I have two separate algorithms (call them "A1" and "A2") which reconstruct the $(x, y)$-position of an event in a particle detector. I can test both of these algorithms on simulated events from a very accurate Monte Carlo of the experiment. Note that A1 and A2 work on different observables in the detector and their errors are not correlated (though the observables themselves are correlated.) There is no systematic bias with either algorithm and so -- in aggregate -- the reconstruction error in $x$ and $y$ is approximately zero over all events.
Say A1 reconstructs a given MC event at some position $(x_1, y_1)$, and A2 reconstructs the same MC event at some different position $(x_2, y_2)$. I run A1 and A2 on every MC event, and end up with two distributions: one which gives the distance (scalar distance, not vector) from the true MC position of the event to $(x_1, y_1)$ for all events, and one which gives the distance from the true MC position of the event to $(x_2, y_2)$ for all events. Since this distance is necessarily non-negative, these distributions have some positive mean value, and some RMS.
This is all fine: these two distributions each have a mean (which characterizes the accuracy of the algorithm) and an RMS (which characterizes the precision of the algorithm), and the two distributions are more or less Gaussian. Next, I want to use these algorithms A1 and A2 on real data from the detector, and use the properties of these MC distributions to put a limit on the uncertainty of my reconstructed positions.
My question is this: knowing the RMSes and means of the A1 and A2 distance distributions, when I use A1 and A2 on real data, I should be able to find a "best fit" point and put some uncertainty on it. One one hand, I feel like I should just average the measurements and sum the errors in quadrature, but this feels incorrect for some reason (perhaps because the mean of A2 tends to be much higher than the mean of A1).
Is this the correct way to go about analyzing this data? Am I overthinking this?