An Improved Method for Measuring the Height of Quad-rotor Aircraft

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1 A Improved Method for Measurig the Height of Quad-rotor Aircraft Yi Huag School of Iformatio Sciece & Egieerig, Cetral South Uiversity, Chagsha, Hua, Chia Hua Keyshare Iformatio echology Co., Ltd, Chagsha, Hua, Chia Yoggag Li & Ximi Cheg School of Iformatio Sciece & Egieerig, Cetral South Uiversity, Chagsha, Hua, Chia ABSRAC: he air pressure sesor provides high-precisio height iformatio by temperature compesatio, but it is easily iterfered by eviromet, ad the precisio is decreased by the height. his paper presets a ew approach for measurig the height of quad-rotor aircraft, usig the air pressure seor, GPS ad accelerometer data. he proposed algorithm which is based o discrete Kalma filterig results i elimiatig iterferece from evirometal chage o the air pressure sesor. he algorithm was tested extesively i simulatios ad experimets, the results show that this method ca get more accurate height iformatio, ad fully meet the demads of flight cotrol of quad-rotor aircraft. Keywords: quad-rotor aircraft; pressure sesors; discrete Kalma filter; height measuremet INRODUCION With the developmet of the iertial measuremet uit, the attitude cotrol ad trajectory tracig of quad-rotor aircraft are gradually resolved, maig the aircraft achieve autoomous flight. he height measurig uit is required to provide real-time ad accurate flight altitude, especially i low altitude. herefore, how to use the limited airbore equipmet o the four-rotor aircraft to obtai accurate ad reliable iformatio is the ey to the research. GPS ca provide positioig iformatio for the four-rotor aircraft, but its log respose time ad error rage ca t meet the real-time requiremets ad the accuracy. If the umber of star searches ot satisfies the requiremet, it will seriously affect the accuracy of height iformatio; the pressure sesor has advatages of small volume, low power cosumptio, characteristics of short respose time, high reliability, high measuremet accuracy ad wide measurig rage which are widely used i the four-rotor aircraft, but the pressure highly susceptible to the evirometal wid ad measured from the data cotais all ids of oise, ad the error icreases with the decreasig height. Accelerometer ad gyroscope iertial uit ca be reactio to the height of dt time the aircraft chages, ad the error after dampig treatmet of the aircraft will appear less. herefore, combiig GPS with differet characteristics of the pressure sesor ad accelerometer iertia uit ca get high accuracy from the aspect of height iformatio. I this paper, we first establish a reasoable ad accurate motio model for the pressure sesor, GPS ad iertial sesor uit, ad the we carry out the data fusio with the discrete Kalma filterig algorithm. Fially, we compare the measured height of radio module to demostrate the feasibility of this method. 2 DAA PROCESSING AND MODELING OF AIR PRESSURE SENSOR I the gravity field, the atmospheric pressure decreases with altitude, ad the height iformatio of the aircraft ca be obtaied by usig this priciple. he relatioship betwee the stadard ad height is expressed as follows: β R/ g PH ( ) ] b β 0, H Hb β Pb b β () 0, H Rb I P Hb g PH 43

2 I this formula, P H represets the correspodig pressure value whe the height is H; P b ad b respectively represet the air pressure ad temperature whe the surface height is H b ; βrepresets the vertical temperature gradiet; G represets the gravity acceleratio; R represets the air specific gas costat. I practical use, the pressure ad temperature are easily affected by the eviromet which could result i height error. From the formula of partial derivatives, we ca coclude: he relatioship betwee temperature ad height is proportioal, but the atmospheric pressure ad height is iversely. herefore, the wid iterferece will lead to a lower measured pressure; as a result, the height of iformatio is higher tha the actual height. We eed to hadle this problem. Read raw data from the pressure sesor ad use the average filter: p t i t i i p i he measuremet equatio is as follows: (2) H h h' λ (3) baro b I this formula, h b represets the true altitude; h represets the error of system; λ represets the oise of measuremet. 3 DAA PROCESSING AND MODELING OF GPS military use, ad the frequecy of its update ca t meet the real-time requiremets of aircraft. his research selects the Ublox-GPS module ad carries o the low-pass filter processig to the GPS height iformatio. he GPS sigal is aalyzed by Fourier aalysis of the height measuremet data collected at 50Hz frequecy, ad the cutoff frequecy is 0.5. he spectrum diagram is as Figure. he measuremet equatio is as follows: HGPS hg λ (4) 2 I this formula, hg represets the true altitude, ad λ 2 represets the oise of measuremet. 4 DAA PROCESSING AND MODELING OF ACCELEROMEER he accelerometer is measured by the liear acceleratio of the vertical groud motio to measure the height of the flight. We respectively use the strap-dow type ad the three-directio lie acceleratio sesor alog the three axes of the aircraft-fixed coectio, which calculate the three directios of the lie acceleratio. I this study, the sesor with three axes ad three-axis accelerometer, which ca directly measure the acceleratio of the vertical directio, is used for MPU6000. he itegral equatio is as follows: adt ε h dt ε ( adt ε ) dt ε (5) I this formula, a represets the t momet of acceleratio; represets speed; h represets altitude; ε ad ε 2 represet the error of system. Due to the height of the accelerometer measuremets that will have a cumulative error over time, it is required to combie with other high sesors. he measuremet equatio of accelerometer is show as follows: az a' λ (6) 3 I this formula, a represets the actual vertical acceleratio, ad λ 3 represets the measuremet oise. Figure. Frequecy spectrum aalysis of GPS altitude. GPS is the global positioig system. he localizatio priciple is based o the measuremet of the itersectio to determie the locatio of the itersectio method. But the accuracy of the GPS developers to the civilia use is far less tha the accuracy of its ow 5 SOFWARE FLOW-CHAR OF DAA FUSION ALGORIHM I this flow chart, H baro represets the altitude of barometer; H GPS represets the altitude of GPS; H represets the height value resultig from the data fusio. 44

3 6 IMPLEMENAION OF HE DISCREE KALMAN FILERING ALGORIHM he priciple of Kalma filter is the liear miimum variace estimatio, ad the estimatio criterio is based o the miimum variace. his study uses adaptive KF to realize mutual compesatio of the height from GPS ad pressure sesors. () he establishmet of system state equatio ad measuremet equatio he height h, vertical velocity Z ad acceleratio a are regarded as the state variables. he state equatio of this system is show as follows: h 0 0 h 0 z 0 0 z 0 w a z a ' [ ] (7) Accordig to the aforemetioed aalysis of the height, we establish a system of measuremet equatio as follows: H baro 0 0 h λ H 0 0 λ GPS z 2 a z 0 0 a ' λ 3 (8) (2) Desig of Kalma filter State equatio ad observatio equatio of discrete Kalma filter are as follows: ( ) X AX Bu( ) (9) Z ( ) H X v( ) (0) I the formula, the oise of the system u() ad the observatio oise v() are ot related to the Gauss white oise, ad the correspodig covariace is respectively Q() ad R(). E{u()}0; E{u()u() } Q()δ j ; E{v()}0; E{v()v() } R()δ j. he system samplig frequecy is 50Hz, so the state trasitio matrix is A , the oise matrix is B ad the measuremet matrix is H 0 0. herefore, accordig to the 0 0 priciple of Kalma filter: a) he predictio equatio of momet is as follows: X ( ) AX ( ) () b) he state update equatio is as follows: X ( ) X ( ) K ( Z( ) H X ( )) (2) c) he gai equatio is as follows: K P H '( H P H R ) (3) d) he estimatio error variace is as follows: P ( I K H ) P (4) e) he error covariace update is as follows: P AP A BQ B (5) 7 SIMULAION RESULS o verify the validity of this study, a simulated test was carried out i MALAB. he variace of w was 00; the variace of λ was 200; the variace of λ was 80; the variace of λ was 0.0. Because of 2 3 the high error of GPS, it is ot suitable to be used directly for data fusio. herefore, the adaptive factor σ is used to determie the ifluece of the curret eviromet o the height of the barometer. Give the iitial state of the filter as follows: P(0) ; x(0) (6) he algorithm simulatio curve is show i Figures (2) to (4): 45

4 the maximum close to the true height value. he error is relatively serious whe the samplig poits are i the rage of 2,300-2,800. herefore, the discrete Kalma filter with the additio of the adaptive factor ca get more accurate height iformatio, which satisfies the precisio requiremet of the four-rotor aircraft. Figure 2. Barometer height, GPS height, fusio height ad radio altitude. Figure 3. Fusio height ad radio altitude. Figure 4. he error betwee the fusio height ad the radio altitude. 8 CONCLUSION From the simulatio results, we ca coclude that the height of the pressure sesor is close to the real height i the case of the outside eviromet. However, the height of GPS with poor accuracy is highly variable. Whe there is wid that forms the exteral eviromet, the height of the pressure sesor is icreased, but the GPS height is decreased. Due to the additio of the adaptive factor, the fusio height will be adjusted accordig to the tred of the GPS fusio results, with REFERENCES [] Isidori A, Marcoi L, & Serrai A Robust oliear motio cotrol of a helicopter. IEEE rasactios o Automatic Cotrol, 48(3): [2] Shi J, Noami K, Fujiwara D, et al Model-based optimal attitude ad positio cotrol of a small-scale umaed helicopter. Robotica, 23(): [3] Yoghog Hu. 2006, Applicatio of data fusio approach o altitude locatiofor small aircraft. Computer Measuremet & Cotrol, 4(0): [4] James F. MeLella & Joh Schlepper, 994. GPS/Barometry Height-Aided Positioig System, IEEE 994 Positio Locatio ad Navigatio Symposium. [5] McLitoc, D. & M uttle GPS ad barometry for mic positioig, preseted at the SPM opograpllcal Worshop, he Hague, Netherlads. [6] Scott Burgett et al Device ad Method for Calibratig ad Improvig the Accuracy of Barometric Altimeters with GPS-Derived Alitudes, Uited States of America,A,US 2004/09676 A. [7] Grewal. Adrews Kalma Filterig--heory ad Practice Usig MALAB, Joh Wiley. [8] W. ag, G. Howell, & Y.H. sai Barometric altimeter short-term accuracy aalysis, IEEE Aerospace ad Electroic System Magazie, 20(2): [9] Kigsto D B, & Beard R W Real-time attitude ad positio estimatio for small UAs usig lowcost sesors //AIAA 3rd "Umaed Ulimited" echic a Coferece. Chicago, USA: [0] Sog Ebi, Zhu Yumi, Zhou Jie, et al Optimality of Kalma filterig fusio with cross-correlated sesor oises. Automatic, 43(8): [] R.E. Kalma & R.W. Koepce, 958. Optimal Sythesis of Liear Samplig Cotrol System Usig Geeralized Performace Idexes, RANS. ASME, 80, pp: [2] S. adooro el al Rescue Robotics-DD Project o Robots ad Systems for Urba Search ad Rescue- Spriger Lodo, [3] H. Naaishi, H. Hashimoto, N. Hosoawa, K. Ioue & A. Sato Autoomous flight cotrol system for itelliget aero-robot for disaster prevetio, Joural of Robotics ad Mechatroics, 5(5): [4] Li Z, Lili X, Famig L, & Yi C Applicatio of UKF for MEMS IMUs ad fluxgate sesors based attitude ad headig referece system of carriers. Chia: ICIEA d IEEE Coferece. [5] B. Eli & L.D. Reid Dyamics of Flight -Stability ad Cotrol- 3rd. Editio, Joh Wiley & Sos Ltd. [6] Qi Yogyua Iertial Navigatio. Beijig: Sciece Press. [7] Qi Yogyu & Zhag Hogyue Kalma Filterad Itegrated Navigatio. Northwester Polytechical Uiversity Press. 46

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