A Vision Based Method for Aircraft Approach Angle Estimation

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1 ISSN -9825, CODEN RUXUEW Joral of Software, Vol.7, No.5, ay 26, pp ttp:// DOI:.36/jos7959 Tel/Fax: by Joral of Software. All rigts resered., +, ( ( ), 8) A Visio Based etod for Aircraft Approac Agle Estimatio ZHU Hai-Jiag, WU F-Cao +, HU Za-Yi (Natioal Laboratory of Patter Recogitio (Istitte of Atomatio, Te Ciese Academy of Scieces), Beijig 8, Cia) + Correspodig ator: P: , Fax: , fcw@lpr.ia.ac.c, ttp:// Z HJ, W FC, H ZY. A isio based metod for aircraft approac agle estimatio. Joral of Software, 26,7(5): ttp:// Abstract: A algoritm for estimatig aircraft approac agle sig compter isio is proposed i tis paper. Drig te ladig of a aircraft, te descet of te aircraft may be approximately cosidered as a pre traslatio motio. I tis case te epipole as te same coordiates i all images ad is called te Focs-of-Expasio (FOE), ad te aisig lie of te grod plae is termed te Horizo. Frtermore, ow te Focs-of-Expasio ad te Horizo are extracted from a few calibrated seqetial images is first itrodced, te te aircraft approac agle is deried from tese parameters. Simlated ad real experimets alidate tis algoritm. Key words: aircraft approac agle; FOE (focs-of-expasio); orizo :.,.,, FOE(focs-of-expasio), Horizo. FOE Horizo,.. : ;FOE(focs-of-expasio);orizo : TP39 : A 2, (maed aerial eicle, UAV),. [,2]., [3]. GPS(global positioig system) INS(iertial aigatio system).,,, [5]. GPS, Spported by te Natioal Natral Sciece Fodatio of Cia der Grat Nos.6754, ( ); te Natioal Hig-Tec Researc ad Deelopmet Pla of Cia der Grat No.22AA42223 ( (863)) Receied ; Accepted 25--2

2 96 Joral of Software Vol.7, No.5, ay 26,...,,.,,., [6].,, 3 : (pricipal poit).,.,.,,,,...,,,,,., (epipole) ( ), FOE(focs-of-expasio).,, (pricipal axis, )., FOVC(field of iew ceter)., Horizo.,., P P, FOE, W ; P V, VP V, VP ( ); P,P,,P t,t,,t ; FOVC. α. Time t Camera cetre t P t P P FOE FOVC VP Image plae W α Grod plae V Fig. Geometry of te aircraft approac agle

3 : ,P ;Horizo ;FOE ;VP., α β, β. [],, β FOE VP. Horizo P (Camera cetre) FOE β VP Grod plae W α Fig.2 Image plae V easremet of te approac agle α 2 α K, w=k T K, FOE VP e, β T T T e ( K K ) e w cos( β ) = = () T T T T T T e ( K K ) e ( K K ) e w e w β, α. 2 FOE VP., [2]. 2, FOE, VP. FOE VP, (). [3,4] FOE., FOE VP. X, x, 2 x, :sx=hx,,h, 3 3 ;s. H = x=[,,] T [ ] T , 33 s = x =,,, H i 32 32, H 2., x i x (i=,2,,), : i =. = A = (2) [ ] T = ;

4 962 Joral of Software Vol.7, No.5, ay 26 = A. A, H.,, 4 H., 4, 4 3 []., H. [5], 3 l.,, ; l. Fig.3 Geometry of Homograpy H 3 H H H U=U V, : [ ] 3 2 U = ( i U i );V 3 3, = 3 2 λ λ λ V.,λ I (i=,2,3) H,. λ 2 =λ 3, λ FOE; λ 2,λ l Horizo. [5],, w. l p p, l p =w p (3), Horizo, (3) VP. :, 4 3, 4., 4, P4P [6] FOE VP 4, π Z=, 4, H π, H π =K[r,r 2,t], :K ;r,r 2 R ;t., H π R t. R,R 2 t,t 2 2, 2 3 l

5 : 963 : T e = K ( R2R ) ( t2 R2R t), e ( 2 = K t2 R2R t)., R R 2, e =e 2 =K(t 2 t ), FOE., VP. 3,. (), [2] ; (2), (2) H; (3), FOE Horizo;, (3) VP; (4),.2 (). 4 4., f =2, f =,s=, =32, =24. (), 4 A,B,C,D, 4 Z=, 4 X A =[,,] T,X B =[4,,] T,X C =[5,2,] T,X D =[2,3,] T. r=(.8568,.3549,.374) T, θ =.5325π ( r θ R). α [5,75 ], α =,r=z/ta(α),z=2. C =(.77r,.77r,z) T t =R C ; 2 C 2 =(.47r,.47r,.667z) T t 2 =R C 2., 6 6., σ(2.)., FOE VP,.,, P4P 4(a) 4(b)., RS(root mea sqare), 5(a) 5(b) P4P RS., ; RS, RS P4P. (2)., 6. 2,3,,6.,,,.5.. 6,, 6(a) 6(b) 5,3,45, RS.,,, RS.

6 964 Joral of Software Vol.7, No.5, ay ea of te approac agle ea of te approac agle Noise (pixel) Noise (pixel) (a) Or metod (a) (b) Based o P4P metod (b) P4P Fig.4 Te aerages of te estimated approac agle der differet oise leels RS error 5 RS error Noise (pixel) Noise (pixel) (a) Or metod (a) (b) Based o P4P metod (b) P4P Fig.5 Te RS errors of te estimated approac agle der differet oise leels 5 RS

7 : 965 ea of te approac agle (degree) Te mber of images Te mber of images (a) Te aerages of te estimated approac agle (a) (b) Te RS errors of te estimated approac agle (b) RS Fig.6 Te aerages ad te RS errors of te estimated approac agle der differet mber of images RS,,,,...,, 7 6, 5 ; 8 2 6, 35. [2], Cay, 4 ( ); FOE Horizo,., 5.37, ,. RS errors (pixeeels) Fig.7 Te st image seqece of te lab. scee 7

8 966 Joral of Software Vol.7, No.5, ay 26 Fig.8 Te 2d image seqece of te lab. scee 8 2,,, 72.6,, 3 9 ( )., FOE Horizo; ,. Fig.9 Te 3rd image seqece of te lab. scee 9 3 5,.,.,,...,. Refereces: [] Ster D, Hamel T, aoy R. Visal seroig based o omograpy estimatio for te stabilizatio of a x4-flyer. I: Proc. of te 4st IEEE Cof. o Decisio ad Cotrol, Vol ttp://

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