How to apply kalman filter on rotation matrix?

Why is the Kalman filter called a 'filter'? What do we filter with it?

• Answer:

  The omniscient Wikipedia says: The Kalman filter, also known as linear quadratic estimation (LQE), is an http://en.wikipedia.org/wiki/Algorithm that uses a series of measurements observed over time, containing http://en.wikipedia.org/wiki/Statistical_noise (random variations) and other inaccuracies, and produces estimates of unknown variables that tend to be more precise than those based on a single measurement alone. More formally, the Kalman filter operateshttp://en.wikipedia.org/wiki/Recursion on streams of noisy input data to produce a statistically optimal http://en.wikipedia.org/wiki/Estimation_theory of the underlying http://en.wikipedia.org/wiki/State_space_(controls). The filter is named for http://en.wikipedia.org/wiki/Rudolf_E._K%C3%A1lm%C3%A1n, one of the primary developers of its theory. Simply put, Kalman filter is used to estimate the underlying states based on a stream of NOISY data. The key word here is "noisy". It is precisely this noise that the Kalman filter tries to filter out!