Technical Provisions for Mode S Services and Extended Squitter

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DRAFT - Working Paper ASP TSGWP11-01 for review by the TSG during the meeting in June 2011 in Paris C-46 Technical Provisions for Mode S Services and Extended Squitter 2. Because the higher-order bits are not transmitted, it follows that multiple locations on the earth will produce the same encoded position. If only a single position message were received, the decoding would involve ambiguity as to which of the multiple solutions is the correct location of the aircraft. The CPR technique includes a provision to enable a receiving system to unambiguously determine the location of the aircraft. This is done by encoding in two ways that differ slightly. The two formats, called even-format and odd-format, are each transmitted fifty percent of the time. Upon reception of both types within a short period (approximately 10 seconds for airborne formats and 50 seconds for surface formats), the receiving system can unambiguously determine the location of the aircraft. 3. Once this process has been carried out, the higher-order bits are known at the receiving station, so subsequent single message receptions serve to unambiguously indicate the location of the aircraft as it moves. 4. In certain special cases, a single reception can be decoded into the correct location without an even/odd pair. This decoding is based on the fact that the multiple locations are spaced by at least 360 NM. In addition to the correct locations, the other locations are separated by integer multiples of 360 NM to the north and south and also integer multiples of 360 NM to the east and west. In a special case in which it is known that reception is impossible beyond a range of 180 NM, the nearest solution is the correct location of the aircraft. 5. The parameter values in the preceding paragraph (360 and 180 NM) apply to the airborne CPR encoding. For aircraft on the surface, the CPR parameters are smaller by a factor of 4. This encoding yields better resolution but reduces the spacing of the multiple solutions. C.2.6.2 CPR ALGORITHM PARAMETERS AND INTERNAL FUNCTIONS The CPR algorithm shall utilize the following parameters whose values are set as follows for the Mode S Extended Squitter application: 1. The number of bits used to encode a position coordinate, Nb, is set as follows: For airborne encoding, used in the ADS-B Airborne Position Message and the TIS-B Fine Airborne Position Nb = 17 Message: For surface encoding, used in the ADS-B Surface Position Message and the TIS-B Fine Surface Position Nb = 19 Message: For intent encoding: Nb = 14 For TIS-B encoding, used only in the TIS-B Coarse Nb = 12 Airborne Position Message: Draft Note 1.— The Nb parameter determines the encoded position precision (approximately 5 m for the airborne encoding, 1.25 m for the surface encoding, 41 m for the intent encoding and 164 m for the TIS- B encoding). 2. The number of geographic latitude zones between the equator and a pole, denoted NZ, is set to 15. Note 2.— The NZ parameter determines the unambiguous airborne range for decoding (360 NM). The surface Latitude/Longitude encoding omits the high-order 2 bits of the 19-bit CPR encoding, so the effective unambiguous range for surface position reports is 90 NM. The CPR algorithm shall define internal functions to be used in the encoding and decoding processes. a. The notation floor(x) denotes the floor of x, which is defined as the greatest integer value k such that k ≤ x. Note 3.—For example, floor(3.8) = 3, while floor(-3.8) = -4. b. The notation |x| denotes the absolute value of x, which is defined as the value x when x ≥0 and the value –x when x < 0. DRAFT - Working Paper ASP TSGWP11-01 for review by the TSG during the meeting in June 2011 in Paris
DRAFT - Working Paper ASP TSGWP11-01 for review by the TSG during the meeting in June 2011 in Paris Appendix C C-47 c. The notation MOD(x,y) denotes the “modulus” function, which is defined to return the value ⎛ x ⎞ ⎝ y ⎠ ( x, y) = x − y ⋅floor⎜ ⎟ MOD where y ≠ 0 . Note 4.—The value y is always positive in the following 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 remainder of (x+360°) divided by y. For example, ( − 40° , 6° ) = MOD( 320° , 6° ) = 2° MOD . d. The notation NL(x) denotes the “number of longitude zones” 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, NL ( lat) ⎛ ⎜ ⎡ ⎛ ⎛ π ⎞ ⎞⎤ ⎜ ⎢ ⎜ 1− cos⎜ ⎟ ⎟⎥ ⎜ ⎢ ⎜ ⎝ 2 ⋅ NZ = floor 2π ⋅ arccos 1− ⎠ ⎟⎥ ⎜ ⎢ ⎜ ⎛ ⎞ ⎟ 2 π ⎥ ⎜ ⎢ ⎜ cos ⎜ ⋅ lat ⎟ ⎟⎥ ⎝ ⎣ ⎝ ⎝180° ⎠ ⎠⎦ where lat denotes the latitude argument in degrees. For latitudes at or near the N or S pole, or the equator, the following points are defined: For lat = 0 (the equator), NL = 59 For lat = +87 degrees, NL = 2 For lat = -87 degrees, NL = 2 For lat > +87 degrees, NL = 1 For lat < -87 degrees, NL = 1 Note 5.— This equation for NL() is impractical for a real-time implementation. A table of transition latitudes can be pre-computed using the following equation: Draft −1 ⎞ ⎟ ⎟ , ⎟ ⎟ ⎟ ⎠ ⎛ ⎞ ⎜ ⎛ π ⎞ 1− cos⎜ ⎟ ⎟ 180 ° ⎜ ⎝ 2 ⋅ NZ ⎠ ⎟ for NL = 2 to 4⋅NZ –1, lat = ⋅ arccos π ⎜ ⎛ 2π ⎞ ⎟ ⎜ 1− cos ⎟ ⎜ ⎜ ⎟ ⎟ ⎝ ⎝ NL ⎠ ⎠ and a table search procedure used to obtain the return value for NL( ). The table value for NL = 1 is 90 degrees. When using the look up table established by using the equation above, the NL value is not expected to change to the next lower NL value until the boundary (latitude established by the above equation) has actually been crossed when moving from the equator towards the pole. C.2.6.3 CPR ENCODING PROCESS The CPR encoding process shall calculate the encoded position values XZi and YZi for either airborne, surface, intent, or TIS-B 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 intent always uses the even format (i = 0), whereas the airborne, surface, and TIS-B encoding use both even (i = 0) and odd (i = 1) formats. a. Dlati (the latitude zone size in the N-S direction) is computed from the equation: Dlat i = 360° 4 ⋅ NZ − i DRAFT - Working Paper ASP TSGWP11-01 for review by the TSG during the meeting in June 2011 in Paris
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Technical Provisions for Mode S Services and Extended Squitter

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