Polarimetric Target Detector by the use of the Polarisation Fork

Transcription

1 Polrimetri rget Detetor y the use of the Polristion For Armndo Mrino¹ hne R Cloude² Iin H Woodhouse¹ ¹he University of Edinurgh, Edinurgh Erth Oservtory (EEO), UK ²AEL Consultnts, Edinurgh, UK POLinAR009 / he University of Edinurgh

2 Mthemtil formultion POLinAR009 /

3 ingle (oherent) trget ttering mtrix: VH ttering vetor: re, 4 ( Ψ) [,, ] Bsttering & reiproity POLinAR009 / re, ttering mehnism: U ( φ, τ, ν ) ( Ψ) [, ] 6 Huynen prmeters: 0 m [ U ( φ, τ, ν )] exp( jξ ) m m Polristion For: 0 X C tn γ, X, C, m m X - pol Nulls Co - pol Nulls X - pol Mx

4 Prtil trget: rget Cohereny Mtrix he seond order sttistis re neessry. [ C] [ C ] Lexiogrphi sis [ C ] L Clssil formultions: Puli sis [ C ] P ( )( ) ( ) ( )( ) ( ) ( ) ( ) POLinAR009 4/

5 Polrimetri Detetor γ Polrimetri oherene: i( ) i i( ) i ( ) ( ) i( ) i ( ) Where: i ( ) j [, ] j, j, Demonstrtion: In the new sis rget: ) A hnge of sis where the trget to detet is one xes [,0,0 ] i ( ) ) he Polristion For (or Huynen prmeters) is slightly hnged to otin: Pseudo trget: [, ] P,,, C i ( ) P P 0 0 POLinAR009 5/

6 POLinAR009 6/ Polrimetri Detetor,0,0 p,, ( ) ( ) ( ) p p p p C C C γ, C i i p ( ) ( ) ( ) ( ) ( ) ( ) C i i p p R R R R R R C i i C,,,, ) Evlution of the polrimetri oherene ( ) p > γ, Detetor (first ttempt):

7 POLinAR009 7/ ( ), i i p γ ( ) ( ) ( ) ( ) ( ) ( ) i R R R R R R Where: Polrimetri detetor If the omponents of the sttering vetor re unorrelted, the ross produts orrespond to noise residul terms (ising low oherene). If the omponents re orrelted the ross produt is not 0 nd the oherene is ised up/down depending on how they sum with phse. After normlistion for:

8 POLinAR009 8/ Bis removl P P P d P P P γ P ( ), p d γ ( ) ( ), p d γ Detetor: 4) Definition of new opertor tht wors on trget powers Where: ( ) p d > γ,

9 hreshold seletion POLinAR009 9/

10 mple detetor Approximtion: γ (, ) x E[ x] d p E E E E γ d E E CR CR E E CR CR mple detetor mplitude POLinAR009 0/ CR CR CR

11 Detetor mplitude CR Detetor: rndom vrile Rndom oherene tndrd devition Detetor mplitude i N( 0, ˆ σ ) r N( 0, ˆ σ ) Averge window 5x relistions r ji CR POLinAR009 / CR CR CR

12 Vlidtion POLinAR009 /

13 Full-polrimetri Dtset DLR: E-AR L-nd Lndserg AROM projet POLinAR009 /

14 Detetion P Multiple refletion Oriented dipole [,, ],, L Odd-oune Even-oune Horizontl dipole Vertil dipole POLinAR009 4/

15 rihedrl CR Open field: multiple refletion L-nd 5x5 ree Wolf Metlli net rihedrl CR Red : ; Green : ; Blue : POLinAR009 5/ Red: Even-oune Green: 0 Red: Odd-oune

16 rihedrl CR Open field: oriented dipoles L-nd 5x5 ree Wolf Metlli net rihedrl CR Red : ; Green : ; Blue: POLinAR009 6/ Red: Horizontl dipole Green: 0 Red: Vertil dipole

17 Forested re: multiple refletion L-nd 5x5 Red : ; Green : ; Blue : POLinAR009 7/ Red: Even-oune Green: 0 Red: Odd-oune

18 Forested re: oriented dipole L-nd 5x5 Red : ; Green : ; Blue: POLinAR009 8/ Red: Horizontl dipole Green: 0 Red: Vertil dipole

19 Comprison with Polrimetri Whitening Filter (PWF) L. M. Nov, M. C. Burl, nd M. W. Irving, "Optiml Polrimetri Proessing for Enhned rget Detetion," IEEE rns. POLinAR009 Aerospe 9/ nd Eletroni ystems, vol. 0, pp. 4-44,99.

20 L-nd Open field 5x5 PWF POLinAR009 0/ Red: Even-oune Green: 0 Red: Odd-oune

21 L-nd Forest: POLAR 5x5 PWF POLinAR009 / Red: Even-oune Green: 0 Red: Odd-oune

22 Conlusions A trget detetor ws developed sed on the unique polrimetri for (PF) of the single trget (similrly the Huynen prmeters n e used). he mthemtil formultion rried out is generl, nd so n e pplied for ny single trget of interest (s long s the PF is nown). he vlidtion ws hieved over two tegories of trgets: multiple refletion nd oriented dipoles, with results in line with the expeted physil ehviour of the trgets. A supplementry theoretil vlidtion is rried out, where the lgorithm is ompred with the Polrimetri Whitening Filter (PWF). POLinAR009 /

23 hn you very muh for your ttention! POLinAR009 /

24 Uniqueness of detetion We pss with projetion to the spe of Power: C R Defined sis ê i eˆ ˆ ˆ e e C the sttering vetor in is represented y: [, ], C he projetive spe is otined with the opertor: P ii e ˆi C R his is sujetive opertion, hene the vetor in P is uniquelly defined one we selet the vetor in the -D omplex spe (nd we set sis). he detetion is unique sine the detetion rule is defined on the power (CR or pe) nd the Power spe is uniquelly relted with the trget spe (we need only rel numers). POLinAR009 4/

25 Uniqueness of detetion P [,, ] 0 [ ],0, 0 0 [ 0,0 ], [ P] POLinAR009 5/

26 Coherene: rndom vrile Coherene mplitude Rndom oherene CR Coherene mplitude 5x5 0.5 tndrd devition 50 relistions CR CR CR CR POLinAR009 6/

27 Entropy estimtion POLinAR009 7/