With the modernization of GPS and the deployment of Galileo expected soon, there will be an increase in the number of precise or carrier phase signals arriving from space which are at our disposal. One method of utilizing these signals is to form carrier phase linear combinations which: 1) reduce ionospheric delay; 2) reduce receiver noise; 3) increase the wavelength of the observable. This means improved position capability and more reliability for these space based systems. This report focuses its investigation on those combinations which mitigate ionospheric delay, reduce receiver noise and perform best under typical survey conditions. The derivation of the characteristics for the linear combinations is performed including the second and third order ionosphereic delay amplification factors. A number of conclusions are reached. It is possible to more effectively reduce the effect of the ionosphere by using three frequencies rather than two frequencies. Care must be taken in understanding the effects of the linear combinations on the higher order terms especially for very precise applications. Concerning receiver noise, it was shown theoretically that although the triple frequency narrow-lane combination does improve the precision of the measurement it is more effective to use the three frequencies independently to improve the precision in the position domain. Finally it was shown through the use of simulated modernized GPS observations that linear combinations can be very effective in reducing the errors present in satellite positioning.
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