State estimation is a problem that occurs in many fields.  A very well known solution to 
the state estimation problem
occurs when the system satisfies a linear Markovian model and disturbances have a 
Gaussian distribution.  This leads
to the celebrated Kalman filter.   

In this seminar, we will study the problem of state estimation in the presence of 
constraints.  Two types of constraints
will be considered, namely integral and finite alphabet constraints on disturbances and 
finite alphabet constraints on
observations.  We will show how rolling horizon optimization techniques and Markov 
Chain Monte Carlo methodologies
can be utililzed to solve these problems.

The talk will be illustrated by a number of examples including control over network 
communications systems and air/fuel
ratio control in automobile engines