Gradient Flows in Filtering and FisherRao Geometry
Abstract
Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and a systematic way to formulate and solve the same for linear Gaussian systems has appeared in our previous work where the gradient flows were realized via proximal operators with respect to Wasserstein metric arising in optimal mass transport. In this paper, we derive the evolution equations as proximal operators with respect to FisherRao metric arising in information geometry. We develop the linear Gaussian case in detail and show that a template two step optimization procedure proposed earlier by the authors still applies. Our objective is to provide new geometric interpretations of known equations in filtering, and to clarify the implication of different choices of metric.
 Publication:

arXiv eprints
 Pub Date:
 September 2017
 arXiv:
 arXiv:1710.00064
 Bibcode:
 2017arXiv171000064H
 Keywords:

 Mathematics  Optimization and Control;
 Computer Science  Systems and Control