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This lecture delves into the Kalman Filter (KF), a powerful tool for modeling noisy linear dynamics and hidden states that are continuous and Gaussian. Real-world applications such as control systems and tracking are explored, using examples like Columbus's voyage to demonstrate how measurements can reduce uncertainty in estimates. We cover the fundamental tasks of filtering, prediction, and smoothing, as well as the derivation of the general equations and their multidimensional interpretations. Additionally, we discuss the connection to the EM learning algorithm and provide engaging demos and visuals.
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Lecture 17 Kalman Filter
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.
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.
