I have two 2D Gaussian random variables. I'd like to find the weighted average of the two (based on their covariance matrix around the mean, meaning that the mean of the final Gaussian should be closer to the one with the smallest variance). What is the proper way of doing that? Any pointer to web urls around this topic would be highly appreciated.
Clarification: I have a robot that has two sensors. The robot reads two bi-variate normal observations of an object. I want to find the location of the object by finding the weighted mean of the two samples. So I want my final location that I calculate to be closer to the observation that has a smaller spread. What is the proper way of doing that?