SEA SURFACE ALTIMETRY BASED ON AIRBORNE GNSS SIGNAL MEASUREMENTS

Transcription

1 IP Annals of the Photogammety, emote ensing and patial Infomation ciences, Volume I-7, XXII IP Congess, 5 August eptembe, Melboune, Austalia EA UFACE ALTIMETY BAED ON AIBONE GN IGNAL MEAUEMENT K. Yu, C. izos, A. Dempste chool of uveying and patial Infomation ystems, Univesity of New outh Wales, ydney, NW 5, Austalia (kegen.yu, c.izos, a.dempste)@unsw.edu.au KEY WOD: ea uface Altimety, GN eflectomety, Aibone Expeiment, LiDA Measuement ABTACT: In this study the focus is on ocean suface altimety using the signals tansmitted fom GN (Global Navigation atellite ystem) satellites. A low-altitude aibone expeiment was ecently conducted off the coast of ydney. Both a LiDA expeiment and a GN eflectomety (GN-) expeiment wee caied out in the same aicaft, at the same time, in the pesence of stong wind and athe high wave height. The sea suface chaacteistics, including the suface height, wee deived fom pocessing the LiDA data. A two-loop iteative method is poposed to calculate sea suface height using the elative delay between the diect and the eflected GN signals. The peliminay esults indicate that the esults obtained fom the GN-based suface altimety deviate fom the LiDA-based esults significantly. Identification of the eo souces and mitigation of the eos ae needed to achieve bette suface height estimation pefomance using GN signals.. INTODUCTION GN- is a pomising technique that can be exploited to emotely sense a ange of geophysical paametes, as oiginally poposed by Matin-Neia (993). One specific application aea of GN- is sea suface altimety. Compaed to ada altimety, GN altimety is able to povide much lage data coveage due to the fact that the aibone o spacebone eceive can eceive signals tansmitted fom multiple GN satellites and eflected ove a lage sea suface aea. The cuent ada altimetes ae not able to measue mesoscale pocesses that ae the dominant eo souce in global climate modelling, while GN altimety povides a potential and inexpensive way to measue such pocesses. A quite compehensive teatment of the theoy of GP-based ocean altimety is povided by Hajj and Zuffada (3). Also, a numbe of expeiments unde diffeent scenaios wee conducted by eseaches and epoted in the liteatue. GP altimety expeiment ove a lake was caied out by Teuhaft et al (). Bidge-based expeiments wee epoted by ius et al (). Aibone expeiments wee caied out and epoted by Lowe et al () and ius et al (). esults of EA s spacebone PAI expeiments and altimete in-obit demonstato wee epoted by Matin-Neia et al (). In this pape we investigate sea suface altimety using GN signals. One study is how the altimety pefomance is affected by the suface oughness, especially when the suface wave height is athe high, owing to stong local wind and/o swells. A low-altitude aibone expeiment was conducted in June by a UNW-owned light aicaft flying off the coast of ydney when the sea suface was athe ough. A LiDA expeiment was conducted in the same aicaft, whose fist objective was to monito the ydney coastal aeas to povide infomation fo futue infastuctue development; and the second one was to estimate the sea suface height as a efeence to the esults geneated fom the GN-based altimety. A two-loop iteative method is poposed to estimate the suface height using the aival time diffeence between the diect and eflected GN signals. This method is compaatively simple and can be eadily implemented. Though pocessing the expeimental data it is demonstated that the LiDA data not only can seve as a efeence fo mean sea level (ML), but they also povide the statistics of the sea suface oughness, including the significant wave head (WH), the oot-mean-squae (M) wave height, and the maximum wave height. Note that thee ae a significant numbe of epots in the liteatue on using LiDA fo sea suface topogaphy (eineman et al 9 and Vbancich et al ). It is obseved that thee is good ageement between the wave head statistics calculated fom the LiDA data and those obtained fom a Waveide buoy. In the case of GN-based altimety, some peliminay esults ae poduced. Compaed to the esults obtained fom the LiDA data, the estimation eo associated with the GN-based method is lage. Finding the eo souces and mitigating the estimation eos is the topic of ongoing wok. The emainde of the pape is oganised as follows. The following section pesents the basic theoy of GN-based altimety and descibes a two-loop iteative method fo calculating suface height. ection 3 descibes the aibone GN expeiment and the LiDA expeiment. ection 4 pesents expeimental and estimation esults, and ection 5 concludes the pape.. GN-BAED EA UFACE ALTIMETY. Fundamentals The pinciple of the GN altimety is quite simple, as illustated in Figue. The eceive may be eithe on an aibone o on a spacebone platfom, and eceives the signals tansmitted by thee GN satellites and eflected by the wate o ice suface. Depending on the suface oughness each signal may be eflected at many suface points and eceived by the eceive via the down-looking antenna. Howeve, the suface point of inteest is the specula point fom which the signal popagation path length is the minimum. The sea suface height is calculated by measuing the delay of the diect signal and that of the eflected signal. The delay o code phase of the diect signal can be eadily detemined by coss-coelating the eceived signal with a code (C/A-code o P-code) eplica. The 347

2 Deivative of Delay Wavefom Coelation Powe Nomalised Coelation Powe Coelation Powe IP Annals of the Photogammety, emote ensing and patial Infomation ciences, Volume I-7, XXII IP Congess, 5 August eptembe, Melboune, Austalia delay is simply estimated as the time point whee the cosscoelation eaches the maximum. On the othe hand the detemination of the delay of the eflected signal can be moe complex. In the case whee the eceive altitude is vey low such as aound tens of metes, the method used fo diect signals can be diectly applied to eflected signals (Matin- eina ). It is a fact that due to suface oughness the delay of the specula eflection point does not coespond to the peak of the coss-coelation. Howeve, at such low altitudes, the oughness-induced eo is smalle than the obsevation noise hence it can be ignoed. As fo aibone altimety a few kilometes o spacebone altimety of seveal hundeds of kilometes above the sea, the displacement between time point of the peak of the coss-coelation and that of the delay can be significant. To detemine the tue delay of the signal eflected at the specula point, the deivative of the delay wavefoms can be exploited (Hajj & Zuffada 3, ius et al ). That is, the time point of the peak of the deivative of the wavefom coesponds to the delay of the eflected signal. Figue : Pinciple of GN altimety In the case of an ideally pefect smooth sea suface, the eflected signals would have a tiangle coelation function which is the same as the diect signals. Thus the eflected signal has a delay wavefom and its deivative as illustated in Figue. In this idealised case the delay of the eflected signal can be eadily detemined eithe fom the delay wavefom o fom the deivative of the wavefom GN AT# P GN AT# Figue. Delay wavefom and its deivative of a GN signal eflected fom a pefectly smooth sea suface. The uppe plot of Figue 3 shows the delay wavefom that is geneated using data logged duing an aibone expeiment. The sampling fequency of the IF data is MHz, coesponding to a esolution of 8.33 metes, which is too lage in tems of sea suface altimety. Thus intepolation of the samples is equied to obtain a much highe esolution. Fom the uppe plot in Figue 3 the effect of the intepolation can be eadily obseved. The post-intepolation delay wavefom was poduced using the Matlab libay function INTEP. The P eceive GN AT#3 P3 deivative of the post-intepolation delay wavefom is shown in the lowe plot of Figue 3. In this case the displacement between the peak of the wavefom and the peak of the deivative of the wavefom is.33 code chips, coesponding to 8.4 nanoseconds o metes intepolated wavefom deivative of wavefom oiginal afte intepolation Figue 3. Intepolation of delay wavefom (top) and deivative of delay wavefom (bottom). ince the position of the GN satellite is known and the position of the eceive can be detemined using the diect signals associated with such as eight o even moe satellites, the distance between the GP satellite and the eceive can be eadily detemined as: t ( x xt ) ( y yt ) ( z zt ) () whee x, y, z ) and x, y, z ) ae the positions of the ( ( t t t eceive and the satellite, espectively. Thus with the knowledge of the elative delay ) of the eflected signal with espect to ( d the diect signal, the total distance ( t ) fom the GN tansmitte though the specula eflection point and to the eceive can be eadily detemined as: ˆ cˆ () t t whee c is the popagation speed of light and ˆ d is the estimate of d. As a consequence the position of the specula eflection point on the sea suface can be calculated by solving the nonlinea equation: t t ( x ( x t t x ) ( y y x ) ( y y t d ) ( z z ) ( z z whee x, y, z ) is the position of the specula eflection ( point on the sea suface. In Figue 4 point is the specula eflection point in the ough sea suface, whose altitude ove the WG84 ML is to be estimated. The actual sea suface can be significantly diffeent the WG84 ML whee the altitude is defined as zeo, although the diffeence of the sufaces (actual sea suface, ML and geoid) is ignoed in some cases. A numbe of notations o symbols in the figues ae defined as: = satellite elevation angle at the eceive, = incident angle at specula point h = WG84 altitude of the eceive = distance fom specula point to the WG84 ML t ) ) (3) 348

3 IP Annals of the Photogammety, emote ensing and patial Infomation ciences, Volume I-7, XXII IP Congess, 5 August eptembe, Melboune, Austalia. Poposed Iteative Method Clealy the aim is to detemine the paamete and a two-loop iteative method is poposed hee to solve the poblem. pecifically the inne loop is fo calculating the position of the specula point, while the oute loop is fo selecting the suface height. Initially, a guess of the sea suface height is given based on some pio infomation about the suface height in the aea of inteest. In the event that thee is no elevant pio infomation, the initial value may be simply set at zeo, i.e. the specula point is assumed to be on the suface of the WG84 geoid suface whee the altitude is zeo. Fo a given suface height, say, the coodinates of the specula point can be detemined by minimising the total path length defined by (3). Then the minimum path length ( t ) is compaed with the measued actual path length ˆ ( t ) given by (). If t ˆ t, then the tentative suface height is inceased by an incement. Othewise, it is deceased. The pocedue continues until the diffeence between the two path lengths is sufficiently small. To educe the computational complexity, a simple technique may be used. Fo instance, if ˆ, the tentative suface height t is inceased by a elatively lage incement such as 4 metes. At the next iteation of the oute loop if ˆ, the incement is deceased by half of the pevious incement. In this way, the pocess will quickly convege to the steady state. Note that the specula eflection must satisfy nell s Law, i.e. the two angles ( and in Figue 4) between the incoming wave and the eflected wave, sepaated by the suface nomal must be equal. Thus the esults should be tested to see if this Law is satisfied. Fom GN satellite Figue 4. Geomety of the eceive, WG84 mean sea level, ough sea suface, diect and eflected signal paths. A method fo detemining the specula point on the WG84 suface with a zeo altitude can be found in Gleason (9). Hee the modified vesion of the method is given to accommodate the non-zeo altitude value. Fom (3) the patial deivatives with espect to the coodinates of the specula point can be detemined as: t ea uface WG84 ML with zeo altitude. t eceive h t u t u x u xt t, u { x, y, z} which can be ewitten in a vecto fom as: T d (5) t whee,, and T ae the position vectos of the specula point, the eceive and the tansmitte, espectively. Equation (4) is the basis to geneate an iteative solution to the minimum path length. That is, at time instant n the specula point position is updated accoding to: n n d (6) whee is a constant which typically should be set as a lage value as the flight altitude inceases. The initial guess of the specula point can be simply the pojection of the eceive position on the suface. At each iteation, a constaint must be applied to estain the specula point on the suface that is metes above o below the WG84 suface which has a zeo altitude if is a positive o negative numbe. That is, the specula point position is scaled accoding to: ' n n ( ) (7) n whee the adius of the Eath at the specula point is calculated by: e WG 84 z, acsin awg 84 e (cos ) (8) WG 84 whee e WG and a WG metes. ince the altitude of the WG84 ML is zeo, the WG84 altitude of the specula point (point ) is equal to. Clealy, the altitude of a single specula point cannot be teated as the estimate of the mean sea suface height. Howeve, a easonable estimate of the mean suface height will be poduced though the geneation and subsequent pocessing of the altitude estimates of many specula points ove a peiod of time. 3. LOW-ALTITUDE AIBONE EXPEIMENT A low-altitude aibone expeiment was conducted by a UNWowned light aicaft off the coast of ydney between Naabean Beach and Palm Beach on the 4 th of June. Both the LiDA expeiment and the GN- expeiment wee caied in the same aicaft at the same time. Due to the equiement of the LiDA expeiment, the aicaft flight height was below 5 metes. Figue 5 shows the light aicaft used fo the expeiment, which can accommodate fou people. Figue 6 shows the GP softwae eceive and the LiDA equipment secued in the aicaft. The LiDA device is a iegl LM- Q4i lase scanne and the lase wavelength is 95nm. This device is extemely ugged and thus ideally suited fo aibone expeiment. The maximum measuement ange is aound 65m and anging accuacy is about mm. The LHCP (light hand ciculaly polaised) and HCP (ight hand ciculaly polaised) antennas and the low noise amplifie (LNA) ae also secued eithe on the top o on the bottom of the aicaft as shown in Figue 7. The diect signal was captued via (4) 349

4 Wind Diection (deg) Wind peed and Gust (m/s) Wave Peiodss (sec) Wave Heights (m) IP Annals of the Photogammety, emote ensing and patial Infomation ciences, Volume I-7, XXII IP Congess, 5 August eptembe, Melboune, Austalia the zenith-looking HCP antenna, wheeas the eflected signal was eceived via the nadi-looking LHCP antenna. Both signals wee pocessed though the softwae eceive, which has fou F font-ends to geneate the IF signals that wee logged to a laptop fo subsequent pocessing WH M wave height maximum wave height Figue 5. Light aicaft used fo conducting the expeiment. 6 zeo cossing peiod 4 significant peiod peiod of waves with most enegy Figue 9. Wave heights and peiods duing the day when the expeiments wee conducted. Figue 6. GP softwae eceive (left font) and LiDA equipment (ea) secued in the aicaft. Figue. ea suface conditions viewed fom the aicaft. 4. EXPEIMENTAL EULT 4. LiDA Expeimental esults Figue 7. HCP antenna (left), LHCP antenna (middle) and low noise amplifie (ight). The wind and wave conditions duing the expeiment day ae shown in Figues 8 and 9, espectively. The wind data wee povided by the Austalian Bueau of Meteoology, while the wave data wee povided by Mak Kulma fom the Manly Hydaulics Laboatoy, ydney, New outh Wales. It can be seen that the wind was stong with speeds between 7.m/s (6km/h) and 3.9m/s (o 5km/h). The sea suface was athe ough with the WH (significant wave height) between.65m and 4.8m and the maximum wave height was geate than 6m. Figue shows the sea suface conditions viewed fom the aicaft Gust peed Figue 8. Wind speed and diection duing the day when the expeiments wee conducted. Figue shows the esults elated to 3983 points on the sea suface fom pocessing of the LiDA data. The uppe plot shows the WG84 altitudes of the suface points and thei mean (dashed staight line), while the lowe plot shows the diffeence when the altitudes ae subtacted by the mean of the altitudes. That is, the lowe plot shows the suface elevation vaiation with espect to the measued ML which is calculated as 3.444m. The standad deviation of the ML estimate is.38metes, mainly contibuted to by the suface oughness. This ML estimate can be employed as a efeence when evaluating the pefomance of the GN-based altimety. These samples wee taken between 5:7:55 and 5:3:38, fo duation of 3 min 43.3 sec. The Waveide buoy-based wave height measuements (see Figue 9) indicate that duing this peiod the WH, M (oot mean squae) wave height, and maximum wave height wee 4.m,.7m, and 6.4m, espectively. Figue shows the wave heights deived fom the LiDA suface points shown in Figue. A wave is defined as the potion of the wate between two successive zeo-upcossings elative to the ML. The wave height is simply calculated as the vetical displacement between the cest and the tough of the wave. Using these LiDA-based wave heights the WH, M wave height, and maximum wave height ae calculated as 3.7m,.6m, and 6.78m, espectively. It can be seen that these LiDA-based statistics of the wave height measuements have good ageement with those of the Waveide buoy-based measuements. Note that the distance between the location of the Waveide buoy and the location whee the pesented data wee collected is between.45km and.5km. Due to this location diffeence some small vaiations of the wave statistics ae expected. Figue 4 shows the cumulative distibution function (CDF) of the measued wave heights. It can be seen that the measued wave heights closely follow the ayleigh distibution whose CDF is given by 35

5 Cumulative Distibution Function Aicaft Altitude (m) Wave Heights (m) Aicaft Velocity (m/s) elative Elevation(m) Altitude of Points(m) IP Annals of the Photogammety, emote ensing and patial Infomation ciences, Volume I-7, XXII IP Congess, 5 August eptembe, Melboune, Austalia { exp( x /( ))} whee the distibution paamete.8m is calculated fom the measued wave heights. This is in ageement with those esults epoted in the liteatue (Longuet-Higgins 95, Dean & Dalymple l99). GN satellite is assigned with one specific PN code with a unique code numbe to distinguish fom each othe Time (min) Time (min) Figue. WG84 altitudes of the sea suface points (top) and elative sea suface elevation (bottom) measued by LiDA Figue 4. Expeimental location. The data collected ove 5 seconds between points A and B. Table. atellite elevation angles (deg) at Points A and B. atellite Point A Point B Wave ample Numbe Figue. Wave heights deived fom the LiDA suface points Measued Theoetical Wave Height (m) Figue 3. Cumulative distibution functions of the measued wave heights and the ayleigh vaiable. 4. GN- Expeimental esults Figue 4 shows the shot flight tack segment elative to the coastal aea ove the duation of about 5 seconds. The distances between the Waveide buoy and the two points A and B ae.98 km, 8.97 km, and 9.54 km, AB AW espectively. The satellites with elevation angles geate than 4 degees ae listed in Table, whee two angle values ae fo points A and B espectively. ince the duation is just 5 seconds, the elevation angle of each satellite changes little. Figue 5 shows the flight height and the aicaft speeds ove the duation of 5 seconds. The flight height was just aound 3 metes, equivalent to about one C/A (coase/acquisition) code chip. The C/A code is a deteministic sequence of 3 bits, which is called pseudoandom noise (PN) code. Each BW Time (sec) Figue 5. Aicaft altitude and speed ove the duation of 5 seconds. Figue 7 shows the delay estimates of the eflected signal elative to the diect signal associated with two satellites (PN# and PN#8). The delays wee estimated based on the delay wavefoms of the diect and eflected signals as mentioned ealie. The wavefoms wee poduced by coheent integation of the eceived signals ove millisecond and then combined though non-coheent integation ove second. Ove the peiod of 5 seconds, the elative delay vaies significantly. Ongoing wok will focus on why the elative delay changes so much. Cetainly, the suface oughness will affect the delay estimation, but the impact should not be so much. Figue 8 shows the sea suface height estimates associated with the two satellites. The means of the estimates ae 8.6 metes and 5.4 metes espectively, while the standad deviations ae 7.4 metes and 7.4 metes espectively. Clealy, the estimation esults do not have good ageement with the esults povided by the LiDA expeiment. This will be the subject of futhe investigation. A numbe of factos may contibute to such an outcome. The suface oughness is one, as aleady mentioned. The second facto may be the delay estimation eo, and anothe facto is that we have not pefomed a caeful calibation fo the elative positions of the zenith-looking antenna and the nadi-looking antenna. Futhe, the numbe of samples used fo the estimation may not be sufficient. To 35

6 Altitude Estimate (m) Altitude Estimate (m) Delay (m) Delay (m) IP Annals of the Photogammety, emote ensing and patial Infomation ciences, Volume I-7, XXII IP Congess, 5 August eptembe, Melboune, Austalia achieve accuate suface altimety, all these issues need to be consideed PN# PN# Time (sec) Figue 6. Delay of the eflected signal elative to the diect signal associated with two satellites. 4 PN# PN# Time (sec) Figue 7. uface height estimates using signals associated with two satellites (P# and PN#8). 5. CONCLUDING EMAK In this pape we investigated sea suface height estimation based on GN signal measuements. A LiDA expeiment and a GN- expeiment wee conducted in the same aicaft at the same time. By pocessing the data obtained fom the LiDA expeiment, the statistics of the wave heights wee poduced, showing good ageement with the esults obtained fom a neaby Waveide buoy. Infomation about the sea suface height was also deived fom the LiDA data. GN-based suface height estimation was pefomed by estimating the elative delay between the diect and the eflected signals. A two-loop iteative method was poposed to calculate the suface height. The esults obtained fom the GN altimety did not have good ageement with the LiDA-based esults. Ongoing wok will focus on finding the eo souces and impoving the estimation accuacy. ACKNOWLEDGEMENT EFEENCE Dean,.G. and Dalymple,.A., 99. Wate Wave Mechanics fo Enginees and cientists, Wold cientific, ingapoe. Gleason,.T., Gebe-Egziabhe, D., 9. GN Applications and Methods, Atech House. Hajj, G.A. and Zuffada, C., 3. Theoetical desciption of a bistatic system fo ocean altimety using the GP signal, adio cience, 38(5), pp. -. Longuet-Higgins, M.., 95. On the statistical distibution of the heights of sea waves, Jounal of Maine eseach, (3), pp Lowe,.T., Zuffada, C., Chao, Y., Koge, P., LaBecque, J., Young, L.E.,. 5-cm-pecision aicaft ocean altimety using GP eflections, Geophysical eseach Lettes, 9(), Matín-Neia, M., 993. A passive eflectomety and intefeomety system (PAI): Application to ocean altimety, EA Jounal, 7(4), pp Matin-Neia, M., Capaini, M., Font-ossello, J., Lannelongue,., Vallmitjana, C..,. The PAI concept: An expeimental demonstation of sea suface altimety using GP eflected signals, IEEE Tansactions on Geoscience and emote ensing, 39(), 4-5. eineman, B.D., Lenain, L., Melville, W.K., 9. A potable aibone scanning Lida system fo ocean and coastal applications. Jounal of Atmospheic and oceanic technology, 6(), ius, A., Cadellach, E., Matın-Neia, M.,. Altimetic analysis of the sea-suface GP-eflected signals. IEEE Tansactions on Geoscience and emote ensing, 48(4), 9 7. ius, A., Nogues-Coeig, O., ibo,., Cadellach, E., Oliveas,., Valencia, E., Pak, H., Taongi, J.M., Camps, A., Mael, H.V.D., Bee..V., Altena, B., Matin-Neia, M.,. Altimety with GN- intefeomety: Fist poof of concept expeiment, GP olutions, DOI.7/s Teuhaft,., Lowe,.T., Zuffada, C., Chao, Y.,. -cm GP altimety ove Cate Lake, Geophysical eseach Lettes, 8(3), Vbancich, J., Lieff, W., Hacke,J,. Demonstation of two potable scanning LiDA systems flown at low-altitude fo investigating coastal sea suface topogaphy. emote ensing, 3(9), The authos would like to acknowledge that this eseach wok was caied out fo the A Fomation Flying Poject which was funded by the Austalian pace eseach Pogam (AP) and fo the AC Discovey Poject DP87738 (Envionmental Geodesy: Vaiations of ea Level and Wate toage in the Austalian egion). The authos would also like to thank thei colleagues M. Pete Mumfod, M. Geg Nippad and Pof. Jason Middleton fo conducting the aibone expeiments. 35