Showing papers by "Martin Morf published in 1980"

Doubling algorithms for Toeplitz and related equations

Abstract: A new class of doubling or halving algorithms for solving Toeplitz and related equations is presented. For scalar n by n Toeplitz matrices, they require O(n \log^{2}n) computations, similarly to the HGCD (half-greatest-common-divisor) based algorithm of Gustavson and Yun. However, these new algorithms are based on the notions of "shift" or displacement rank 1 \leq \alpha \leq n , an index of how close a matrix is to being Toeplitz, requiring O(\alpha^{d} n \log^{2}n) operations, ( d \leq 2 ). A basic version of a doubling algorithm for such "α-Toeplitz matrices" is presented, and the applications of these results to related problems are mentioned, such as the inversion of banded-, block- and Hankel matrices.

Recursive ladder algorithms for ARMA modeling

Abstract: The extension of the all-pole (AR) exact least-squares ladder algorithms to the pole-zero (ARMA) case is presented. The algorithms are based on a general set of recursions obtained by a geometric approach. The recursions obtained are square-root normalized and have much simpler structures than the unnormalized case. The white input as well as the possibly non-white unknown input case are discussed.

Source location from time differences of arrival: Identifiability and estimation

Abstract: A new framework is presented for the problem of estimating source location from a set of time difference of arrival (TDOA) measurements. First the conditions under which the source coordinates are identifiable are derived and geometrically interpreted. Then it is shown that the source location can be found, when it is identifiable, by estimating the coefficients of a set of linear relationships, with the number of equations being equal to the number of stations.

State-space structures of ladder canonical forms

Abstract: LADder form MOdeling (LADMO) is attracting an increasing amount of interest. The use of ladder forms (also referred to as lattice filters) is growing in the area of estimation, system identification, signal processing and related applications. While the advantages offered by ladder form implementations are by now quite well known, very little attention has been paid in the literature to the properties of the ladder forms from a system theoretic point of view.

A tree classification of algorithms for Toeplitz and related equations including generalized Levinson and doubling type algoritms

Abstract: A survey of several methods for matrix inversion currently used in linear estimation is presented. The algorithms considered belong to two classes: order recursive and function recursive. For each class a tree representation of the performed operations helps in classifying the various algorithms. Novel stochastic derivations and interpretations of the update equations are introduced that provide new insights into the structure of these procedures.