10,155 research outputs found
Parameter estimation via differential algebra and operational culculus
Parameter estimation is approached via a new standpoint, based on differential algebra and operational calculus. Some applications such as, the estimation of a noisy damped sinusoid, the analysis of chirp signal, the detection of piecewise polynomial signals and their discontinuities are presented with numerical simulations
COMPARISON ON DIFFERENT DISCRETE FRACTIONAL FOURIER TRANSFORM (DFRFT) APPROACHES
As an extension of conventional Fourier transform and a time-frequency signal analysis tool, the fractional Fourier transforms (FRFT) are suitable for dealing with various types of non-stationary signals. Taking advantage of the properties and non-stationary features of linear chirp signals in the Fourier transform domain, several methods of extraction and parameter estimation for chirp signals are proposed, and a comparative study has been done on chirp signal estimation. Computation of the discrete fractional Fourier transform (DFRFT) and its chirp concentration properties are dependent on the basis of DFT eigenvectors used in the computation. Several DFT-eigenvector bases have been proposed for the transform, and there is no common framework for comparing them. In this thesis, we compare several different approaches from a conceptual viewpoint and point out the differences between them. We discuss five different approaches, namely: (1) the bilinear transformation method, (2) the Grunbaum method, (3) the Dickenson-Steiglitz method, also known as the S-matrix method, (4) the quantum mechanics in finite dimension( QMFD) method, and (5) the higher order S-matrix method, to find centered DFT (CDFT) commuting matrices and the various properties of these commuting matrices. We study the nature of eigenvalues and eigenvectors of these commuting matrices to determine whether they resemble those of corresponding continuous Gauss-Hermite operator. We also measure the performance of these five approaches in terms of mailobe-to-sidelobe ratio, 10-dB bandwidth, quality factor, linearity of eigenvalues, parameter estimation error, and, finally peak-to-parameter mapping regions. We compare the five approaches using these several parameters and point out the best approach for chirp signal applications
Classification of chirp signals using hierarchical bayesian learning and MCMC methods
This paper addresses the problem of classifying chirp signals using hierarchical Bayesian learning together with Markov chain Monte Carlo (MCMC) methods. Bayesian learning consists of estimating the distribution of the observed data conditional on each class from a set of training samples. Unfortunately, this estimation requires to evaluate intractable multidimensional integrals. This paper studies an original implementation of hierarchical Bayesian learning that estimates the class conditional probability densities using MCMC methods. The performance of this implementation is first studied via an academic example for which the class conditional densities are known. The problem of classifying chirp signals is then addressed by using a similar hierarchical Bayesian learning implementation based on a Metropolis-within-Gibbs algorithm
Gravitational waves from coalescing binaries: detection strategies and Monte Carlo estimation of parameters
The paper deals with issues pertaining the detection of gravitational waves
from coalescing binaries. We introduce the application of differential geometry
to the problem of optimal detection of the `chirp signal'. We have also carried
out extensive Monte Carlo simulations to understand the errors in the
estimation of parameters of the binary system. We find that the errors are much
more than those predicted by the covariance matrix even at a high SNR of 10-15.
We also introduce the idea of using the instant of coalescence rather than the
time of arrival to determine the direction to the source.Comment: 28 pages, REVTEX, 12 figures (bundled via uufiles command along with
this paper) submitted to Phys. Rev.
Degeneracy between mass and spin in black-hole-binary waveforms
We explore the degeneracy between mass and spin in gravitational waveforms
emitted by black-hole binary coalescences. We focus on spin-aligned waveforms
and obtain our results using phenomenological models that were tuned to
numerical-relativity simulations. A degeneracy is known for low-mass binaries
(particularly neutron-star binaries), where gravitational-wave detectors are
sensitive to only the inspiral phase, and the waveform can be modelled by
post-Newtonian theory. Here, we consider black-hole binaries, where detectors
will also be sensitive to the merger and ringdown, and demonstrate that the
degeneracy persists across a broad mass range. At low masses, the degeneracy is
between mass ratio and total spin, with chirp mass accurately determined. At
higher masses, the degeneracy persists but is not so clearly characterised by
constant chirp mass as the merger and ringdown become more significant. We
consider the importance of this degeneracy both for performing searches
(including searches where only non-spinning templates are used) and in
parameter extraction from observed systems. We compare observational
capabilities between the early (~2015) and final (2018 onwards) versions of the
Advanced LIGO detector.Comment: 11 pages, 9 figure
Parameter estimation on gravitational waves from neutron-star binaries with spinning components
Inspiraling binary neutron stars are expected to be one of the most
significant sources of gravitational-wave signals for the new generation of
advanced ground-based detectors. We investigate how well we could hope to
measure properties of these binaries using the Advanced LIGO detectors, which
began operation in September 2015. We study an astrophysically motivated
population of sources (binary components with masses
-- and spins of less than )
using the full LIGO analysis pipeline. While this simulated population covers
the observed range of potential binary neutron-star sources, we do not exclude
the possibility of sources with parameters outside these ranges; given the
existing uncertainty in distributions of mass and spin, it is critical that
analyses account for the full range of possible mass and spin configurations.
We find that conservative prior assumptions on neutron-star mass and spin lead
to average fractional uncertainties in component masses of , with
little constraint on spins (the median upper limit on the spin of the
more massive component is ). Stronger prior constraints on
neutron-star spins can further constrain mass estimates, but only marginally.
However, we find that the sky position and luminosity distance for these
sources are not influenced by the inclusion of spin; therefore, if LIGO detects
a low-spin population of BNS sources, less computationally expensive results
calculated neglecting spin will be sufficient for guiding electromagnetic
follow-up.Comment: 10 pages, 9 figure
Online identification of a two-mass system in frequency domain using a Kalman filter
Some of the most widely recognized online parameter estimation techniques used in different servomechanism are the extended Kalman filter (EKF) and recursive least squares (RLS) methods. Without loss of generality, these methods are based on a prior knowledge of the model structure of the system to be identified, and thus, they can be regarded as parametric identification methods. This paper proposes an on-line non-parametric frequency response identification routine that is based on a fixed-coefficient Kalman filter, which is configured to perform like a Fourier transform. The approach exploits the knowledge of the excitation signal by updating the Kalman filter gains with the known time-varying frequency of chirp signal. The experimental results demonstrate the effectiveness of the proposed online identification method to estimate a non-parametric model of the closed loop controlled servomechanism in a selected band of frequencies
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