If you mean building a GPS decoder (like the module below) from scratch, this is like asking is it possible to build a car.
Short answer... No.
They used a premade GPS module like the Parallax one pictured below, the data comes out serial NMEA @4800 baud. This is easy to decode with any microcontroller, most of the data you can throw away.
**broken link removed**
Sample data looks like this.
GGA - essential fix data which provide 3D location and accuracy data.
$GPGGA,123519,4807.038,N,01131.000,E,1,08,0.9,545.4,M,46.9,M,,*47
Where:
GGA Global Positioning System Fix Data
123519 Fix taken at 12:35:19 UTC
4807.038,N Latitude 48 deg 07.038' N
01131.000,E Longitude 11 deg 31.000' E
1 Fix quality: 0 = invalid
1 = GPS fix (SPS)
2 = DGPS fix
3 = PPS fix
4 = Real Time Kinematic
5 = Float RTK
6 = estimated (dead reckoning) (2.3 feature)
7 = Manual input mode
8 = Simulation mode
08 Number of satellites being tracked
0.9 Horizontal dilution of position
545.4,M Altitude, Meters, above mean sea level
46.9,M Height of geoid (mean sea level) above WGS84
ellipsoid
(empty field) time in seconds since last DGPS update
(empty field) DGPS station ID number
*47 the checksum data, always begins with *