RTCA Special Committee 186, Working Group 3. ADS-B 1090 MOPS, Revision B. Meeting #30. An Expanded Description of the CPR Algorithm

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1 WP30-12 August 18-21, 2009 RTCA Specal Commttee 186, Workng Group 3 ADS-B 1090 MOPS, Revson B Meetng #30 An Expanded Descrpton of the CPR Algorthm Prepared by Al Marshall Senss Corporaton SUMMARY Ths paper s ntended to become an nformatve Appendx on the CPR encodng and decodng algorthms. The algorthms are descrbed wth dagrams, text and equatons n a manner that s easer to understand than the necessarly terse descrpton n Appendx A. No new requrements or test procedures are proposed.

2 2 1 Purpose The purpose of ths appendx s to provde explanatons and dervatons of the Compact Poston Reportng (CPR) equatons gven n Appendx A. CPR encodng and decodng can be mplemented wthout usng any of the nformaton n ths appendx but, f a CPR mplementaton has problems, the nformaton n ths appendx may be helpful n resolvng the ssue. 2 Motvaton for Compact Poston Reportng CPR) was developed for ADS-B messages broadcast on the 1090 MHz Extended Squtter (ES) datalnk to reduce the number of bts requred to convey partcpant lattude and longtude. Poston resoluton for ES messages s approxmately 5.1 meters for arborne partcpants and 1.3 meters for surface partcpants (see Secton 3). The crcumference of the earth s approxmately klometers so m/5.1 m = ~ dscrete poston values poston values would requre 23 bts n a message. Longtude s expressed over a range of 360 so longtude would requre the full 23 bts. Lattude s expressed over a range of 180 so only dscrete poston values or 22 bts would be requred. Followng smlar reasonng, surface poston would requre 25 bts for longtude and 24 bts for lattude. CPR conveys poston wth 17 bts each for lattude and longtude plus 1 CPR format bt. Table 2-1 Message bts requred for poston encodng wth and wthout CPR Arborne Poston Surface Poston Wthout CPR Wth CPR Bts Saved wth CPR Lattude Longtude CPR Fmt 0 1 Total Lattude Longtude CPR Fmt 0 1 Total CPR saves 10 bts per poston message for arborne partcpants and 14 bts per poston message for surface partcpants. Poston messages are broadcast twce per second under most condtons so CPR saves 20 bts/second for arborne partcpants and 28 bts/second for surface partcpants. The maxmum message transmsson rate allowed for each 1090ES ADS-B partcpant s 6.2 messages/sec. Of the 112 bts n each ES message, only 56 are avalable for the ADS-B payload. The frst 5 ADS-B payload bts are reserved for the message type so 51 bts from each message are avalable for data. 51 bts/message multpled by 6.2 messages/sec s 316 bts/second. CPR saves 6% - 9% of the avalable bts for other uses. 3 CPR Coordnate System CPR can be thought of as a coordnate system and a set of coordnate transformaton algorthms. The coordnate system s sphercal and comparable to the lattude/longtude reference system commonly used for navgaton. The coordnate transformaton algorthms convert between lattude/longtude and CPR coordnates. The coordnate transformaton algorthms are commonly called CPR encodng and CPR decodng.

3 In the CPR coordnate system, the globe s dvded nto zones. Lattude zones start at the equator and go to both poles. Longtude zones start at the Prme Merdan and proceed eastward around the globe. Lattude zones are approxmately 360 nautcal mles (NM) n heght measured n the north-south drecton. Longtude zones are approxmately 360 NM n wdth measured n the east-west drecton. The number of longtude zones s reduced as one moves from the equator to the poles to mantan approxmately constant zone wdth. There are two sets of slghtly dfferent szed zones n both lattude and longtude. One set of zones s called even and the other s called odd. Fgure 3-1 and Fgure 3-2 depct lattude and longtude zones on a global scale where the red lnes represent even zone boundares and the blue lnes represent odd. 3 Fgure 3-1 Lattude Zone Boundares (Red s Even; Blue s Odd)

4 4 Fgure 3-2 Longtude Zone Boundares (Red s Even; Blue s Odd) Each zone s dentfed wth a zone ndex number. Imagne a talor s tape measure marked wth even and odd lattude zones as shown n the left sde of Fgure 3-3. The tape measure has 4NZ = 60 even zones and 4NZ-1 = 59 odd zones numbered begnnng wth zone ndex 0. The zone boundares wll lne up at the begnnng and end of the tape measure but nowhere else. The tape measure s wrapped around the globe startng wth zone ndex 0 extendng north from the equator. The tape passes over the north and south poles and returns to the equator as shown on the rght sde of Fgure 3-3.

5 5 Fgure 3-3 Lattude Zone Indexng Longtude zone ndexng s the same as lattude zone ndexng except zone ndex 0 s just east of the Prme Merdan and the zone numbers ncrease n the eastward drecton. As mentoned above, the number of longtude zones around the globe vares wth lattude and ths s reflected n the zone ndex numbers. Lattude and longtude zones are dvded nto bns. Each zone contans 2 Nb equal szed bns. The value of Nb vares wth the type of poston beng encoded. Bns are numbered startng wth 0 at the southern edge of lattude zones and the western edge of longtude zones. More detals on szng are provded n the followng sectons. Every pont on the globe s dentfed n the CPR coordnate system wth a lattude zone ndex, lattude bn number, longtude zone ndex, longtude bn number and CPR format (even or odd zone sze). 3.1 Lattude Zones Lattude zones are symmetrcal about the equator. The heght of a lattude zone s called Dlat. The subscrpt has a value of 0 to ndcate the heght of an even zone or a value of 1 to ndcate the heght of an odd zone. Dlat s defned n terms of the constant NZ. NZ s the number of even lattude zones n one quadrant of the globe and has a value of 15. The lattude zone sze, Dlat, s determned wth Eq 1. Dlat = NZ NZ = 15 = 0 for even encodng = 1 for odd encodng Eq 1 [A a] Snce there are 4 quadrants around the globe, there are 60 even lattude zones and 59 odd zones. Even lattude zones are approxmately 360 nautcal mles (nm) NM hgh and odd lattude zones are approxmately 366 NM hgh measured n the north-south drecton.

6 6 The defnton of Dlat s depcted n Fgure 3-4. Dlat = NZ Fgure 3-4 Defnton of Lattude Zone Szes Lattude zones are dvded nto bns. There are 2 Nb bns n each lattude zone. Each lattude bn s dentfed by the nteger bn number YZ. YZ s the bn number relatve to the southern edge of the lattude zone (n both the northern and southern hemspheres). The subscrpt ndcates whether the value of YZ s relatve to an even zone (=0) or an odd zone (=1). The CPR decodng algorthms produce a lattude value (a real number) from YZ whch s the lattude at the centerlne of the bn. Ths value s called the bn centerlne lattude.

7 Fgure 3-5 shows the relatonshp between lattude bns and zones. 7 Fgure 3-5 Lattude Zones and Bns The bn heght, whch s equal to the encodng resoluton, s the lattude zone heght dvded by the number of bns per zone. Secton A defnes the number of bts used for encodng to be 17 for arborne poston, 19 for surface poston and 12 for Coarse TIS-B poston. The resultng bn szes are shown n Table 3-1. Table CPR Lattude Encodng Resoluton Zone sze (degrees) Bn sze (degrees) Bn Sze (meters) Poston Type Nb bns/zone Even Odd Even Odd Even Odd Arborne E E Surface E E Coarse TIS-B The CPR encodng algorthm transforms lattude nto even and odd bn numbers. Fgure 3-6 s an example showng even and odd bn numbers for arborne poston at N. Red lnes delmt the even zone and blue lnes delmt the odd zone. The pont of nterest, colored magenta, s n even bn number and odd bn number Fgure 3-6 YZ for Even and Odd Lattude Zones at N Although not produced by the encodng algorthm, the zone ndex number for both the even and odd zones at the lattude n Fgure 3-6 s 7.

8 8 3.2 Longtude Zones and Bns Longtude zones and bns are smlar to lattude zones and bns. For a gven poston type (.e. arborne, surface, coarse TIS-B), the number of bns per longtude zone s equal to the number of bns per lattude zone. The man dfference between lattude and longtude zones s that the number of longtude zones crclng the globe s a functon of lattude. The CPR coordnate system keeps the encodng resoluton (.e. bn wdth n meters) as close to a constant as possble everywhere on the globe. Snce the number of bns per zone s fxed, the zone wdth (n NM) must also reman close to constant. The dstance around the globe along lnes of constant lattude s smaller near the poles than near the equator. The CPR algorthm keeps the longtude bn and zone wdth approxmately constant by reducng the number of zones as lattude ncreases. Fgure 3-7 Reducton n Number of Longtude Zones at Hgh Lattudes Note that the lnear (not angular) wdths of the longtude zones n Fgure 3-7 are all approxmately equal and that the number of zones around the globe decreases as the magntude of lattude ncreases. The number of even longtude zones at a lattude s called NL. The lattudes at whch the number of longtude zones changes are called NL Transton Lattudes. These are represented by black lnes of constant lattude n Fgure 3-2 and Fgure 3-7. NL Transton Lattudes generally do not concde wth lattude zone boundares. For all CPR computatons, NL s calculated usng the recovered lattude Rlat. Rlat s obtaned by convertng a bn number to a bn centerlne lattude. The ratonale for ths s dscussed n Secton 4. The equaton for the number of longtude zones (NL) as a functon of lattude s specfed n Eq 2:

9 For Rlat = 0 (the Equator), NL = 59 For Rlat = +87 or lat = -87, NL = 2 For Rlat > +87 or lat < -87, NL = 1 For all other lattudes (-87 < Rlat < 0 and 0 < Rlat < +87 ): 1 π 1 cos 2NZ NL( Rlat ) = floor 2π arccos 1 2 π cos Rlat Eq 2 [A d] Note n Eq 2 that NL s nversely proportonal to the magntude of the recovered lattude and that the result of the computaton on the rght hand sde s quantzed by the floor functon. As the magntude of the recovered lattude ncreases (.e. from the equator to the poles), NL changes after the recovered lattude crosses the NL Transton Lattude. Ths s llustrated n Fgure 3-8. NL Transton Lattudes Equato r Fgure 3-8 NL Values and Transton Lattudes A rearranged verson of Eq 2 gves NL Transton Lattudes as a functon of the number of longtude zones. The rearranged equaton s presented n Eq 3: lat NL Transton π 1 cos arccos NZ = = for NL to NZ π π 1 cos NL Eq 3 [A1.7.2.d, note 5] The longtude angular zone wdth, Dlon (n degrees of longtude) depends on the value of NL and s gven by Eq 4: Dlon = 360 NL ( Rlat ) 360,, when when NL NL ( Rlat ) ( Rlat ) > 0 = 0 Eq 4 [A d] A vsual representaton of these equatons s shown n Fgure 3-9. Red lnes are even longtude zone boundares and blue lnes are odd longtude zone boundares. Black lnes of constant lattude are the transton lattudes defned by Eq 3.

10 10 Fgure 3-9 Even and Odd Longtude Zones Wth Transton Lattudes Zone ndexng for longtude s smlar to lattude except that zone ndex 0 extends east from the Prme Merdan and the tape measure contnues eastward around the globe, returnng to the Prme Merdan. The number of zones on the tape measure vares wth recovered lattude as descrbed above. Longtude zones are dvded nto bns n the same manner as lattude zones except that bn number zero s located at the western edge of each zone and bn numbers ncrease to the east. Even bn numbers are represented by the varable XZ 0 and odd bn numbers are represented by the varable XZ 1. Fgure 3-10 s an example showng even and odd bn numbers for arborne poston at W. Red lnes delmt the even zone boundary and blue lnes delmt the odd zone boundary. The pont of nterest, colored magenta, s n even bn number and odd bn number Fgure 3-10 XZ for Even and Odd Longtude Zones at W The longtude zone ndex number for both the even and odd zones at the longtude shown n Fgure 3-10 s 33.

11 4 CPR Encodng 11 The frst step of the encodng process s to determne the lattude zone sze Dlat. Dlat s calculated wth Eq 1. The second step of the encodng process converts the nput lattude nto an output bn number YZ. The nput lattude can be any real number between -90 and +90. YZ s lmted to a fnte set of ntegers (0 to ) whch represent bn numbers. Eq 5 converts nput lattude lat nto a bn number YZ. (, Dlat ) Nb MOD lat YZ = floor 2 Dlat Eq 5 [A b] The modulus functon returns the number of degrees between the southern edge of the zone contanng lat and lat. Dvdng ths by the lattude zone sze Dlat produces the fracton nto the zone or zone fracton of the nput lattude. The product of the zone fracton and the number of bns n the zone (.e., 2 Nb ) s approxmately the bn number of the nput lattude. The product s not necessarly an nteger so t s rounded to the nearest nteger by addng ½ and takng the floor of the sum. The thrd step n the encodng process s to recover the bn centerlne lattude of YZ. Because Eq 5 performs roundng, the bn centerlne lattude of YZ wll not equal the nput lattude n most cases. Rlat = Dlat YZ 2 Nb + floor lat Dlat Eq 6 [A c] YZ /2 Nb s the zone fracton of YZ. floor(lat/dlat ) s the zone ndex number. The frst lattude zone north of the equator s ndex number 0. The sum of the terms nsde the parentheses s the number of whole zones plus the zone fracton of YZ. The product of ths sum and Dlat, the number of degrees per zone, s the bn centerlne lattude of YZ. In the fourth step, Rlat from Eq 6 s used to determne NL from Eq 2 or from a lookup table based on Eq 3. Then, Dlon s calculated wth Eq 4. Usng Rlat n the determnaton of NL ensures that the transmtted value of YZ s consstent wth the value of NL used for longtude encodng. The step also ensures that only one value of NL s used for any lattude wthn a sngle lattude bn. The recever only knows the lattude that s recovered from YZ and must determne NL based on ths value alone. If more than one value of NL were used for lattudes n the same bn, the recever would have no relable way to determne whch value of NL was approprate. The next step s to encode the longtude. Ths s done wth Eq 7. (, Dlon ) Nb MOD lon XZ = floor 2 Dlon Eq 7 [A e] Eq 7 works n the same manner as Eq 5 except that the nputs and results are longtude values.

12 12 The fnal step trms YZ and XZ to the number of bts avalable n the poston message. For surface poston, ths fts a 19 bt number nto a 17 bt space by dscardng the 2 most sgnfcant bts. For arborne and coarse TIS-B poston, ths step takes care of the case where the lattude or longtude falls wthn the most northern or most eastern ½ bn n a zone. YZ or XZ calculated from Eqs 5 or 7 would equal 2 Nb n these cases whch s too large be encoded n the respectve poston messages. Ths step drops the most sgnfcant bt leavng only a strng of zero bts for transmsson. See Fgure 4-1 for an example wth lattude. For lattude n shaded regon (most northern ½ bn of lattude zone) Nb MOD( lat, Dlat ) 1 YZ = 2 + floor Dlat 2 YZ wll evaluate to 2 Nb. Max value that wll ft n poston message s 2 Nb -1. YZ = 0 YZ = 2 Nb -1 Dlat Lattude Zone YZ = 2 YZ = 1 YZ = 0 Fgure 4-1 YZ When Lattude s n Northernmost 1/2 Bn of Lattude Zone The followng equatons from secton A.1.7.3f trm YZ and XZ to the approprate number of bts: YZ XZ XZ = MOD YZ = MOD YZ = MOD YZ XZ = MOD YZ = MOD YZ = MOD 17 (,2 ) 17 ( XZ 2 ), 17 (,2 ) 17 ( XZ 2 ), 12 (,2 ) 12 ( XZ 2 ), for Arborne encodng for Surface encodng for Coarse TIS B encodng 5 CPR Decodng Every lattude and longtude can be mapped to a unque trple of zone ndex, bn number and CPR Format. However, only the bn number and CPR Format are transmtted n poston messages. Recevers must recover the lattude and longtude usng only the transmtted bn numbers and CPR Format. Remember that any lattude bn number YZ wll exst n each lattude zone and that there are 15 even and 14 ¾ odd lattude zones n both the northern and southern hemspheres. The ambguty n longtude s smlar except the number of longtude zones vares from 1 to 59 dependng on lattude. The MOPS provdes two methods for recoverng the zone and determnng the poston of a target n secton A.1.7. One method s called Globally Unambguous CPR Decodng and the other s called Locally Unambguous CPR Decodng. These methods are commonly called global decodng and local decodng.

13 Most mplementatons use global decodng to determne poston when a target s frst acqured and then swtch to local decodng for ongong poston updates. Global decodng can determne the locaton of a target anywhere on the globe but must have one even CPR format poston message and one odd CPR format poston message receved wthn 10 seconds of each other to perform a vald decode. Local decodng s lmted to a range of ±½ zone n lattude and longtude from the last poston update but can use an encoded poston of ether format wth no tme lmt between updates Global Decodng for Arborne and TIS-B Poston Global decodng uses the bn numbers from one even poston message and one odd poston message to determne whch zones contan the target and to recover the lattude and longtude. The target could be anywhere on the globe and global decodng wll stll work correctly Arborne and TIS-B Lattude Global Decodng A recever needs to determne the zone ndex of the target because the zone ndex s not transmtted n poston messages. Global decodng works on the dea that the zone ndex s related to the offset between the southern edges of the even and odd zones that contan the lattude bn numbers transmtted n the two poston messages. The prncple s llustrated for lattude n Fgure 5-1. YZ 0 (even bn number) # of Zone Offsets to YZ 0 = ZO YZ0 Even Zone 2 Even Zone 1 P0 Odd Zone 2 P1 Odd Zone 1 YZ 1 (odd bn number) # of Zone Offsets to YZ 1 = ZO YZ1 x = offset between zone southern boundares (n Zone Offsets) x = ZO YZ0 -ZO YZ1 j = x rounded to nearest nteger j = floor(x+ ½) Zone Offset (ZO) Even Zone 0 Odd Zone 0 Equator Fgure 5-1 Prncple of Global Decodng Fgure 5-1 s a magnfed vew of the frst three zones north of the equator n Fgure 3-3. The lattude bn numbers YZ 0 and YZ 1, whch are receved n separate even and odd poston messages, are also shown. Zone Offset (ZO) s the dfference n sze between an even zone and an odd zone. Ths dfference, n degrees, s defned by Eq 8.

14 14 ZO = Dlat ZO = ( 59)( 60) Dlat = = 4NZ 1 4NZ 4NZ(4NZ 1) Eq 8 Observe n Fgure 5-1 that as the zone ndex number ncreases, the offset between zone southern boundares also ncreases by the value of ZO. The dfference n lattude between the southern edges of the even and odd zones wth ndex 1 s ZO and the dfference n lattude between the southern edges of zones wth ndex 2 s 2ZO. The zone ndex number and offset between zone southern boundares are lnearly related. Therefore, the offset between zone southern boundares can be used to determne the zone ndex number. Global decodng s easer to see f the followng two assumptons are made: Assumpton 1. P0 and P1 have the same lattude (e.g. statonary target or one movng due east or due west). Assumpton 2. P0 and P1 are n zones wth the same ndex number. Fgure 5-1 ncorporates these assumptons. The offset between zone southern boundares (x) of the zones wth ndex number 2 (measured n Zone Offsets) s the number of Zone Offsets from the southern edge of the even zone to YZ 0 (ZO YZ0 ) mnus the number of Zone Offsets from the southern edge of the odd zone to YZ 1 (ZO YZ1 ). The result wll be a number that s very close to an nteger, whch s the expected answer, because zones are always offset by an nteger multple of the Zone Offset. If the result (x) s rounded to the nearest nteger (j), the zone ndex number of the even or odd zone contanng P0 or P1 wll be equal to the number of Zone Offsets (j) between the zone southern boundares. The number of Zone Offsets from the southern boundary of the zone to YZ 0 (ZO YZ0 ) or YZ 1 (ZO YZ1 ) s the product of the number of Zone Offsets per zone (ZO ) and the zone fracton of YZ 0 or YZ 1. The number of Zone Offsets per zone s determned wth Eq 9. Dlat ZO = ZO = 360 4NZ 360 ( ) 4NZ 4NZ 1 ( 4NZ 1) 4NZ 1 = 59 when = 0 ( even) = NZ 4NZ = 60 when = ( odd ) ZO 4NZ = 4 1 Eq 9 The zone fracton s the bn number of P0 or P1 dvded by the number of bns n the zone (YZ /2 Nb ). Eqs 10 & 11 defne the number of zone offsets from the southern edge of a lattude zone to a bn wth coordnate YZ. ZO YZ YZ0 = 59 for even zones Nb Eq YZ1 ZOYZ = 60 for odd zones Nb Eq

15 Subtractng Eq 11 from Eq 10 produces the number of Zone Offsets between the southern boundares of the zones contanng P0 and P1. x = ZO YZ 0 ZO YZ1 59YZ0 60YZ x = Nb 2 YZ = Nb YZ Nb 15 Eq 12 The number of Zone Offsets between zone southern boundares must be an nteger because of the way zones are defned. P0 and P1 wll not have exactly the same lattude n most cases because, even f the nput lattudes are equal, the CPR encodng process wll result n the centerlne of the even bn beng a slghtly dfferent lattude than the centerlne of the odd bn. Therefore, x must be rounded to the nearest nteger to determne the true (.e. nteger) number of Zone Offsets between zone southern boundares. Eq 13 rounds the result of Eq 12 to the nearest nteger. The result s the equaton gven n A.1.7.7b. 1 j = floor x YZ0 60YZ1 j = floor Nb Eq 13 [A.1.7.7b] Assumpton 1 s not practcal for real applcatons because arcraft and ground vehcles move durng the perod between poston messages. The roundng performed by Eq 13 wll accommodate up to ½ Zone Offset between P0 and P1. Assumpton 1 can be relaxed to allow up to ½ Zone Offset between P0 and P1 ncludng vehcle movement, poston errors and CPR quantzaton errors. Note: Appendx A, Secton A.1.7.7, Note 2 states that arborne poston global decodes cannot be performed wth even-odd poston message pars receved more than 10 seconds apart because the dstance between the reports for a target movng at 1000 knots could move more must be less than 3 NM n a 10 second perod. The 3 NM lmt comes from the requrement that the lattude (or longtude) change between P0 and P1 not exceed ½ ZO. From Eq 8, ZO ½ ZO NM. Assumpton 2 s also mpractcal because P0 and P1 could end up n zones wth dfferent zone ndex numbers. An example s shown n Fgure 5-2.

16 16 Even Zone 0 Odd Zone 0 Even Zone 1 Odd Zone 1 Even Zone 2 Odd Zone 2 Fgure Ponts n Zones Wth Dfferent Zone Index Numbers In Fgure 5-2, P0 s n a zone wth ndex number 2 whle P1 s n a zone wth ndex number 1. The value of j n Fgure 5-2 wll be -58 because Even Zone 1 s 59 Zone Offsets tall and the bottom of Odd Zone 1 s 1 Zone Offset above the bottom of Even Zone 1. The Modulus functon defned n Appendx A can be used to recover the zone ndex number when the offset between zone southern boundares s negatve. The Modulus functon s repeated n Eq 14. MOD x y ( x, y) = x y floor where y 0 Eq 14 [A c] The value of y s chosen to produce the zone ndex number from j. Fgure 5-3 depcts the relatonshp between j and the ndex number of each zone.

17 17 Fgure 5-3 Relatonshp Between j and Zone Index If y n Eq 14 s replaced wth the number of even (60) or odd (59) zones around the globe (refer to the tape measure n Fgure 3-3) and f x s replaced wth j, Eq 14 becomes: MOD j, Eq 15 4NZ ( j 4NZ ) = j ( 4NZ ) floor The range of j s -59 to +58. The quantty 4NZ- s ether 59 or 60. floor(j/(4nz-)) wll be 0 when j s postve and -1 when j s negatve. When j s postve, the second term of Eq 14 s zero and the zone ndex equals j. When j s negatve, the sgn n front of the second term s postve and the value of the term s 4NZ-. These forms of the equaton match the forms shown n Fgure 5-3. The zone ndex can be determned from j usng Eq 16. Zone Index = MOD Zone Index = MOD ( j,4nz ) ( j,60 ) Eq 16 The lattude s recovered usng the zone ndex and bn number (YZ ). The bn number dvded by the number of bns n a zone equals the zone fracton of the bn number. Multplyng the heght of a zone by the sum of the zone ndex and the zone fracton wll produce the bn centerlne lattude of YZ. Rlat Dlat MOD YZ 2 ( j, 60 ) + = Nb Eq 17 [A c] Rlat 0 s the lattude of the even poston message used n the global decode and Rlat 1 s the lattude of the odd poston message. Recallng the tape measure of Fgure 3-3, the northern hemsphere wll have zone ndex numbers between 0 and 14 and lattude values between 0 and 90. The southern hemsphere wll have zone ndex numbers between 45 and 59 and lattude values between 270 and 360. Lattudes between 90 and 270 are

18 18 nvald. Southern hemsphere lattude values can be put n the range of 0 to -90 by subtractng 360 from the result of Eq 17 or by usng Eq 18. ( + 180,360 ) Rlat = MOD Rlat 180 Eq Arborne and TIS-B Longtude Global Decodng Longtude global decodng s smlar to lattude global decodng n that even and odd messages are used to count zone offsets and determne the zone ndex. The concept of offset between zone southern boundares s replaced wth the dea of offset between zone western boundares. The measured offset s rounded to the nearest nteger, whch s named m nstead of j, and the Modulus functon s used to get the zone ndex from postve or negatve values of m. The rule that the even and odd postons must be wthn ½ Zone Offset of each other also apples to longtude global decodng. The man dfference between longtude global decodng and lattude global decodng s that the number of longtude zones around the globe vares wth lattude. There are always 60 even zones and 59 odd zones around the globe n lattude global decodng. In longtude global decodng, there are between 1 and 59 longtude zones, as depcted n Fgure 3-2. The frst step n longtude global decodng s to ensure that the values of NL for the even and odd postons are the same. If they are dfferent, the Zone Offset szes wll be dfferent and the equaton to compute the number of Zone Offsets wll produce erroneous results. Eqs 17 and 18 wll produce one lattude for each bn number used n the lattude global decode (.e. Rlat 0 and Rlat 1 ). NL for each of these lattudes s computed wth Eq 2. If the NL values are dfferent, the recever must wat untl a par of even and odd messages arrve that produce the same value for NL. If the NL values are the same, longtude global decodng proceeds usng the same logc as lattude global decodng. In Eqs 8 and 9, the factor 4NZ, the number of even lattude zones around the globe, s replaced wth NL, the number of even longtude zones around the globe at Rlat 0 and Rlat 1. Eq 8 for the sze of the Zone Offset becomes Eq ZO = Dlon Dlon0 = for NL NL 1 NL 360 ZO = for NL > 1 NL NL 1 1 > ( ) Eq 9 for the number of Zone Offsets n a zone becomes Eq Dlon NL ZO = = for NL > 1 ZO 360 NL( NL 1) ( NL 1) NL 1 when = 0 ( even) = NL when = 1 ( odd ) NL ZO = for NL > 1 NL Eq 10 for the number of Zone Offsets to an even bn becomes Eq 21. ZO XZ 1 Eq 19 Eq 20 XZ0 = ( NL 1) for even zones Nb Eq

19 Eq 11 for the number of Zone Offsets to an odd bn becomes Eq 22. ZO XZ XZ1 = ( NL) for even zones Nb Eq Subtractng Eq 22 from Eq 21 produces the number of Zone Offsets between the western boundares of the zones contanng P0 and P1. XZ x = ZOXZ 0 ZOXZ1 = ( NL 1) 2 ( NL 1) XZ0 ( NL) XZ1 x = Nb 2 0 Nb XZ ( NL) 2 1 Nb 19 Eq 23 The result of Eq 23 must be rounded to the nearest nteger. Instead of assgnng the result to j, as s done for lattude n Eq 13, the result s assgned to m. 1 m = floor x + 2 ( NL 1) XZ0 m = floor 2 Nb ( NL) XZ Eq 24 [A f] As was the case wth Eq 13, the roundng performed by Eq 24 wll accommodate up to ½ Zone Offset between P0 and P1 ncludng vehcle movement, poston errors and CPR quantzaton errors. m wll behave the same as j n that the value of m wll be negatve when the even and odd longtude zones contanng P0 and P1 have dfferent Zone Index numbers. The Zone Index s recovered from m n the same manner that t s from j. Agan, the term 4NZ s replaced wth NL and j s replaced wth m n Eq 15 to form Eq 25. m MOD ( m, NL ) = m ( NL ) floor NL > 1 Eq 25 NL Eq 16 becomes Eq 26. (, NL ) for > 1 Zone Index = MOD m NL Eq 26 The recovered longtude Rlon s determned n the same manner as the recovered lattude Rlat. XZ Rlon = Dlon MOD( m, NL ) + for NL > 1 Eq 27 Nb 2 Rlon wll be a value between 0 and 360. It can be placed n the range of -180 to +180 wth Eq 28. ( + 180,360 ) Rlon = MOD Rlon 180 Eq 28 Eqs 19, 20, 25, 26 and 27 wll be ndetermnate when NL=1. From Eq 2, NL wll be 1 at lattudes greater than 87 N or less than -87 S. When NL = 1, Dlon, the longtude zone wdth, equals 360 (ref Eq 4) for both even and odd encodng. Wth one zone, there s no need to determne the zone ndex. Longtude can be recovered by multplyng the zone wdth (Dlon ) by the zone fracton (XZ /2 Nb ). Whle ths s a straghtforward approach, the algorthm descrpton n Appendx A does not handle NL=1 ths way.

20 20 When NL s 1, Eq 24 (A.1.7.7f) for m reduces to ether 0 or -1 for all values of XZ and Nb. Secton A.1.7.7g defnes a varable n. n = greater of [NL(Rlat ) ] and 1 Eq 29 Secton A.1.7.7g also defnes a formula for Rlon n terms of m and n. Rlon Dlon MOD m XZ 2 (, n ) + = 17 Eq 30 [A.1.7.7g] When m = 0 and n = 1, MOD(m, n ) equals 0. When m = -1, MOD(m, n ) also evaluates to 0. In ether case, Eq 30 for Rlon reduces to the zone wdth (Dlon ) multpled by the zone fracton (XZ /2 17 ). Ths s the expected result. For values of NL > 1, n wll equal (NL ) and Eqs 27 and 30 wll be equvalent. Secton A.1.7.7e redefnes Dlon n terms of n. Eqs 4 and 31 are equvalent. The reason for the redefnton s not clear. 360 Eq 31 Dlon = n [A e] 5.2 Surface Global Decodng Surface global decodng s the same as arborne and TIS-B local decodng except that the lattude and longtude zone wdths Dlat and Dlon are reduced by a factor of 4. Surface poston encodng s performed wth 19 bts of resoluton (reference Table 3-1) but only the 17 least sgnfcant bts are transmtted n the surface poston message (A.1.7.3f). Droppng the two most sgnfcant bts reduces the number of bns per zone by a factor of 4 but the wdth of the bns must reman the same for both encodng and decodng. Therefore, the lattude and longtude zone wdths Dlat and Dlon used n decodng must also be smaller by a factor of 4. Nb for surface decodng s equal to 17 rather than 19 because the number of bns n each of the reduced sze zones s 2 17 nstead of The smaller zone wdth means that the length of the talor s tape measure descrbed n Fgure 3-3 wll be ¼ of the dstance around the globe. Calculatons for recovered lattude and longtude Rlat and Rlon wll be n the range of 0 to 90 (.e. northern hemsphere and 0 to 90 east longtude). Addtonal solutons wll exst at 90, 180 and 270 from the calculated lattude and longtude. The recever must choose the approprate soluton and that soluton may be n a dfferent quadrant of the globe than the recever. Lattude solutons between 90 and 270 are dscarded. If there were targets broadcastng surface poston messages near ether of the poles, longtude ambguty could be a problem. Ths s an unlkely scenaro. For surface global and local decodng, the lattude zone wdth s gven by Eq 32 (reference Eq 1) Dlat = = 4 4NZ 4NZ NZ = 15 = 0 for even encodng = 1 for odd encodng Eq 32 [A.1.7.8a]

21 Lattude Zone Offset defned n Eq 8 wll also be smaller by a factor of 4. Eqs 9 through 18 are vald for surface global decodng as long as the correct values of Dlat, Nb and ZO are used. Rlat from Eq 17 wll be between 0 and 90. An addtonal soluton n the southern hemsphere wll be located at Rlat 90. The recever must choose the closer of the two. NL s calculated usng Eq 2 and Rlat but the result s the number of longtude zones n one quadrant of the globe rather than the number of zones around the globe. Before proceedng wth longtude global decodng, the recever must verfy that NL(Rlat 0 ) = NL(Rlat 1 ). If not, the decode s aborted and the process s restarted wth a new par of even and odd poston messages. For surface global and local decodng, the longtude zone wdth s obtaned by dvdng Eq 4 by 4. Ths results n Eq 33: 21 Dlon = NL 90 ( Rlat ) 90,, when NL when NL ( Rlat ) ( Rlat ) > 0 = 0 Eq 33 [A.1.7.8e] Longtude Zone Offset defned n Eq 19 wll also be smaller by a factor of 4. Eqs 20 through 27 are vald for surface global decodng as long as the correct values of Dlon and ZO are used. Rlon wll be between 0 and 90. Addtonal solutons wll exst at longtudes of 90, 180 and 270 to the east of Rlon. The recever must choose the approprate longtude whch wll be, n most cases, the closest longtude. 5.3 Arborne and TIS-B Locally Unambguous Decodng Local decodng uses a reference poston and the contents of one poston message to recover the lattude and longtude of the target. The dfference between the target poston and the reference poston must be less than ½ of a zone n both lattude and longtude. The reference poston s usually the last successfully decoded poston receved from the target. Snce ½ of a zone s approxmately 180 nautcal mles for arborne poston and 45 nautcal mles for surface poston, the poston change between two successfully decoded poston messages s unlkely to exceed the ½ zone lmt. The effect of the local decodng algorthm s to create a sldng regon 1 zone wde n lattude and longtude, centered on the reference poston. Because the regon s 1 zone wde, each bn number occurs only once n the regon, ensurng a unque result for each encoded lattude and longtude. Fgure 5-4 llustrates the behavor of the sldng regon for lattude. The number of bns per lattude zone has been reduced to 8 (.e. Nb = 3) to smplfy the fgure. Behavor of the sldng regon s the same for longtude except the fgure s rotated 90 clockwse and references to lattude are replaced wth longtude.

22 22 Sldng regon poston for (YZ=1) < (YZ=2) 1 Lat Zone YZ = 0 YZ = 7 YZ = 6 YZ = 5 YZ = 4 YZ = 3 YZ = 2 YZ = 1 YZ = 0 YZ = 7 YZ = 6 YZ = 5 YZ = 4 YZ = 3 YZ = 2 YZ = 1 YZ = 0 Sldng regon poston for (YZ=2) < (YZ=3) 1 Lat Zone YZ = 0 YZ = 7 YZ = 6 YZ = 5 YZ = 4 YZ = 3 YZ = 2 YZ = 1 YZ = 0 YZ = 7 YZ = 6 YZ = 5 YZ = 4 YZ = 3 YZ = 2 YZ = 1 YZ = 0 Sldng regon poston for (YZ=3) < (YZ=4) 1 Lat Zone YZ = 0 YZ = 7 YZ = 6 YZ = 5 YZ = 4 YZ = 3 YZ = 2 YZ = 1 YZ = 0 YZ = 7 YZ = 6 YZ = 5 YZ = 4 YZ = 3 YZ = 2 YZ = 1 YZ = 0 Fgure 5-4 Local Decodng Sldng Regon Behavor The sldng regon poston changes when lat s moves from one grey regon to another. In the unlkely event that the target poston s more than ½ zone from the reference poston, the target poston wll appear to wrap around the other sde of the ±½ zone regon. For example, f the target was n bn 7 (YZ=7) n the upper zone wth the reference poston between YZ=1 and YZ=2 (see left sde of Fgure 5-4), the recovered lattude would be for YZ=7 n the lower zone. Ths wrap around behavor occurs because the algorthm assumes the target s wthn ½ zone of the reference poston and the only bn number 7 s n the lower zone. In effect, the recovered poston s shfted one zone from the actual poston n the drecton of the reference poston. Some older mplementatons used the recever poston as the reference poston nstead of the last target poston. Surface targets more than ½ zone away (45 nautcal mles) would decode ncorrectly as descrbed above. The local decodng algorthm may be easer to vsualze wth a smplfed example. Imagne a road wth a marker at each klometer statng the number of klometers from the begnnng of the road. A person walkng along the road toward the end, who s known to be wthn ½ km of the 22 km marker, announces they are 0.2 km past the last marker. What s ther locaton relatve to the begnnng of the road? Snce they are wthn ½ km of marker 22 and they are 0.2 km past the last marker, they are 22.2 km from the begnnng of the road. Suppose they had announced ther poston as 0.7 km past the last marker. Ther locaton would be 21.7 km from the begnnng of the road because ths s the only locaton that s both 0.7 km past the last marker and wthn ½ km of 22 km marker. Ths s the logc emboded n the local decodng algorthm Arborne and TIS-B Lattude Local Decodng Local decodng determnes lattude frst n order to compute NL and then determnes longtude. Lattude s calculated from the bn number and CPR format transmtted n the poston message, and the zone ndex, whch s computed from the last known target poston. The algorthm sums the Zone Index of the reference poston (RP) and the dfference between the Zone Indces of the reference poston and the encoded poston (EP) to obtan the Zone Index of the encoded poston.

23 ZI EP = ZI + ΔZI Eq 34 RP RP EP 23 Because the encoded poston s assumed to be wthn ½ zone of the reference poston, the dfference n zone ndces ΔZI RP EP s lmted to -1, 0 or +1. The Zone Index of the reference poston ZI RP s determned wth Eq 35. lat s ZI = RP floor Eq 35 Dlat lat s s the reference lattude. Dlat s the lattude zone wdth from Eq 1. The frst zone north of the equator has an ndex number of zero. Lattude Zone Index numbers south of the equator start at -1 and ncrease n magntude toward the South Pole. Note that southern hemsphere lattude zone ndces for local decodng are numbered dfferently than the zone ndces for global decodng. The dfference between the lattude zone ndces of the reference poston and of the encoded poston (ΔZI RP EP ) s the dfference between the lattude zone fractons of the reference poston and the encoded poston (f RP - f EP ), rounded to the nearest nteger. Ths s shown for f RP > ½ n Fgure 5-5. ±½ zone local decodng regon. Target s assumed to be n ths range of lattude EP2 RP EP1 = Zone Fracton Fgure 5-5 Local Decodng Zone Index Determnaton when f RP > 1/2 f RP s gven by Eq 36. f MOD( lat, Dlat ) s RP = Eq 36 Dlat f EP s gven by Eq 37. f EP YZ = Eq 37 Nb 2

24 24 The RP and EP are assumed to le wthn the ±½ zone local decodng regon (the shaded area n Fgure 5-5), but the RP and EP may be n dfferent lattude zones (e.g. RP and EP2). The dfference n zone fractons s used to determne whether the EP s n the same zone as the RP, one zone to the north or one zone to the south. The converson from the dfference n zone fractons (f RP - f EP ) to the dfference n zone ndces (ΔZI RP EP ) s done by roundng as shown n Eq ΔZI RP EP = floor frp fep + Eq 38 2 If the two postons are n the same zone, the dfference n zone fractons wll always be between -½ and +½. Eq 38 wll produce a dfference n Zone Indces (ΔZI RP EP ) of 0. If EP s n the zone to the north of RP (e.g. EP2 n Fgure 5-5), the dfference n zone ndces ΔZI RP EP s expected to be +1. f EP wll be less than f RP ½ and therefore (f RP f EP ) wll be greater than +½. Applyng Eq 38 for ΔZI RP EP to (f RP - f EP ) wll produce the expected value of +1. Ths value s added to the zone ndex of RP to get the zone ndex of EP (n+1). The case where f RP < ½ s shown n Fgure 5-6. ±½ zone local decodng regon. Target s assumed to be n ths range of lattude EP2 RP EP1 = Zone Fracton Fgure 5-6 Local Decodng Zone Index Determnaton when f RP <1/2 If EP s n the zone to the south of RP (e.g. EP1 n Fgure 5-6), the dfference n zone ndces ΔZI RP EP s expected to be -1. f EP wll be greater than f RP + ½ and therefore (f RP f EP ) wll be less than -½. Applyng Eq 38 for ΔZI RP EP to (f RP - f EP ) wll produce the expected value of -1. Ths value s added to the zone ndex of RP to get the zone ndex of EP (n-1).

25 Eq 38 produces the correct dfference n zone ndces for any two reference poston and encoded poston zone fractons. Substtutng Eqs 35 through 38 nto Eq 34 and rearrangng results n Eq 39. ZI EP = ZI RP + ΔZI RP EP lat s 1 ZI EP = floor + floor frp fep + Dlat 2 Eq 39 lat s MOD( lats, Dlat) YZ 1 ZI = + + EP floor floor [A.1.7.5b] Nb Dlat Dlat 2 2 lat s 1 MOD( lats, Dlat) YZ j = ZI = + + EP floor floor Nb Dlat 2 Dlat 2 The lattude of the encoded poston s the lattude zone wdth, Dlat, multpled by the sum of the encoded poston zone ndex j and the encoded poston zone fracton. Rlat YZ Dlat j + 2 = Nb Arborne and TIS-B Longtude Local Decodng 25 Eq 40 [A.1.7.5c] Local decodng of longtude s smlar to local decodng of lattude. Longtude Zone Wdth s calculated wth Eq 4, whch s repeated n [A.1.7.5d]. Then, the longtude zone ndex s computed usng Eq 41. ZI EP = ZI RP + ΔZI RP EP lon s 1 ZI EP = floor + floor f RP f EP + Dlon 2 lon s MOD( lons, Dlon ) XZ 1 ZI = + + EP floor floor Nb Dlon Dlon 2 2 lon s 1 MOD( lons, Dlon ) XZ m = ZI = + + EP floor floor Nb Dlon 2 Dlon 2 Eq 41 [A.1.7.5e] Eq 41 s the same as Eq 39 except the followng varable substtutons have been made: RP lattude lat s replaced wth RP lattude lon s Lattude Zone Wdth Dlat replaced wth Longtude Zone Wdth Dlon Lattude bn number YZ replaced wth Longtude bn number XZ EP lattude zone ndex j replaced longtude zone ndex m ZI and f n Eq 41 refer to longtude zone ndces and zone fractons whereas the same varables n Eq 39 refer to lattude zone ndces and zone fractons. Longtude zone ndces start at zero on the east sde of the prme merdan and ncrease wth ncreasng east longtude. If RP longtude s between 0 and 360, the longtude zone ndces wll range from 0 to 59 and the recovered longtude Rlon wll be n the range of 0 to 360. If RP longtude s between -180 and +180, the longtude zone ndces wll range from -30 to +29 and the recovered longtude Rlon wll be n the range of -180 to +180.

26 26 The longtude of the encoded poston s the longtude zone wdth, Dlon, multpled by the sum of the encoded poston zone ndex m and the encoded poston zone fracton. Rlon XZ Dlon m + 2 = Nb Eq 42 [A.1.7.5f] 5.4 Surface Local Decodng Surface local decodng s the same as arborne and TIS-B local decodng except that the lattude and longtude zone wdths Dlat and Dlon are reduced by a factor of 4. Surface poston encodng s performed wth 19 bts of resoluton (reference Table 3-1) but only the 17 least sgnfcant bts are transmtted n the surface poston message (A.1.7.3f). Droppng the two most sgnfcant bts reduces the number of bns per zone by a factor of 4 but the wdth of the bns must reman the same for both encodng and decodng. Therefore, the zone wdths for decodng must also be smaller by a factor of 4. Nb for surface decodng s equal to 17 rather than 19 because the number of bns n each of the reduced sze zones s 2 17 nstead of The ±½ zone sldng regon s applcable for surface local decodng, but snce the zone wdth s smaller by a factor of 4, the sldng regon wdth wll be smaller by a factor of 4 also. Ths means that nstead of a surface target needng to be wthn approxmately ±180 nautcal mles of the reference poston, the surface target must be wthn approxmately ±45 nautcal mles. Eqs 34 through 40 are applcable for surface lattude local decodng as long as the reduced lattude zone wdth Dlat from Eq 32 and the correct value for Nb are s used n the calculatons. NL s calculated usng Eq 2 and Rlat but the result s the number of longtude zones n one quadrant of the globe rather than the number of zones around the globe. Eqs 41 through 42 are applcable for surface longtude local decodng as long as the reduced longtude zone wdth Dlon from Eq 33 s used n the calculatons. 6 Addtonal Informaton The precedng sectons descrbe how the CPR algorthms should work..ths secton descrbes specfc ssues that have arsen n terms of the concepts descrbed above. 6.1 NL Transton Lattudes Ths secton defnes the 32 bt Angular Weghted Bnary (32bAWB) nput lattudes at whch the value of NL changes. In 2006, Arservces Australa reported anomales n encoded longtude reported by certan arcraft. The root cause of the longtude jumps was nconsstency between the encoded lattude and the value of NL used to encode the longtude. SC-186 WG3 added the poston reasonableness tests n sectons , and to detect the erroneous longtudes caused by ncorrect NL values as well as erroneous postons caused by undetected bt errors and other mechansms. Durng the revew of ths appendx, SC-186 WG3 requested that a table be added showng the 32bAWB nput lattudes at whch the value of NL changes. The CPR encodng process s descrbed n Secton 4. The relevant steps leadng to the selecton of NL are:

27 1. Determne the lattude zone wdth Dlat (Eq 1) Determne the bn number YZ (Eq 5) 3. Determne the bn centerlne lattude Rlat (Eq 6) 4. Determne NL usng Rlat (Eq 2 or Eq 3) A crucal and commonly msunderstood pont s that the value of NL selected durng encodng s NOT based drectly on the lattude nput to the encoder. NL s determned from Rlat and Rlat s dependent on the nput lattude. The reason for ths s the decoder can determne only Rlat and must use the value of Rlat to determne NL. If the value of NL used durng encodng s not consstent wth the encoded lattude, the decoder wll select a dfferent value for NL and produce an ncorrect longtude. Fgure 6-1 depcts the relatonshps between nput lattude, bn centerlne lattude and the NL transton lattude for even and odd arborne encodng at the 53/52 NL transton (approx 27.9 south lattude). Input lattudes at or above the bn boundary wll have Rlat values (.e. bn centerlne lattudes) above the NL transton lattude and an NL value of 53. Input lattudes below the bn boundary wll have Rlat values below the NL transton lattude and an NL value of 52. Note that lattudes above the bn boundares but below the NL transton lattude stll result n NL=53. An encoder that based NL drectly on the nput lattude, nstead of Rlat, would ncorrectly select NL=52 for these lattudes.

28 28 Fgure 6-1 Example of relatonshps between nput lattude, Rlat and NL Gven the purpose of ths secton and the behavor descrbed above, the 32bAWB lattudes of nterest are the ones that straddle the lattude of the bn boundary closest to each NL transton lattude. The lattude of the closest bn boundary wll depend on the CPR format (.e. even or odd) and the number of bts used for encodng Nb. The process to determne the 32bAWB NL transton boundary lattudes s as follows: 1. Determne the NL transton lattudes usng Eq Determne the bn numbers YZ north and YZ south of the bns that straddle each NL transton lattude (, Dlat ) Nb MOD lat north YZ = 2 north floor + 1 Eq 43 Dlat YZ south (, Dlat ) Nb MOD lat south = floor 2 Eq 44 Dlat

29 3. Determne the bn centerlne lattude Rlat of the straddlng bns usng Eq 6 4. Average the bn centerlne lattudes to get the bn boundary lattude 5. Fnd the 32bAWB NL lattudes that straddle the bn boundary lattude 360 latbn boundary 32bAWB north = celng Eq latbn boundary 32bAWB south = celng Eq Usng Eq 7, verfy that the encoded longtude changes between the 32bAWB lattudes when the nput longtude remans constant. Ths s an ndcaton that NL changed. Eq 44 s the same as Eq 5 except the frst bn wth a bn centerlne at or south of the NL transton lattude s selected. Eq 45 selects the bn just to the north of the bn selected n Eq 44. Specal handlng s requred for the NL transton lattude at 87 south when even CPR format s used. Eq 43 wll select the bn wth a bn centerlne that concdes wth the 2/1 NL transton lattude at 87 south and Eq 44 wll select the bn just to the north. Snce NL s defned to be 2 at 87 south and 2 at the centerlne of the next bn to the north, NL wll not change at the bn boundary between these two bns. Therefore, the northern bn should be at 87 south and the southern bn should be the next bn to the south. The celng functon n Eq 46 produces the number of 32bAWB bns from the equator to the 32bAWB lattude just north of the bn boundary. The number of bns multpled by the heght of each bn (360 /2 32 ) s the north 32bAWB lattude. Eq 46 gves the next 32bAWB lattude to the south. The celng functon s used nstead of the floor functon to address cases where the 32bAWB lattude concdes wth the bn boundary. An nput lattude on the bn boundary should round up to the next more northerly bn. The celng/celng-1 approach provdes a northern lattude on the bn boundary and a southern lattude on 32bAWB bn to the south. Verfcaton usng Eq 7 s performed wth constant nput longtudes of 45 for surface encodng and 180 for arborne and TIS-B encodng. Any value could be used but these values create encoded longtude values that represent ether the edge of a zone or the exact mddle of a zone. Table 6-1 through 29

30 30 Table 6-6 present the northern and southern 32bAWB boundary lattudes for each transton lattude wth even and odd, surface, arborne and TIS-B encodngs. The expected outputs n Table 6-1 are dentcal to those n Table The nput lattudes n Table are the bn centerlnes of the even format, surface encoded bns that straddle each NL transton lattude. The dstance between the bn centerlnes s approxmately 127 cm for even format and 130 cm for odd. The dstance between the 32bAWB boundary lattudes s approxmately 0.93 cm. Even though the separaton between the 32bAWB boundary lattudes s much smaller than the test lattudes n Table 2-130, both sets of lattudes are on opposte sdes of the bn boundary and both wll generate the same values of NL and the same encoded longtudes. Encoders that determne NL ncorrectly from the nput lattude rather than from Rlat wll produce the expected outputs usng the nputs from Table but wll not produce the expected outputs usng the 32bAWB boundary lattudes presented n Table 6-1. Table bAWB boundares for NL Transton lattudes - surface even encodng Input 32bAWB Boundary Lattudes (Input Longtude = 45 ) Expected Outputs South North South North Decmal 32bAWB Decmal 32bAWB Enc Lat Enc Lon Enc Lat Enc Lon DDDDE DDDDE D8948CC D8948CD CFB4BFF CFB4C E F C5E0E C5E0E A B BBA3A BBA3A67 1FD2D FD2E B12CB B12CB78 0C33D C33E A690D A690D9A 184F FA BDA BDA59A ED ED12 0FFBC FFBD A 1B9C B9C B438CC B438CD 071EA EB D E F F34 1DCCA DCCB A1E A1E512 08F8D F8E EF31DD EF31DE 1407D E B7C B7C89 1EF EF8A BAEE BAEF 09C9E C9F D0DF D0DF34 147A A DA DA67 1F F07A B B A A B B FED FED2734 1DCA DCAA F30C7BB F30C7BC 07B B E72DC E72DC D E DB34C DB34C89 1B02F B CF1FC CF1FC89 045B BA C2ED0CC C2ED0CD 0D7C D7C B69A9DD B69A9DE 1661E F 00000