Accurate Estimation of Vehicle Attitude for Satellite Tracking in Ka Band SOTM

Transcription

1 214 UKSim-AMSS 8th Europea Modellig Symposium Accurate Estimatio of Vehicle Attitude for Satellite Trackig i Ka Bad SOTM Salvatore Coco, Gialuca Chisari, Patrizia Di Falco, Eza Iraci ad Simoa Militello DIEEI, Uiversity of Cataia Cataia, Italy coco@dieei.uict.it Atoio Laudai Departmet of Egieerig, Roma Tre Uiversity Roma, Italy alaudai@uiroma3.it Astract The developmet of Satcom o-the-move (SOTM) systems for lad applicatios has led to the use higher frequecy, with ew prolems that SOTM aeroautic systems do ot ow. Aove all, the satellite trackig/poitig is a very critical issue i Ka ad. For this reaso, accurate ope loop systems makig use of iertial measuremet system are fudametal. I order to improve the performace of these ope loop systems ad makig them accurate for Ka ad, ovel solutio i the predictio of the vehicle attitude are studied. I this paper a simple solutio is proposed for the ehacemet of the performace of iertial measuremet system without chagig architecture or addig ew sesors, y usig a tailored filterig ad exteded Kalma filters. Keywords: SOTM; vehicle attitude modelig; satellite trackig; Iertial Measuremet Uit; Kalma Filter I. INTRODUCTION SOTM (Satcom o-the-move) is a acroym used for satellite moile commuicatio: SOTM cosists of ateas mouted o lad platforms, aircraft or ships; these ateas are ale to coect ad commuicate with satellite while the vehicle is o the move [1]. SOTM is a traditioal approach i military applicatios [2]; it is widely used for maritime commuicatio o warship, oth for arrow ad (Imarsat ad UHF) ad roadad (X, Ku ad Ka ads) trasmissios. Recetly, SOTM systems are applied o aircrafts for widespread implemetatio of roadad ad high coectivity commuicatio systems, oth for commercial users ad govermetal authority. The developmet i ateas for satellite commuicatios leads to use this techology also o lad applicatios, such as military ad roadad commuicatios implemetatios for commercial users (for example iteret or TV o the move) [3]. O the other had, govermetal authority for civil protectio is most iterested o SOTM systems for field cotrol, risk maagemet ad emergecy itervetio for the possiility to estalish a coectio ad to maage commuicatios usig lad platform o territory destroyed y a atural disaster [4]. The developmet of SOTM systems for lad applicatios icreased the demad for commuicatio ad ad, cosequetly, the eed of use higher frequecy; it also itroduced ew prolems related to lad SOTM systems that do ot exist i aeroautics applicatios; ideed, i Ka ad the egative effects of the move of the vehicle/platform is icreased ad, at the same time i this ad, the regulatory requiremets aout eam size ad satellite steerig are more costraiig [5-6]. I this cotest, phased array atea ad digital eam-formig ased systems are coveiet i term of size ad performaces, ut they required the study ad the implemetatio of specific trackig algorithm (acquisitio, stailizatio ad trackig of the satellite) [7]. The satellite trackig/poitig i SOTM lad applicatios is a very critical aspect: differetly from aeroautic SOTM systems, the terrestrial oes are iflueced y the trasmissio chael coditios (Lie-Of-Sight/LOS or Not-Lie-Of- Sight/NLOS) ad y the evirometal iterfereces. Geerally, most of trackig methods (step trackig, CONSCAN, etc)[8] are ased o the measures of sigal power coected to small agular movemets (oth i azimuth ad i elevatio) of the receiver atea; i other words, they use small de-poitigs, which allow to fid the higher power directio. All these approaches are for this reaso kow as closed loop trackig methods. Ufortuately, NLOS coditios occur durig the usual operatio (due to the presece of hidrace as uildigs, trees, ridges, tuels, etc,) this causes the immediate failure of trackig system ased oly o the power measures of the received sigal. This drawack is usual overcome y addig to the closed loop trackig system a poitig system realized with a ope loop trackig lock (the so called lid poitig) that gives iformatio (sometimes ot very accurate) aout satellite positios ased o the vehicle attitude gathered from gyroscopes, accelerometers, magetometers ad spatial locatio systems. The closed loop lock ad the ope loop oe ofte iteract i order to improve the performace of the overall trackig system. I Ka ad, the maximum poitig error admitted is oe teth of degree: this foist o the use of very accurate ope loop systems to reduce the applicatio of closed loop approaches [6]. The algorithms preseted i this paper are developed ad hoc to improve the performaces of ope loop lock: i these algorithms the iformatio derived from Iertial Measuremet System (IMS) ad from gyroscopes are coected together y meas of tailored filter to otai a etter estimatio of the vehicle attitude i order to e used i ope loop trackig lock. II. BRIEF DESCRIPTION OF SOTM AND VEHICLE ATTITUDE A schematic represetatio of a SOTM lad system is show i fig. 1. I this picture, the atea is placed o /14 $ IEEE DOI 1.119/EMS

2 vehicle top ad trackig/poitig sesors are located close to it. If the atea were placed o the lad o a fixed platform, it is possile to steer it to the satellite target settlig azimuth (A) ad elevatio (E) agles ad usig polarizatio (V) [9]. I SOTM systems, sice geostatioary satellites are used, these agles deped oly o the platform positio o the lad after the choice of satellite target. Sice atea is istalled o a vehicle, we must settle these agles i the coordiate system of the vehicle itself. I order to do this, it is required to itroduce three referece systems to relate the attitude of the vehicle with that of the atea. The first coordiate system is the local geodesic, amed frame, that is the Est Nord Up frame; its origi is chose as the platform coordiate system origi projectio o the terrestrial geoid. A frame vector is expressed with the superscript, P. Platform coordiate system (vehiclefixed), also idicated as ody coordiate system (-frame), is coected with the vehicle ad aliged with its logitudial (forward), lateral (right) ad vertical (upward) axis. As descried i fig. 1, for sake of simplicity, it egis i the gravity ceter of the atea. The third referece system is the eam coordiate system (s frame); sice i SOTM system atea could e mouted with aritrary positio ad directio, oly z axis is steerig toward satellite target. A vector i s frame is idicated with P s [1-13]. A. Vehicole Attitude The vehicle attitude ca e descried y the followed equatio: s C ( AEV,, ) P = = ( αβγ,, ) ( ψθϕ,, ) s where ( AEV,, ) C C P s (1) C is the trasformatio matrix of coordiates or attitude matrix, geerated from the three agles (A, E ad V), ad that represets s frame orietatio compared to frame. Similarly,,, ad are the atea agles stated i the frame. Whe the vehicle is o the move, the three attitude agles of the vehicle chage cotiuously. The trackig system o the SOTM must check costatly the agles,, to correct the effects o the atea poitig produced y the vehicle attitude variatios: for this reaso, it is possile to steer the atea toward satellite target with precisio oly if the vehicle attitude ca e accurately estimated. I this way, the prolem of atea attitude estimatio is coverted i that of the vehicle attitude valuatio. B. Attitude Represetatio Differet represetatios of the vehicle attitude ca e used to descrie its kiematic, such as Euler agles, quaterios ad Rodrigues formula [9-1]. The fudametal prolem is that each represetatio is sigular or redudat i a specific applicatio. Euler agles are the asic represetatio without redudacies, eve if they preset sigularity whe icliatio agle is aout ± 9. However, this sigularity does ot appear i the case of lad SOTM applicatio. Therefore, Euler agles are the usual choice to defie the vehicle attitude. Figure 1. Schematic represetatio of a lad SOTM system As stated efore, alace matrix C ( ψ, θ, ϕ ), which charts from frame to frame, is produced y the three Euler agles, that is y the yaw agle (), the pitch agle (), ad the roll agle (); it is represeted y the orthogoal matrix show elow: C = cψ cϕ+ sψ sθ sϕ sψ cϕ+ cψ sθ sϕ c s θ ϕ = sψ cθ cψ cθ sθ cψ sϕ sψ sθ cϕ sψ sϕ cψ sθ cϕ cθ c ϕ where c =cos() ad s =si(), with =, or. The kiematic of a solid uit returs ϕ siϕtaθ 1 cosϕ taθω θ = cosϕ siϕ ω y (3) ψ siϕsecθ cosϕ secθ ω z where x, y, ad z are the agular speed of roll, pitch ad yaw expressed i the frame [9-1]. III. ATTITUDE ESTIMATION BY SENSORS The cotiuous chages i attitude of a movig vehicle strogly ifluece the poitig ad trackig of the satellite. The estimatio of the vehicle attitude could e doe y usig gyroscopes, accelerometers, magetometers, ad the gloal positioig system (GPS) [14-16]. A survey of the differet possile approaches ca e foud i [9, 16]. The gyroscopes could e itegrated to give agles, ut they itroduce errors due to gyroscopic ias [17-18]. The accelerometer could aid pitch ad roll agles measurig gravity vector if the vehicle is fixed or o the move at costat speed [16, 19]. The attitude ased o accelerometer is without deviatio, ut it is affected y platform acceleratios ad viratios. The magetometers are widely used, ut they suffer of large disturaces due to ferromagetic materials [19-22]. Also the multi-aselie GPS techology is ale to set the alace, ut it suffers from sigals locks ad from low upgrade frequecy [18, 2]. I the followig a rief recall aout these approaches is proposed with advatages ad drawacks. x (2) 41

3 A. Gyroscopes ased estimatio Gyroscopes are used for the measuremet of the agular speed. It is possile to otai attitude agles y itegratig the gyroscopes measuremets accordig to the (3). Ulucky, the error i the measured data ca determie high mistakes i the log term attitude estimatio. The most commo used gyroscope model is [9-1]: + + ωm = ωt ηω (4) = η (5) where m stads for agular speed measured value, t is the actual agular speed, iflueced y a slow time-variat ias ad y a measuremet oise ; is the white oise that makes the ias slowly variale. ad are idepedet ull-mea Gaussia white oise processes, with stadard deviatio ad. If oe directly itegrates the data measuremets y gyroscopes, errors i the agles come out ad accumulate i time. Cosequetly, it is ot possile to adopt this estimatio as it is. B. Accelerometers ased estimatio The accelerometer ca provide vehicle attitude if acceleratios are cosidered as distur ad the gravity vector is assumed to e the desired variale to e measured. Takig ito accout the system trasformatio (from to frame), the output of the accelerometer ca e modeled as a = C a + g + η (6) ( ) m ody a a ody where g=[,, -g] t is the gravity vector (g=9.81m/s 2 ), is the vehicle acceleratio expressed o the frame, ad a is a zero-mea Gaussia white oise process with covariace matrix Ra = σ 2 ai33. If we sustitute (2) ito (6) we achieve: a mx cosθsiϕ am = a my siθ = g + Caody + ηa (7) a mz cosθ cosϕ If the vehicle is fixed or if it is movig at a costat speed, a = ad the gravity is the oly acceleratio ody source: thus the pitch () ad roll () agles ca e determied y measurig the gravitatioal acceleratio. This approach has a log-term precisio sice the attitude errors do ot icrease with the time. However, the acceleratio of the vehicle a caot always e. The accelerometer ody ased attitude estimate is ievitaly corrupted y acceleratios disturs caused y the vehicle movemet [9]. C. GPS ased estimatio A couple of GPS ateas (also called sigle-aselie GPS) ca e used to estimate with accuracy yaw agle, y usig carrier-phase differetial techology, i which oth GPS ateas capture the same five or more satellites simultaeously. I spite of a commo GPS atea, the sigle-aselie GPS is suject to e affected y ostacles such as trees, uildigs, overpasses ad light poles; i these cases although the satellites are i LOS coditio, the two GPS ateas caot provide the correct yaw agle ad speed. For this reaso, it is ecessary to take care of GPS system work status whe usig it. The GPS system ca also provide two other importat variales: the vehicle speed ad the drift agle. The drift agle is the differece etwee the speed ad the vehicle directios; the it ca e easily otaied whe the yaw agle is availale. However, durig the GPS iterruptios, the vehicle yaw ad drift will ot e availale, ad the speed of the vehicle will e oisy [9, 23]. D. Estimatio y usig Magetometer The magetometer is a typical example of referece sesor for the measuremets of the motio directio. A three axis magetometer measure directly the directio ad itesity of the local magetic field o the sesor frame; this is performed y the comiatio of three sesor elemets mouted o a orthogoal ase. Usually the magetometer is mouted o the vehicle i proximity of the atea, the the sesor frame coicides with vehicle frame ( frame) ad cosequetly a trasformatio is required to chart to frame. The attitude is determied from magetometer y comparig the measured geomagetic field with a referece field determied y a suitale model. Ufortuately, the use of magetometers for attitude determiatio is limited to regios with a strog ad well kow field, ad must e coupled with other sesors, usually accelerometers to provide sufficietly accurate estimatio [19-22]. E. Fusio of data from differet sesors for accurate attitude estimatio I order to fix the aove mistakes whe usig sigularly the metioed sesors, ad i order to accurately estimate the vehicle attitude, the est solutio is to coect together the elemets of these sesors usig a suitale algorithm to verify ad correct all the attitude data. For this reaso, usually the most SOTM employ a referece system (AHRS - Attitude ad Headig Referece System) [9, 18-2, 22, 23], which usually employs specific algorithms (usually ased o Kalma filter [24]) i order to fuse the data from differet sesors ad to improve the estimatio accuracy. O the other had, the high cost of these devices limits the diffusio of the systems SOTM, ad i the case of Ka ad the resultig accuracy is ofte isufficiet. For this reaso i literature differet solutio are proposed to develop low cost systems for attitude estimatio y usig low cost sesors with a limited accuracy, or to improve accuracy y addig multiple sesors with a ot egligile hurdle of the architecture [9]. O the cotrary, we propose a solutio for the ehacemet of the accuracy without modify architecture or addig ew sesors. IV. ENHANCEMENT OF THE ACCURACY OF ATTITUDE ESTIMATION BY USING KALMAN FILTER The solutio proposed uses of the data comig from gyroscopes ad AHRS ad improves the precisio y meas 411

4 of exteded Kalma filter for o liear dyamic systems ad a suitale treatmet of the measured sigals. The exteded Kalma filters, also i adaptive cofiguratio or the so-called usceted Kalma filter, are widely used for this kid of prolems ad we refer to the wide literature for further discussios o this topic [24-28]. The mai ovelty herei proposed is istead the adoptio of a estimator/filter, which provides the oservale data to the Kalma filter lock. A lock diagram is represeted i fig. 2. The IMS seses acceleratios (agular ad liear) ad other quatities ad elaorates these (usually y meas of suitale filter) to retur attitude estimate ( ϕ, θ, ψ ). It also is ale to provide the raw sesed data ad, amog these, the gyroscopes measuremets ( x, y, z ). These latter data are directly used as iput of the exteded Kalma filter for the dyamic system (2), whereas the attitude estimate ( ϕ, θ, ψ ) is give as iput at the estimator lock of fig. 2. This lock uses a temporal series of these data to evaluate a corrected measuremet of attitude ( ϕ, θ, ψ ) to e used as oservale data of Kalma filter. Figure 2. Block diagram descriig the proposed solutio. The output of Kalma is the used as corrected ad real estimatio of the attitude. The actually implemeted formula of the estimator lock is N α = (8) i= 1 λα i N i where stads for, or, ad N i= 1 λ = 1 i. This is doe i order to filter (it correspods to a FIR filter) the frequecy oise due to the samplig frequecy (1 Hz). Usually just N = 2 with = (.25,.75) are good for such purpose. I the test proposed i the validatio sectio these values for have ee used. V. VALIDATION OF THE PROPOSED APPROACH I order to verify the proposed approach a campaig of measuremets were setup at SELEX-ES laoratory i Cataia. I particular, we have used a motio platform (Saricola Simulatio Systems HEXAD-1E)[29] to simulate picht/roll/yaw variatios ad a iertial measuremets device (LadMark 3 GPS/AHRS LN Series)[3], cotaiig gyroscopes, accelerometers, GPS system ad magetic sesors, to perform the measuremets, as i the followig idicated. A. Descriptio of the Platform The HEXAD-1E is a electrically actuated sixdegree-of-freedom motio platform capale of carryig a 1 poud load. It is suitale for a wide variety of equipmet test ad simulatio applicatios. The platform itself uses the classic "hexapod" or "Stewart" cofiguratio of six electric legs to provide cotrolled motio i six degrees of freedom. The platform is cotrolled y a stadard PC-type computer ruig Microsoft Widows XP equipped with custom cotrol software ad a Etheret ealed outoard cotroller i a separate caiet. The software provides a meas of maual cotrol of the platform ad asic performace measuremet tools. A variety of separate custom programs are availale to produce a variety of motio profiles. For example: the aility to store ad replay customer-producer motio profiles; programs to iterface to a host computer for real-time motio cotrol; a Fourier Aalysis program; Wave Form Geerator program ad others. By separately cotrollig the six leg extesios, the platform ca produce motio i ay comiatio of the six spatial axes: surge, sway, heave, yaw, pitch ad roll. B. Descriptio of the Iertial Measuremet System The LadMark 3 GPS/AHRS "LN Series" is a digital 6 Degree of Freedom MEMS (Micro-Electro-Mechaical System) GPS-Aided AHRS that provides velocity ad attitude iformatio: i additio it also provides GPS headig as well as roll ad pitch (degrees) ad GPS altitude (meters) outputs ealig positio determiatio from a kow startig poit. The AHRS 1Hz output is comied with 5 chael C/A code GPS receiver with 4 Hz data update rate. This uit is fully temperature compesated for ias ad scale factor ad correctios for misaligmet ad g- sesitivity. The availale output are gyroscopes measuremets ( x, y, ad z ), accelerometers measuremets ( amx, amy, a mz ), pitch, roll ad yaw agles (estimated y fusio of sesors output y meas of suitale algorithms which compesate temperature drift ad ias). C. Tests performed Before executig the tests, a phase of caliratio of the platform was ecessary i order to exactly idividuate the correspodece etwee the assiged motio profiles ad the real movemets performed y the platform. I order to do this, several profiles cosistig of pure siusoidal pitch, roll, ad yaw separately, ad the comiatios of roll/pitch, roll/yaw ad pitch/yaw were used. These sigals were 412

5 acquired y the iertial measuremets device ad were the aalyzed i frequecy ad i time domai i order to estalish ias of the platform. I additio a accurate procedure ased o the efficiet CFSO 3 optimizatio algorithm [31] was used to sychroize the assiged sigal (pitch, roll ad yaw) with the correspodet measured oe, retured i output y AHRS. I this way, it was possile to idividuate that a ratio of was etwee measured frequecy ad the platform assiged oe. After this phase two log tests were performed y acquirig the two differet pitch/roll/yaw comiatios (as idicated i tales I ad II) for respectively 1 ad 5 miutes. Also these data have ee aalyzed ad sychroized i order to filter oise ad to extract the referece waveforms of pitch, roll ad yaw correspodet to those estalished y the platform. The roll/pitch/yaw agles predicted y usig these measuremets with our approach are compared with those comig from iertial measuremet system (IMS). The results of this compariso are summarized i tale III ad IV ad i the fig. 3 ad 4. I particular tale III ad IV report, respectively, the mea square error (MSE) computed with the formula 1 estimated real MSE = ( ) 2 N xi xi (9) N for estimates achieved with our approach ad with IMS. I almost all the examied case the results are etter tha those comig from IMS. Oly i the case of roll for the test #2 there is a small deterioratio of the performace. This is, o the other had, compesated y the improvemets i the estimatio of the yaw i the same case. It is worth oticig that i all the other case the MSE achieved is lower tha.1%. I additio it is importat to cosider that eig the measuremets performed i laoratory (that is iside a uildig) the GPS system was deactivated ad this iflueces a lot the performace of the system i the estimatio of yaw. The fig. 3 ad 4 show the plot of the asolute error i pitch, roll ad yaw estimatio of our approach (lue) compared with the oe otaied y IMS (red). I almost all the case (excludig the estimatio of yaw), the error is aout.1/.15, that is i the limit of admissile de-poitig for Ka ad, ad which ca e cosidered a satisfactory results. TABLE I. DATA OF TEST #1. Frequecy [Hz] Amplitude ( ) Iitial phase ( ) Pitch.5 2 Roll roll pitch yaw secods Figure 3. Error i roll, pitch ad yaw of the proposed approach (lu) ad of IMS (red) for test #1. TABLE III. MEAN SQUARE ERROR ON TEST #1. Proposed approach IMS MSE Pitch.1.1 MSE Roll.9.16 MSE Yaw pitch roll yaw secods Figure 4. Error i roll, pitch ad yaw of the proposed approach (lu) ad of IMS (red) for test #2. Yaw TABLE II. DATA OF TEST #2. Frequecy [Hz] Amplitude ( ) Iitial phase ( ) Pitch.3 5 Roll Yaw TABLE IV. MEAN SQUARE ERROR ON TEST #2. Proposed approach IMS MSE Roll.1.1 MSE Pitch.8.2 MSE Yaw

6 VI. CONCLUSIONS I this paper a simple solutio has ee proposed for the ehacemet of the accuracy of attitude estimatio of terrestrial SOTM system i Ka ad. This solutio does ot modify the architecture of the system ad makes use of data from IMS, of a exteded Kalma filter ad of a lock called estimator which operates a sort of filterig of data comig from IMS. The proposed approach has ee validated y usig laoratory measuremets performed y meas of a motio platform simulatig real coditios ad a IMS. Further developmet will regards the optimizatio of the filterig of the estimator, the hardware/firmware implemetatio of the proposed approach ad the testig o a real lad SOTM system. ACKNOWLEDGEMENTS This work has ee partly fuded y the Programma Operativo Nazioale Ricerca & Competitività withi the project PON1_683 SIGMA. The authors would like to thak Barara Maifrei ad Sergio Rochi for the collaoratio durig the measuremet campaig performed at Selex ES laoratory. REFERENCES [1] Gozalez, Lio, et al. 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