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Understanding the Kalman Filter: Applications and Mathematical Foundations

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  1. Lecture 17 Kalman Filter

  2. KF • KF is a ``factor analyzer through time’’: hidden states are continuous and gaussian. • KF are used to model noisy linear dynamics. Real world examples include control (``the eagle has landed’’), tracking (vision) etc. • Example Columbus discovers the Americas. Wind and waves make his estimate of his position increasingly uncertain. Measurements decrease uncertainty. • This can be written in terms of the kalman gain factor.

  3. KF • In multidimensional setting the equation have the same form and interpretation: • There is evolution which increases uncertainty and measurement which decreases it. • 3 tasks: filtering, prediction, smoothing. • Derivation of general equations. • Smoothing harder. Its also the E-step in the EM learning algorithm. Very similar as in HMMs: forward-backward recursions. • M step: analytical updates for A,B,R,Q,mu,Sigma. • demos, movies.

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