Exponential Fourier Densities on a Riemannian Metric and Optimal Estimation for Axial Processes.

Several models, which are believed to be generic for the estimation of discrete-time axial processes, are proposed. By introducing axial exponential Fourier densities and axial exponential trigonometric densities, finite-dimensional recursive schemes are obtained for updating the conditional density functions. The underlying idea is the closure properties under the Bayes rule of the various combinations of these exponential densities. An estimation error criterion, which is compatible with a Riemannian metric, is introduced. It is shown that the corresponding optimal axial estimates can be easily computed. Author