Kalman filter achieves convergence of state vector by using sensor observations.
Assuming a sensor such like velocity sensor, giving two axis velocity information in X-axis as well as Y-axis(see edit for one more example to capture essence of my question)
I can always design kalman filter in such a way that X-axis and Y-axis velocity are taken as two different scalar sensor readings and also a kalman filter where I take them as a vector sensor reading.
From both theoretical and practical aspects Is there any thing I am losing by taking X-axis and Y-axis as independent readings?
Or taking them together helps in converging faster? What is a better approach? And Why?
Edit: Assume one is in a airplane and a camera captures an image and tells latitude and longitude of nadir. With this data I would like to correct my State vector. Now if I use latitude as a different reading and longitude as a different reading than using both of the data. Will I lose anything? As pointed by an answer below if the signal model has an interaction among the components of reading I lose that interaction. Now do latitude and longitude have an interaction? How do I capture this interaction mathematically with H matrix?