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Blind separation of delayed sources based on second-order Taylor approximation

Li H., Shen Y., Wang J.

Przegląd Elektrotechniczny

2013

R. 89, nr 1b

253--256

Conventional linear instantaneous mixing model becomes unsuitable if propagation time delays are taken into account. A blind separation algorithm based on second-order Taylor approximation for delayed sources (SOTADS) is presented, under the constraint that time delays are small in comparison with the coherence time of each source. Simulation results validate that the proposed algorithm performs superior than related approaches even when the constraint is violated.

Zaprezentowano algorytm ślepej separacji bazujący na aproksymacji Taylora drugiego rzędu dla źródeł z opóźnieniem SOTADS. Założono że czas opóźnienia jest mały w porównaniu z czasem koherencji obu źródeł.

An improved constrained nonlinear state estimator for target tracking

Stubberud A. R., Stubberud S. C.

Systems Science

2004

Vol. 30, no 4

31-39

In a series of earlier papers, the first author developed an estimator which generates an optimal sequential estimate of the state of a linear discrete-time dynamic system in which the state is subject to an instantaneous constraint. In the third paper of the series, an extended estimator, based on the optimal linear estimator, was developed for the constrained nonlinear estimation problem. In this paper, the extended nonlinear estimator is revised. One of the critical steps in the development of an extended estimator is the quasi-linearization step. In this step, the terms in the Taylor series expansion which have been evaluated at some nominal state trajectory are instead evaluated at the most recent 'best' available state estimate. In developing the estimator, the point in the development at which the quasi-linearization takes place is not fixed. In the earlier paper, the quasi-linearization is performed about midway through the overall development. In this paper, the quasi-linearization is taken at the last possible point in the development. The result is an improved version of the extended constrained nonlinear sequential estimator.