I'm a statistician conducting an analysis on animal movement based on data collected using ATS Wildlink 500 collars. As part of this analysis, I'm estimating GPS error assuming that the error in the measurement is normally distributed with the mean being the true location (x and y) with some standard deviation that is equal in the x and y dimension. I'm ignoring accuracy at this point, or rather, I'm assuming that bias is zero.
Obviously, there is way more to this, but as a first cut analysis, I'm happy with this assumption. However, the one thing that I want to capture at this stage is the likely degradation in precision based on the number of satellites associated with a given GPS fix. What I'm looking for is a simple relationship between the number of satellites and the standard deviation of the GPS error given that the fix was successful. Less than a minimum number of satellites (4) and the error is infinite (i.e. the fix fails). So really I'm just looking for the relationship when the number of satellites is above this number (say between 4 and 12).
Is it linear? Sigma = A + B * X, where is X is the number of satellites?
Exponential? Something like: Sigma = exp(A + B*X)
Unfortunately, I don't have raw data where I could investigate this relationship myself and I'm having trouble finding good resources online. So I'm going to have to fit this relationship blind to a certain extent. I'm just looking for a general guideline on how precision improves with increasing number of satellites.