3533 0 ① Country dance algorithm Country dance algorithm Algorithm:forward pass computes,backward pass does b Country dance algorithm linear Gau (TT)O=fia model and sen Kalman filters m1 Country dance algorithm Country dance algorithm Country dance algorithm Can avoid storing all forward messages in smoothing by running forward algorithm backwards: f1:t+1 = αOt+1T > f1:t O−1 t+1 f1:t+1 = αT > f1:t α 0 (T > ) − O1 −1 t+1 f1:t+1 = f1:t Algorithm: forward pass computes ft , backward pass does fi , bi Chapter 15, Sections 1–5 19 Country dance algorithm Can avoid storing all forward messages in smoothing by running forward algorithm backwards: f1:t+1 = αOt+1T > f1:t O−1 t+1 f1:t+1 = αT > f1:t α 0 (T > ) − O1 −1 t+1 f1:t+1 = f1:t Algorithm: forward pass computes ft , backward pass does fi , bi Chapter 15, Sections 1–5 20 Country dance algorithm Can avoid storing all forward messages in smoothing by running forward algorithm backwards: f1:t+1 = αOt+1T > f1:t O−1 t+1 f1:t+1 = αT > f1:t α 0 (T > ) − O1 −1 t+1 f1:t+1 = f1:t Algorithm: forward pass computes ft , backward pass does fi , bi Chapter 15, Sections 1–5 21 Country dance algorithm Can avoid storing all forward messages in smoothing by running forward algorithm backwards: f1:t+1 = αOt+1T > f1:t O−1 t+1 f1:t+1 = αT > f1:t α 0 (T > ) − O1 −1 t+1 f1:t+1 = f1:t Algorithm: forward pass computes ft , backward pass does fi , bi Chapter 15, Sections 1–5 22 Country dance algorithm Can avoid storing all forward messages in smoothing by running forward algorithm backwards: f1:t+1 = αOt+1T > f1:t O−1 t+1 f1:t+1 = αT > f1:t α 0 (T > ) − O1 −1 t+1 f1:t+1 = f1:t Algorithm: forward pass computes ft , backward pass does fi , bi Chapter 15, Sections 1–5 23 Kalman filters Modelling systems described by a set of continuous variables, e.g., tracking a bird flying—Xt = X, Y, Z, X˙ , Y˙ , Z˙ . Airplanes, robots, ecosystems, economies, chemical plants, planets, . . . t Z t+1 Z t X t+1 X t X t+1 X Gaussian prior, linear Gaussian transition model and sensor model Chapter 15, Sections 1–5 24