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Kalman Filter and Orthogonal Projections

A linear Kalman filter has a simple geometric interpretation in terms of vector projections. This applet explorers the geometry behind a recursive estimation of a random variable x from two noisy measurements and . Geometrically, we obtain the orthogonal projection of x onto followed by the orthogonal projection of the result on the plane spanned by and . You can grab the picture with a mouse and move it around to have a better look. See the attached text for details.