WSEAS TRANSACTIONS on ELECTRONICS
frequency of a given primary clock. The GPS receiver dual carrier phase measurement and the oscillation frequency of the master clock are used to achieve the frequency stabilizing and time synchronization. The clock error between satellites and receivers can be estimated through the GPS carrier phase observation. A master atom clock replaces the satellite atom clock, to estimate frequency error between the receiver and master atom clock. The extension control law and extension neural network are employed to implement the controllers in this system. The oscillation frequency of the GPS receiver is synchronized with the master atom clock frequency. The position precision can be improved by reducing the frequency error between the receiver and master atom clock. 
This paper is organized as follows:
1) Section 2 describes GPS carrier phase observation.
Section 3 derives the extension controller.
Section 4 depicts the extension neural network.
Section 5 discusses the experimental results.
Section 6 gives our conclusions.
2 GPS Carrier Phase Observation
The phase difference between the GPS satellite’s carrier phase and the reference frequency of its GPS receiver oscillator can be expressed as follows:  
: Carrier phase of the R-th receiver station to observe the S-th satellite.
: Carrier phase of the S-th satellite time transmission in t epoch.
: The phase of R-th receiver produced at T epoch
If we consider the phase relationship between the GPS carrier phase frequency and the oscillator, the above equation can be rearranged using
( ) ( ) S S R R t T φ φ Φ = −
( ) ( ) ( ) S R T t f T t φ φ = + ⋅ −
The propagation delay errors contain the ionosphere delay effect, the troposphere error and the uncertain error. It can be formulated as follows:
( ) S S S S S R R R R i o n t r o p c d t d T N d d ρ λ Φ = + S − + − +
S R ε +
S R ρ : T h e d i s t a n c e b e t w e e n t h e S - t h s a t e l l i t e a n d t R-th receiver h e
dtS : Clock bias of the S-th satellite
R d T
: The clock difference between the GPS time and the R-th receiver clock.
R S N
: Initial carrier phase integer ambiguity
λ : The GPS L1 carrier phase wavelength
S R ε : U n c e r t a i n e r r o r a m o u n t
: Speed of light
S i o n d : I o n o s p h e r i c d e l a y
t S r o p d
: Tropospheric delay
The wide lane method is used to dispel the ionospheric and tropospheric delay errors, and formulate a new relationship with the carrier phase. This is expressed as follows:
fL1 = =Φ 1 L1 c −Φ − fL2 2 L2 ρ S R 1 2 1 1 ( ) L L L L N N c f f α + + ( fL1 − − − fL2 )Δ δ −
Δδ : Time difference between the satellite and receiver
α : Total ions number in the path
1 L f : T h e f r e q u e n c y o f L 1 c a r r i e r p h a s e
1 L f : T h e f r e q u e n c y o f L 2 c a r r i e r p h a s e
NL1 : The integer ambiguity of L1
: The integer ambiguity of L2
Issue 7, Volume 4, July 2007