# How to sum two covariance matrices

I'm doing a kalman filter and I need to sum two covariance matrices (Q1 and Q2) regarding two uncertainties I need to join. I'm tracking the position of an object from a referencial with a changing position and orientation. As the position of the moving referential also has an uncertainty, it also has a covariance matrix. Both covariances matrices are 2x2 matrices, regarding the covariance in x, y, xy. So, the first covarience (Q1) refers to the uncertainty of the position of the moving object I'm trying to track. The second covariance (Q2) is the uncertainty of the position of the moving referencial in with I do the observation of the moving object. The total covariance will just be Q1+Q2, or do I need to do anything else?

• I am confused on what you are asking. You can add two matricies of the same size because matrix addiition is well defined. But why are you doing that in the first place?
– Josh
Apr 10, 2017 at 1:37
• The nature of your question is becoming clearer, but it's still difficult to decipher. I suspect you will need to explain how the variables for the one covariance matrix are related to the variables for the other--otherwise, it will be impossible to know what needs to be done.
– whuber
Apr 10, 2017 at 13:57