GPS operates by sending radio-frequency signals (in the microwave range, 1.2 - 1.6 GHz) from a constellation of satellites to the receiver. If the power line interfered with these signals, it could potentially cause either a reduced accuracy in the calculation of the position, or even an erroneous position. Does this happen in practice? There are two possible mechanisms to consider:
Screening of the satellite signal by the physical presence of the power line
A power line is similar to any other physical structure. We know that buildings, trees etc can sometimes stop the GPS receiver from picking up the satellite signals. Potentially, the same effect could occur inside the body of a pylon. But calculations show that the conductors of a power line are too thin to have any significant effect. This has been confirmed by measurements: driving under the conductors of a power line made no measureable difference to the signal strength detected by a GPS receiver.
Radio-frequency interference produced by the power line itself
High-voltage power lines can produce corona, which does cause the line to emit some radio-frequency EMFs. All power lines can sometimes have arcing on their fittings, which likewise produces radio-frequency EMFs. But again, calculations show that it would have to be really extreme even to be big enough potentially to cause problems, and in practice, tests have not detected any interference with GPS.
Some systems for obtaining greater accuracy from GPS use a separate signal from another satellite or from a local transmitter set up either by the user themself or more centrally for groups of users. This should not be subject to interference from the power line unless the line of sight between the GPS receiver and the base station is blocked temporarily, which could happen with any type of obstruction.
Right up close to a pylon, there might be some degradation in GPS performance, just as there can be some degradation close to buildings and trees. Other than that, there is no evidence of power lines interfering with GPS.
Other effects of power lines on agriculture
One use of GPS is in agriculture, sometimes referred to as "precision agriculture". See also the evidence on whether power lines have any other effects, on animals, crops etc.
Abstracts of relevant publications
Power Delivery, IEEE Transactions on, 2002, 17 (4) 938 - 944
Use of Global Positioning System (GPS) receivers under power-line conductors
Silva, J.M.; Olsen, R.G.
The use of Global Positioning System (GPS) technology continues to grow and accuracy augmentations will generate ever more innovative applications. The issue of GPS use under or near electric power lines has been raised since some GPS documents have vague warnings about such use. First, GPS and the satellite microwave signals used to determine position, velocity, and time are described. Then, the potential effects of electromagnetic interference and/or signal scattering from overhead conductors are evaluated analytically and with some practical measurements under transmission lines. This work demonstrates that it is unlikely that power line conductors will interfere with use of the GPS satellite signals.
Note: the following paper refers to a system of differential GPS used in America but now increasingly superseded by more accurate systems such as RTK.
Power Delivery, IEEE Transactions on, 2002, 17 (2) 326 - 333
Evaluation of the potential for power line noise to degrade real time differential GPS messages broadcast at 283.5-325 kHz
The new Nationwide Differential Global Positioning System network uses the 283.5-325 kHz band to broadcast differential GPS (DGPS) correction messages. Concern has been expressed that power line corona and gap discharge noise could degrade the performance of DGPS receivers using this band. Previous work on power lines and the AM broadcast band identified corona and gap discharges as broadband noise sources in the LF/MF bands. The potential to locally degrade performance of DGPS receivers relatively close to some power facilities appears possible for certain situations. The extent of any DGPS interference problem will depend on receiver/antenna design and placement, signal strength, power line design, weather conditions, and characteristics of the noise source. Also affecting DGPS receiver performance can be the presence of any nearby nonpower line RF noise sources;such as electronic devices or equipment internal to the user's vehicle.