A boater recently commented about the speed of his boat while a GPS position solution was being obtained, possibly implying that the boat speed might influence accuracy of the deduced position from GPS. There is little influence on the speed of the GPS receiver on Earth on a slowly moving boat in the position solution using GPS because the other element in any range solution used to establish that position, the GPS satellite, is in very rapid motion relative to the receiver.
A GPS satellite has an orbital height above Earth of about 12,550-Miles.
The radius of the Earth is about 3,963-miles at the equator.
The GPS satellite orbital period is about 12-hours.
From the above three factors we can deduce the approximate speed of travel of a GPS satellite. We assume a circular orbit and use the Earth radius at the equator. We calculate the circumference of the orbital path in miles and divide by the time in hours to travel that path:
Earth radius + orbital height = radius of orbital path
3,963 + 12,550 = 16513-miles radius
Circumference of circle = 2 × π × radius
Circumference of orbital path = 2 × π × 16513-miles radius
Circumference of orbital path = 103,754-miles
Speed = Distance ÷ Time
Speed = 103,754-miles ÷ 12-hours
Speed = 8,464-miles-per-hour
If a boat is moving at a slow speed, say 8.4-MPH, the satellites are moving one-thousand times faster. On that basis, any motion on the boat does NOT have an effect on the solution of the range from the satellite to the GPS receiver.
In GPS position finding, the method used is to measure a range, in this case the range from the GPS receiver to the satellite transmitting the signal. Modern GPS receivers calculate a new position once per second or faster. We can then look at how much change in location will occur in a period of one second.
We know the satellite is traveling at 8646-mles-per-hour. In one second the satellite movement will be
8646-miles/1-hour × 1-hour/3600-seconds × 5280-feet/1-mile = 12,680-feet
If the boat travels at 8.646-miles-per-hour, then in one second the boat will travel
8.646-miles/1-hour × 1-hour/3600-seconds × 5280-feet/1-mile = 12.68-feet