Calculating GPS uncertainty as a function of general position and time

Question

Is it possible to calculate the uncertainty in a GPS measurement at a given point at a given time by taking into account the number and positioning of the GPS satellites overhead?
People throw around general numbers (plus/minus 5m is common), but it seems to me it would clearly be a function of the two factors mentioned above. Why does nobody ever do this analysis?
There are also other, separate factors that introduce a variable amount of uncertainty, such as time delay for signal propagation in the ionosphere. Is this correction (and its uncertainty) similarly known and charted by any agency? Could this be included in an uncertainty analysis?

fastest · Answer

As far as I understand, there are at least two different aspects to be taken into account:

The measurement errors on the signals that are broadcast by the GPS/GNSS satellites and observed by the sensor. Those can vary according to the type of the signal observed (e.g., pseudorange or phase or doppler measurements) and to the characteristics of the media that the signals pass through.
The errors on the position that is computed (or estimated) based on the acquired measurements. Those can vastly vary and are normally measured in terms of precision (i.e., how much is the position repeatable) and of accuracy (i.e., how much is the position close to the true position).

The topic is ample (and quite fun) to explore. I can suggest the next references as good places where to start from:

Signals and measurement errors.
Receiver noise
Positioning error

Good luck and enjoy the exploration.

Calculating GPS uncertainty as a function of general position and time

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