keyword: ynthetic aperture onar, circular SAS, bathymetry, height-map

2 (a) (b) Fig.1: (a) circular SAS geometry. (b) Moaic of idecan imagery, circle radiu i approximately 70 m and relative depth 10m below the onar. 1. INTRODUCTION Circular ynthetic aperture onar (CSAS) can be ueful for identification of underwater object a cattering feature are collected a wide range of view-angle. In addition, there i potential for a large improvement in image reolution. The combination of high-reolution imagery and the ability to meaure variation in the cattering trength a a function of viewangle increae the information content. For example, many feature on a target have trong angular dependence mooth urface give high backcatter in the pecular direction and little echo in other direction. Information of thi type offer the poibility of meauring urface orientation, roughne and poibly penetration into object urface. CSAS however, i very difficult to implement in practice becaue SAS motion and environmental contraint increae dramatically (ee ection 2, [1, Chapter 7]). Depite thi, the poible benefit to target-identification provide incentive enough to attempt CSAS. Example of CSAS from the literature include [2] and [3]. Whilt impreive, the reult have been obtained through ue of navigation beacon placed inide or near the imaging cene [3] or tationary experimental etup [2]. Ue of beacon in the cene of interet olve many problem but limit the uefulne of the method. There are no publihed reult to the author knowledge that implement ucceful CSAS without ue of additional navigation beacon. We preent a SAS proceing chain intended to provide CSAS imagery without ue of a beacon. In ection 2 we give background to the CSAS imaging problem and preent navigation, ound-peed and topographical accuracy contraint. We preent modified micronavigation and autofocu method in ection 3.1, 3.2 and 3.3. Reult and an analyi of the on-going work follow in ection 4, through 6.

3 (a) (b) (c) Fig 2:. 20 cm by 20 cm ynthetic coherent CSAS image of a ingle-point catterer at 70 m range and 10 m depth relative to the onar. Image are diplayed in log intenity with 50 db dynamic range from peak. (a) No error. (b) height error of 10 cm. (c) ound-peed error of 1.5m/ 2. CIRCULAR SAS CONSTRAINTS Circular SAS ha much tighter motion and environmental contraint than traditional ynthetic aperture imagery. Thi i due to the violation of along-track cylinder-ymmetry aumption that are allowable in tripmap SAS [4]. Thu to prevent lo of phae-coherence, coherent imaging mut be accurate to λ/8 over the entire circular aperture. For a 100 khz SAS, for example, even λ/4 require better than 3 mm poition accuracy and 0.06 m/ oundpeed accuracy. Becaue of the non-traight aperture path, relative bathymetry i alo required. In the previou example, for a target at 70 m range and 10 m below the onar require a height accuracy of about 5 cm. To demontrate the effect of imilar error in imaging geometry we have imulated a mall cene containing a ingle point catterer on the ea-floor at 28 m with a 10 m relative depth from a model HISAS-1030 SAS. Reult are preented in fig. 2. The firt image (2a) i of the cene without induced error. Image reolution i at pixel reolution and Airy pattern idelobe taper rapidly to below -50 db. In the econd and third image (2b-2c) we have deliberately ued inaccurate imaging parameter, in thi cae a height error of 10 cm and a ound-peed error of 1.5 m/ repectively. The reult of uing incorrect parameter i to limit real image reolution to the ize of the 2-way lant-plane range error. In both cae the reolution i everely degraded. Slowly-varying navigation error will caue a geometrical degradation effect imilar to that hown above. Incorrect imaging parameter caue ignificant reolution degradation in addition to that uffered though inaccurate navigation. However, a noted in Carrara [5, Chapter 5], rapidly varying navigation-error will caue increaingly evere degradation. 3. METHOD A hown in ection 2, lant-range to the cene need to be accurately known. Beacon meaurement along-with accurate bathymetry i able to provide lant-range to ub-millimetre accuracy. Our goal i to duplicate thi accuracy uing the onar data itelf.

4 3.1. Micronavigation Uing the definition in [6] we regard micronavigation a operating on redundant element and autofocu a operating on cene redundancy. Mot SAS micronavigation cheme aume a quai-linear ping-to-ping movement with little angular change. For CSAS thee aumption are invalid and mut be altered. We have implemented a variant of the diplace ping imaging autofocu (DPIA) algorithm [7] whereby all ping-to-ping image are beamformed onto a common image grid fixed in global poition. A the inertial navigation ytem (INS) provide accurate meaure of ping-to-ping diplacement thi information i ued in the beamforming tep to remove geometrical inaccuracie. We firt form an interferogram from image f ( p, and f ( p 1, from redundant element in adjacent ping and noted that it phae x, x ) i related to poition error via with * f ( p, f ( p 1, 2k r( x, x, x ) ( ( x, x ) (1) 0 r x, x, x ) ( x x ) ( x x ) ( x x x ) ( x x x ) (2) ( where x x, y, z i the image coordinate, k0 2 fc / c frequency of the received echo and, c, ound-peed and x, y, z, where f c, i the center-of-ma x i the average poition of the overlapping element for ping p and, x, i the unknown diplacement from ping p to ping p+1. We olve for the unknown x uing an iterative earch method where the difference between predicted and meaure interferogram 2 ( x, x, x ) ( meaured (3) i minimized with repect to x. For every pair of ping a new interferogram i created and the earch run again. The pair-wie etimate of x are then integrated p x ˆ ( p) x( p) (4) 0 to give a navigation error etimate x ˆ ( p) which i ued to correct the INS-provided navigation olution Image correlation Even after the micronavigation ha been ued, the navigation ytem uffer drift. To aid navigation and improve total image focu we have choen to employ technique baed in autofocu. Due to the lack of common autofocu method for circular geometrie we choe to ue non-coherent image correlation to generate a navigation olution. The method i related

5 to multi-aperture map-drift [5, Chapter 6.2] and operate by aligning image from ubaperture. The intenity image from each individual ub-aperture i, f ( i,, i 2D cro-correlated with all other image f ( giving Y ( i, ) f ( i, f ( (5) where the peak-location in Y ( i, ) a a function of 2D lag give the image hift xˆ ( i, j) and repreented cro-correlation. In the current implementation, we weight individual correlation by a modified ignal-to-noie ratio w and multiply by the curvature of the crocorrelation function at it peak. Thu from each image-pair, a ingle etimate of movement in x and y i obtained, along with a weighting in each direction w. To etimate the relative poition of each image, we ue a weighted leat-quare olution for poition. Thi i accomplihed by forming difference equation in matrix form [5, page. 258], A for each image pair and uing a peudo-invere via x T 1 T et y( A wa) wa (6) with y xˆ ( i, j) and weight w. Traditionally in map-drift the movement between image i aigned to a linear-phae error (which caue along-track image diplacement). Thi i neceary for generating coherent CSAS imagery. Intead we ue the x et etimate to hift ub-aperture image and combine them incoherently. Thi i a clear weakne in the method and we aim to provide navigation etimate in future work Height-map correlation A the HISAS-1030 i an interferometric SAS, we alo have the poibility of running ub-aperture height-map correlation. Ue of height map for the ub-aperture-image alignment provide a redundant ource of information. Whilt operating in imilar fahion to image correlation, height-map correlation ha an important advantage: height-map look the ame from all direction and are obtainable in cene containing only peckle (within peckle induced height-map noie). Normally thee type of cene caue de-correlation in map-drift and provide no ueful information. In addition, height-map comparion allow traightforward meaurement of vertical diplacement, omething very challenging in image-baed correlation. We generate the height-map correlation function Y ( i, ) via the ad-hoc Y ( i, ) b( i, b( b( i, b( (7) where b(i, i the complex interferogram created from ub-aperture i. The ret of the method proceed a for image correlation.

6 4. RESULTS We have implemeted a time-domain beamformer to generate imagery on the graphic proceor unit (GPU). The GPU-baed beamformer operate between time fater than it C language equivalent on a Compaq 8510W laptop with an NVIDIA quadro FX 570M. Thi allow traight-forward (and fat) beamforming of acoutic data onto an arbitrary imaging grid. For the reult preented here, we ued a data-et collected at 180 m depth in the area outide of Horten, Norway with the HISAS-1030 onar. The data collection wa obtained on January 17, 2008 with the Hugin 1000-MR [4] a the carrier platform. The cene of interet contain 2115 ping of 32-element multiple-receiver SAS data in a circle around an unidentified object. The data pan 540 degree of circle with a radiu of approximately 70 m. Due to the difficulty of keeping a table long-term track for the 8 minute circle-duration the overlapping circle region i offet by 1-2 metre. A chematic of the cene i hown in fig. 1. We aumed that the navigation i accurate enough on hort time cale to obtain the HISAS-1030 theoretical trip-map reolution of 2 cm by 2 cm. We then made 30 image, each containing 71 ping paced uniformly over 540 degree 18 degree of angular coverage for each image. Each ub-aperture image ha a theoretical reolution of approximately 2 cm by 2 cm and at 1024 by 1024 pixel cover jut over 20 m by 20 m. All image are proceed onto a flat ground-plane at the average ea-floor depth m. (a) (b) (c) (d) Fig. 3: Incoherent CSAS image, log intenity with 35 db dynamic range from peak: (a) original INS navigation, (b) after micronavigation, (c) after micronavigation and image correlation, (d) after micronavigation and height-map correlation.

7 (a) (b) (c) Fig 4: Etimated navigation error. Blue repreent northing, green eating, and red depth all in metre:(a) micronavigation etimated error againt ping, (b) image correlation etimated error againt image number, (c) height-map correlation etimated error againt image number. All 30 image were then added incoherently to give a emi-coherent image for comparion imagery. The object of interet i not covered in the entire circular aperture. Lacking a full circular aperture coverage, we preume only incoherent imaging will work without cauing exceive ide-lobe. We made a reference image uing the navigation olution provided by the INS ytem onboard the collection AUV. Thi image i hown in fig. 3a. A oppoed to the image hown in fig. 2 we ee replica of the object. Thi i due to the uneven cene viibility noted above. Five to ten of the image cover only mall part of the cene thu intead of getting donut-like point-pread-function one get cene replica. Thee replica are widely diplaced in poition indicating large navigation-error. Uing the micronavigation technique outlined in ection 3.1 we generated a ping-by-ping navigation error etimate (ee fig. 4a) and ued thi to generate a new image hown in fig. 3b. We then ued the image-correlation correlation routine of ection 3.2 on the image obtained in fig. 3b the image hown in fig 3c i formed. The equivalent image when uing height-map correlation i hown in fig. 3d. Image poition error etimate from the method are hown in figure 4b and 4c a a function of image-number. 5. ANALYSIS Increaingly accurate incoherent image over thoe from INS navigation are available from micronavigation and image-correlation repectively. Height-map correlation alo improve the final reult, although it eem to not have the accuracy of image-correlation for thi data-et. Thi trait i perhap to be expected. Scattering trength in particular i trongly dependent on local lope of the cene. Imagery thu ha a large ignal at point of changing bathymetry and will a a conequence have better cro-correlation propertie. That aid, a better method for height-map correlation may provide a better navigation-error etimate. We etimate the total reolution of the bet reult (in fig. 3c) to be on the order of 10 cm. Given that all of the imagery i generated on a flat eafloor at m and the object i etimated from height-map to be >0.4 m high, 10 cm accuracy correpond to that expected from the imaging height inaccuracy predicted in ection 2. A we have contrained the navigation to only cae where bathymetry i well known, our current technique can not get better accuracy. To olve thi problem, one need to form the image onto an accurate digital terrain map (DTM). Typically, DTM are not available in 2 cm by 2 cm reolution with 5 cm height-

8 accuracy. In order to generate uch a DTM, one need to ue SAS-generated height-map. In addition, each image need to be regitered accurately to the height-map for thi to work, alo a non-trivial undertaking. Overcoming thee limitation will probably require a combined height/navigation/ound-peed etimation procedure. 6. SUMMARY Uing micronavigation and autofocu we have produced a ueful incoherent CSAS image without a beacon over 540 degree of motion and for 20 degree coherent aperture. The wort-cae reolution of the image i approximately 10 cm. Obtained reolution i not contant throughout the image and i highly dependent on cene difference from the aumed height-map. We have hown that it i poible to ue height-map correlation a the bai for an independent navigation data-ource although on the dataet invetigated; the accuracy of image diplacement meaure wa poorer than with thoe generated from image amplitude. Future method hould concentrate on improving micronavigation accuracy to provide a better tarting point. We recommend combining ound-peed, relative-height and relativepoition etimation technique to olve the tight coupling between error in each domain in CSAS. A method of linking ub-aperture image diplacement and navigation error i alo trongly deirable in order to compare image correlation reult with micronavigation and allow image correlation to be ued for improving overall vehicle navigation. REFERENCES [1] M Soumekh, Synthetic Aperture Radar Signal Proceing, with MATLAB Algorithm, Wiley Intercience, 1999 [2] B G Ferguon, R J Wyber, Application of acoutic reflection tomography to onar imaging, The Journal of the Acoutical Society of America, 117(5), , [3] S K Mitchell, K N Scarbrough, S P Pitt, T L Kooi High Reolution Circular SAS with Controlled Focu, In The International Conference on Synthetic Aperture Sonar and Synthetic Aperture Radar, Lerici, Italy, September, [4] R E Hanen, H J Callow, T O Sæbø, S A Synne, P E Hagen, T G Foum, B Langli Synthetic Aperture Sonar in Challenging Environment: Reult from the HISAS 1030, In Underwater Acoutic Meaurement (in print) [5] W G Carrara, R S Goodman, R M Majewki, Spotlight Synthetic Aperture Radar Signal Proceing Algorithm, Artech Houe, 1995 [6] D Billon and M A Pinto. Some general conideration for ynthetic aperture onar deign. In Proceeding of the IEEE OCEANS'95 Conference, volume 3, page , 1995 [7] P T Gough, M A Miller, Diplaced ping imaging autofocu for a multi-hydrophone SAS, IEE Radar Sonar Navigation, 151(3), , 2004