Toeplitz vs. Hankel

This paper explores similarities and differences of different types of stochastic modeling, namely the traditional covariance modeling based on Schur-Levinson theory vs. partial moment matching. The first case leads to positive definite Toplitz matrices, while the second case handles positive definite Hankel matrices (or generalized versions ot those). In both cases a special type of interpolation problem is solved, from which general solutions can be derived. However, the differences between the two problems and their solution methods soon appear. In the multi-dimensional Hankel case, a joint pdf has to be determined, while in the (generalized) Schur-Levinson case, only second order data is handled. In contrast to the traditional Schur-Levinson approach, the non-linear, non-Gaussian estimation filter is a derivative of the model filter and not vice versa. Some results presented here for the multivariate Hankel case are believed to be new.