> If Q and R are constant (as is usually the case), the gain quickly converges,
You also need for measurements to be equally spaced. Often they are – you might get an alternating pattern of measurement and observation – but often they're not, in which case the Kalman filter gives extra weight to new measurements coming in if it's been a while since it last had one (because that will have allowed the uncertainty to grow).
The Kalman filter also allows you to take into account measurements that are more uncertain in one direction than another. Think of cameras with visual recognition, which tell you a precise angle but only a rough distance estimate. If you have a couple of those and suitable measurement error matrices then the Kalman filter will automatically do a sort of triangulation.
Add a bonus, you can also use the covariance matrix of the target as information in its own right. But, as you say, often parameters are tuned for getting a good result rather than reality so the target uncertainty isn't always especially meaningful.
You also need for measurements to be equally spaced. Often they are – you might get an alternating pattern of measurement and observation – but often they're not, in which case the Kalman filter gives extra weight to new measurements coming in if it's been a while since it last had one (because that will have allowed the uncertainty to grow).
The Kalman filter also allows you to take into account measurements that are more uncertain in one direction than another. Think of cameras with visual recognition, which tell you a precise angle but only a rough distance estimate. If you have a couple of those and suitable measurement error matrices then the Kalman filter will automatically do a sort of triangulation.
Add a bonus, you can also use the covariance matrix of the target as information in its own right. But, as you say, often parameters are tuned for getting a good result rather than reality so the target uncertainty isn't always especially meaningful.