1,134 research outputs found
A Computationally Efficient algorithm to estimate the Parameters of a Two-Dimensional Chirp Model with the product term
Chirp signal models and their generalizations have been used to model many
natural and man-made phenomena in signal processing and time series literature.
In recent times, several methods have been proposed for parameter estimation of
these models. These methods however are either statistically sub-optimal or
computationally burdensome, specially for two dimensional (2D) chirp models. In
this paper, we consider the problem of parameter estimation of 2D chirp models
and propose a computationally efficient estimator and establish asymptotic
theoretical properties of the proposed estimators. And the proposed estimators
are observed to have the same rates of convergence as the least squares
estimators (LSEs). Furthermore, the proposed estimators of chirp rate
parameters are shown to be asymptotically optimal. Extensive and detailed
numerical simulations are conducted, which support theoretical results of the
proposed estimators
Statistical Gravitational Waveform Models: What to Simulate Next?
Models of gravitational waveforms play a critical role in detecting and
characterizing the gravitational waves (GWs) from compact binary coalescences.
Waveforms from numerical relativity (NR), while highly accurate, are too
computationally expensive to produce to be directly used with Bayesian
parameter estimation tools like Markov-chain-Monte-Carlo and nested sampling.
We propose a Gaussian process regression (GPR) method to generate accurate
reduced-order-model waveforms based only on existing accurate (e.g. NR)
simulations. Using a training set of simulated waveforms, our GPR approach
produces interpolated waveforms along with uncertainties across the parameter
space. As a proof of concept, we use a training set of IMRPhenomD waveforms to
build a GPR model in the 2-d parameter space of mass ratio and
equal-and-aligned spin . Using a regular, equally-spaced grid of
120 IMRPhenomD training waveforms in and ,
the GPR mean approximates IMRPhenomD in this space to mismatches below
. Our approach can alternatively use training waveforms
directly from numerical relativity. Beyond interpolation of waveforms, we also
present a greedy algorithm that utilizes the errors provided by our GPR model
to optimize the placement of future simulations. In a fiducial test case we
find that using the greedy algorithm to iteratively add simulations achieves
GPR errors that are order of magnitude lower than the errors from
using Latin-hypercube or square training grids
Building a stochastic template bank for detecting massive black hole binaries
Coalescence of two massive black holes is the strongest and most promising
source for LISA. In fact, gravitational signal from the end of inspiral and
merger will be detectable throughout the Universe. In this article we describe
the first step in the two-step hierarchical search for gravitational wave
signal from the inspiraling massive BH binaries. It is based on the routinely
used in the ground base gravitational wave astronomy method of filtering the
data through the bank of templates. However we use a novel Monte-Carlo based
(stochastic) method to lay a grid in the parameter space, and we use the
likelihood maximized analytically over some parameters, known as F-statistic,
as a detection statistic. We build a coarse template bank to detect
gravitational wave signals and to make preliminary parameter estimation. The
best candidates will be followed up using Metropolis-Hasting stochastic search
to refine the parameter estimation. We demonstrate the performance of the
method by applying it to the Mock LISA data challenge 1B (training data set).Comment: revtex4, 8 figure
Bayesian inference on compact binary inspiral gravitational radiation signals in interferometric data
Presented is a description of a Markov chain Monte Carlo (MCMC) parameter
estimation routine for use with interferometric gravitational radiational data
in searches for binary neutron star inspiral signals. Five parameters
associated with the inspiral can be estimated, and summary statistics are
produced. Advanced MCMC methods were implemented, including importance
resampling and prior distributions based on detection probability, in order to
increase the efficiency of the code. An example is presented from an
application using realistic, albeit fictitious, data.Comment: submitted to Classical and Quantum Gravity. 14 pages, 5 figure
A stochastic template placement algorithm for gravitational wave data analysis
This paper presents an algorithm for constructing matched-filter template
banks in an arbitrary parameter space. The method places templates at random,
then removes those which are "too close" together. The properties and
optimality of stochastic template banks generated in this manner are
investigated for some simple models. The effectiveness of these template banks
for gravitational wave searches for binary inspiral waveforms is also examined.
The properties of a stochastic template bank are then compared to the
deterministically placed template banks that are currently used in
gravitational wave data analysis.Comment: 14 pages, 11 figure
Parametric Estimation of Harmonically Related Sinusoids
Mud-pulse telemetry is a method used for measurement-while-drilling (MWD)in the oil industry. The telemetry signals are corrupted by spurious mud pump noise consisting of a large number of harmonically related sinusoids. In order to denoise the signal, the noise parameters have to be tracked accurately in real time. There are well established parametric estimation techniques for determining various parameters of independent sinusoids. The iterative methods based on the linear prediction properties of the sinusoids provide a computationally e±cient way of solving the non linear optimization problem presented by these methods. However, owing to the large number of these sinusoids, incorporating the harmonic relationship in the problem becomes important.
This thesis is aimed at solving the problem of estimating parameters of harmonically related sinusoids. We examine the efficacy of IQML algorithm in estimating the
parameters of the telemetry signal for varying SNRs and data lengths. The IQML algorithm proves quite robust and successfully tracks both stationary and slowly varying
frequency signals. Later, we propose an algorithm for fundamental frequency estimation which relies on the initial harmonic frequency estimate. The results of tests performed on synthetic data that imitates real field data are presented. The analysis of the simulation results shows that the proposed method manages to remove noise causing sinusoids in the telemetry signal to a great extent. The low computational complexity of the algorithm also makes for an easy implementation on field where
computational power is limited
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