How can I mathematically compare two measurements to improve accuracy?

Question

I have two different techniques for measuring geolocation accuracy. I am asked to combine two different measurements in any way that might improve accuracy. Say I have an error of n1 using measurements A and an error of n2 using measurements B. Can I do better than both n1 and n2 by using both sets of information? Any suggestions or techniques that could be implemented in Python or MATLAB are greatly appreciated.

Answer 1

The standard way of doing this is to use the weighted mean value $$ \bar X = \frac{\sum_i w_i X_i}{\sum_i w_i} $$ where the weights $w_i$ are the inverse variance, $w_i = 1/\sigma^2_i$.