Aspects Regarding Fly Control of Quadcopter

Recen Inno a ions in Mecha onics (RIiM) Vol. 3. (2016). No. 1-2. DOI: 10.17667/ iim.2016.1-2/7. Aspec s Rega ding Fly Con ol o Quadcop e End owednes Kuan ama Enginee ing Doc o al School Uni e si y o O adea 1 Uni e si ăţii S ., O adea, Romania end owedne[email p o ec ed]m Ioan Ta ca1, Radu Ta ca2, Dan C aciun3 Mecha onics Depa men Uni e si y o O adea 1 Uni e si ăţii S ., O adea, Romania 1nelu @uo adea. o, 2 a ca@uo adea. o, 3danc [email protected] Abs ac —Quadcop e is one o Unmanned Ae ial Vehicle (UAV) which has wo pai s o iden ical ixed pi ched o o p opelle s. I can ly au onomously based on p e-p og ammed ligh o manually con olled by a emo e, and e e y mo emen achie ed by a ying he speed o each o o independen ly. The o ien a ion o quadcop e axes ela i e o a e e ence line and i s di ec ion o mo ion a e known as a i ude. Fly con ol ac o s a e a ec ed by a i ude de e mina ion which can be calcula ed om 3 possible angles using combined measu emen . Gy oscope and accele ome e a e p ima y senso s o con ol quadcop e a i ude, bu magne ome e senso and GPS also used o enhance he s abili y du ing ligh . This pape will ocus on de ails o unc ion and ma hema ical o mula o e e y ac o ega ding ly con ol and compa a i e da a o 2 ypes o o ien a ion senso used in his sys em. Keywo ds—quadcop e ; a i ude; gy oscope; ly con ol; o ien a ion senso I. INTRODUCTION Quadcop e is classi ied as Unmanned Ae ial Vehicle which is li ed by 4 o o s, as i s name sugges . I s mo emen can be di ec ed by con olling he angula speed o each o o . The o o s a e connec ed wi h he p opelle s, and he each pai o opposed simila p opelle a e o a ing in he same di ec ion ( wo clockwise and wo coun e clockwise). The mos impo an aspec s needed o be conside ed when designing quadcop e a e ela ed o i s ligh s abili y: wha ac o s a e a ec ing i and how hey in luence he s abili y. Main opics ega ding quadcop e s a e ela ed o hei a i ude; ma hema ical o mulas and ligh con ol aim o con ol hei a i ude. A i ude is a posi ion o he body (ine ial ame) o he o ien a ion o quadcop e axes ela i e o a e e ence line and i s di ec ion o mo ion. Quadcop e a i ude can be measu ed using MEMS (Mic o Elec o Mechanical Sys em) senso . This senso canno accomplish same accu acy as Kalman il e o complemen a y usion algo i hms which a e used o p o ide mo e accu a e and eliable in o ma ion in he MEMS a i ude de e mina ion sys ems [1]. Senso sys em is a undamen al pa o UAV, including quadcop e , ha ing hei ole in calcula ing accu a e a i ude by measu ing h ee angles, using combined measu emen s such as he gy oscope/gy o a e, accele ome e and magne ome e [2]. These senso s measu e h ee-axis angula a es, h ee-axis appa en accele a ion, and Ea h’s magne ic ield wi h espec o he quadcop e ’s body ame. In o de o achie e he bes e alua ion o a i ude angles om hese senso s, i is essen ial o use hese measu emen s in a seamless manne while conside ing he di e ence be ween each senso ’s signal speci ica ions. I is possible o use a a e gy o o ob ain a i udes, by in eg a ing he igid body's kinema ic equa ions, while accele ome e s p o ide g a i y di ec ion. Wi h high quali y gy oscope and app op ia e ini ial alues, hese assessmen s can be e y accu a e o e long pe iods o ime. On he o he hand, accele ome e s signals p esen di ec alues o il angles [3]. When quadcop e shi s om one posi ion o he o he , he wing on espec i e side will slan sligh ly in he mo ing di ec ion as seen on Fig.1. The esul ed angle is an impo an ac o in de e mining he quadcop e s abili y. Each mo emen ’s angle has o be con inuously moni o ed by he o ien a ion senso un il he s abili y is achie ed. Wi h he ligh con ol senso s' help, quadcop e will adjus i s posi ion acco dingly, e en in he case o na u al dis u bances o p opelle ai low. These aspec s e eal he impo ance o quadcop e ligh con ol. Fig. 1. Illus a ion o a i ude quadcop e mo emen II. ATTITUDE PARAMETERIZATION AND REPRESENTATION P ope es ima ion o a i ude angles and posi ion o quadcop e a e he mos impo an ac o in ligh con ol na iga ion. De e mina ion o ligh a i ude also in ol es he compu a ion o quadcop e ’s pi ch angle, oll angle, and heading angle. Bo h pi ch angle and oll angle can be compu ed by measu ing accele a ions and body a es om accele ome e s and a e gy os, while heading angle can be measu ed by calcula ing he magne ic heading. Ha ing known he accele a ion on h ee axes (pi ch, oll, and yaw a e in o ma ion), he pi ch and oll angles can also be de e mined ei he by compu ing he g a i a ional accele a ion componen s Recen Inno a ions in Mecha onics (RIiM) Vol. 3. (2016). No. 1-2. DOI: 10.17667/ iim.2016.1-2/7. on he body axes, o by using he Eule qua e nion me hod. The la e me hod, howe e , p o ides low noise con en s and as esponse o changes in he inpu signals, bu ends o d i wi h ime due o gy o bias e o s [4]. The absolu e linea posi ion o he quadcop e is de ined in he ine ial ame x, y, z axes wi h Eule (£). The a i ude is de ined in he ine ial ame wi h h ee Eule angles: Pi ch angle (θ) de e mines he o a ion o he quadcop e a ound he y-axis, while Roll angle (ɸ) a ound he x-axis and Yaw angle (ψ) a ound z-axis. Using concep o kinema ic mo ing ame, quadcop e mo emen om ini ial posi ion o desi ed posi ion can be calcula ed as seen on Fig. 2. Fig. 2. Illus a ion o quadcop e o ien a ion The Eule o mula (1) can be used o calcula e he o a ion o he quadcop e ame h oughou each axis as well as he ma ix mul iplica ion esul o R oll, Rpi ch, Ryaw: (1) Whe e symbol ‘s’ ep esen sine and ‘c’ ep esen cosine. To ge he desi ed quadcop e mo emen (based on each mo emen angle), he angula mo emen o e e y o o mus gene a e app op ia e h us . The h us mo emen in (2) is p oduced by each o o h ough he o que applied by o o which d i en by elec onic speed con olle s. The o o speed is ωi and he li cons an o quadcop e is b ha depends on he ai densi y a ound p opelle . (2) Fly con ol, especially he a i ude measu emen senso , holds an essen ial pa o moni o e e y a i ude and o ien a ion o quadcop e in o de o i o ly s able e en h ough dis u bance. III. QUADCOPTER FLY CONTROL MEASUREMENT In e ms o quadcop e a i ude, o ien a ion and mo emen posi ion ha e o be moni o ed con inuously using o ien a ion measu emen such as accele ome e and gy oscope senso . Accele ome e is used o measu e accele a ion om quadcop e mo emen , whe eas gy oscope is used o measu e he angula a e as seen in diag am block on Fig. 3. Magne ome e and GPS as posi ion senso s a e used o imp o e he accu acy o o a ion and posi ion o quadcop e . By using hese senso s, one can p ecisely e alua e quadcop e speed, posi ion and o ien a ion and help s abilizing quadcop e mo emen . Fig. 3. Quadcop e ligh con ol uni Accele ome e and gy oscope as o ien a ion senso s a e called s ap down sys em in which he ine ial senso s a e di ec ly a ached o he ehicle ame. These senso s unc ion as he ull dynamic mo ion o he ehicle. The ela ionship be ween he body- ixed ame and he na iga ional ame mus be main ained compu a ionally on boa d. A. Quadcop e a i ude es ima ion based on Accele ome e Accele a ion is he a e o eloci y change wi h ime o he a e o change o dis ance wi h squa ed ime. To de e mine speci ic accele a ion, an accele ome e is used. As a measu e senso , accele ome e can calcula e he di e ence be ween ehicle’s accele a ion and g a i y accele a ion. To be able o de e mine h ee-dimensional accele a ion ec o , accele a ion can be calcula ed based on New on’s second law o mo ion which ela es o ce (F), mass (m), and accele a ion (a). Accele ome e is going o be used in ine ial na iga ion; he e o e, accele a ion wi h espec o he ine ial ame is needed. The ou pu o accele ome e is measu emen o he di e ence be ween he ac ual ehicle accele a ion (a) and he g a i a ional accele a ion (g) (3) In (3), F is he speci ic o ce. I is necessa y o know he magni ude and o ien a ion o he g a i y ec o g wi h espec o he accele ome e inpu axis in o de o compu e he accele a ion componen s om he accele ome e ou pu s. The ou pu o accele a ion on a igid body is he e o e gi en by (4). (4) Whe e am is he measu ed accele a ion and Fg is he o ce due o g a i y and F is he ex e nal o ce. One can use (4) o calcula e he g a i a ional e ec when he ex e nal o ces equals o ze o. I is assumed ha he axes o he accele ome e a e aligned wi h he body- ame axes and ha he accele ome e has been p ope ly calib a ed o emo e misalignmen e o s and c oss-axis sensi i i y. Y X ψ X X Y Z Z Z Gy oscope Accele ome e Accele a ion (m/s2) Angula Ra e ( ad/s) Na iga ion Algo i hm A i ude ( ad) Veloci y (m/s) Posi ion (m) Magne ome e & GPS Z’ (c) Pi ch mo emen ψ Y’ X’ (a) Yaw mo emen Y’ ϕ ϕ Z’ X’ θ θ (b) Roll mo emen Y )FF( m 1 ag m  )ga(F  2 i .bT             cccsscssscsc cssssccsccss ssccc R Recen Inno a ions in Mecha onics (RIiM) Vol. 3. (2016). No. 1-2. DOI: 10.17667/ iim.2016.1-2/7. In he h ee axis accele ome e , (ax, ay, az) ep esen he accele a ion measu ed in he body ame axes. In he ine ial ame, he o ce o g a i y is in z-axis. Using (4) and he o ce o g a i y, he accele a ion in he body ames is gi en by (5). (5) The symbol Ri ep esen he o a ion ma ix om he ine ial o he body- ixed e e ence ame, which come om calcula ion be ween Pi ch and Roll (Rx, Ry), as in (1). Since he accele a ions in s able ligh egimes a e usually small compa ed o he g a i y accele a ion, neglec ing he linea accele a ion is a classical assump ion [5]. No malizing he ec o o accele a ion measu emen s acili a es o exp ess he oll and pi ch angles as (6). (6) Whe e ϕ is he oll angle and θ is he pi ch angle ela i e o he g ound. Quadcop e s a e di e en om g ound ehicles because o he h us equi ed o keep hem ai bo ne. The accele ome e s in s ap down sys ems measu e he esul an o g a i a ional and o he accele a ions ac ing on he body o which he senso s a e a ached. The idea o his me hod is o ega d he accele ome e s as inclinome e s, which p o ide an absolu e e e ence o he a i ude by ela ing he body o ien a ion o he g a i y ec o . I is assumed ha he body is no mo ing o is mo ing a cons an speed, so ha he accele a ion due o he ea h’s o a ion is negligible and he g a i y is he only sou ce o accele a ion, also known as Co iolis accele a ion [6]. The accele ome e s can p o ide e y accu a e measu emen s o a i ude, bu he accele ome e - based a i ude is sensi i e o ex e nal accele a ion and ib a ion. B. Quadcop e a i ude es ima ion based on gy oscope Gy oscope is he angula a e senso which is used o measu e he a e o o a ion a ound he senso axis in quadcop e . Theo e ically, when in eg a ing he signal om he gy oscope, one can acqui e he angula change o e a pe iod o ime. In Fig. 2 can be seen he illus a ion o quadcop e ’s o ien a ion and posi ion, he e e ence ame X, Y, and Z is aligned wi h he p incipal (main) axis o he body. In s ap down sys ems, gy oscopes measu e he angula a es o h ee axes o he body wi h espec o he ine ial coo dina e ame. Wi h hese measu emen s o angula a es in body coo dina es, he a i ude o he quadcop e can be de i ed by in eg a ing he igid body kinema ic equa ions, s a ing om a known ini ial a i ude a a gi en poin in ime. The a i ude o a body wi h espec o he ine ial coo dina e ame is de ined by Eule o mula. Examina ion o small changes in each Eule angle and he e ec s on he angula ec o a e based on kinema ic mo ing ames heo em. The con inuous ime nonlinea igid body kinema ic equa ion in s a e space ep esen a ion is shown in (7) and (8). (7) (8) Whe e p, q, a e he angula a es measu ed by gy oscopes in he body coo dina e ame. Using his equa ion, he measu emen esul om gy o senso will be compa ed wi h desi ed a i ude o quadcop e . C. Quadcop e a i ude es ima ion based on magne ome e Magne ome e s a e commonly used o measu e Ea h’s local magne ic ield ec o hus de e mine he di ec ion in which magne ic no h lies. A 3 axis magne ome e can measu e magne ic ield in ensi y in 3 dimensions. These poin s a e e e ed o as he magne ic poles. Magne ic ield lines a y bo h in s eng h and di ec ion abou he ace o he ea h. The di ec ion and s eng h o he ea h’s magne ic ield (H) can be ep esen ed by he h ee axis alues Hx, Hy, and Hz. The Hx and Hy in o ma ion can be used o de e mine compass headings in e e ence o he magne ic poles. The a i ude is es ima ed by wo successi e qua e nion o a ions. The i s o a ion is he one be ween magne ic ield ec o measu ed by he magne ome e in i s e e ence sys em and he ea h’s magne ic ield ec o es ima ed by a model. The second o a ion is by sub ac ing he cen ipe al accele a ion om he accele a ion measu ed by he accele ome e [8]. The magne ome e -based a i ude de e mina ion is widely used o spacec a as well as quadcop e [9]. In quadcop e , hese me hods a e based on he qua e nions a i ude ep esen a ion. The in o ma ion abou oll and pi ch angle can be ex ac ed om g a i y poin s which head o he local e ical down di ec ion. The magne ome e is used o measu e quadcop e ’s magne ic ield in ensi y in 3 dimensions. The declina ion (δ) and inclina ion (Ƞ) a e modeled and p o ided by he Wo ld Magne ic Model (WMM) o he Na ional Geophysical Da a Cen e (NGDC). F om his model, he magne ic ec o , which is exp essed in local na iga ion ame, can be known. In addi ion, he yaw, pi ch, and oll angle is de e mined by he magne ome e measu emen s. The g a i y ec o o he ea h is always poin ing o a local e ical down di ec ion. In con as , he di ec ion o he magne ic ec o o he ea h a ies wi h posi ion on he ea h. In yaw mo emen , he di ec ion o he magne ic ec o is exp essed by he declina ion and inclina ion o he local na iga ion ame in Fig. 4.                     coscosg- cossing- sing a a a z y x                               coscos cossinsin R; g 0 0 R a a a ii z y x                                                                           coscossecsin0 cossincos0 sin01 q p 0 0 0 0 R0 0 RR q p xyx                                  q p seccossecsin0 sincos0 ancos ansin1    Recen Inno a ions in Mecha onics (RIiM) Vol. 3. (2016). No. 1-2. DOI: 10.17667/ iim.2016.1-2/7. Fig. 4. Magne ic ec o o he ea h on local na iga ion ame The magne ome e -based yaw angle in quadcop e is de e mined wi h he Ea h’s magne ic ield. Ho izon al di ec ion o he Ea h’s magne ic ield is poin ing owa d he magne ic no h o he Ea h. Magne ic no h is de ia ed om ue no h. I s de ia ion is e e ed as a declina ion angle and a ies wi h i s posi ion on he Ea h. The yaw angle de e mina ion om he magne ome e measu emen is conduc ed as shown in (9) and (10): (9) (10) Whe e Hb is he magne ome e measu emen ec o in body ame and δ is he declina ion angle o he ea h’s magne ic ield. The angle ψ can be calcula ed using he equa ion abo e based on illus a ion in Fig. 4. Ob iously, he e o o oll and pi ch angle a ec s he accu acy o he de e mined yaw angle. The e o e, he magne ome e -based yaw aiding me hod should be applied wi h a alid oll and pi ch angle in o ma ion. Example o magne ic oll angle de e mina ion can be seen in Fig. 5. Fig. 5. Magne ic oll angle de e mina ion The heading-down plane and he X, Y, and Z plane a e iden ical, and H ep esen s he p ojec ed magne ic ec o on his plane. Angle ȠT can be calcula ed by ans o ming he magne ic ec o om he magne ic ield model o he heading- down ame. Angle λ is de e mined by he magne ome e measu emen s, which a e ans o med om he body ame o he X’, Y’, and Z’ ame. Likewise, he oll angle can be de e mined by sub ac ing ȠT om λ. This p ocess is gi en by (11): (11) The accu acy o magne ic ec o is limi ed o abou 1o in oo mean squa e by he modeling esolu ion, a ia ion abou ime and ex e nal dis u bances [10]. The magne ic ield is easily dis u bed by he en i onmen , hus he magne ome e -based a i ude me hod should be applied wi h an app op ia e calib a ion and dis u bance de ec ion. The λ and ȠT angle can be calcula ed using igonome y o kinema ic mo ing ame heo em. D. GPS-based a i ude GPS holds an impo an ole in a i ude es ima ion because o i s long- e m accu acy in eading quadcop e ’s posi ion and eloci y. La ge e o s in low-cos ine ial senso s can be coun e balanced by da a upda es acqui ed om GPS. Fo small scaled o a y-wing ai c a , an a i ude es ima ion me hod using he eloci y measu emen s wi h single an enna GPS was p oposed; he ime lag o he es ima ed a i ude was compensa ed wi h he help o measu emen s om gy oscopes by using he complemen a y il e [11]. A GPS ecei e calcula es i s posi ion by using a me hod called T ila e a ion which is shown in Fig. 5. Many ila e a ion algo i hms ha e been p oposed o de e mine loca ion accu a ely. GPS ecei e calcula es he posi ion, eloci y and ime based on he da a om he GPS Sa elli e. Fig. 6. T ila e a ion The 3D mul i-la e a ion uses he ollowing s anda d equa ions: (12) Whe e, (13) F om his heo y o ila e a ion, he syn hesized a i ude is called he pseudo-a i ude. I consis s o an equi alen oll angle abou he eloci y ec o o he quadcop e , an equi alen pi ch angle de ined as he ho izon al ligh pa h angle and an equi alen yaw angle de ined as he e ical ligh pa h angle. S anda d equa ion usage and qua e nion o quadcop e a e wo o he mos popula app oaches which a e used o calcula e pseudo a i ude. The qua e nion and Eule angles a e bo h common ep esen a ions o he a i ude. The qua e nion, which ep esen s a o a ion abou a speci ic axis, is de ined in e ms o ou pa ame e s in a column ec o as seen in (14). (14) One essen ial cons ain o he qua e nion in he applica ion is ha i s no m should be equal o uni y. The qua e nion uni s om q1 o q3 a e called he ec o pa o he qua e nion, while H δ Ƞ X Y ϕ ȠT H λ Y Z Z’ Y’ GPS ecei e (X, Y, Z) D1 D4 D3 D2 (X1, Y1, Z1) (X2, Y2, Z2) (X3, Y3, Z3) (X4, Y4, Z4) X kqjqiqq 310     = ).Z Z- 2(Z + ).YY - 2(Y + X1).X - 2(X = ).Z Z- 2(Z + ).YY - 2(Y + X1).X - 2(X = ).Z Z- 2(Z + ).YY - 2(Y + X1).X - 2(X 14144 13133 12122 )Z-(Z-)Y-(Y-)X-(X - )D - (D )Z-(Z-)Y-(Y-)X-(X - )D - (D )Z-(Z-)Y-(Y-)X-(X - )D - (D 2 4 2 1 2 4 2 1 2 4 2 1 2 4 2 1 2 3 2 1 2 3 2 1 2 3 2 1 2 3 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1     b H cossin0 sincos0 001 cos0sin 010 sin0cos H                               x y H H a c an Recen Inno a ions in Mecha onics (RIiM) Vol. 3. (2016). No. 1-2. DOI: 10.17667/ iim.2016.1-2/7. q0 is he scala pa . The inpu s a e he angula a es measu ed by he gy oscopes and he eloci y wi h espec o g ound in No h-Eas -Down di ec ion coo dina es acqui ed om he GPS ecei e , and he ou pu s a e he es ima ed oll angle, pi ch angle, and yaw angle, compu ed om he qua e nion es ima ed o he Eule angles can be de i ed by using: [12] (15) IV. ATTITUDE AND ORIENTATION SENSOR The o ien a ion senso s compa ed in his esea ch a e he GP9 and UM7 senso . They use hei own a i ude es ima ion in conjunc ion wi h he onboa d accele ome e s, in o de o measu e changes in eloci y. These eloci y es ima es a e hen compa ed o eloci ies epo ed by he GPS and p essu e senso s. Since a i ude inaccu acy is a majo sou ce o eloci y measu emen e o , i is possible o measu e a i ude by compa ing he accele ome e -based eloci y wi h GPS-based eloci y. In Table 1 de ail in o ma ion o GP9 and UM7 AHRS elec onic sys em can be seen. TABLE I. COMPARISON BETWEEN TWO ATTITUDE SENSOR Compa ison GP9 UM7 Powe consump ion < 150mA a 5.0V du ing GPS seek. < 100mA a 5.0V wi h GPS lock 50mA a 5.0V Ope a ing empe a u e -40C o +85C -40 o +85 C Communica ion 3.3V TTL UART 3.3V TTL UART, SPI bus Ra e o measu es o ien a ion, eloci y, and posi ion 500 Hz 500 Hz S a ic pi ch/ oll accu acy +/- 2 deg ee +/- 2 deg ee Dynamic pi ch/ oll accu acy +/- 1 deg ee +/- 4 deg ee S a ic yaw accu acy +/- 5 deg ee +/- 5 deg ee Dynamic yaw accu acy +/- 1 deg ee +/- 8 deg ee Resolu ion < 0.01 deg ees 0.01 deg ee Da a ou pu a e 0 o 255 Hz, selec able da a 0 Hz o 255 Hz (bina y packe s) 1 Hz o 100 Hz (NMEA packe s) I can be concluded ha GP9 has highe le el o sensi i i y o dynamic mo emen wi h less powe consump ion. Da a ou pu a e in he o m o accele a ion, angula a es, magne ic ield, ba ome ic p essu e, GPS al i ude, posi ion, eloci y, a i ude (qua e nion, Eule Angle). Bo h senso and p ocessing yield excellen gy o bias s abili y o e empe a u e. Adjus able low- pass il e and Kalman il e se ings p o ide cus omizable pe o mance o a ious applica ions. S a es and senso da a synch onized o GPS posi ion and eloci y using op ional ex e nal GPS module allows o alignmen calib a ion and hi d-o de bias and scale ac o empe a u e compensa ion o accele ome e s, gy os, and magne ome e . Magne ome e so and ha d-i on calib a ion can be pe o med h ough he se ial in e ace so wa e. V. CONCLUSION Fligh con ol plays an indispensable ole in managing quadcop e ligh s abili y. Gy oscope and accele ome e a e jus enough o moni o quadcop e ’s posi ion and mo emen o ien a ion, bu o coun e he e o ac o and ou side dis u bance, addi ional senso s such as magne ome e and GPS a e needed. While gy oscope compa es he angle be ween he ini ial posi ion and he desi ed posi ion, magne ome e compa es each ini ial and al e ed angle wi h ea h magne ic ield in o de o ge he changes in angle. Wi h his da a, he esul om gy o and magne ic senso can be compa ed o ge be e eading. GPS has accu a e eading on quadcop e posi ioning and mo emen . Senso o ien a ion GP9 has highe p ecision on a i ude changes eading, compa ed o UM7. ACKNOWLEDGMENT This wo k has been unded unde he LEADERS - E asmus Mundus G an (ag eemen numbe 2014-0855/001-001) by Eu opean Commission, h ough he Educa ion, Audio isual and Cul u e Execu i e Agency, in he Ac ion Plan 2 o he yea s 2014-2018. REFERENCES [1] Shiau, J. K., & Wang, I. C. (2013). Unscen ed Kalman Fil e ing o A i ude De e mina ion using MEMS Senso s. Jou nal o Applied Science and Enginee ing Vol.16 No.2, 165-176. [2] M.G.Ea l, & D'And ea. (n.d.). Real Time A i ude Es ima ion Techniques applied o a Fo Ro o Helicop e . IEEE Con e ence on Decision and Con ol Vol.4 (pp. 3956-3961). Alan is-Bahamas: IEEE. [3] Sanca, A., Fe ei a, J., & Ja ie , P. (2012). Real Time A i ude Es ima ion Scheme o Hexa o o Mic o Ae ial Vehicle. 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(2010). The US/UK Wo ld Magne ic Model o 2010- 2015. NOAA Technical Repo NESDIS/NGDC. [11] Tenn HK, J. S. (2009). Pi ch and Roll A i ude Es ima ion o a Small- scaled helicop e using single an enna GPS wi h Gy oscope. GPS Solu ions, 209-220. [12] Bea d, D. B. (2004). Real-Time A i ude and Posi ion Es ima ion o Small UAVs Using Low-Cos Senso s. AIAA 3 d (pp. 1-9). Chicago, Illinois: Ame ican Ins i u e o Ae onau ics and As onau ics.                                                       )qq(21 )qqqq(2 an ))qqqq(2(sin )qq(21 )qqqq(2 an 2 3 2 2 3021 1 2031 1 2 2 2 1 1032 1