## 6 Coding

03.323GPPRelease 98TSUniversal Geographical Area Description (GAD)

## 6.1 Point

The co-ordinates of an ellipsoid point are coded with an uncertainty of less than 3 metres

The latitude is coded with 24 bits: 1 bit of sign and a number between 0 and 2^{23}-1 coded in binary on 23 bits. The relation between the coded number N and the range of (absolute) latitudes X it encodes is the following (X in degrees):

except for N=2^{23}-1, for which the range is extended to include N+1.

The longitude, expressed in the range -180°, +180°, is coded as a number between -2^{23} and 2^{23}-1, coded in 2’s complement binary on 24 bits. The relation between the coded number N and the range of longitude X it encodes is the following (X in degrees):

## 6.2 Uncertainty

A method of describing the uncertainty for latitude and longitude has been sought which is both flexible (can cover wide differences in range) and efficient. The proposed solution makes use of a variation on the Binomial expansion. The uncertainty *r*, expressed in metres, is mapped to a number K, with the following formula:

with C = 10 and x = 0,1. With 0 £ K £ 127, a suitably useful range between 0 and 1800 kilometres is achieved for the uncertainty, while still being able to code down to values as small as 1 metre. The uncertainty can then be coded on 7 bits, as the binary encoding of K.

Table 1: Example values for the uncertainty Function

Value of K | Value of uncertainty |

0 | 0 m |

1 | 1 m |

2 | 2,.1 m |

– | – |

20 | 57,.3 m |

– | – |

40 | 443 m |

– | – |

60 | 3 km |

– | – |

80 | 20 km |

– | – |

100 | 138 km |

– | – |

120 | 927 km |

– | – |

127 | 1800 km |

## Altitude

Altidude is encoded in increments of 1 meter using a 15 bit binary coded number N. The relation between the number N and the range of altitudes *a *(in metres) it encodes is described by the following equation;

except for N=2^{15}-1 for which^{ } the range is extended to include all greater values of *a.*

The direction of altitude is encoded by a single bit with bit value 0 representing height above the WGS84 ellipsoid surface and bit value 1 representing depth below the WGS84 ellipsoid surface.

## Uncertainty Altitude

The uncertainty in altitude, h, expressed in metres is mapped from the binary number K, with the following formula:

with *C* = 45 and *x* = 0,.025. With 0 £ K £ 127, a suitably useful range between 0 and 990 meters is achieved for the uncertainty altitude,. The uncertainty can then be coded on 7 bits, as the binary encoding of K.

Table 2: Example values for the uncertainty altitude Function

Value of K | Value of uncertainty altitude |

0 | 0 m |

1 | 1,.13 m |

2 | 2,.28 m |

– | – |

20 | 28,.7 m |

– | – |

40 | 75,.8 m |

– | – |

60 | 153,.0 m |

– | – |

80 | 279,.4 m |

– | – |

100 | 486,.6 m |

– | – |

120 | 826,.1 m |

– | – |

127 | 990,.5 m |

## Confidence

The confidence by which the position of a target entity is known to be within the shape description, (expressed as a percentage) is directly mapped from the 7 bit binary number K, except for K=0 which is used to indicate ‘no information’, and 100 < K ≤128 which should not be used but may be interpreted as “no information” if received.

## Radius

Inner Rradius is encoded in increments of 5 meters using a 16 bit binary coded number N. The relation between the number N and the range of radius *r *(in metres) it encodes is described by the following equation;

Except for N=2^{16}-1 for which^{ }the range is extended to include all greater values of *r.* This provides a true maximum radius of 327,.675 meters.

The uncertainty radius is encoded as for the uncertainty latitude and longitude.

## Angle

Offset and Included Aangle areis encoded in increments of 21 using an 98 bit binary coded number N in the range 0 to 179. The relation between the number N and the range of offset (ao) and included (ai) angles *a *(in degrees) it encodes is described by the following equations;

Offset angle (ao)

2 N <= ao < 2 (N+1) Accepted values for ao are within the range from 0 to 359,9…9 degrees.

Included angle (ai)

2 N < ai <= 2 (N+1) Accepted values for ai are within the range from 0,0…1 to 360 degrees.