Exact filtering in exponential families:discrete time

An exact filter is an algorithm for calculating the a-posteriori distribution of the state ξ n of a process, given observations ηt, …,ηnup to time n. We describe a method to determine an appropriate algorithm for processes, where the distributions involved are members of exponential families, The resulting algorithm consists essen tially of a prediction term, combined with an affine transformation depending on the chosen model.