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e) The notation MOD(x,y) denotes the "modulus" function, which is defined to return the value
MOD(x,y) = x - y - floor t)w here y # 0.
Nore 4.- The value y is always positive in thefollowing CPR algorithms. When x is non-negative, MOD(x,y) is equivalent
to the remainder of x divided by y. When x represents a negative angle, an alternative way to calculate MOD(x,y) is to return
the rtnzairzder of (x+360°) divided by y.
For example, MOD(40°,6") = MOD(32Oo,6") = 2".
f) The notation NL(x) denotes the "number of longitude zoncs" function of the latitude angle x. The value returned by NL(x)
is constrained to the range from 1 to 59. NL(x) is defined for most latitudes by the equation,
- 1
1 - cos -
YL(lat) = floor 2 ~ a-rc cos
(2 .;z) [ [ [co:(6- llatllj7]
where lat denotes thc latitude argument in degrees. For latitudes ai or near the N or S pole, where the above formula would
either be undefined or yicld NL(1at) = 0, the value returned by the NL( ) function shall be 1. Likewise, at the equator, where
the above formula might otherwise yicld NL(ht) = 60, the value returned by the NL( ) function shall be 59.
Note 5.- This equation for NL( ) is impractical for real time implementation. A table of transition latitudes can be precomputed
using the following equation:
!at = -'80" . arc cos N Z - 1,
and a table search procedure used to obtain the return value for NLO. The table value for NL = I is 90 degrees.
2.6.3 CPR ENCODING PROCESS
The CPR encoding process shall calculate the encoded position values XZ, and YZi for either airborne, surface or TCP, TCP+l
latitude and longitude fields from the global position lat (latitude in degrees), lon (longitude in degrees), and the CPR encoding
type i (0 for even format and 1 for odd format), by performing the following sequence of computations. The CPR encoding for
TCP, TCP+l shall always use the even format (i = 0), whereas the airborne and surface encoding shall use both even (i = 0) and
odd (i = 1) formats.
a) Alati (the latitude zone size in the N-S direction) is computed from the equation:
Alut, = -360"
4. NZ- i
Ei(t he Scoordinate within the Zone) is then computed from Alnt; and lat using scparate equations:
For airborne encoding:
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Annex 10 - Aeronauticul Telecommunicatio~is Volume 111
( , MOD(lat.Alntj)
For surface encoding: YZi = floor 2 .
Alat,
,, MOD(lat,Alnto)
For TCP, TCP+ I encoding: YZo = floor (2 - Alat;
b) Rlat, (the latitude that a receiving ADS-B system will extract from the transmitted message) is then computed from lat, YZi.
and Alat, using separate equations:
For airbomc encoding: Rlnti. Alat, - (3 +floor
For surface encoding:
YZ.
For TCP, TCP+I encoding: Rho. Aloto . (j+ floo r(*))
2 Alate
c) Aloni (the longitude zone size in the E-W direction) is then computed from Rlat, using the equation:
I 3600 when NL(Rloti) - i > 0
NL(Rlat,) - i
lion; =
1 360°, when NL(R1at;)- i = 0
d) XZi (the &-coordinate within the Zone) is then computed from lon and Aloni using separate equations:
For airborne encoding:
17 MOD(lon,Alon,) xzi = floor (2 . Alan;
MOD(lon,Aloni) 1
For surface encoding: XZ! = floor (219 * Aloni
+ i)
For TCP, TCP+ 1 encoding:
e) Finally, limit the values of XZ, and Yq to fit in the 17-bit or 14-bit field allotted to each coordinate:
For airborne encoding: YZ; = MOD(YZ~, 217),
xz, = MOD(XZ;, 217)
For surface encoding: YZ, = MOD(YZ~, 217),
xz, = MOD(XZ,, 217)
For TCP, TCP+l encoding: YZo = MOD(YZo, 214),
XZ, = MOD(X~2,1 4)
2.6.4 LOCALLYUN AMBIGUOUS CPR DECODING
The CPR algorithm shall decode a geographic position (latitude, Rlat, and longitude, Rloni,) that is locally unambiguous with
respect lo a reference point (lat,r, lon,) known to be within 180 NM of the true airborne position (or within 45 NM for a surface
message).
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No. 77
Part I Annex 10 - Aeronaulical Telecommlinications
Note.- This reference point nzay be a previously rracked position thuf hus been confirmed by global decoding (see 2.6.7) or it
muy be the own-uircraft position, which would be used for decoding a new tentutivz position report.
The encoded position coordinates XZi and YZi and the CPR encoding type i (0 for the even encoding and 1 for he odd encoding)
contained in a Mode S extendcd squitter message shall be decoded by performing the sequence of computations givcn in 2.6.5 for
the airborne and TCP, TCP+1 format types and in 2.6.6 for the surface format type.
2.6.5 COMPUTATIONFOSR THE
AIRBORNE MESSAGE AND TCP, TCP+l MESSAGE
The following computations shall be performed to obtain the decoded latituddlongilude for the airborne and TCP, TCP+I message
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