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.