Position fixing in three dimensions may involve the measurement of distance ( or range ) to at least three satellites whose X Y and Z positions is known in order to define the user’s Xp Yp and Zp position
In its simplest form the satellite transmits a signal on which the time of its departure from the satellites modulated the receiver in turn notes the time of arrival of this time mark then the time which it took the signal to go from satellite to receiver is called the delay time the measured range R is obtained from
If the error in R due to clock bias is r and is constant throughout then :
where Xn Yn Zn = the coordinates of satellites 1,2,3 and 4 ( n = 1 to 4 )
Xp Yp Zp = the coordinates required for point P
Rn = the measured ranges to the satellites
Solving the four equations for the four unknowns XpYp Zp and R also solves for the error due to clock bias
Whilst the use of pseudo range is sufficient for navigational purposes and constitutes the fundamental approach for which the system was designed a much more accurate measurement of range is required for positioning in engineering surveying measuring phase difference by means of the carrier wave in a manner analogous to EDM measurement does this as observational resolution is about 1%of the signal wavelenght the following table shows the reason for useing the carrier waves this is referred to as the carrier phase observable
Carrier phase is the difference between the incoming satellite carrier signal and the phase of constant frequency signal generated by the receiver it should be noted that the satellite carrier signal when it arrives at the receiver is different from that initially transmitted because of the relative velocity between transmitter and receiver this is the well known Doppler effect the carrier phase therefore changes according to the continuously integrated Doppler shift of the incoming signal this observable is biased by the unknown offset between the satellite and receiver clocks and represents the difference in range to the satellite at different times or epochs the carrier phase movement although analogous to EDM measurement is a one way measuring system and thus the number of whole wavelengths ( N ) at lock on is missing this is referred to as the integer or phase ambiguity the value of N can be obtained from GPS network adjustment or from double differencing or eliminated by triple differecing
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