Passive Aircraft Altimetry using GPS as a Bistatic Radar : A simulation model
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(190) P _ NQAPN ` _ rR X s |ZTP"S^V P}h0V % ZTART`h
(191) "`fS
(192) RAMORPPWDh[PP}h0NQTPP Md SY[ZA`yVUR Ph V`yZAX RTh"M
(193) WTMOV `i_ SY`NQR"PXUP"V MdlVYR[R _`iR S [S^XYxTPxANQs S V _ XUP"VUVUMd`yR|\ q `iR _ g
(194) q S^Pc_ X X AP V ZTRTh j Aq `fS `fS q W[_ X MO`iRAPh _rsys ` Xk_ MpVUMrhAMOV q _ _rsysi_ q sy_ _ q _ _ TP"` q IXM s XY`iNQPXYPV o + A`
(195) kXYV MORTSYNQ` X SV MdhAMdV x Z s SYPS T` s P 3:c MdRThkWTMOV _ NQP"XYP"V MdVYP MrSYSY` Pp`iRTS^XYVUZANQP"RIXUS X APQP P,
(196) XYV N|M RAP"XY`
(197) M PSXYV MOR~S^NQ`yX^XYP}h W% XAP|ao
(198) "MdR WDPh[x P"XYP,
(199) XYg P}h RQNe` s ` X MOV M xTxAs `
(200) "sMOXY` _ RT_ S`yXLq `fS _ \ XUP"R h[P}g S^`iVUMdW s P7`yX |M x MrSYSY` g PS [S^XYPN MOR~h SYZ
(201) MOR3M s XYPVYR~MXY` g PcX _ XAPao _ Z s htW~PWDP"RTP 2
(202) "`iM s RTPM X M8
(203)
(204) N `iS 3X T`iS.`fSX Z~S^PQM WA`fS^XUMXU`.
(205) V MdhAMdVcM XY`iNQPXUP"V,0 AP"VUP MkS^` R~M `iS XU VUMdRTSYNe`yX^XUPh_ \ V _ N_ MkxAsh[` 1DPVYPRIX.S _ ZA_ V
(206) P8DVUP+~P
(207) XUPh MOXcX AP q V _ s ZARTh MORTh X AP"R<VYP,
(208) P` gq Ph3s W% XAP MdP"V _dxAs MORAP |\M s S _ M3h[`iVYP,
(209) XpSY` q RTM s `fSVUP
(210) P` g Ph0l` X `iS xD_ SUSY`yW s PQ\ _ V X AP Md`yV
(211) V M\ X X _
(212) M s
(213) Z s MXUPXAP AP"` q IX _ g PV q V _ ZARTh|W%|ZTSY`yR q XAPh[`21 P"VUP"R
(214) P.`yR MOVUVY` g M s XY`iNQP Lj AP.VUMrhAMOV SY` q RTM s SD` sis X APR R _ X WDPXUVUMdRTS^NQ`yX^XUPh W%eX TP.Md`yV
(215) V M\ X MdRThQX AP.S5[S XUP"N ` sys WDP x MrSYSY` g P P}S^`fh[PScV MdhAMdVwSY` RTM SZ~S^P}h3`yR V Mdh[`
(216) NQNpZART`.
(217) MXY` R~ScS5[S XUP"N|ScMdVYPeM S VYP TP
(218) XYP}h MX XB AP q V _ ZARTh0SY`yR
(219) "q P X As P}S^P<S^` q RTM s S|MdVY_ P XU_ VUMdRTSYNe`yX^XUPh _ _ RP s P,
(220) XUV _ NQM q RAP"XY`s
(221) "_ M g PSQNpZ
(222) VUPSYP"N W `yR X S^P \-V MdhAMdV j A`iS PMdhTSLX X TP`fh[PM X TMOX XAPSYPcSY` RTM SD
(223) MOR|WDPcZ~S^P}hQ\ V XAP x ZTV s xD_ q SYP _ \w_ MWA_ `fS X MXU`.
(224) x MrSYSY` g Ps VUMrhAMOVLS5_ [S XUP"N n` q RTM s S\ V _ N SYMOq XYP sis s ` XUPS`iRQX AP ! sy_ WT_ M s #SYZ_
(225) S^ `yXY`M|_ RTS [`yR S^qXYPN %[ S XUP"N ! # & \ Z s 2~sys XAPtRTP
(226) P}SYSUMOV VYP *rZT`yVUP"NQP"RIX S MdRTh-
(227) "MdRFWDPkZ~S^P}h `yR aPSYPMOV
(228) _ R Z~S^`iR q ! # SY` q RTM s S VUP+TP,
(229) XUPh \ V _ N q V _ ZAR~h TMdS W~PP"R qr_ `iR q _ R \ _ VpX AP s MdS^Xh[P,
(230) "MdhAP R ) MOVYX R[ :aP`yV M x V _rx~_ S^P}h XAP ZTSYP _ \D! # tSY` q RTM s SVUP+~P
(231) XUPht\ V _ N. .
(232) . C @"zB-G;ld@8?BDC. _ \
(233) "PS^MOP}R M S^SYZAZAVYV^\?\?M/M8
(234) "
(235) PP S T\ P"_ ` VQISYXUMOS XY P sis J` XUK PtM P"sVUXY`y`iNQNQP"PRIXUX V5M V \?S j XTTPtMOXpN|XMOA`iRFP `iVURIP+XYTP"P,VU
(236) PXUS^PXhFSYMd` SpRT`yM R S X AMdPkVYP S^PS^XYRTV SY`yRR q _PR Z P"VUP h[P ` q P"VUPh `yR x TP"R¼s x Øa_nZA_ WDP"V M8
(237)
(238) `fh[PRrX NQP}MdSYZAVYP}h q XAs P VYP TP
(239) XY` _ RTq S s _ \ V _ _ N q X AP _
(240) P}MORs g j TPL`ihAPMX ZTSYPX AP VYP TP
(241) XYPhSY` RTM S \ VvMO`iV
(242) V M\ XvM XY`iNQPXUV5 MrS-h[`fS5
(243) "ZTSUS^P}hcW%MX "WDP"V. P"X M s .`iR _ LMOR~h3PK x P"VU`yNQq P"RIX s M s _ VYP}S^Z s XUS
(244) _ R 2 s VUNQPh X A`iScXAP _ V5 MOX "WDP"V q P"X M sq M S h[PVY` P}h S NQP X AP VYP"XY`
(245) "M VYP}S^Z X S
(246) R
(247) "P"VURA`yR M/
(248)
(249) ZAV M/
(250) /DM X Z 3XAP XYP
(251) TRA`8*IZAP X _ s _PS^XY`iN|Mg XYP.X A_ P AP"` q IX_ \ V _ N(X s AP
(252) _ s VYVUP s M_ XU` _ R|\ ZAR
(253) q XY` _ R MdS *IZA`ysXYP _SY`yN q xAs P j T`iS
(254) R
(255) P X MdSw\ ZTV^X AP"Vh[P P Ph MdRTh PKAMONQ`iRAPh `yRpS^XYZ~h[`yP}S P"V-W X MdRTh MdRThS^P}M&. W% Md_ S^XYPVUSx P"X M s l`iR Or g si_d j x TP p`iR g P}S XU` q MXYP}h SYP g P"V M s NQPX _ g _ hAS __ \DP}S s XU`yN|MXU`yR q X AP TP"` q IX\ V _ N X APVUP+TP,
(256) XYP}h SY` q RTM s x MdV^X s ;`yX AP syxQ_ \DMX AP _ VYP"XY`
(257) "M s N _ h[P s \ _ VVYP TP
(258) XYP}h ! # pSY` q RTM s S j$ _ P"K x PVY`iNQP"RIXUM s ~` q rX S
(259) _ R 2 VUNeP}hX APX AP _ VU`yP}SMdRThX APVYP}S^Z s XU`yR q xXAP"`fVYSa\ _ MOVUVUN|PM MOR`iS
(260) "P R _ \ X `iAR P| WA`fS X MXU`.
(261) |M s XU`yNQPXUP"V M xAx P}MOVUPh X _ WDP SYMOXY`fS \ n`iR q 6AZTV^X AP"V; _ VUm3`yR _ qr_ q j TPt`fh[PM \ VeX A`iSeX APSY`fS VY` `iRTMOXYPS \ V N [MdMdW \ VUSeb IR~MONQ`.
(262) S b ' MdR? \. XAPNQ` s `yXUMOV_ M xAxAs `.
(263) MXY` _ R~S_ h[P gq P si_dx PhkMX_ X T`iS
(264) _ N Bx Md_ R?_ \ PMXUZAVUPcXAP XYV MdhAB ` XU` _ RTM s ao _ P q `iR RTM g ` q MXU` _ R S5nS^XYPN|S\ _ V Ne`fSUS^` s P}S X; _ Z s h WDPe`yRIXYPVYP}S XU`yR q X _ `iR g PS^XY` q MOXYPpX AP xD_ SUSY`yWA` s ` XU`yP}S _ \ZTS^`iR q M x MrSYSY` g P.M s XU`yNQP"XYP"V`iRTS^XYP}Mdh . .
(265) p . j TP x ZAV xD_ SYP _ \ X A`fS X TPSY`iS TMrS W~PP"R X _ P"K[MdNQ`yRAP|MdRTh
(266) ~MOV M/
(267) XUP"VU` P XAPQZTS^P _ \$! # . MrSMQWA`fS X MXY`
(268) V MdhAMdVM XU`yNQP"XYP"VcS [S^XYP"N [`yR
(269) "P X A`fS`fh[PMQ`fSRAP `yX T`yR b[\
(270) ZTS TMdS N|Md`yR s FWDP"PR _ R x P"VY\s _ VUNQ`yR q MdR `iRA` XU`iM s S^XYZTh(8MdRTh x VYP x MOVU`iR q \ _ VQ\ ZAV^BXAP"V|VU_ PSYPMdV
(271) 6TZAVYX APVYN _ VUP/?`yX A`iR XAP.XY`iNQP s `yNQ`yXUS _ \-X APcX TPSY`iSnX AP AP` q rXNQPMrS^ZAVUP"NQPRrXNQPX _ h ~MdSWDP"P"R|P"KAMONQ`yRTPh` XeVUPS x P
(272) XX _ h[`21 P"VUP"RIX x MdVUMdNQPXYPVUSOSYZ
(273) |MdSX TPX3 x P _ \ q V _ ZTRTh
(274) _ g PVMdRTh XYP"VUV MO`iR g MOVU`fMXY` _ R~S 6TV _ N(X TP _ VU` q `yRTM s x ZAV x~_ S^P.X3 _eqr_ M s S TM g P.PNQP"V q Ph- cbj AP g P P syN _rx hAMdP RTh Np`yZ~N S xAX s P"W~NQP P"
(275) RIXtN M SYP`yXYN P Z P"s MR XY` Z_ RE N X _ h[PN|s MO\ mr_ P VQAX APP3` IVUP+Xk~NQP
(276) PXUMrPS^h ZTVY! PNe# EPRISYXU` S q RTM s P"S V _ s _ xAs _ q _ q _g gh[MO` 1DVnPVY`yR PRIq X YX PV VYV MO`iP"R VYXY`iPnSP MOg VUPP VUMh[s P}S^X3`i V xMOWPS P _\ n`yq R V
(277) _ PZANQRTh MdR%
(278) _ g SYP`iN VUSP` q
(279) "4MOXY` MRTXUSP"V _ ` VeWD\ _ PVUh PS^XRA'P8{X `yAX P SY`yN Z s MOXY` _ x R _dN x _ h[P s ` sis WDP hAPSY` q s RAPhtX _ W~P MdS ~PK[`yW xTs Pps 2 MrS xD_ _ SUS^`iW s P/sy~s ` P ~` X _ S _ Z s h WDPPMdS5QX _ hAP g P sy_rx MdRTht`yN xAs P"NQP"RIXaP q AMQRAP N _ h[P s \ _ VaSY` q RTM s S5
(280) MX^XUP"VU`yR q .
(281) . ~B =:;v@}8?BDC 9FHI@B-G NQSYPP X X Th P eN j _ ThAPeP s NQX _ P"X x PV^h \ _ S VY N Z S^`ihNpZWDs PQMOXYP ` _ M RTSZTMOMdXYRTPhkhP g M`yX s ZTMVYXUP}P S X APP
(282) X.AX P"` q h[I`2Xa1 NQP"VUPP"MrRIS^X ZAVUP"MdNQVUMdPN RrX PXUP"V S w_ SYZ
(283) <MrSaXUP"VUVUMd`y_ R g MdVY_`fMXUs ` _ RTS _ V g s `fhnX _ \ MORIXYPRARTM x
(284) _ g PVU_ M q P cj APeRnx ZANpWDP"V _M \ MOx ` MOMdV W MONQPtP"XUXY`yP"NQV SP µMORTØh S S
(285) P"RAR~P3MOVUP ` _ M ScZT`iRMO
(286) XYs` ZTRhAPNQh P`yR<X X Th0P S^X `iTNpP Z As MP"XU` ` _ IRTX SNQMOVUP}PQMdSYh[ZAPVY
(287) "P}`ihh[P}h ` W?X XX AAPP SY`yg N Z s s MOXYs ` _ RkN _ hAP s
(288) _ N _ x MOVUPg h sX _ X T_ P XYVUZAP AP"_ ` q IX ` sys WDPq ZTSYPh . . j TPkSY`yN Z MXY` R N h[P ~MdS W~P,
(289) NQPkMORF`iN V^X MORIX MdV^X \XAP XAPSY`fS W X h[ZAPtX. VUP+*IZA`iVUP"NQP"s RIXUSv_ \ V _ N _ B bs OMORTh S^`iR_
(290) "P `yX`iSXAPx~S __rs Z[XU` _ Rpx NQPX _ _ h
(291) _ SYP"R j AP_ SY`iNpZ s MXU` _ R_ N _ h[P s `yXUSYP s \v`fSR _ XS^Z xTx~_ S^P}h|X _ WDP.M x MOVYX _ \lM s MOV q PV S5nS^XYPN IWTZ[X XAP 2 RTM s M s XU`yNQPXUP"V NQ` q IXaWDP . ' "t e! 2 j TP.S _ds Z[XY` _ RtNQPX _ h TMdS WDP"P"RtX _ h[P g P si_dx MpSY`yN Z s MOXY` _ RtN _ h[P s _ \-XAP x V _ W s PN ?`yX hAPS
(292) VU` XU` RTS \ X AP ! S^` RTM -X AP V ZARTh VUP+~P
(293) XU` R MdRTh<X AP|VUP
(294) "P"` PV Qj APQW~PR[ P 2 XUSx ` X _ X A_`fSQNeP"X _ # h MOVUP3q S^P g s PVUM s Eq j __ S _ds g PtX AP x _ V _ W s PN MORTM s IXU`.
(295) g M sis _ Z s h W~P X _n_ h[`29
(296) "Z s XkMORTh R _ X ~PK[`yW s P3PR _ Z q _ NQP MdRTM s IXY`
(297) "M s N _ h[P s S TM g P WDP"P"Rh[P g P s _rx
(298) "PP}MOh0R<[WAS^Z[ZAXVY\?XM/A
(299) "PPS MdVYP.`yXZT SYZTM M sis P"RA_ PR VUs M M SY`ixANpxAZs `
(300) "MMOXUW ` s PcR `yRN
(301) PhAV^P X MO``iXR `f
(302) "S MrS^P}S SU S^s`i`yW mrP.PpSYX ` q RTSYM`yN s SZ VYP MTXYPP
(303) AXYP}Ph` rMXX _NQP}MdSYZAVYPNQP"RIXUS P"VcS^P P"V q M X3 sPS \ s V ZA_ RTh3MOR~_ h XYs PVYV MO`iRxD~_ MdRTh*s`yX _ S P
(304) `fs M X3 P}S q \ XUP"VUVUMd`yR g MOVU`fMXY` _ _ R~g S LXc`ig SaM s S s _ PxMrS X_ _ q
(305) T_ MdR q P h[` 1 P"VUP"RIX x MOV MONQP"XYP"V S s `imdx PX AP;s `fhnx X __ \ XAP MORIXUP"RARTMeWDPMdN _ VX AP x~_ P"V _ \vX AP S^` q R~M s S AMdRThtS^XYZ~h( X APP+1 P
(306) X _ \X A`fS ØR X AP"V M V M8
(307) p`fSX M8
(308) XYZ~M WAZA` hQM AP` rXLM XU`yNQPXUP"V MdRTh PV^\ VYN VYP}M NQPMrS^ZAVUP NQPRr_ X S AxA`
(309) x _ M s S _ TMdS _ WDP"PR h sis _ RAP s vWTZ[Xq X A`fS;s _ Z s h W~PQX _nx _
(310) _ _ S^X s MOR~h<s M s S _ s P}SYS ~PK[`yW s P Lo _ P g PVIX _ g M s `fhAMXUP X AP SY`iNpZ s MXU` _ RtN _ h[P s nX T`iS`fSRAP,
(311) P}SYSUMOV . 't" 3
(312) . ! j T`iS XAPSY`fS TMrS NQMd`yR <W~PP"R-
(313) R
(314) PRIXYV MXYP}h R h[P P `iR M3S^`iN P WAZ[X \ Z \ ZAR
(315) . XU` _ RTM s S^`iNpZ s MXU` _ R N _ h[s P s j AP A_ P` q IXLNeP}MdSYZAVU_ P"NQP"RIXg NQsi_dPx X _ q h ~MdS _ xAR ss pW~PP"R|PKAsys MdNe`iRAP}h WTVY`iP+kMORThtXAP"VUP `fSaS XU` N Z
(316) kX h TP"VUP MOR%tSY`yN `
(317) "MOXY` RTS ~M P W~PP"R h RAP X XAPS^`iNpZ s MOXY` _ R N _ h[P s dh[sis ZTP X _ XAP _ s `iNQ_ ` XUPhQS5
(318) _dx P _ \TX TP xAXAs P2 SY`iS 46_ _ VP"K[Mdg N xAs P8N _ _ hAP s `yR _q XAP q V _ ZARTh3MdRTh VYP TP
(319) XY` _ RTS _ \XAP ! # S^` q RTM s MdVYPpM xAx V _ K[`yN|MXUPh"`yX s PSUS
(320) _ N xAs PK N _ h[P s S j TPaS^`iN xAs ` 2
(321) MXY` _ R~S _ \DX APN _ h[P s MOVUPh[P}S5
(322) "VY`iWDPheN _ VUP `iR|h[PX MO` s `yR # TM x XYPV .
(323) . . . t"! . C @"zB-G;ld@8?BDC. j TP _ [Z X s `iRAP _ l\ X APVUPS^X _ \X A`fSVUP xD_ VYX`fSXAP \ _dsisy_ `iR q . >@HIz h[P}S5
(324) "VY`iW~P}SX AP x V _ W s PN `iR q P"RAPVUM s . > x @VHI_ z W s P"N q ` g P}SX AP RAP,
(325) P}SYSUMOV XAP _ VYP"XY`
(326) "M s mnR _ s Ph q P|RAP"P}h[PhFX _ ZAR~h[P"V S X MORTh X AP. >SY@` HIq zRTM s MOh[R~P}h S5
(327) "X VYA`iW~PP}P+Sa1 X PA
(328) PQX _NQ\PR X _ `f_ S^hTP Sc`iRkZ~S^X P}Ah3PX VU_ P
(329) "PP"S^` XYg `iP"N|V MXUPpXAP TP"` q IXc\ V _ N XAPQVYP,
(330) P"` g P}h. > @HIz h[P}S5
(331) "VY`iW~P}S-X AP hAPSY` q RpMORThp`yN xAs P"NQPRrX MXU` _ R _ \[X APSY`iNpZ s MXU` _ R N _ hAP s ZTSYPh . > MO@R~HIhz
(332) TMd
(333) VU_ M8RI
(334) XUXUMOP"`iVURT` S PVYP}X S^AZ P s X ASLP"\ ` Vq _ IN XaNQh[`P1 MrP"S^VUZAP"VURIP"XNQSYP`iNpRrX Z S s MXU` _ RTS Z~S^P}h|X _ P g M s ZTMOXYPX AP.N _ hAP s. > @HIz SYZANQNQMdVY8` "P}S X APVUPSYZ s XUS\ V _ N X AP SY`yN Z s MOXY` _ RTS . > @HIz q ` g P}S X AP
(335) _ R
(336) s ZThA`yR q VUP"N|MOVUm[S _ RkX AP X APSY`fS . . .
(337) . C . . # RTSY`ih[PV X AP S5
(338) "P"RTMdVY` h[P}S5
(339) "VY`iWDPh|`iR"6` ZAVUP. ¢ØRkMdP"VU`iM P A`
(340) P/nP [MdR MOPV MdRAP/ f` S _ n`iR q _ g P"VXAP q V _ ZA_ R~hpMXLM
(341) PV^X MO`iR Tq P"` q IX j AP! # s gS^` q R~M ss `iSXUVUq MdRTSYNe`yX^XUP_rh xA\s V _ N MQSUMXUP `yXYP;`yX 3MORkP P MOXY` R MOR P PV V ZARTh \ 7 TMdRThtVYP}M/
(342) AP}S XAPVUP
(343) P` P"V\ V N X3 _ h[` si1 s P"VUP"RIXh[`iVUP
(344) XU` _ s RTg S _ _ RAPh[`iVYqrP,s
(345) X_ S^g ` q RTM q sT__ RQX _dx _ _ \wX TPcMOPV _rxAs MORAPaMdRTh _ RAPcgVYP TP
(346) XY_ P}h SY` q RTM s \ V _ N X AP q V _ ZTRTh j TP X MdSYm3\ _ V.XAPAP"` q IX NQPMdSYZAVUP"NQP"RIX S5nS^XYPN
(347) "M sys Ph X AP M XU`yNQP"XYP"V,T`fSX PS^XY`iN|MXYP \ V N,XAPSYP SY` RTM S j AP N|MO`iR x V _ W s P"N)`iS _
(348) MORkX A`fS WDs P h _ RAP/TMdRTh _ ` X" ~MXaZAR
(349) "P"_ VYXUMd`yRIX3 q s. . !#"$ ¥§ w22{ }+ y. .
(350) .
(351) zB =?Hn9B DHrz
(352) -8:H8@ . GPS satellite. . Propagation path. . $ ! v. a L"! #. . Receiver. Height Correlation function. w7 -zg}+ w -|xy'ª w22{L} y. "# e . \lX AP h[`iVYP,
(353) XS^` q R~M s MOVUVY` g P}S MOX XU`yNQP MdRTh|XAP.VYP TP
(354) XYPhtS^` q R~M s MXXY`iNQP Ò IX AP AP` q rX _P g P P"VvMX XYA` P R q VMO_ R ZAR~P h;
(355) "MOP"RpV W~P$V
(356) "ZAM R~s
(357) "h0Z ns MOVYPXYP}MOh XY`\ V _PcN X X AX TP P XY`iMdNQP"VPhAP sMOMRT/P/ 7 [`fS mnÒ R RI\AX TX TP PASUP"M` XUPIsiX s `yXY
(358) "P MdR S WDs P.g PS^XY`i_NQMOXYP}h|qds W% _ Xg APc\q _dsi_ sy_ `iR q VUs P s MXUg ` _ RTS_ T` x nMdSUSYZA_dNQxAs`yR q X TMOX XAP.hA_ P s M `fS NQP}MdSYq ZAVYP}hQX _ XAP S _ VYXYP}S XVUP+TP,
(359) XY` _ R SYÓ `yR 7 j _._ W[X MO`iRpX APXY`iNePh[P s M X AP x V _dx P"VYXY`iPS _ \TX AP ! # pS^` q RTM s
(360) "MOR W~PZTSYPh ¢Ø S
(361) AP"N|MXU`.
(362) gMe`iPS
(363) "_ M \DX PAh PaS
(364) PRTMOVU` _ `fSLS _ Re`y3R `i6S$` q
(365) ZAM VU
(366) PZ M XUP h0 % TP"ARQ`
(367) X T`fPaSS^ZT` q S^P}RTh|M s X MOVUXUVYVU` g M8P}
(368) SmQMMdXRTX h TPVY
(369) "P,MO
(370) XYP"Pc` g X PAVP SY` q RT_ M s sy js AP X _dx _ \[X TP \ ZAR
(371) XY` _ R ` sys M xTs x V s _ K[`iN|MXYP s
(372) _ VYVUPS xD_ RTh._ X _ X AP XU`yNQP si_ _ \~MdVYVU` g M s oP"R
(373) "P/-`y\ W X X AP
(374) VYVUP MXU` R \ ZAR
(375) XU` R \ V NX AP|h[`iVYP,
(376) X S^` R~M MORTh X AP
(377) VUVYP MOXY` R \ ZTR
(378) XU` _ R \ V _ _ N X AP VYP T_ P
(379) XYPs htS^_ ` q R~M s MOVUP _
(380) "M s
(381) "Z _ s MXYP}h0IX AP`yVX _dx qS7` s sys WDPMXX3 _ _ h[`21 s P"VUP"_ RIX XU`yNQP}S j APQh[` 1DPVYPR
(382) PeW~P"X3 PP"R3X APSYP X3 _ XY`iNeP}S ` sis W~P X APQh[P s M WDPX3P"P"R X AP X3 _ SY` q RTM s S S^PP 6` q ZAVUP 8 R _ V h[P"VX _
(383) _ N x PRTSUMXYP \ _ VaX APeP s P g MXU` _ R MOR qrs P _ \X APQSYMOXYP sys ` XUP/~X APeMOR qrs P 7 TMrSX _ WDPmnR _ R \` Xa`fSR _ XmnR _ RkPKAM8
(384) X s /nXAP MOR qds P.N ZTS^XaW~PP}S XU`yN|MXUPh j TP"VUPQMdVYP X AP"V V W PNQScX TMX
(385) N `
(386) "MOXYPeX TPQS
(387) PRTMOVU` R 6` ZAVUPQ X AP|SY` RTM. \ V _ N XAP q _ V _ ZARTh x `iS_ _ s R s VUP+TP,
(388) XYP}_ h MOxAX s _ RAP xD_ `iRIX M S _ _
(389) "M sys Phq S x P
(390) "Z s MO VkVYP TP
(391) XYq ` _ R s o _ P g PVdX AP.S^` q RTM s `fS _ \ XYPR VUP+TP,
(392) XYP}h MXN|MOR% xD_ `iRIXUS(
(393) "MOZ~S^`iR q M P sys mnR _ x V _ W s P"N
(394) M P}h3NpZ XU` MOX V M MXY` R S^PP6` ZAVUP ? cbcP P"RTh[`iR R ZAR~h[Z MXY`iR X AP XUP"VUsisVUMd`yR<`iSs MdRTx h Tx MX_rmnx `iRTq h _ _\ q V _ ZARTh
(395) q _ g PVX AP"VUPQ`iSwx X AP|NpqtZ s _ XY` x MOX _ x V _ W s P"s N
(396) MOq R W~P N _ VYP _ V s PSUS x V _ R _ ZAR
(397) P}h j AP VYP,
(398) P` g Ph
(399) _ VUVYP s MOXY` _ R|\ ZTR
(400) XU` _ R"` sis W~P MeSYZAN _ \lN|MOR%
(401) _ VUVYP s MOXY` _ Rt\ ZAR
(402) XY` _ RTSDMOXch[` 1DPVYPRIXaXY`iNQPph[P s M[S j APpS TM x P` sis
(403) TMdR q PMdRThkX APpX _rx
(404) MOR _
(405)
(406) ZTVaMXM s MOXYPVXY`iNeP8A`iRrXUV _ h[Z
(407) `iR q MORkP"VUV _ V`iRkX AP XU`yNQP h[P s M 6TZAVYX APVYN _ VUP/nX AP SY` q RTM s ` sys W~P h[`fS^XYZAVUW~P}h W% R _ `fSYP`yRkX TPVYP,
(408) P"` g PV j A`fS ` sys `yRIXYV _ hAZ
(409) P MdRtZAR
(410) P"VYXUMd`yRIX3 `iRkX AP TP"` q IXNeP}MdSYZAVUP"NQP"RIX( T`.
(411) TMdSX _ W~P MdRTM s "P}h . . . . ! "#.
(412) . . . .
(413) . Hn>A6};lz{8:Cl Hn8? D @ . 1.2. Direct signal. 1. Reflected signal. Correlation function. 0.8. 0.6. 0.4. 0.2. 0 ∆t −0.2 1. 2. 3. 4. 5. 6 7 Time delay [µs]. 8. 9. ! ¥§ zB2}2~%a|§-2{ |§yB { }' 2
(414) - Pªpyz . y'ª '{L}+2. 10. 11. w-y'2}+ y'{ ªs {w- y{ . .
(415) . "!$#&%'(#&)*',+&-.'(0/1(0#&%-.2*-.34#&),56+&5 75 8 #&5 9. :%/;2"(.!=<.
(416) . zB =?Hn9B DHrz
(417) -8:H8@.
(418) . j _ WDPaMOW s PX _
(419) "VYP}MXYPMdRQM8
(420)
(421) "ZAVUMOXYPS^`iNpZ s MOXY` _ RQN _ hAP s `yXL`iSLRAP
(422) "PSUSYMdV5X _ ZARTh[PVUS^XUMdRThpX AP
(423) N RAPRrX S \X AP V W P"N [P [XAP ! kS5[S XUP"N,MdRThtX APVUP+TP,
(424) XU` R \vXAPpSY` RTM S R _ X AxD`f_ S
(425) TM x XU_ P"V,TXAP x hA_ `21 P"s VUP"RIXc`yXYq PN|ScMdVYP# XUVYP}MXUPh _ RAPpW% _ RAP8 ~MXc_ P"K[`i_ S^XY`iR q XAqP _ VY`is PS XAP"VUP MdVYPeMORTh _ X AP* _ VYmk`iR3X A`fS
(426) "MrS^P .P}Mdh[PVUSa\?MONQ` s `fMOV ` X XAP XAP _ VY`iPS
(427) "MdR V WTMOW VYP}Mdh3`yX *rZT`.
(428) m s kWTZ[X S _ Z s h x M R _ XY`
(429) P X _ XAP|M xAxTs `
(430) "MOXY` _ R _ \LX APN1`yR X A`fS Xx AP_ SY`fS s . . ak . # RTSY`ih[PV X AP V W PN
(431) MrS h[P}S5
(432) "VY`iWDPh`iR # T M x XYPV j AP N _ h[P s _ Z s h
(433) _ RTSY`iS^X _ \ P}SY_ SYP"RIXU`iM sys |X TVYPx P _ x MOs VYXUS j^S XYAVUZP
(434) XYXUVZAMOVYRTP8SY NQ` XYXY`iP"R Vq MdRT! ht# \ VYP SU*rMZTXYP"P Rsys
(435) `yXY P MORTj hkAM `fS S `yR
(436) s Z~SYh[`yXYP` SeR `iN \xDX_ AVYXUP MdSURIMX XUP `fSYSY`yZAXYP PS s `ymrPtSY` q RTM s x~_ s _exD_ _ _ sis XY j V APh[Zx
(437) "MOP X S Ne_ \cP|X Ah[P`fS^X SY` qVYXYRT` M sR XUX VUM g X P As P`yR SYq ` X RT_ M XlAWAP Z[VYX P,
(438) XPA` P g P"N|V EMO`iRj AP V MOW XYN P"N _ S x `fS APXAVYP"P V ` sys ZT`iRTR[h _ _ _ q s x _ s q _ VUP+_TP,
(439) XY` _ R _ j AP VUP
(440) P` g P"V,n`yR
(441) s Z~h[`yR q X AP MdRrXUP"RAR~M . j T`iS
(442) TM XUP"V` XYVUPMOX X TP h[` 1DPVYPRrX `iSUS^ZTPSpMdRTh<X AP X AP _ V RAPPh[P}h X _ ZTRTh[P"V S^XUMOR~h. P}M/
(443) x V _ W x s P"N `iRksisX AP \ _rsysi_ `iR q M .
(444) . HnBTz>. . S^XUMdlRTHh X A P SY` 6q >-RT6M @s HnS^9 XYVUZ
(445) j XUZA_ VUW~P/P xDMd_ W s PPVX _ MdRTN h _ hA\ VYP P s *rX ZTTP"P R
(446) ! # PSYSY` q `ih[RTP}M Ss nX `AX`fS`fSnX RTAPP
(447) P}N SYSU_ MOS^VX `yNX _ xDZA_ RTVYXUh[MdPRrV^X . `fSUS^ZAP `iS-X AP VYP,
(448) P"` g PV-MORTh.XAP
(449) _ VUVYP s MOX _ V~XTMX x V _ hAZ
(450) P}B S X AP7
(451) _ VYVUP s MXU` _ R\ ZAR
(452) XY` _ R j AP}S^P x MOVYXUSMOVUPh[`fS5
(453) "ZTSYSYPht`iR3[P
(454) XU` _ Rk pX _dq P"X APV ` X _ X TP"VaMdS x P
(455) X S _ \lX AP ! # tS5[S XUP"N ØcSaX AP SY` q RTM s XYV M g P s S\ V _ N)XAP SUMXUP sis `yXYPpX _ X AP VYP,
(456) P"` g PV~` X ` sis xMdVYMdlPcSUHS.N X >[A@}hAV 9FP_ Z PB~q hk6 MdlXSAHIh[P zP H s MMQdP"`yV RtS X _ A\P X SYA` P RTMOM XYN S _ S MOx X A PLVYP o !. PP"RAP"PV,VUdM `isyRts 3X XAA`fSP|X P"AVUP}V S^_ `fVUS ScX `iARrP XUV P+_ 1 h[PZ
(457)
(458) XUPS h \vAX PAVYPP MOXYN _ S _ x APs VYP MOVUP
(459) _ s R~S^`fh[P"VUPhkMdSq RAP qds s ` q `yx W s PMdSMe_ VUPSYgZ s X _ \vX TP hA`iS
(460) ZTSUSY` _ Rt`iR [P
(461) XU` _ _ Rk ØZTSYP\ Z X \ Vh[PS
(462) VU`yWT`yR X TP V M MOXY` R \-X APSY` RTM M\ XUP"V `y X T>AMrSCXYClV HnM = g P 9 s P}B-h GlXHnA=:V 6 _ Z q XAPMOs XYN _I__rSs x _APVYPMOR~h `fSVUq P+TP,
(463) XUxPh|_dMx XXq AP q_ V _ _ZARTh0O`fSXq APX s TP _ V _SYZ\
(464)
(465) TMOMdRTSRA\?P Mrs h[N `yR _ hA P ns S P,
(466) XY j ` AR3`fSL X AeP `i_ SV5h[Ph[``sy
(467) "s MOM XYP}s S h _ X W~Pc
(468) RATPMO
(469) "RAPRTSUSYP MdV5N h[AP P"S R XYVUPMOXY`iR q _ X AP"VSYZAW P
(470) XUS q _ _ s _ s GSMOVUPc N _ h[6}8?P Ds PClh >A=:6XXYZARFVURTnS P,
(471) _ XUZA` _XR X _ W~ &PvN Mt_ hAVU`iP S
(472)
(473) ZT_ SUR SYg` _ P"R<RA`i`fP"S RIXAP X s_ h h[_ P}R S5
(474) "VY`i_ W~ P VUP+~B-PGl
(475) XUHnP=:h 8?C! # ztH S^` Hnq dR~@M Hns XAPVUP
(476) P` g PhkS^` q R~M s `yRkXUP"VUNQS _ \ xD_ P"V,nMrSM|S^ZTN _ \N|MOR%
(477) _ VYVUP s MXU` _ R|\ ZAR
(478) XY` _ RTS j
(479) "M
(480) "Z MOXYPQX AP
(481) VYVUP MXU` R \ ZAR
(482) XY` R \X AP|VUP ~Pl
(483) XUH PhQ8:SY6"` q @}RT>[M@8:s X Tz>APGlVYP,>A
(484) z P"` H g wP}h ;>[xD@_ 8: B~PC VLMdSM._ \ ZARs
(485) XY` s _ R _ \ h[P s M_\ V _ s N X_ APah[`iVYP,
(486) X _ SY` q _ RTM s NpZ~S X WDP hAPXYPVYNQ`iRAPh j T`iS
(487) "MOR3WDPph RAP W%kZTS^`iR X APpWA`fS^XUMXU`.
(488) VUMrhAMOVP *rZ~MXY` R \ V N)VUMrhAMOV XAP _ V5 Ø \ ZAV^X AP"V`yR g P}S XU` q MXU` _ R _ _ \lX A`fS
(489) MORkq W~P \ _ ZARThk`yR nP,
(490) XU` _ R _ _ j APtN S Xeh[`29
(491) "Z X MdV^X X
(492) M
(493) Z MXUP `yRFX APtVUMrhAMOV P *IZTMXU` R. `ftzSXBDA;lPpCVUP+G ~Pz{
(494) H XU` _ HnR O@_ 8:\B~X C TP SY` q RTM s MO_ XXAP q V _ ZTs RThx anP g _ P"V M s-s x MOVs MONQPXUP"V S
(495) _ RrXUVY`iWAZ[XUPX _ X _AP VUP+~P
(496) XUPh x~_ P"V,nP q rX APMXYXYPRIZ~MXY` _ Rt`yRtX TP q V _ ZARTh MdRTh X AP S5
(497) MX^XUP"VU`yR q _ \-X AP SY` q RTM s xD _ T`.
(498) P" V.`f`ySR h hA`2RA1 P P"VU`iP"R RIXnPh[
(499) `yXYVU` P
(500) R3XY` _ RT S j A`fS
(501) _ N xAs PK3`iSUSYZAP ~MdSX _ WDPePKAMONQ`iRAPh X _ V _ Z q s / _ _ Ø
(502) NeN R V W P"N7`iRFVUMrh[`
(503) NeN ZARA`
(504) "MOXY` RTS S [S^XYP"N|S `iSp\?MdhA`yR A`
(505) `fSe>AMdGhA8?Ch[VU PSUSYPh `i_REnP,
(506) _ XY` _ Rx _ s j APVYPkMOVU_ P SY_P g PVUM s X3 x PS _ _ \\?MdhA`yR q h[P x P"R~h[`yR qq _ RFX AP
(507) ~MOV M/
(508) XUP"VU`iS^XY`
(509) "S _ \aX AP
(510) TMORARTP s LP q `y\X TP q V _ ZARTh \ P}MXYZTVYP}S s MOV q P g MdVY`fMXU` _ RTS _ V X AP S x P"Ph A`
(511) <X AP MdP"V _dxAs MORAPpXYV M g P s S `yX |j AP|N|MO`iR P+1 P
(512) X _ \ \?Mrh[`yR q ` sis W~P MkV MOR[ h _ N s g MdV5n`iR q SY` q RTM s X AP MON xAs `yXYZTh[PMdRTh x ~MdSYP` sys WDP TM g PcMrSS^X _
(513) TMrS XU`.
(514) g MOVU`iMdW s P}S o P PVOh[ZTP X X AP
(515) N PKpRTMOXYZAVUP \~\?Mdh[`iR OX APVYP$` R W~PM h[`fS5
(516) "ZTSUS^` _ RQMOW _ Z[X XA_ P x V g _ W s P"N)MORT_ hk`yXa`iS_ R _ XaxAs `yN xAs P"NQPRrXU_Phk`iRtX Aq P SY`yN Z s MOXY` _sysARk_ N s _ hAP s 5_t\LC X @THnPeCMdClRr>AXU6 P"RAR~ j M TP
(517) _ VUg PP"
(518) "V P"M ` g q `yP.R qWDP"MO`iRIR XUq P"RAX ARTPeMXYN ZT_ VYRAS^XcP}h `iN _ x~Z[_XV^X X _ MORIW~X P x_ \MdVUq MdVUNQPMOPXXYPSY`V q IRAØ` 2
(519) "RTMdMORVU
(520) V P8_ { X AMOP$RIXUP"`fRAhnRTX M
(521) PVUM P TMdSM MOV PV MORIXUP"RARTM MO`iR MdRThQX TP"VUP\ VUPX APcSY` RTM X R `iSYPVUMOXY` `fS WDPXYXYP"V, WT_ Z[g X _ R<q XAP _ X AsPV q TMOR~h sy_ SYMOqXYP sys ` XUP MOR qds PS.XYP_ RTh X _
(522) "MOqZ~S^P|s PVY_ V _ V _S kj A`fS_ `iSpW~P,
(523) "MdZTS^P XAPpS x P,
(524) Z s MOVVYP TP
(525) XY` _ R A`.
(526) `fSX APpS _ VYXYP}S XXUVUM g P s Ph x MX 3W?tX TP VYP TP
(527) XYP}hkSY` q RTM s N|M R _ X|W~P*
(528) "M x XYZTVYP}h W% X TP MdRIXYP"RTRTM ØaR `yRIXUV _ h[Z
(529) XY` _ R _ R MORIXYPRARTMdSe`fS q ` g P"R `yR [P
(530) XU` _ R3 . .
(531) Mean anomaly (deg). C @zB-Gl;O@}8?BDC. . @B. . 180 150 120 90 60 30 0 −30 −60 −90 −120 −150 −180. Equator. A. B Plane. C. D. $ #"$ y{2 }+ y{ y'ªO ¬®d¡}+- 22 ! $ (' !e 2 e . . . ! # `fStMFS5[S XUP"N+h[P g P si_dx Ph W% X AP bP x MOVYXYNQPRrX _ \pbcP\ PRTS^P b _ b |X _ q ` g P _ V s h(`ihAP/~M8
(532)
(533) "ZAVUMOXYP xD_ SY` XU` _ RA`iR q o _ P g P"V,A`iR X A`fSaXAPSY`fS ! # k`fSaR _ XZTSYPh3\ _ VXTMX xTZAP"` V xDI_ X SYP MO W RTP S XUPV MrhEZARTX hFAP \
(534) V|TMOMOV R M/
(535) MOXYPPVYVY`f`fM S XU`.
(536) S P A_ `.\
(537) P8XALP \ ! Ve# P"KAMON S^` q R~P M s MdR`fS MdZ~P"S^V P}h X MO_ RAP NQ P}j MdSYAZAPVYVYP P"\ X AVUPP SYP g q P"V M s h[P"_XUMdg ` s SLq MOW _ _ ZAX7! _ # QMdVYP s P\ X _s Z[g XrWAZ[s XL\ _ VL_ XAPa`iRrXUP"xAVUsPS^XYP}h VUPMrh[_dP"xAVs XAP"VUPMdVYPN|MO_ R% XUPKnXaW _I_ m[S _ RtX AP SYZAW P,
(538) XTP q lMdRTh !
(539) RTS^`fS^XUS \ X AVUP"P S^P NQP"RIXUS X AP<S M8
(540) P SYP NePRIXX TP ZTSYP"VtSYP NQP"RIXtMOR~hEX AP
(541) _ # RIXYV _ds _ SYP q NQP"RI_ X kj AP S x M/q
(542) P SYP q NQP"RIX `iS x VYP x VYP}S^Pq RIXYPh W% XAP SUMXYP sys `yXYq PS _ VUWA`yXY`iR q X AP P}MOVYX dX APZ~S^PV S^P q NQP"RIX SMOVUPX APVUP
(543) "P"` g P"V SZTSYPheX _ R~M g ` q MOXYPMOR~hpX AP
(544) _ RIXYV _ds SYP q NQPRrX hAPM s S$`yX kX APN|MdRTM q P"NQP"RIX _ \X APSUMXYP sys `yXYPS R s |X TP S x M8
(545) PMOR~h ZTSYP"VaSYP q NQP"RIXaMOVUP _ \`iRIXYPVYP}S X APVYP j TPQ\ _dsisy_ `iR q S^P,
(546) XU` _ RTSh[PS
(547) VU`iW~PQX AP S x M/
(548) P SYP q NQP"RIXwX AP ! # <SY` q RTM s MORTh MkX3 x `.
(549) M s. ! # tVYP,
(550) P"` g PV `iR q PRAP"V M s . . .
(551)
(552). 1
(553)
(554) .
(555) . 6` q ZAVUP S _ aS M x `
(556) XYZTVYP _ \wX TPcSUMXYP sys `yXYP
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