857 research outputs found
On Minimal Spectral Factors with Zeroes and Poles lying on Prescribed Region
In this paper, we consider a general discrete-time spectral factorization
problem for rational matrix-valued functions. We build on a recent result
establishing existence of a spectral factor whose zeroes and poles lie in any
pair of prescribed regions of the complex plane featuring a geometry compatible
with symplectic symmetry. In this general setting, uniqueness of the spectral
factor is not guaranteed. It was, however, conjectured that if we further
impose stochastic minimality, uniqueness can be recovered. The main result of
his paper is a proof of this conjecture.Comment: 14 pages, no figures. Revised version with minor modifications. To
appear in IEEE Transactions of Automatic Contro
On the Factorization of Rational Discrete-Time Spectral Densities
In this paper, we consider an arbitrary matrix-valued, rational spectral
density . We show with a constructive proof that admits a
factorization of the form , where is
stochastically minimal. Moreover, and its right inverse are analytic in
regions that may be selected with the only constraint that they satisfy some
symplectic-type conditions. By suitably selecting the analyticity regions, this
extremely general result particularizes into a corollary that may be viewed as
the discrete-time counterpart of the matrix factorization method devised by
Youla in his celebrated work (Youla, 1961).Comment: 34 pages, no figures. Revised version with partial rewriting of
Section I and IV, added Section VI with a numerical example and other minor
changes. To appear in IEEE Transactions of Automatic Contro
New mechanization equations for aided inertial navigation systems
Inertial navigation equations are developed which use area navigation (RNAV) waypoints and runway references as coodinate centers. The formulation is designed for aided inertial navigation systems and gives a high numerical accuracy through all phases of flight. A new formulation of the error equations for inertial navigation systems is also presented. This new formulation reduces numerical calculations in the use of Kalman filters for aided inertial navigation systems
Hierarchical theory of quantum dissipation: Partial fraction decomposition scheme
We propose a partial fraction decomposition scheme to the construction of
hierarchical equations of motion theory for bosonic quantum dissipation
systems. The expansion of Bose--Einstein function in this scheme shows similar
properties as it applies for Fermi function. The performance of the resulting
quantum dissipation theory is exemplified with spin--boson systems. In all
cases we have tested the new theory performs much better, about an order of
magnitude faster, than the best available conventional theory based on
Matsubara spectral decomposition scheme.Comment: 8 pages, 3 figures, submitted to Chemical Physics special issue
"Dynamics of molecular systems: From quantum to classical
Theory, design and application of gradient adaptive lattice filters
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