Stochastic Systems Group  

Professor Sanjoy Mitter
LIDS
In this lecture I present a variational interpretation of nonlinear path estimation. This is a consequence of the fact that the conditional distribution corresponding to the optimal path estimation is obtained by minimizing an appropriate Free Energy and hence has a representation as a Gibbs distribution. The duality between Free Energy and Relative Entropy can then be exploited to shed further light on the optimal path estimator. This solves a longstanding open problem of giving a rigorous treatment of the BrysonFrazier smoothing view of the Kalman filter. Here however we solve the problem even in nonlinear situations. Time permitting, I shall discuss the concept of stochastic dissipativeness and how this provides a framework for discussing the stability of the filter against various perturbations. These ideas have connections to recent work in nonequilibrium statistical mechanics.
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