An Azimuth Antenna Pattern Estimation Method Based on Doppler Spectrum in SAR Ocean Images

Transcription

1 Aticle An Azimuth Antenna Patten Estimation Method Based on Dopple Spectum in SAR Ocean Images Hui Meng,,3, Xiaoqing Wang, * and Jinsong Chong,, * National Key Laboatoy o Science and Technology on Micowave Imaging, Beijing 9, China; menghui@mails.ucas.ac.cn Institute o Electonics, Chinese Academy o Sciences, Beijing 9, China 3 School o Electonics, Electical and Communication Engineeing, Univesity o Chinese Academy o Sciences, Beijing 9, China Institute o Micoelectonics o Chinese Academy o Sciences, Beijing 9, China * Coespondence: wangxiaoqing@ime.ac.cn (X.W.); lily@mail.ie.ac.cn (J.C.); Tel.: (X.W.); (J.C.) Received: 9 Januay 8; Accepted: Apil 8; Published: 3 Apil 8 Abstact: In synthetic apetue ada (SAR) ocean emote sensing, it is vey diicult to estimate an accuate azimuth antenna patten (AAP) om low-scatteing SAR images without stong scatteing tagets. Theeoe, an azimuth antenna patten estimation method based on Dopple spectum in SAR ocean images is poposed in this pape. In ode to peseve the complete AAP inomation, an azimuth unweighted matched ilte is used to e-image the SAR aw data in the poposed method. Then, the shape acto o AAP can be obtained by linea statistics o the elationship between Dopple cente and edge equency spectum in Dopple spectum o each distance gate. In addition, the impact o the uniomity and signal-to-noise atio o SAR ocean images on the estimation esults ae also analyzed by simulation. Finally, the easibility o poposed method is veiied by data om ERS- (Euopean emote sensing satellite (ERS) was the Euopean Space Agency s ist Eath-obseving satellite). Expeimental esults show that the AAP estimated by poposed method has a good estimation esult. Keywods: azimuth antenna patten; Dopple spectum; low-scatteing egion; SAR Ocean images. Intoduction In synthetic apetue ada (SAR) images, the accuate knowledge o the antenna pattens is o geat signiicance o pecise image pocessing and calibation []. Cuently, whethe aibone o spacebone SAR, azimuth antenna patten (AAP) monitoing is all mainly peomed by exploiting tanspondes [], which ae quite expensive to be deployed and maintained. Fo the cuent spacebone SAR, the antenna patten changes little and does not equie eal-time calibation. Fo aibone SAR, it is necessay to peom a e-calibation test in evey light expeiment, which makes it vey impotant to measue the eal-time values o the AAP. Theeoe, in ode to educe the complexity and cost o the antenna calibation, it is wothwhile to extact the accuate inomation o the antenna patten om SAR images. Cuently, seveal methods have been poposed o estimating the AAP om SAR images. Fo example, in 3, Guaniei, A.M. et al. [3,] poposed a method to estimate the AAP om a stong point taget in SAR images. In 7, Tan, H. et al. [5] poposed a new simulated method to estimate the AAP using a stong point taget. In this pape, the two-way AAP is estimated by applying the shot-time Fouie tansom to the oiginal echo o the stong taget. Fom to, Guccione, P. et al. [6 8] poposed a method to estimate the AAP using the pesistent stong point scattees. The tagets they use in this method have instead the ollowing two eatues: () multiple Sensos 8, 8, 8; doi:.339/s88

2 Sensos 8, 8, 8 o 8 images need to be collected in the same aea; () the stong scatteing tagets contained in the image should have spasity and time stability. The above methods o estimating AAP om SAR images all have one thing in common: that is, the SAR image used to estimate the antenna patten must contain at least one stong scatteing point taget with time stability. Howeve, when we estimate the AAP om SAR ocean images, thee is usually no stong scatteing taget with time stability. Theeoe, the methods above cannot wok. In ode to estimate the AAP moe conveniently om ocean SAR images, an AAP estimation method based on Dopple spectum in SAR ocean images is poposed in this pape. The pocedue o the poposed method is as ollows. Fistly, the elationship between the AAP and the Dopple spectum is deduced by analyzing the composition o the Dopple spectum o the SAR images. Secondly, the pope model paametes ae estimated via the elationship between Dopple cente spectum and edge spectum. Finally, the eal value o the AAP is calculated by substituting the estimated AAP paametes into the model. In addition, the accuacy o the estimated AAP is indiectly veiied by compaing the eal Dopple spectum with the Dopple spectum calculated by the estimated AAP. The est o this pape is oganized as ollows. Section gives the details o the methods and pinciples used in this method. In Section 3, simulation analysis o the applicability o the poposed method ae pesented. In Section, two eal SAR data ae used as examples o expeimental validation. Finally, conclusions ae pesented in Section 5.. Azimuth Antenna Patten Estimation Method Based on Dopple Spectum.. The Pinciple o the Poposed Method... Analysis o Dopple Spectum Composition Fom the SAR imaging theoy, it is well known that the shape o system noise, azimuthal ambiguity, and the backscatteing signal pesent dieent pattens in the Dopple spectum o the SAR aw signal (hee, it is supposed that the ange match ilteing and ange cell migation coection have been done), i.e., the system noise powe density is a cetain constant in the Dopple spectum, wheeas the shape o the Dopple spectum o the backscatteing signal and azimuthal ambiguity depend on the antenna patten: the backscatteing signal and azimuthal ambiguity coespond to the main lobe and side lobe espectively. Theeoe, the Dopple spectum o the SAR aw signal can be expessed as [9] n N E p, x, y x nd, y nd P nf () F x y a n whee x y ae the cente positions o the aea upon which the Fouie tansomation is applied; x y, and ae the coodinates in the light and look diections espectively, ees to the mathematic expectation, denotes the Dopple equency, and denotes the azimuth powe spectum o the SAR aw signal. Pa is the powe spectum unction o an ideal point taget with a db nomalized ada coss-section (NRCS), its shape is detemined by the two-way AAP. Futhe, is the Dopple centoid, ees to the pulse epeat equency o the SAR system, N is the intinsic noise loo o the SAR system, x ndx, y ndy F p E is the mean NRCS o the pixels located between x ndx L /, y nd y and x ndx L /, y nd y ( L is the data length o calculating the Dopple spectum), D x and D y ae the displacements between the position o the azimuth ambiguity signal and the eal taget position in the light and look diections, espectively. They can be witten as [] RF F R Dx, Dy () V V

3 Sensos 8, 8, 8 3 o 8 whee is the slant ange o the taget, is the ada wavelength, and is the velocity o the SAR platom. Geneally, in Equation (), among the azimuthal ambiguity signals, only the ist azimuth antenna side-lobes, which coespond to n = and, ae stong enough that cannot be omitted [9]. Hence, Equation () can be simpliied as R,,,, E p x y x y P x D y D P F N x Dx, y Dy Pa F F a x y a Equation (3) indicates that the shape o the aveaged powe spectum o backscatteing signal, azimuth ambiguity and system noise ae detemined by the AAP ( P a ) and... Methods and Solutions to Estimate the Antenna Patten om the Dopple Spectum D x In geneal, (o example, D y D x L D x I the data length o calculating the Dopple spectum is much lage than ) and SAR image scatteing intensity in the obsevation aea is elatively uniom, the xdx, y Dy and xdx, y Dy can be appoximated by whee Hence, Equation (3) becomes N / F x Dx, y Dy x Dx, y Dy x, y () E p x P P F P F a a a (5) F is the aveage o the noise. Hee, Equation (5) has been suiciently aveaged. Then, on the basis o Fomula (5), the deivation pocess o estimating the antenna patten om the SAR image is as ollows. can have multiple unknown paametes. Theeoe, we assume that the two-way AAP is Pa expessed as Pa ( ) Pa ( b, b,, bm, ) (6) whee b, b, b3,, b m epesent the paametes o AAP, m is the numbe o paamete. Howeve, in geneal, the numbe o the AAP paametes ae limited. The Gaussian model [] o the model [3,7,8] is chosen as the AAP model. The ideal antenna patten powe spectum is the sinc sinc model (o example, sinc L ant v, L ant is the antenna length) [7], especially o satellites such as ERS (Euopean emote sensing satellite (ERS) was the Euopean Space Agencys ist Eath-obseving satellite), RADARSAT (RADARSAT is a Canadian emote sensing Eath obsevation satellite pogam oveseen by the Canadian Space Agency), Envisat (Envionmental Satellite) and most o the aibone SAR. Theeoe, the applicability o this method is to estimate the AAP using the one paamete model as an example (in Appendix A, the method o estimating multi-paamete AAP will be given). The ollowing section will show how to estimate the AAP om a one-paamete estimation model. Since we ae studying a single-paamete AAP estimation method, let m =. It is ound though obsevation that Equation (5) can be simpliied as an equation containing only two unknowns, AAP and system noise. theeoe, the Equation (5) can be simpliied by choosing two dieent equency points in the Dopple spectum (o example, and ), then the ollowing linea elationship is deived out. whee N E p E p E p (7) F V N N. (3)

4 Sensos 8, 8, 8 o 8 Pa Pa F Pa F P P F P F P P F P F a a a a a a (8) Equation (7) indicates that the elationship between E p and E p E p is linea, in which the constant tem depends on the noise loo, and the linea coeicient depends on Pa [see Equation (8)]. Theoetically, i thee ae moe than two suiciently aveaged Dopple specta, and N moe pecise estimation o and selected to make E p E p N can be esolved by equation system (7). Moe Dopple specta will esult in a N. To incease the estimation pecision, as lage as possible while and should be E p as small as possible (in Appendix B, the inluence o Dopple equency point selection on AAP estimation accuacy is analyzed: that is why and F / ae selected in this pape). Ate estimating, Pa can be obtained uthe. in ode to simply the eading, the one paamete model is selected to estimate the AAP. Theeoe, the two-way AAP model chosen in this pape is shown as sinc whee, a can be solved by b 3 PRF/ asinc d 3 PRF/, Pa asinc b v b L ant is the scale acto [], equency. Substituting Equation (9) into Equation (8), Equation (8) becomes F 3 F asinc asinc b b F F 3F asinc asinc asinc b b b (9) is the Dopple () whee is the slope o the Equation (7), the ight side o Equation () is a unay unction o b. In geneal, the F s cove the ange o:.9b F.5b [], in this case, the above unction is monotonically inceasing. Theeoe, the acto b can be obtained om Equation () by dichotomy, and then model can be obtained by Equation (9). At the same time, the one-way AAP can be calculated out. Stictly speaking, P a P a depends on the slant ange o the taget: o example, α is a unction o the slant ange. In act, when the image scatteing value distibution is homogeneous, the dieences in α between dieent ange cells can be omitted. In many cases (such as the second example in Section ) the dieences in α between dieent ange cells cannot be omitted. Theeoe, the entie image can be divided into subsets, then α and can be estimated om the subset with homogeneous... Method Flow Chat and Summay P a The azimuthal matching iltes o the standad imaging algoithm o commecial SAR poducts ae geneally weighted iltes, which does not satisy the basic equiements o the poposed method (the AAP inomation o the single-look complex (SLC) image obtained ate weighted ilteing will be distoted). Theeoe, in ode to etain the complete AAP inomation, the ollowing steps ae taken: in the ist step, in SAR imaging, an unweighted azimuthal matching ilte must be applied to the SAR aw data, and the SLC image o SAR data is obtained. In the second step, the Dopple cente equency must be estimated om the SLC image. Then, the Dopple centoids o the SLC image can be shited to the zeo-equency. In the last step, the Dopple spectum is calculated once evey L pixels in the azimuthal data o each distance gate o the new SLC image. Then, the azimuth Dopple spectum obtained om each distance gate is aveaged sepaately to obtain a new ange-dopple image. By the statistics o the elationship between the Dopple cental equency and the edge equency in evey distance gate, the linea acto is obtained. Finally, the appopiate AAP model is chosen to estimate the AAP o the SAR image.

5 Sensos 8, 8, 8 5 o 8 The poposed method is summaized in Figue. SAR Raw Data 3. Estimate the AAP.SAR imaging Imaging algoithm (the azimuthal matching ilte should be an unweighted ilte) Calculate Dopple specta by all o the pixels o the entie single-look complex image SAR single-look complex image Dopple centoids o all ange cells Calculate P PF and P F o each spectum Apply Fouie tansomation in light diection Fit the linea elation between P PF and P F, and estimate the vaiables α and N in equation (7). Shit the Dopple centoids to zeo Shit the Dopple spectum centoid to zeo Apply invese Fouie tansomation in light diection AAP Model Use equation () to compute the spectum shape acto b α N Dopple-centoid-shited single-look complex image Pa() Figue. The low chat o the poposed method. SAR: synthetic apetue ada; AAP: azimuth antenna patten. 3. Simulation Analysis o the Applicability o the Poposed Method 3.. Paametes Settings o the Simulation In ode to satisy the appoximation o Equation (), the atio o the aveage NRCS o the ambiguous signal position to that o the tue taget position is chosen as.9 in this section. The simulation paametes ae shown in Table. Table. Paametes o the simulated data. Paametic Name Paametic Symbol Paametic Value Pulse epetition equency Numbe o Dopple spectum pixels Simulation epeat numbe F (Hz) Azi _ len 8 Repeat _ numbe 8 Look numbe o SAR image M Signal-to-Noise Ratio SNR 5 db AAP scale acto Ratio o the scatteing values o the blued signal and the eal taget position b x Dx, y Dy / x, y.89 F.9

6 P(-F/) Dopple spectum intensity Sensos 8, 8, 8 6 o Simulation Results Based on the paametes in Table, we can geneate simulation data o the Dopple powe spectum as shown in Figue. Dopple spectum intensity 6 x Dopple equency(hz) (a) 6 x Dopple equency(hz) (b) Figue. Simulated Dopple powe spectum. (a) Beoe multi-looking; (b) ate multi-looking. We assume that the simulated powe spectum is P, and then use the same method to geneate seveal Dopple powe specta to om a two-dimensional equency domain image. The statistical elationship between P P F / and P F / om this simulated two-dimensional image is shown in Figue 3. 7 x P()-P(-F/) x Figue 3. Relationship between P P F and P F o the simulated data. Fom Figue 3, it can be seen that the elationship between P P F and P F / is a linea elationship, appoximately. This esult validates the coectness o Equation (7). The vaiable in Equation (7) is the slope o the itted line in Figue 3. The scale acto b is calculated by the Equation (), and then the AAP can be obtained by substituting b into Equation (9). The compaison between the estimated two-way AAP and theoetical two-way AAP model is shown in Figue. In addition, by substituting the estimated AAP into Equation (3), the powe spectum can be obtained. The compaison chat between the estimated Dopple powe spectum and simulated one is shown in Figue 5.

7 Nomalized antenna gain(db) Sensos 8, 8, 8 7 o 8 - Theoetical model Poposed method Dopple equency(hz) Figue. The compaison between the estimated two-way AAP and theoetical two-way AAP model. Dopple spectum intensity 6 x 5 3 estimated powe spectum simulated powe spectum Figue 5. The compaison between the simulated powe spectum and estimated powe spectum. Figue 5 shows that the estimated Dopple powe spectum is vey close to the simulated oiginal powe spectum. This esult shows the easibility o the poposed method Peomance Analysis Dopple equency(hz) To uthe conim the eectiveness o the poposed method, 8 andom Monte Calo expeiments ae peomed. The mean and the oot mean squae eo (RMSE) o the estimated esults ae shown in Table. Table. The peomance analysis o the poposed method. Mean AAP Paametes RMSE Real Value Estimated Value b/ F Fom Table, it can be seen that the mean o the estimated value is vey close to the eal value, and that the RMSE o the paamete estimation achieved by the poposed method is athe low. The esults show that the poposed method is vey accuate.

8 The RMSE o estimated b/f Sensos 8, 8, 8 8 o Applicability Analysis o the Poposed Method The inluence o the uniomity o SAR image intensity and signal-to-noise atio (SNR) on the estimation accuacy is mainly analyzed in this Section The Inluence o SAR Image Uniomity on Estimation esults In ode to satisy the appoximation o Equation (), the SAR ocean image intensity used to estimate the antenna patten should be appoximately uniom. Theeoe, the inluence o the intensity homogeneity o SAR maine images on the estimation esults is analyzed in this section. Geneally, SAR signals ae aected by not only additional noise but also multiplicative speckle noise. As an example, we assume that the SAR signals can be descibed by a gamma distibution [3]. The pobability distibution unction o the SAR signal intensity can be expessed as whee I is the SAR signal intensity, The mean o the distibution unction is / / N () ( N) N N I ( I,, N) I e is the scale paamete, N, and its standad deviation is N is the numbe o multi-looking. N. Theeoe,. As we all know, o a SAR image, the geate the numbe o multi-looking, the smoothe the image, and the stonge the image uniomity is. Fo ease o undestanding, the impact o SAR image uniomity on the estimation esults is simulated below. Among them, the uniomity o SAR images is mainly caused by the change o multi-looking. Accoding to Equation (), the inluence o the uniomity o SAR image intensity on the estimation esults is simulated, the simulation paametes ae shown in Table 3. / Table 3. The simulation paametes in Figue 6. The aveage o the scatteing coeicient ( Values SNR N ) The standad deviation o the scatteing coeicient ( ). Simulation epeat numbe 8 The aveage o the scatteing coeicient in Table 3 is a ixed value. When changing the value o, the cuve o the RMSE o the estimated is shown in Figue 6. b/ F.5 X:. Y: / Figue 6. The RMSE o the estimated RMSE RMSE=. b/ F as a unction o.

9 Sensos 8, 8, 8 9 o 8 As can be seen om Figue 6, the lage the atio o the vaiance o the image scatteing coeicient to the mean value, the lage the eo o the estimation value. The dashed ed line in Figue 6 is the RMSE theshold calculated when the estimated eo is equal to 5% o the tue value. This means that when is less than o equal to., the estimation esult is consideed to be moe accuate. This means that the moe uniom the SAR ocean image selected o estimating the antenna patten, the close the estimation esults ae to the eal value The Inluence o the SNR o SAR Image on Estimation Results The simulations wee peomed unde dieent SNRs. The paametes o the simulations ae given in Table. Table. Simulation paametes. Values db x D, y D N.9 x, y N x, y N x y Simulation epeat numbe 8 Pixel numbe used o calculating one Dopple spectum 8 Accoding to the paametes in Table, the eect o SNR on estimation accuacy is shown in Figue estimated values b/f =.8895 eal values. b/f.9 X:.865 Y: SNR(dB) Figue 7. The compaison o estimated esults and eal values. The blue solid line is the eal values o simulation data, the blue dotted line is the estimated values which is estimated by the poposed method, the ed dashed line is the eeence value ( b F =.8895) which is 5% lage than the eal values. The values between ed dashed line and blue solid line ae consideed to be moe accuate esults. SNR: signal-to-noise atio. Fom Figue 7, it can be seen that with the inceasing o SNR, the estimated values ae close to eal values. When the SNR is lage than.865 db, the elative eo between the estimated esult and eal value is less than 5%. Theeoe, it can be consideed that the estimated esult eaches enough estimation accuacy.. Validation o the Poposed Method Based on Spacebone SAR Data In this section, two ERS- satellite SAR images will be used to estimate the AAP. The satellite paametes o ERS- ae shown in Table 5. /

10 Sensos 8, 8, 8 o 8 F Table 5. The elated SAR paametes o the ERS-. Pulse Repetition Platom Velocity Antenna Length Pulse Width Bandwidth Wavelength Fequency ( ) (V) (m/s) (m) ( μs ) (MHz) (m) L a The theoetical scale acto b can be calculated om the paamete values in, which is.89. F.. The SAR Ocean Images Pepocessing o Expeimental Validation Figue 8 is a SAR ocean image acquied by ERS- on 9 June 8 nea the Taiwan in China. Thee is a lage aea o uniom scatteing SAR ocean image in Figue 8. Figue 8. ERS- SAR image nea the Taiwan in China collected on 9 June 8, at :5 UTC. The ed dashed ame, Fame A, in Figue 8 will be used o validation. Thee ae 35 pixels in the look diection and,336 pixels in the light diection in the SLC image o Fame A. The pocedue o estimating AAP om Fame A in Figue 8 is as ollows. The ist step is to estimate the Dopple centoid o each ange cell [, 9], and then shiting the Dopple spectum centoid o the SLC image to zeo. Although ocean cuents can lead to an additional local shit o the Dopple centoid [9 ], howeve, the Dopple shit esulting om the ocean cuent is geneally less than 5% o the pulse epetition equency, which can be neglected in the method poposed in this pape. The second step is to calculate Dopple specta om the SLC image. In this example, each Dopple spectum is a 8-point discete spectum that is aveaged by times in the light diection and 3 times in the look diection. Then, we can obtain 5 Dopple specta. The azimuthal length used o calculating one Dopple spectum is about km (o example, L = km). wheeas D is only about 5.67 km. In this case, L and D x satisy the appoximation condition o Equation () (o example, L D x ). Figue 9 is an ocean image acquied by ERS- on 3 Apil 5 in the South China Sea. Thee ae 9 pixels in the look diection and 8,695 pixels in the light diection in the SLC image used in this Figue. Fom Figue 9, the SAR ocean image in this example contains some egions with poo uniomity, theeoe, we select two egions as shown in Fame B and Fame C o x

11 P(-F /) Sensos 8, 8, 8 o 8 veiication and compaison. Fame B is an aea with poo uniomity and Fame C is an aea with stong uniomity. Then, the two aeas will be uthe pocessed. Figue 9. ERS- SAR ocean image o South China Sea collected on 3 Apil 5, at :8 UTC. As in the ist example, the ist step is to estimate the Dopple centoid o each ange cell, and then shit the Dopple spectum centoid o the SLC image to zeo equency. The second step is to calculate Dopple specta om the SLC image. Each Dopple spectum in this example is also a 8-point discete spectum, which is aveaged by times in the light diection and 7 times in the look diection. We can obtain 9 Dopple specta om the SLC image in Fame B and Fame C, espectively. The azimuthal length used o calculating one Dopple spectum also satisy the appoximation condition o Equation () (o example, L D )... The Expeimental Veiication Results Denoting P / and P P F P E p, the elationship between P F / o Fame A, B and C ae depicted in Figue. as the shited Dopple spectum x 8 x 6 measued value linea itted value P()-P(-F /) 5 6 x 5 (a)

12 P(-F / ) Sensos 8, 8, 8 o 8.5 x 5 measued value linea itted value 8 x measued value linea itted value P(-F / ) P( ) - P(-F x 5 / ) (b) Non-uniom aea (Fame B) (c) Uniom aea (Fame C) Figue. The compaison o statistical esults between the uniom and non-uniom scatteing egions in the second example. (a) Relationship between P P F / and in Fame P F A, and the goodness o it o the cuve is.999; (b) Relationship between P P F / / and in Fame C, and the goodness o it o the cuve is.998. P F / P P F / and in Fame B, and the goodness o it o the cuve is.995; (c) Relationship between P F / P( ) - P(-F / ) x 6 Fom Figue, the statistical esults o egions with non-uniom scatteing (Fame B) ae moe scatteed, wheeas statistics o uniom egions (Fame A and Fame C) ae close to linea itting cuves. Howeve, it can be seen that the elationship between P F / and P P F / is all vey close to a linea unction in those thee aeas. Ate obtaining, the scale actos b.9f, b.93f and b.9f can be obtained espectively om Fame A, Fame B and Fame C by solving Equation (). In ode to bette elect the estimation accuacy o the poposed method, the AAP chaacteistics ae shown in Table 6 by compaing the measued values o Ottawa tansponde [], the estimated values o the poposed method, and the theoetical calculated values. Table 6. The AAP chaacteistics measued with Ottawa tansponde, the estimated values and the theoetical values. Tansponde values Estimated values Theoetical values Mainlobe Width ( ) Fame A Fame B Fame C PSLR(Peak Sidelobe Ratio) (db) ISLR (Integal Sidelobe Ratio) (db) Mainlobe Width ( ) PSLR (db) ISLR (db) Mainlobe Width ( ) PSLR (db) ISLR (db) Fom Table 6, it can be concluded that the AAP obtained by tansponde ae vey consistent with those estimated by the poposed method. The esults o estimated AAP ae compaed with the esult measued by Ottawa tansponde, which is shown in Figue.

13 Nomalized antenna gain(db) Nomalized antenna gain(db) Sensos 8, 8, 8 3 o Theoetical model Poposed method Ottawa tansponde antenna pointing angle( ) (a) Uniom aea (Fame A) Nomalized antenna gain(db) Theoetical model Poposed method Ottawa tansponde antenna pointing angle( ) antenna pointing angle( ) (b) Non-uniom aea (Fame B) (c) Uniom aea (Fame C) Theoetical model Poposed method Ottawa tansponde Figue. The compaison chat between the estimated AAP model, the esult measued by Ottawa La tansponde and theoetical one-way model ( sinc ( ), is the length o antenna). (a) The V estimated AAP om Fame A; (b) the estimated AAP om Fame B; (c) the estimated AAP om Fame C. It is obvious to see om Figue that the AAP estimated om Fame A and Fame C is close to the esult measued by Ottawa tansponde than that estimated om Fame B. Fom the simulation data in Section 3, we also know that the poposed method has highe estimation accuacy. Theeoe, om the analysis o Dopple spectum in Figue, it can also be concluded that the estimated AAP model is moe suitable o eal SAR data than the theoetical AAP. In Figue, the centoids o the measued and the estimated specta ae both shited to zeo. Figue shows that the spectum model estimated by the poposed method is supeio to the theoetical spectum model. In addition, the estimated spectum o the uniom scatteing egion (Fame A and Fame C) is close to the SAR eal Dopple spectum than that o the non-uniom egion (Fame B). This shows the easibility o the poposed method. At the same time, Figue also shows that the sinc model is moe suitable o the two-way AAP modeling o ERS- data. In the above expeiment, the numbe o pixels used to calculate the Dopple spectum is chosen as 8, and which satisy the appoximate condition o Equation (). When the numbe o pixels used to calculate the Dopple spectum is changed, the estimation accuacy also will be changed. The esults ae shown in Table 7. L a

14 Sensos 8, 8, 8 o 8 7 x x 6 Dopple spectum intensity measued spectum estimated spectum (Fame A) theoetical spectum Dopple equency(hz) (a) Dopple spectum intensity measued spectum estimated spectum(fame B).5 estimated spectum(fame C) theoetical spectum Dopple equency(hz) (b) Figue. The compaison between the estimated spectum, measued spectum and theoetical spectum. (a) Fame A in Figue 8; (b) Fame B and Fame C in Figue 9. Table 7. The eect o the numbe o pixels used to calculate the Dopple spectum on the estimation esults o. b F / Numbe o Pixels Used to Calculate the Dopple Spectum Fame B (Non-uniom aea) Fame C (Uniom aea) Ate the analysis o the esults in Table 7, we can get the ollowing conclusions: () The moe uniom the selected image aea, the highe the estimated accuacy is; () Unde the same degee o uniomity, the moe pixels used to calculate the Dopple equency, the bette the estimation eect. 5. Conclusions In ode to solve the poblem that AAP cannot be estimated om low-scatteing SAR images without stong scatteing tagets, an AAP estimation method based on the Dopple spectum in SAR ocean images is poposed. The pocedue is as ollows. Fist o all, the egion o the SAR ocean image with moe uniom scatteing intensity is selected. Then, the powe spectum o each distance gate can be calculated espectively. Secondly, two equency points ae selected om the powe spectum o each distance gate o mathematical statistics. Lastly, the shape acto o AAP is estimated based on the linea elationship o the statistical esults, and then AAP is obtained. In addition, the accuacy o the estimated AAP is indiectly veiied by compaing the eal Dopple spectum with the Dopple spectum calculated by the estimated two-way AAP. At the same time, we also veiy the accuacy o the one-way AAP estimated by the poposed method though compaison with tansponde values. In Appendix A, the estimation method o multi-paamete AAP is given. In Appendix B, the selection o two equency points in the above estimation pocess is analyzed by the simulation, and the conclusion is that when the Dopple cente equency and the Dopple spectum edge equency ae selected, the estimation esult is the closest to the tue value. In ode to analyze the pacticability and easibility o the poposed method, the inluence o the uniomity o SAR image intensity and SNR on the estimation accuacy is simulated in this pape. Ate simulation, we conclude that the RMSE o the estimation esults is lage when the uniomity o the SAR ocean image intensity is getting wose. When / =., the RMSE o the estimation esult eaches the theshold, which is calculated when the estimated eo is 5 pecent o the tue value. This theshold is limited to the conclusion which simulated by the Gamma distibution. In addition, the poposed method is also validated though simulation expeiments and eal SAR data. The veiication esults ae in good ageement with the theoetical analysis. Meanwhile, when the inluence o SNR on the estimation accuacy is simulated, the value when the estimated eo is 5% o the tue value is selected as the theshold. Theeoe, we conclude that the poposed method can

15 Sensos 8, 8, 8 5 o 8 achieve good estimation esults when the SNR is moe than.865 db; when the SNR is lowe than.865 db, the estimation eo is lage. Howeve, the method we developed in this study is based on the condition that we have a known SAR AAP model. Fo an SAR image with unknown AAP model, the theoy and method poposed in this pape need to be uthe impoved. Theeoe, moe common AAP models ae unde study and will be pat o the utue wok. Autho Contibutions: Hui Meng and Xiaoqing Wang conceived and peomed the expeiments; Xiaoqing Wang and Jinsong Chong supevised and designed the eseach and contibuted to the aticle s oganization; Hui Meng dated the manuscipt, which was evised by all authos. All authos ead and appoved the inal manuscipt. Conlicts o Inteest: The authos declae no conlict o inteest. Appendix A. Multi-Paamete AAP Estimation Method In this appendix, a multi-paamete AAP estimation method o m in Equation (6) is given. In ode to estimate the whole unknown paametes o AAP, we select equency points on the Dopple spectum, o example,,,, m, substituting them into Equation (5), the ollowing equation can be deived m numbe o dieent N E p E p E p F N E p 3 E p E p 3 F (A) N E p m E p E p m m F whee Pa Pa F Pa F Pa 3 Pa 3 F Pa 3 F Pa Pa F Pa F Pa Pa F Pa F P P F P F P P F P F a a a a 3 a 3 a 3 (A) Pa m Pa m F Pa m F m Pa Pa F Pa F Pa m Pa m F Pa m F Equation (A) indicates that the elationship between E p m and E p E p m is linea. This is consistent with the analysis o Equation (7). Accoding to the analysis in Appendix B, in Equation (A) is selected as Dopple cente equency ( ) position,,, m ae selected as the Dopple spectum edge position as a as possible. Substituting Equation (6) into Equation (A), Equation (A) becomes

16 b/f b/f b/f Sensos 8, 8, 8 6 o 8 Pa b, b, bm, Pa b, b, bm, F Pa b, b, bm, F,,,,,,,,,,,,,,,,,, Pa b, b, bm, 3 Pa b, b, bm, 3 F Pa b, b, bm, 3 F,,,,,,,,,,,,,,,,,, Pa b b bm Pa b b bm F Pa b b bm F Pa b b bm Pa b b bm F Pa b b bm F Pa b b bm Pa b b bm F Pa b b bm F Pa b b bm 3 Pa b b bm 3 F Pa b b bm 3 F (A3) Pa b, b, bm, m Pa b, b, bm, m F Pa b, b, bm, m F,,,,,,,,,,,,,,,,,, m Pa b b bm Pa b b bm F Pa b b bm F Pa b b bm m Pa b b bm m F Pa b b bm m F To solve all the unknown vaiables om Equation (A3), the Newton iteative method can be adopted. Then, the AAP can be obtained when all the vaiables that have been solved ae substituting into Equation (6). Appendix B. The Inluence o Dopple Fequency Point Setting on AAP Estimation Accuacy In this appendix, the inluence o Dopple equency point setting on AAP estimation accuacy will be veiied by simulations. The linea elationship statistics o Equation (7) is made by selecting two equency points ( and ) in the Dopple spectum. Among them, is chosen as the ollowing ive dieent equency positions. They ae the spectum let edge (the ist equency point), the 3th equency point, Dopple centoid (the 6th equency point), the 9th equency point and the spectum ight edge (the 8th equency point). taveses the entie spectum. The estimated esults o b/ F ae shown in a, b, c, d, e in Figue A b/f..9 estimated values eal values..9 estimated values eal values X: Y: (Hz) (a) (Hz) (c) estimated values eal values (Hz) (b) estimated values eal values (Hz) (d)

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