time of transmission of the signal can be multiplied by the speed of light to yield an approximation of

the range between the satellite and receiver. The biases for carrier beat phase measurements are the

same as for pseudoranges, although a higher accuracy can be obtained using the carrier. A more exact

range between the satellite and receiver can be formulated when the biases are taken into account during

derivation of the approximate range between the satellite and the receiver.

and carrier beat phase measurement in both absolute and relative positioning surveys can be improved

through processing that incorporates differencing of the mathematical models of the observables.

Processing by differencing takes advantage of correlation of error (such as GPS signal, satellite

ephemeris, receiver clock, and atmospheric-propagation errors) between receivers, satellites, and

epochs, or combinations thereof, to improve GPS processing. Through differencing, the effects of the

errors common to the observations being processed are greatly reduced or eliminated. There are three

broad processing techniques that incorporate differencing--single, double, and triple. Differenced

solutions generally proceed in the following order: differencing between receivers, between satellites,

and between epochs.

a. Single Differencing. There are three general single-differencing processing techniques--between

receivers, between satellites, and between epochs.

(1) Between Receivers. Single differencing the mathematical models for pseudorange (C/A- or

P-code) carrier phase observable measurements between receivers will eliminate or greatly reduce

satellite clock errors and a large amount of satellite orbit and atmospheric delays.

(2) Between Satellites. Single differencing the mathematical models for pseudorange or carrier

phase observable measurements between satellites eliminates receiver clock errors. Single differencing

between satellites can be done at each individual receiver during observations as a precursor to double

differencing and to eliminate receiver clock errors.

(3) Between Epochs. Single differencing the mathematical models between epochs takes

advantage of the Doppler shift (apparent change in the frequency of the satellite signal by the relative

motion of the transmitter and the receiver). Single differencing between epochs is generally done in an

effort to eliminate cycle ambiguities. Three forms of single-differencing techniques between epochs are

intermittently integrated Doppler, consecutive Doppler counts, and continuously integrated Doppler.

b. Double Differencing. Double differencing is a differencing of two single differences. Double-

difference processing techniques eliminate clock errors. There are two general double-differencing

processing techniques--receiver time and receiver satellite.

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