Nonlinear parameter estimation in statistical manifolds

Many nonlinear parameter estimation problems can be described by the class of curved exponential families. The latter are fundamental concept in the framework of Information Geometry. This paper shows that when a closed-form statistical model is available the problem can be mapped onto the corresponding statistical manifolds via fixed parameterizations and thus solved optimally through a manifold gradient method. The solution process involves a dual projection which iteratively operates under the e-connection and m-connection in the flat manifolds with the coordinate systems in which the Cramér Rao Bound is attained. An example of tracking a moving target by two bearings-only sensors with location uncertainties is presented to demonstrate the efficiency and optimality of this manifold based method as well as the associated geometrical interpretation.