I believe you get much better accuracy with more than 4 satellites. On our survey grade GPS, we could possibility get a 3D fix with only four satellites but we would have to be in a wide open field. When in vegetation or close to vegetation we need 10-12 satellites to keep a fixed position. In the field or on a boat the higher number of satellites will not only improve accuracy in calculations, it will help keep the accuracy when you may lose connection with a satellite. What happens when the motor gets in the way when your boat turns or you go into a small creek channel that is vegetated with large trees on both sides of your boat... You will most likely lose the signal to some satellites and keep the others.
In order for our survey grade GPS to reach sub-centimeter accuracy... It has fixed base stations it communicates with through radio waves on top of cell phone towers. This further increases the horizontal accuracy of the calculations. If only four satellites would give these type results then that would be great.. But it does not. There is always room for an increase in accuracy.
You mentioned earlier that there were not enough satellites to possibility connect 12 satellites at one time.. Have you thought about the Russian's GLONASS (21 satellites plus 3 spares) or Europe's Galileo (27 satellites plus 3 spares - Not active yet)? The US satellites (GPS - 24 operating satellites) are not the only satellites in orbit. Our survey grade GPS uses both US GPS satellites and GLONASS satellites. Along with the corrections made from the base stations in order to get the desired results.
GLONASS - Summary
ESA - Navigation - The future - Galileo - What is Galileo?
Global Positioning System
Also, the added accuracy of more satellites can stem from the location of the satellites. If all the satellites were closely grouped together then your accuracy would be poor. The further they are spread out the better the accuracy. Also, how can the average of 12 calculations not be better than the average of 4 calculations? Doesn't the standard deviation improve with the increase in calculations (or in this case satellites)? How about WAAS.... Why was WAAS needed if 4 satellites were accurate enough?
Navigation Services
There are many things that can cause variations in results with GPS measurements such as solar flares... When this happens with 4 satellites being averages to get the results the results would be off. Now when you have 12 satellites and you have a solar flare that affects one... the average is much better which improves accuracy.
Four satellites is a minimum requirement to get results... In the case of satellites, more is always better.
DoubleG


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