Out of curiosity how many satellites are required to give a accurate 10Mhz, is it just one or are others needed? I thought the reason for more than one is because the satellite will eventually move out of the antenna reception depending on the time of the day etc, so for a continuous lock you would want more than one.
The first thing to do is a location survey, i.e. to precisely measure the antennas position.
When the location of the antenna is known (and fixed), then a single satellite is sufficient to determine the time precisely.
Simple mathematical reason: the triangulation needs 4 satellites to solve the equations for the 4 dimensions: X,Y,Z, and c*t.
Therefore, if 3 variables are known, the 4th variable can be calculated from one satellite.
As the GPS signal is disturbed (jitter) on the path to the receiver, more satellites will add stability to the time signal, anyhow.
8 channels are fully sufficient to get a very stable time signal.
Additionally the number of visible satellites is limited, especially, as you may want to filter out satellites which are lower than 20° over horizon.. this avoids reflected signals.
Instead you want to receive the signal directly, only.
Therefore, you receive rarely more than 6 satellites.
Frank