> Do I understand it correctly that Kalman filters are supposed to give a better estimate of a value from noisy observations than just averaging the observations?
Yes, but with a big caveat. Your observations are related by something like the transition mechanism. You can't just apply a Kalman filter to every problem and expect to get better results.
A Kalman filter is traditionally used in estimating something that moves over time (but can be used for more than just this). Think a person moving in a video, or some other sort of random walk. By assuming some sort of relationship between two successive timepoints/measurements, like speed and current heading, we can blend the information from a model for motion with the model from noisy measurements to get a better estimate of the position/value or of the entire motion history.
If that motion model is meaningfully incorrect, then you don't get improved estimates.
A lot of the ways that people have extended them have to do with incorporating more sophisticated motion models, like dealing with wheel slippage in robotics, so your heading direction might have error now, etc.
Yes, but with a big caveat. Your observations are related by something like the transition mechanism. You can't just apply a Kalman filter to every problem and expect to get better results.
A Kalman filter is traditionally used in estimating something that moves over time (but can be used for more than just this). Think a person moving in a video, or some other sort of random walk. By assuming some sort of relationship between two successive timepoints/measurements, like speed and current heading, we can blend the information from a model for motion with the model from noisy measurements to get a better estimate of the position/value or of the entire motion history.
If that motion model is meaningfully incorrect, then you don't get improved estimates.
A lot of the ways that people have extended them have to do with incorporating more sophisticated motion models, like dealing with wheel slippage in robotics, so your heading direction might have error now, etc.