779 research outputs found
Application of asymptotic expansions of maximum likelihood estimators errors to gravitational waves from binary mergers: the single interferometer case
In this paper we describe a new methodology to calculate analytically the
error for a maximum likelihood estimate (MLE) for physical parameters from
Gravitational wave signals. All the existing litterature focuses on the usage
of the Cramer Rao Lower bounds (CRLB) as a mean to approximate the errors for
large signal to noise ratios. We show here how the variance and the bias of a
MLE estimate can be expressed instead in inverse powers of the signal to noise
ratios where the first order in the variance expansion is the CRLB. As an
application we compute the second order of the variance and bias for MLE of
physical parameters from the inspiral phase of binary mergers and for noises of
gravitational wave interferometers . We also compare the improved error
estimate with existing numerical estimates. The value of the second order of
the variance expansions allows to get error predictions closer to what is
observed in numerical simulations. It also predicts correctly the necessary SNR
to approximate the error with the CRLB and provides new insight on the
relationship between waveform properties SNR and estimation errors. For example
the timing match filtering becomes optimal only if the SNR is larger than the
kurtosis of the gravitational wave spectrum
Target Localization Accuracy Gain in MIMO Radar Based Systems
This paper presents an analysis of target localization accuracy, attainable
by the use of MIMO (Multiple-Input Multiple-Output) radar systems, configured
with multiple transmit and receive sensors, widely distributed over a given
area. The Cramer-Rao lower bound (CRLB) for target localization accuracy is
developed for both coherent and non-coherent processing. Coherent processing
requires a common phase reference for all transmit and receive sensors. The
CRLB is shown to be inversely proportional to the signal effective bandwidth in
the non-coherent case, but is approximately inversely proportional to the
carrier frequency in the coherent case. We further prove that optimization over
the sensors' positions lowers the CRLB by a factor equal to the product of the
number of transmitting and receiving sensors. The best linear unbiased
estimator (BLUE) is derived for the MIMO target localization problem. The
BLUE's utility is in providing a closed form localization estimate that
facilitates the analysis of the relations between sensors locations, target
location, and localization accuracy. Geometric dilution of precision (GDOP)
contours are used to map the relative performance accuracy for a given layout
of radars over a given geographic area.Comment: 36 pages, 5 figures, submitted to IEEE Transaction on Information
Theor
Frequentist and Bayesian Quantum Phase Estimation
Frequentist and Bayesian phase estimation strategies lead to conceptually
different results on the state of knowledge about the true value of the phase
shift. We compare the two frameworks and their sensitivity bounds to the
estimation of an interferometric phase shift limited by quantum noise,
considering both the cases of a fixed and a fluctuating parameter. We point out
that frequentist precision bounds, such as the Cram\`er-Rao bound, for
instance, do not apply to Bayesian strategies and vice-versa. Similarly, bounds
for fluctuating parameters make no statement about the estimation of a fixed
parameter.Comment: 4 figure
A Hybrid Global Minimization Scheme for Accurate Source Localization in Sensor Networks
We consider the localization problem of multiple wideband sources in a
multi-path environment by coherently taking into account the attenuation
characteristics and the time delays in the reception of the signal. Our
proposed method leaves the space for unavailability of an accurate signal
attenuation model in the environment by considering the model as an unknown
function with reasonable prior assumptions about its functional space. Such
approach is capable of enhancing the localization performance compared to only
utilizing the signal attenuation information or the time delays. In this paper,
the localization problem is modeled as a cost function in terms of the source
locations, attenuation model parameters and the multi-path parameters. To
globally perform the minimization, we propose a hybrid algorithm combining the
differential evolution algorithm with the Levenberg-Marquardt algorithm.
Besides the proposed combination of optimization schemes, supporting the
technical details such as closed forms of cost function sensitivity matrices
are provided. Finally, the validity of the proposed method is examined in
several localization scenarios, taking into account the noise in the
environment, the multi-path phenomenon and considering the sensors not being
synchronized
The noise properties of 42 millisecond pulsars from the European Pulsar Timing Array and their impact on gravitational wave searches
The sensitivity of Pulsar Timing Arrays to gravitational waves depends on the
noise present in the individual pulsar timing data. Noise may be either
intrinsic or extrinsic to the pulsar. Intrinsic sources of noise will include
rotational instabilities, for example. Extrinsic sources of noise include
contributions from physical processes which are not sufficiently well modelled,
for example, dispersion and scattering effects, analysis errors and
instrumental instabilities. We present the results from a noise analysis for 42
millisecond pulsars (MSPs) observed with the European Pulsar Timing Array. For
characterising the low-frequency, stochastic and achromatic noise component, or
"timing noise", we employ two methods, based on Bayesian and frequentist
statistics. For 25 MSPs, we achieve statistically significant measurements of
their timing noise parameters and find that the two methods give consistent
results. For the remaining 17 MSPs, we place upper limits on the timing noise
amplitude at the 95% confidence level. We additionally place an upper limit on
the contribution to the pulsar noise budget from errors in the reference
terrestrial time standards (below 1%), and we find evidence for a noise
component which is present only in the data of one of the four used telescopes.
Finally, we estimate that the timing noise of individual pulsars reduces the
sensitivity of this data set to an isotropic, stochastic GW background by a
factor of >9.1 and by a factor of >2.3 for continuous GWs from resolvable,
inspiralling supermassive black-hole binaries with circular orbits.Comment: Accepted for publication by the Monthly Notices of the Royal
Astronomical Societ
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