More on Orbits, Part 2

I should add a note here about how to identify the satellites. All the satellites transmit on the same frequency, and each satellite has a unique pseudo-random noise (PRN) code that spreads its message data over a wide bandwidth. This is a direct sequence spread spectrum method known as CDMA. There are 32 unique codes so there will be up to 32 active satellites, and they are identified in the almanac by their PRN codes.

The GPS almanac references its time relative to the start of a GPS week. This week starts at midnight UTC time on the first day of the calendar week (Saturday night turning into Sunday morning.) The orbital parameters given in the almanac are valid at the reference time, or epoch, which is given as "Time of Applicability". This time is the number of seconds after the start of the referenced GPS week.

The satellite position is given as mean anomaly at the epoch, on the line in the almanac file that starts with "Mean Anom". Mean anomaly is an angle measurement that increases linearly over time. We get the current mean anomaly using the difference between our time of interest t and the epoch t_oe:

t_k = t - t_oe

Then the current mean anomaly is

M = M₀ + n * t_k

There is our mean motion n from the previous post. Now we have an angle measurement that will help us find the position of the satellite in its orbit at time t.