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Modern Geomatics Technologies and Applications

codes, the 0s and 1s that are the codes. In any case, the most commonly used spread spectrum modulation technique is known
as binary phase shift keying (BPSK). This is the technique used to create the NAV Message, the P(Y) code and the C/A code.
The binary biphase modulation is the switching from 0 to 1 and from 1 to 0 accomplished by phase changes of 180º in the carrier
wave. PRN codes are a sequence of zeroes and ones, each zero or one referred to as a “chip”. These codes are combined and
modulated with the navigation data and sent to the ground.
5. Gold code polynomial for other GNSS satellites systems

In the all GNSS systems, the structure of PRN codes generation is conceptually similar, while, the form of using
mathematical equations in the production of these codes is slightly different. Gold code generator polynomial for BeiDou
satellites systems are as Equations 10 and 11 [12]:

( ) = 1 + + + + + + (10)

( ) = 1 + + + + + + + + (11)

With initial states
(0) = {0,1,0,1,0,1,0,1,0,1,0}
(0) =
The range codes are different from GPS even for the same taps, because the polynomials and their initial states are different.
In similar, gold code generator polynomial for GLONASS satellites systems are as Equations 12 and 13 [6, 12]:

(X) = 1 + X + X (12)
G

(X) = 1 + X + X (13)
G

6. Conclusion
In this research, not only, the PRN codes generation for GNNS satellites using different polynomials is presented and
discussed but also, this paper demonstrates a practical application of mathematics in the Geomatics and engineering. The GNSS
uses of satellites to provide autonomous Geo-spatial positioning. The GNSS satellites continuously transmit signals at two or
more frequencies. These signals contain pseudorandom noise (PRN) codes and navigation data to allow users to compute both
the travel time from the satellite to the receiver and the satellite coordinates at any time. Each satellite within a GNSS
constellation has a unique PRN code that it transmits as part of the C/A navigation message. This code allows any receiver to
identify exactly which satellite(s) it is receiving.
The PRN codes have special mathematical properties which allow all satellites to transmit at the same frequency without
interfering with each other. These codes also allow precise range measurements between satellite and user receivers. PRN codes
generator contains two shift registers known as gold polynomials. To the all GNSS systems, the structure of the PRN code
generation using polynomials is conceptually similar, while, the form of using mathematical equations in the production of these
codes is slightly different. The PRN code generator contains two shift registers always has a feedback configuration with the
polynomials equations. They is set by choosing specific tap outputs and combining them with exclusive OR operation. The shift
registers, which are used for code generation, can be described by polynomials. The essential qualities of the PRN sequences are
defined by the correlation measures. Two infinite random sequences should be uncorrelated. The closer a given PRN sequence
comes in a truly random sequence, the better the PRN sequence is. In this research, PRN codes generation of GNNS Satellites
using different polynomials is presented and discussed. Furthermore, this paper demonstrates a realistic application of
mathematics in the Geomatics and engineering.

References
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