I'm trying to understand how I can update a Kalman filter with a state variable for position and velocity when I only measure position. I have a covariance matrix of the position measurements. But what does the overall covariance matrix of the measurements look like where velocity is unmeasured?
It seems that zeros would send the gain with respect to velocity to favor the measurement, which would drive the velocity estimates toward whatever value I input for the velocity measurements.
I have a similar problem where I am trying to fuse alternating measurements where I either have X and Y but no Z or X and Z but no Y. I would expect a single filter to fuse the two sets of measurements if I do this right, but I don't have a full grasp on how to handle to covariance terms involving the unmeasured property.