3D Visualization of Radar Coverage Considering Electromagnetic Interference

Transcription

1 3D Visualizaion of adar Coverage Considering Elecromagneic Inerference HANG QIU,,3 LEI-TING CHEN,3 GUO-ING QIU CHUAN ZHOU,,3 School of Compuer Science & Engineering, Univeiy of Elecronic Science and Technology of China, Chengdu, CHINA School of Compuer Science, Univeiy of Noingham, Noingham, UNITED KINGDOM 3 rovincial Key Laboraory of Digial Meida, Chengdu, CHINA qiuhang@uesc.edu.cn Absrac: -adar plays an imporan role in many domains, such as arge searching, arge racking and dynamic obecs deecion. However, he elecromagneic informaion of radar is invisible and full of changes in real ime, which resrics use o plan and design he radar sysems. In recen yea, wih he developmen of ineracive visualizaion echnology, 3D visualizaion of he absrac informaion of radar coverage under he influence of complicaed environmen becomes a hospo. In his paper, we presen a mehod o represen radar coverage considering he elecromagneic inerference. Based on he radar equaion, from he pepecives of pich and azimuh angles o achieve 3D modeling of radar coverage hrough discree subdivision, and he radar model possesses self-adapabiliy o differen levels of deail. The 3D radar deecion range under he influence of elecromagneic inerference is analyzed and addressed based on radar amming model. Experimens demonsrae ha our mehod no only can efficienly complee he hree-dimensional modeling of radar, bu also visually show he rue radar coverage under he influence of complex elecromagneic environmen. Key-Words: - 3D visualizaion, radar coverage, levels of deail (LOD), elecromagneic inerference, nonuniform sampling Inroducion adar bea grea applicaion values in civil and miliary fields such as meeorological deecion, ocean waves measuring, air raffic conrol, and so on. adar uses elecromagneic waves o idenify range, aliude, direcion, or speed of boh moving and fixed obecs, including airplanes, ships, clouds, and invisible obsacles. A radar sysem has a ransmier ha emis microwaves or radio waves, which are emied in cerain phase and frequency. When he waves hi an obec, hey are scaered in all direcions and parly refleced back wih a sligh change of wavelengh if he arge is moving. The received signals can be amplified in he anenna configuraion and hen in he receiver o deec obecs a disance. adar s elecromagneic informaion is invisible and full of changes in real ime. The radiional D radar coverage diagrams drawn by hand or aimed by compue have some eviden shorages: D curve canno inuiively represen radar elecromagneic informaion; D radar coverage diagrams canno represen he effecs of amming coming from differen direcions or disance. In recen yea, exensive works [-4] made effo o express he radar elecromagneic informaion in hree-dimensions. Based on differen heories and applicaion purposes, he 3D visualizaion mehods for radar coverage can roughly be classified ino hree following caegories. () adar Equaion-based Mehod The principle of his mehod includes wo seps: fily, he radar s coverage is calculaed by employing he radar equaion. Secondly, according o he specific faco hose affec he radar coverage, such as errain occlusion, elecromagneic inerference and amospheric effecs, he model boundary poins are revised o achieve 3D visualizaion of coverage under differen circumsances. Based on radar equaion, Zhang e al. [5] implemened he 3D visualizaion of he search radar by using Malab and C program. Lin e al. [6] adop radar equaion o calculae verex coordinaes of lobe, and consruc 3D represenaion of radar deecion range. Above-menioned researches confine he radar elecromagneic environmen o pure free space, which has no regard o oher faco such as errain occlusion and amospheric effecs. Kosic e al. [7] and ancic e al. [8] considered heses environmenal influences and realized he 3D E-ISSN: Volume 0, 04

2 display of radar coverage by overlapping D deecion graph. Meng [9] applied radar equaion o represen 3D radar model in free space and implemened he influence of amosphere and errain by revising he boundary verices of he radar model. Based on his mehod, [0] presened novel revised algorihm under errain occlusion. Chen e al. [] proposed beam-drawing mehods in spaial domain, and presened corresponding model revised algorihm considering he influence of errain. Mos recenly, Yang e al. [] and Li e al. [3] designed and realized he represenaion of 3D elecromagneic siuaion for miliary applicaions. () arabolic Equaion-based Mehod The parabolic equaion-based mehod esimaes he paern propagaion facor by parabolic equaion fi, and hen calculaes he radar coverage by radar equaion. Neverheless, parabolic equaion-based mehod has high compuaion complexiy and i is no based on acual elecromoive paramee. Awadallah e al. [4] applied parabolic equaion o research radar-propagaion-model in hreedimension space. Yang e al. [5] considered he effec of mos real environmen faco wih parabolic equaion, and visualized he 3D radar maximum deecion range. (3) Advanced ropagaion Model-based Mehod In advanced propagaion model-based mehod, differen compuaional models are employed wih differen elecromagneism regions according o he propagaion aenuaion compuaional models. Alhough his mehod is faser han parabolic equaion-based mehod, i is very ime consuming and has relaively high demand on model precision. Based on advanced propagaion model, [6, 7] discussed he radar 3D visualizaion approaches in complicaed environmen. Chen e al. [8] pu forward GU-based hardware-acceleraed algorihm o handle wih he limied rendering speed. Zhang e al. [9] described he algorihm for 3D visualizaion of radar deecion range based on revised advanced propagaion model. In his paper, we presen a mehod for 3D visualizaion of radar coverage under he influence of elecromagneic inerference based on radar equaion. We focus on simulaing he essenial behaviou of radar and looking for he righ compromise beween realism and efficiency. The res of he paper is organized as follows. Secion briefly depics he radar-amming model. Secion 3 discusses he hybrid sampling-based radar 3D modeling mehod in free space. Secion 4 focuses on he specific implemenaion approach. Secion 5 gives he acceleraion sraegy for 3D visualizaion of radar. Secion 6 presens experimens o illuminae he performance of our mehod. The conclusion of his paper is given in Secion 7. The Model of adar Jamming The radar ha deecs in a fixed direcion wih specific pich (θ) and azimuh (φ) angles is deermined by Equaion (): / 4 GG rσλ F Fr (, ϕ) = 3 (4π ) r θ () where (θ, φ) is he disance beween radar source and he arge wih specified pich and azimuh angles. r is he receiving erminal power. is he ransmier power. G is he ransmiing anenna power gain. Gr depics he receiving anenna power gain. σ is he radar arge s cross secion. λ is wavelengh. F is paern propagaion facor from ransmiing anenna o he arge, and F r is paern propagaion facor from arge o he receiving anenna. aern propagaion faco F r andf are space coordinaes-relaed variables, which are funcions of he space-vecor (θ, φ). We only need o consider variables in his par and simplify he calculaion. Therefore, Equaion () can be rewrien as ( θ, ϕ) max F r ( θ, ϕ) F ( θ, ϕ) = () where max is he radar s maximum radiaion range in free space when F r and F are a he maximum, which equals o. The exising radar s ransmiing and receiving anennas are ofen he same anenna. So we can furher se F r = F. Then, he final equaion of radar range calculaion is: F( θ, ϕ) = (3) max In free space, radar elecromagneic waves ransmi in he form of spherical surfaces. The ouer surface is deermined by he range equaion above wih varying pich and azimuh angles. adar can be affeced by a variey of elecromagneic inerferences, such as sand-off amming, random amming, self-defense amming and so on. In his paper, we focus on sand-off amming. As shown in Fig., assume ha he ammer and radar are in saionary sae and he arge is a dynamic obec. The angle beween E-ISSN: Volume 0, 04

3 amming signal and he direcion of radar anenna is α. Fig. The principle of sand-off amming In general, when radar deecs or racks a arge, he main lobe of radar poins o he arge. A he same ime, in order o proec he arge, he anenna of ammer poins o radar, which plays he role of suppression. Therefore, here are wo signals received by he radar receiver, i.e. response signal from arge and amming signal from he r ammer. Based on he radar equaion, expressed as: G σλ 3 4 ( 4π ) can be = (4) is he radar ransmied power. anenna gain. σ depics radar cross secion. G is he is he disance beween radar and he arge. The amming signal r can be calculaed as: r G G λ γ ' ( 4π ) = (5) is he ransmied power of he ammer. G is he anenna gain. depics he disance beween ammer and radar. γ is he polarizaion coefficien. ' G is he radar anenna gain in he direcion of he ammer. According o he differen performance of radar, when he value of amming signal is far less han he value of response signal, he amming signal can be auomaically filered. However, when response signal conforms o a cerain relaionship wih amming signal, he receiver canno differeniae hese wo signals, which leads o he deviaion of radar deecion. To measure he performance of he amming effec and he ani-amming capabiliy, power crierion is usually applied, which depics he power relaionship beween response signal and amming signal in effecive amming siuaion. K is suppression coefficien ha can be expressed as follows: K = (6) s The value of suppression coefficien depends on he amming signal s modulaion and he ype of radar. The smaller he suppression coefficien is, he woe he ani-amming capabiliy is. For paricular radar and ammer, he suppression coefficien is fixed. According o Equaion (4), Equaion (5) and Equaion (6), he radar amming equaion can be expressed as follows: G G ' 4 r = G σ G 4πγ K When he power raio is greaer han suppression coefficien, he effecive amming is generaed. The space ha saisfies amming equaion is called suppressing zone. To calculae he effecive deecion range of radar under he siuaion of amming and visualize he boundary of radar sampling poins, we se he value of / equals o suppression coefficien K. Thus, he effecive deecion range of radar can be calculaed as: 4 K G σ = πγ 4 G G r (7) 0 (8) G is a variable, which relaed o he angle α beween amming signal and radar anenna, as shown in Fig.. According o he empirical formula of anenna gain, G ( α ) can be expressed as: G ( α) = G θ0.5 G ( α) = k G α θ0.5 G ( α) = k G 90 0 α θ θ 0.5 α 90 / α / According o he differen values of α, he curve of radar deecion range can be achieved, as shown in Fig.. (9) E-ISSN: Volume 0, 04

4 G n, ( α) = G θ0.5 G n, ( α) = k G α θ0.5 Gn, ( α) = k G 90 0 α θ θ 0.5 α 90 / α / () Fig. Schemaic diagram of proeced area The curve defines he effecive radar deecion range and he amming range of ammer. When he arge moves ino he shadow area ( / < K ), he amming signal canno suppress he response signal, and he arge can be deeced by radar. This area is called exposed area. When he arge leaves exposed area / > K ), he amming signal can suppress he ( r response signal, and he arge canno be deeced by radar. This area is called proeced area. When r / = K, 0 is he boundary beween proeced area and exposed area. From he viewpoin of ammer, 0 is he minimum amming disance, which usually called exposed radius. When muliple amming sources exis, he suppression of ammer in one paricular direcion can be equivalen o numeral superposiion of all he amme suppressions in his direcion. Thus, he amming equaion for muliple amming sources can be expressed as follows: G n n 4 r, k, k, k, i, π = (. k= r, s k= G σ k, γ 4 G. G k, r ) K (0) The boundary of exposed area can be calculaed as: 4 n k, Gk, γ k = K ( G σ k=, 4π G k.. G k,, ) () 3 Hybrid Sampling-based adar 3D Modeling in Free Space To visualize he radar coverage under he influence of elecromagneic inerference, we apply radar equaion-based mehod. Fily, we consider he 3D modeling of radar coverage in free space. Secondly, according o he model of radar amming, we revise he 3D model boundary poins o achieve he visualizaion of radar coverage under he influence of elecromagneic inerference. In his secion, we give deails of 3D modeling of radar coverage in free space. As menioned in Secion, radar elecromagneic waves ransmi in he form of spherical surfaces in free space. The ouer surface is deermined by he range equaion expressed by Equaion (3) wih varying pich and azimuh angles. Therefore, based on he idea of discree sampling and approximaion, he ouer boundary surface can be sampled by using he radar range equaion. Each discree vecor (θ, φ) and he deecion range ( θ, ϕ) ogeher forms a 3D poin (θ, φ, ). The discree boundary poins consiue he necessary grid for drawing he corresponding radar coverage for 3D visualizaion. As shown in Fig. 3, he radar elecromagneic waves form an ouer surface cenred a he radar ransmier/receiver, where θ and φ correspond o he radar s pich and azimuh angles respecively. G k, is a variable, which relaed o he angle α n beween nh amming signal and radar anenna. G ( α ) can be depiced as: n n Fig. 3 Schemaic diagram of he radar spherical coordinae sysem Assuming he radar model is scanning omnidirecional, he pich angle is in he range of [-90, E-ISSN: Volume 0, 04

5 90 ] and he azimuh angle is a circle in he range of [0, 360 ]. We dissec he whole sphere in pich and azimuh direcions. Azimuh dissecion: perpendicular o he plane of azimuh, he sphere is spli ino n slicesα n. Each slice corresponds o a azimuh angle ϕ. n ich dissecion: saring from he cenre of he radar, m veco are range-calculaed corresponding o a unique pich angleθ m. The issue boils down o how o deermine he angle sampling seps. Uniform sampling is a naural choice, as shown in Fig. 4. (a) ich angle sampling (b) Azimuh angle sampling Fig. 4 The uniform sampling mehod Uniform sampling is easy o implemen. However, some feaure poins on he radar beams may be los beween he sampling seps. Meanwhile, here are also many poins whose deecion range is 0, which lead o unnecessary calculaion. In his paper, we presen a hybrid sampling mehod: in he pich direcion, sampling is separaed ino subregions respecively based on he characerisics of he radar beams; in he azimuh direcion, sampling is in accordance wih errain resoluion, as discussed in deail below. 3. Azimuh Sampling In he azimuh direcion, sampling sep lengh is deermined by he errain revoluion, as shown in Fig. 5. he errain grid. The horizonal axis of he radar s coordinaes coincides wih one of he errain grid lines. The deecion range of he radar s maximum radiaion direcion max is aken as a radius o form a circle, which is used o obain he minimum square-shaped errain grid ABCD ha compleely cove he circle. The errain is divided ino n n grids wih he resoluion of β. Then, connecing he cenre and he square s border grids forms he ineecion poins and he azimuh sampling seps. The angle ϕn beween he adacen conneced lines is he acual azimuh sampling sep lengh. No maer wheher he peripheral grid is angenial o he circle or no, he angle divisions are symmeric along horizonal and verical direcions. Therefore, we only need o precompue /8 of he sampling direcions. Sep. Azimuh dissecion: he pre-compued sampling sep lenghs ϕn are used o accomplish discree dissecion. The number of dissecions is expressed as variable ieces, which will be used in he daa srucure discussed in following secion. The above-menioned mehod implemens oneo-one correspondence beween he radar s azimuh sampling and he errain grid, which improves selfadapabiliy of he radar model o differen errain resoluions. When discreizaion is compleed, he coninuous spherical shell is divided ino a number of veco. The vecor ( θ i, ϕ ), or simply i,, corresponds o he radar deecion range, which deermines a boundary poin θ, ϕ, ).Subsiuing each ( i i, direcion s corresponding vecor θ, ϕ ) ino ( i Equaion (3), we can obain he maximum deecion range corresponding o he vecor. As shown in Fig. 6, considering he exreme case, i. e. he radius of radar is smaller han he disance of adacen errain sampling poins, we sill can use 8 poins o represen he radar deecion range. Fig. 5 Deermine azimuh sampling sep lengh The procedure includes wo seps: Sep. re-compuing of sep lengh: The radar s cenre O is iniialized a some ineecion of Fig. 6 Azimuh angle sampling in special circumsance E-ISSN: Volume 0, 04

6 3. ich Sampling Mos of he radar coverage informaion is concenraed wihin he half-power lobe, i.e. beween wo 3dB aenuaion poins, as shown in Fig. 7. Sep. Calculaion of elevaion_sep We apply he proporional relaionship beween sampling sep lengh and curvaure radius o conver he sampling sep lengh in azimuh angle o elevaion_sep. The curvaure radius of curve in azimuh angle is. The curvaure radius of curve in pich angle is max changing. As shown in Fig. 8, we use he wo 3dB aenuaion poins B, C and he boundary poin of iniial pich angle o calculae he corresponding curvaure radius _elevaion. Fig. 7 Sub-regional sampling in pich angle Beyond his zone, here are many poins wih deecion ranges close o 0. Therefore, we apply 3dB aenuaion poins as boarder marke o divide radar coverage ino hree disinc areas in pich direcion, and sample hem separaely using wo differen mehods. The radar half-power beamwidh is defined as he degree of angle beween he wo 3dB aenuaion poins from he origin, by which wo 3dB aenuaion poins a pich angles ω andω can be deermined. As shown in Fig. 6, he farher away he range direcions are from he boundary lines hrough he wo 3dB aenuaion poins, he closer he range deecions are owards 0, hus fewer samplings are needed. Therefore, uniform sampling is employed wihin inerval[ ω, ω ] o guaranee ha he main feaure, shape, and resoluion of he radar deecion informaion are acquired. In he inerval [0, ω ) and ( ω,90 ], sampling seps are auomaically augmened according o he angle away from he boundary lines o he horizonal or verical axis. The specific sampling mehods are as follows: θ i+ θi + ( θi θ0 )/ m θi ω, θi < ω = θi + elevaion _ sep ω θi < ω (3) where θ i θ is he difference beween he pich 0 angle and he iniial elevaion angle. elevaion _ sep is he sep lengh when fully uniform sampling is employed. m is he proporional coefficien, which deermines variaion of sampling sep lengh. The number of sampling in pich angle direcion is indicaed as variable Laye. Equaion (3) is used o auomaically calculae corresponding acual number of sampling poins. The procedure includes hree seps: Fig. 8 Calculaion of curvaure radius The smaller he curvaure radius is, he smaller he sampling sep lengh is. Thus, he relaionship beween curvaure radius and sampling sep lengh in azimuh and pich angle can be expressed as: elevaion _ sep az _ sep _ elevaion k = (4) max Sep. Calculaion proporional coefficien m The value of m affecs he number of sampling poins and is value depends on elevaion_ sep. According o piecewise funcion, in order o achieve smooh ransiion beween uniform sampling zone and non-uniform sampling zone, he sampling sep lengh mus be coninuous in piecewise funcion. Assume ha he 3dB aenuaion poin ω is he piecewise poin of piecewise coninuous funcion. Thus, he m can be calculaed as: m θ0 ω elevaion_ sep = (5) Sep 3. ich dissecion u he value of elevaion_ sep and m ino Equaion (3), sampling sep lengh can be achieved. 4 The endering of adar 4. Discree-side endering As menioned in Secion, we dissec he whole sphere in pich and azimuh direcion. Thus, we E-ISSN: Volume 0, 04

7 apply an array FixBound [ Laye][ ieces] o sore each sampling poin s coordinaes in he radar coordinaes sysem, which is calculaed as: FixBound[ ]. x = _ max[ ] cosθ cosϕ FixBound[ ]. y = _ max[ ] sinθ (6) FixBound[ ]. z = _ max[ ] cosθ sinϕ Here we redefine an array Bound[ Laye][ ieces ] o sore each discree poin s coordinaes in he world coordinaes sysem as follows o improve he efficiency: FixBound[ ]. x = FixBound[ ] + posiion _ x FixBound[ ]. y = FixBound[ ] + posiion _ y (7) FixBound[ ]. z = FixBound[ ] + posiion _ z When he radar sysem is moving in he virual scene, he cener or origin changes, bu he coordinaes of boundary sampling poins remain he same, which are sored in he array FixBound beforehand. Accordingly, we only need o adus Bound o renew he coordinaes of boundary poins in he world coordinaes sysem. When he discree boundary poins are obained, he discree grid verices can be calculaed. In he azimuh direcion, he poins are conneced o form a coil according o heir posiions in he space, as shown in Fig. 9 (a). In he pich direcion, he poins are conneced o form a beam ring, as shown in Fig. 9 (b). Finally, we ge a gridded radar coverage mesh, as shown in Fig. 9 (c). (a) Azimuh angle sampling (C) Spaial drawing effec (b) ich angle sampling Fig. 9 adar coverage mesh as discree verices 4. Implemenaion of Jamming Effec We use coil in he azimuh direcion as he basic processing uni and apply amming equaion o calculae he posiion of each sampling poins in real ime. In each frame, we revise he poins o he exac posiion in he curve boundary as shown in Fig., and connec he discree poins o consruc mesh. To improve clariy, le us ake an example. Assume θ / < α 90, he specific seps are as follows. 0.5 < Sep. Invarian pre-compuaion Equaion (8) can be rewrien o Equaion (8) when all he paramee of radar and ammer are known. Where = α C 0 (8) G γ 4πKθ 0.5 C =. C is a invarian, GK σ which relaed o he paramee of radar, arge and ammer. Sep. Sampling poins revision in pich direcion According o he pich dissecion, differen pich angle corresponds o differen Azimuh coil. The sampling poins in a coil have he same pich angle. We can use Equaion (6) o calculae deecion range direcly. All he sampling poins in Azimuh coils are calculaed in sequence, and he final radar deecion boundary is achieved. Sep 3. Mesh consrucion of discree poins Connec he sampling poins in pich and azimuh direcion and consruc 3D mesh. 5 LOD-based Acceleraion Sraegy To show he deails of he radar coverage, a single radar model needs numerous poins o express. When he viewpoin is far away from he model, he employmen of high-resoluion model descripion is unnecessary. Our consideraion is o make he model s resoluion aduss auomaically according o he viewpoin orienaions. Our view-dependen model approach is as follows. The disance beween he viewpoin and he radar s cener is colleced in real-ime, which is used o decide he model s levels of deail. Blending is used for swiching beween levels of deail o achieve smooh ransiion, as shown in Fig. 0. Fig. 0 View-dependen level of deail When he disance beween viewpoin and radar cenre is ( 0 ~ k ), he level l = 0, and he original model resoluion is rendered. When he disance is ( k ~ k ), he level l =, and he simplified model is rendered. When he disance is ( k ~ k ), he level 3 E-ISSN: Volume 0, 04

8 l =, he simplified model based on level is rendered and so on. Assume ha he curren level is l, and he direcion of azimuh angle begins wih 0. The poins numbered m = l i ( i is posiive ineger, and m ieces ) are needed o render and he rendering l sep in azimuh angle is. () l = 0, all he poins are rendered, as shown in Fig. (a). () l =, i skips sampling poins, as shown in Fig. (b). (3) l =, i furher skips sampling poins based on medium resoluion model, as shown in Fig. (c). Fig. Model wih muliple levels of deail Theoreically, he procedures described above are endless. We se a hreshold o avoid he unlimied simplificaion of model. The discree levels of deail may make he ransiion visible. To avoid popping arifacs appearing, seamless ransiion scheme is indispensable. Assume ha he disance beween viewpoin and radar isdis, he whole area is divided ino n levels by he boundary poins k 0,k, k,k 3,,k n. We accomplish smooh ransiion by esablishing a ransiion zone beween each adacen levels. Transparency of he verices and lines in he ransiion zone changes wih disance. For level l, in he ransiion zone, he poins l + numbered i are needed o be rendered in level l + and he alpha values of hese poins are se. l The poins numbered (i + ) will be simplified in level l + and he corresponding alpha values can be calculaed as: fade = dis k k k l (9) l + Where dis kl depics he disance beween model and he ransiion zone. kl k is he lengh + l of he ransiion zone. l 6 Experimens and Discussions We use OpenGL on C++ plaform o implemen he mehod presened in his paper, and carry ou relaed experimens on C. The compuer configuraion used for experimens is Windows X operaing sysem, Inel enium 3.4 GHz CU, G memory, and ATI FireGLV300 graphics card. In he experimens, we selec Gaussian paern funcion commonly used in he radar equaion: k F = e θ ( k = 4ln θ b, where θ b is he beamwidh). The paramee of radar and ammer are shown in Table and Table respecively. arameer Name Transmied power Frequency Anenna gain Anenna side lobe gain ulse repeiion frequency Sysem loss Table. adar aramee Values 4000kw 3000MHz 40dB -0dBi 50HZ db robabiliy of deecion 0.9 robabiliy of false alarm 0-6 Verical beam widh 30 Elevaion 30 Anenna speed 36 /s Table. Jammer aramee arameer Name Transmied power Iniial disance Anenna gain Sysem loss Values 000kw 85km 5dB 7dB olarizaion coefficien Suppression coefficien To esify he advanage of radar modeling based on our hybrid sampling, we carried ou conras experimens beween our work and he pure-uniform sampling mehods [9, 0, ] wih he sampling paramee shown in Table 3. Table 3. Sampling aramee Uniform arameer Name Hybrid Sampling Sampling esoluion of Terrain 3km 3km 3km 3km Sampling sep in pich angle (rad) (rad) Sampling sep in azimuh angle π/ ~ (rad) Number of samplings in azimuh angle Number of samplings in azimuh angle Iniial pich angle π/6 π/6 E-ISSN: Volume 0, 04

9 Three-dimensional visualizaion performances of radar coverage by our mehod in differen environmens are shown in Fig. and Fig. 3. Fig. 3D visualizaion of radar coverage in free space (a) Single source inerference (b) Muli-source inerference Fig. 3 3D visualizaion of radar coverage under he influence of elecromagneic inerference To esify he performance of our mehod, fily, we consruc a scene, fix he viewpoin and esimae he maximum modeling capabiliies of he mehods above-menioned. Experimenal resul is shown in Fig. 4. rada is up o 05, hybrid sampling sill has 50 frames per second. We also carried ou a series of pressure ess on hese wo mehods wih rada scanning along pich angle and horizonal movemen in free space. The resuls are shown in Fig. 5 and Fig. 6. Fig. 4 ressure es of uniform and hybrid sampling s in free space Obviously, our mehod is more effecive han uniform sampling approach. When he number of Fig. 5 Comparison of he frame raes when rada are in pich scanning E-ISSN: Volume 0, 04

10 6 Conclusion Visualizaion of elecromagneic informaion is a research hospo in he field of scienific compuaion visualizaion. This paper presens a mehod for hree-dimensional visualizaion of radar coverage considering he elecromagneic inerference, which ensures invariabiliy of radar s feaure and shape while grealy cus he compuing expense. I is more pracical in real ime applicaions ha reflec radar coverage. Fig. 6 Comparison of he frame raes when rada in movemen To esify he efficiency of our LOD-based acceleraion sraegy, fily, we applied he paramee shown in Table 4 o consruc he full resoluion model of radar. Table 4. aramee lis arameer Name esoluion of errain Sampling sep in pich angle Sampling sep in azimuh angle Number of sampling in azimuh angle Number of sampling in pich angle Iniial pich angle Values 4000kw 3000MHz 40dB -0dBi 50HZ db Table 5 depics he number of sampling poins of differen levels of deail. Table 5. Number of sampling poins Level Number of sampling poins l = l = 6008 l = 8004 l = l = We rendered 0 rada in a scene. All he rada are in saionary sae, and he fly-hrough pah is predefined. We did wo groups of experimens wih and wihou LOD acceleraion sraegy. We sampled 5000 frames in each scene respecively, and achieved he average frame rae. The resuls are shown in Table 6. Table 6. Average rendering speed wih/wihou LOD LOD Sae on off Average rendering speed 73.9 fps 4.4 fps Acknowledgemen: The auho wish o hank he anonymous reviewe for heir horough review and highly appreciae he commens and suggesions, which significanly conribued o improving he qualiy of his paper. This work is suppored by Naional High Technology esearch and Developmen rogram of China (No. 0AA0503), roec on he Inegraion of Indusry, Educaion and esearch of Guangdong rovince (No. 0B ) and he pre-research proec (No ). eferences: [] Y. M. Lin, F. Zhang, W. Hu, A novel 3D visualizaion mehod of SA daa, In roc. adar03, Xi an, China, 03, pp. -4. [] D. Fernando, N. D. Kodikara, C. Keppiiyagama, 3D radar modeling virual mariime environmen for he saic environmen percepion, In roc. OBINONETICS 3, Yogyakara, Indonesia, 03, pp [3] Q. S. Mahdi, Modeling of 3D pencil beam radar (B) volume coverage and 3D DMC, In roc. LAC 0, Loughborough, UK, 00, pp [4] L. S. Yang, J. Xu, X. Gao, e al, A novel hreedimensional coverage visualizaion sysem of need rada based on ArcObecs, In roc. adar 09, Guilin, China, 009, pp. -5. [5] W. Zhang, B. L. Chen, S. H. Jin, The visual echnology of he deecion range in search radar, Modern adar, No.3, 000, pp (in Chinese) [6] W. M. Lin, D. Q. De, Three-dimensional display of radar survey scope using OpenGL echnique, Journal of Wuhan Univeiy of Technology, Vol.6, No., 00, pp (in Chinese) [7] A. Kosic, D. ancic, adar coverage analysis in virual GIS environmen, In roc. E-ISSN: Volume 0, 04

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