Tsinghua University and Beijing Institute of Mathematical Sciences and Applications
Colloquium Tea held at 4:00 pm in 101A Crowley Hall
Complete Solution to the Most General Nonlinear Filtering Problems and Its Implementation
The famous filtering problem of estimating the state of a stochastic dynamical system from noisy observations is of central importance in engineering. This problem is reduced to solve the Duncan-Mortensen-Zakai (DMZ) equation which is satisfied by the unnormalized conditional density of the state given the observation history. We first introduce a very general class of finite dimensional filters which include Kalman filter and Benes filter as special cases. For general nonlinear filtering problems, solving the DMZ equation can be reduced to solving a Kolmogorov forward equation off-line, and this is the so-called Yau-Yau algorithm. At last, we shall introduce two of our recent works. One is based on the recurrent neural networks, and the other is based on the optimal transportation.