• Jeremy West
  • Wednesday, November 10. 4-5 p.m.
  • EH 3866

The Kalman filter is one of the most prominent algorithms of the last century. It has been used in applications ranging from finance to signal processing to missile guidance. The Kalman filter is usually derived as a Bayesian filter on a linear system. However, in this talk we will show that the Kalman filter arises naturally as the solution of a weighted recursive least squares problem and that it can be derived from Newton’s method. The realization of the Kalman filter from Newton’s method shows the connection between the Kalman filter and the wide array of contraction mapping and Newton-like numerical methods, perhaps most importantly, the implicit and inverse function theorems. This observation not only yields a simple and intuitive derivation of the Kalman filter, but provides insights that allow for significant generalizations. In particular, we will examine predictive and smoothed estimates, fading-memory estimates, and estimators for nonlinear systems.