4,602 research outputs found
Weiss–Weinstein Bound on Multiple Change-Points Estimation
In the context of multiple change-points estimation,
performance analysis of estimators such as the maximum likelihood
is often difficult to assess since the regularity assumptions
are not met. Focusing on the estimators variance, one can, however,
use lower bounds on themean square error. In this paper,we derive
the so-called Weiss–Weinstein bound (WWB) that is known to be
an efficient tool in signal processing to obtain a fair overview of the
estimation behavior. Contrary to several works about performance
analysis in the change-point literature, our study is adapted to multiple
changes. First, useful formulas are given for a general estimation
problem whatever the considered distribution of the data.
Second, closed-form expressions are given in the cases of Gaussian
observations with changes in the mean and/or the variance, and
changes in the mean rate of a Poisson distribution. Furthermore, a
semidefinite programming formulation of the minimization procedure
is given in order to compute the tightest WWB. Specifically,
it consists of finding the unique minimum volume covering the set
constituted by hyperellipsoid elements that are generated using the
derived candidateWWBmatrices w.r.t. the so-called Loewner partial
ordering. Finally, simulation results are provided to show the
good behavior of the proposed bound
Bayesian Bounds on Parameter Estimation Accuracy for Compact Coalescing Binary Gravitational Wave Signals
A global network of laser interferometric gravitational wave detectors is
projected to be in operation by around the turn of the century. Here, the noisy
output of a single instrument is examined. A gravitational wave is assumed to
have been detected in the data and we deal with the subsequent problem of
parameter estimation. Specifically, we investigate theoretical lower bounds on
the minimum mean-square errors associated with measuring the parameters of the
inspiral waveform generated by an orbiting system of neutron stars/black holes.
Three theoretical lower bounds on parameter estimation accuracy are considered:
the Cramer-Rao bound (CRB); the Weiss-Weinstein bound (WWB); and the Ziv-Zakai
bound (ZZB). We obtain the WWB and ZZB for the Newtonian-form of the coalescing
binary waveform, and compare them with published CRB and numerical Monte-Carlo
results. At large SNR, we find that the theoretical bounds are all identical
and are attained by the Monte-Carlo results. As SNR gradually drops below 10,
the WWB and ZZB are both found to provide increasingly tighter lower bounds
than the CRB. However, at these levels of moderate SNR, there is a significant
departure between all the bounds and the numerical Monte-Carlo results.Comment: 17 pages (LaTeX), 4 figures. Submitted to Physical Review
Some results on the Weiss-Weinstein bound for conditional and unconditional signal models in array processing
International audienceIn this paper, the Weiss-Weinstein bound is analyzed in the context of sources localization with a planar array of sensors. Both conditional and unconditional source signal models are studied. First, some results are given in the multiple sources context without specifying the structure of the steering matrix and of the noise covariance matrix. Moreover, the case of an uniform or Gaussian prior are analyzed. Second, these results are applied to the particular case of a single source for two kinds of array geometries: a non-uniform linear array (elevation only) and an arbitrary planar (azimuth and elevation) array
Contributions aux bornes inférieures de l’erreur quadratique moyenne en traitement du signal
A l’aide des bornes inférieures de l’erreur quadratique moyenne, la caractérisation du décrochement des estimateurs, l’analyse de la position optimale des capteurs dans un réseau ainsi que les limites de résolution statistiques sont étudiées dans le contexte du traitement d’antenne et du radar
Performance bounds on matched-field methods for source localization and estimation of ocean environmental parameters
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2001Matched-field methods concern estimation of source location and/or ocean environmental
parameters by exploiting full wave modeling of acoustic waveguide propagation.
Typical estimation performance demonstrates two fundamental limitations.
First, sidelobe ambiguities dominate the estimation at low signal-to-noise ratio (SNR),
leading to a threshold performance behavior. Second, most matched-field algorithms
show a strong sensitivity to environmental/system mismatch, introducing some biased
estimates at high SNR.
In this thesis, a quantitative approach for ambiguity analysis is developed so that
different mainlobe and sidelobe error contributions can be compared at different SNR
levels. Two large-error performance bounds, the Weiss-Weinstein bound (WWB)
and Ziv-Zakai bound (ZZB), are derived for the attainable accuracy of matched-field
methods. To include mismatch effects, a modified version of the ZZB is proposed.
Performance analyses are implemented for source localization under a typical shallow
water environment chosen from the Shallow Water Evaluation Cell Experiments
(SWellEX). The performance predictions describe the simulations of the maximum
likelihood estimator (MLE) well, including the mean square error in all SNR regions
as well as the bias at high SNR. The threshold SNR and bias predictions are also
verified by the SWellEX experimental data processing. These developments provide
tools to better understand some fundamental behaviors in matched-field performance
and provide benchmarks to which various ad hoc algorithms can be compared.Financial support for my research was provided by the Office of Naval Research
and the WHOI Education Office
Lower Bounds on Exponential Moments of the Quadratic Error in Parameter Estimation
Considering the problem of risk-sensitive parameter estimation, we propose a
fairly wide family of lower bounds on the exponential moments of the quadratic
error, both in the Bayesian and the non--Bayesian regime. This family of
bounds, which is based on a change of measures, offers considerable freedom in
the choice of the reference measure, and our efforts are devoted to explore
this freedom to a certain extent. Our focus is mostly on signal models that are
relevant to communication problems, namely, models of a parameter-dependent
signal (modulated signal) corrupted by additive white Gaussian noise, but the
methodology proposed is also applicable to other types of parametric families,
such as models of linear systems driven by random input signals (white noise,
in most cases), and others. In addition to the well known motivations of the
risk-sensitive cost function (i.e., the exponential quadratic cost function),
which is most notably, the robustness to model uncertainty, we also view this
cost function as a tool for studying fundamental limits concerning the tail
behavior of the estimation error. Another interesting aspect, that we
demonstrate in a certain parametric model, is that the risk-sensitive cost
function may be subjected to phase transitions, owing to some analogies with
statistical mechanics.Comment: 28 pages; 4 figures; submitted for publicatio
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