6 research outputs found
A NEW DERIVATION OF THE BAYESIAN BOUNDS FOR PARAMETER ESTIMATION
International audienceThis paper deals with minimal bounds in the Bayesian context. We express the minimum mean square error of the conditional mean estimator as the solution of a continuum constrained optimization problem. And, by relaxing these constraints, we obtain the bounds of the Weiss-Weinstein family. Moreover, this method enables us to derive new bounds as the Bayesian version of the deterministic Abel bound
Entanglement-assisted multi-aperture pulse-compression radar for angle resolving detection
Entanglement has been known to boost target detection, despite it being
destroyed by lossy-noisy propagation. Recently, [Phys. Rev. Lett. 128, 010501
(2022)] proposed a quantum pulse-compression radar to extend entanglement's
benefit to target range estimation. In a radar application, many other aspects
of the target are of interest, including angle, velocity and cross section. In
this study, we propose a dual-receiver radar scheme that employs a high
time-bandwidth product microwave pulse entangled with a pre-shared reference
signal available at the receiver, to investigate the direction of a distant
object and show that the direction-resolving capability is significantly
improved by entanglement, compared to its classical counterpart under the same
parameter settings. We identify the applicable scenario of this quantum radar
to be short-range and high-frequency, which enables entanglement's benefit in a
reasonable integration time.Comment: 18 pages, 9 figure
A Fresh Look at the Bayesian Bounds of the Weiss-Weinstein Family
International audienceMinimal bounds on the mean square error (MSE) are generally used in order to predict the best achievable performance of an estimator for a given observation model. In this paper, we are interested in the Bayesian bound of the Weiss–Weinstein family. Among this family, we have Bayesian Cramér-Rao bound, the Bobrovsky–MayerWolf–Zakaï bound, the Bayesian Bhattacharyya bound, the Bobrovsky–Zakaï bound, the Reuven–Messer bound, and the Weiss–Weinstein bound. We present a unification of all these minimal bounds based on a rewriting of the minimum mean square error estimator (MMSEE) and on a constrained optimization problem. With this approach, we obtain a useful theoretical framework to derive new Bayesian bounds. For that purpose, we propose two bounds. First, we propose a generalization of the Bayesian Bhattacharyya bound extending the works of Bobrovsky, Mayer–Wolf, and Zakaï. Second, we propose a bound based on the Bayesian Bhattacharyya bound and on the Reuven–Messer bound, representing a generalization of these bounds. The proposed bound is the Bayesian extension of the deterministic Abel bound and is found to be tighter than the Bayesian Bhattacharyya bound, the Reuven–Messer bound, the Bobrovsky–Zakaï bound, and the Bayesian Cramér–Rao bound. We propose some closed-form expressions of these bounds for a general Gaussian observation model with parameterized mean. In order to illustrate our results, we present simulation results in the context of a spectral analysis problem
Statistics of the MLE and Approximate Upper and Lower Bounds - Part 1: Application to TOA Estimation
In nonlinear deterministic parameter estimation, the maximum likelihood
estimator (MLE) is unable to attain the Cramer-Rao lower bound at low and
medium signal-to-noise ratios (SNR) due the threshold and ambiguity phenomena.
In order to evaluate the achieved mean-squared-error (MSE) at those SNR levels,
we propose new MSE approximations (MSEA) and an approximate upper bound by
using the method of interval estimation (MIE). The mean and the distribution of
the MLE are approximated as well. The MIE consists in splitting the a priori
domain of the unknown parameter into intervals and computing the statistics of
the estimator in each interval. Also, we derive an approximate lower bound
(ALB) based on the Taylor series expansion of noise and an ALB family by
employing the binary detection principle. The accurateness of the proposed
MSEAs and the tightness of the derived approximate bounds are validated by
considering the example of time-of-arrival estimation
Weiss-Weinstein bound of frequency estimation error for very weak GNSS signals
Tightness remains the center quest in all modern estimation bounds. For very
weak signals, this is made possible with judicial choices of prior probability
distribution and bound family. While current bounds in GNSS assess performance
of carrier frequency estimators under Gaussian or uniform assumptions, the
circular nature of frequency is overlooked. In addition, of all bounds in
Bayesian framework, Weiss-Weinstein bound (WWB) stands out since it is free
from regularity conditions or requirements on the prior distribution.
Therefore, WWB is extended for the current frequency estimation problem. A
divide-and-conquer type of hyperparameter tuning method is developed to level
off the curse of computational complexity for the WWB family while enhancing
tightness. Synthetic results show that with von Mises as prior probability
distribution, WWB provides a bound up to 22.5% tighter than Ziv-Zaka\"i bound
(ZZB) when SNR varies between -3.5 dB and -20 dB, where GNSS signal is deemed
extremely weak.Comment: 35 pages, 13 figures, submitted to NAVIGATION, Journal of the
Institute of Navigatio
Abstracts of papers submitted in 1987 for publication
This volume contains all abstracts submitted for
publication during calendar year 1987 by the staff and students
of the Woods Hole Oceanographic Institution. Because some of
the abstracts may not be published in the journal to which they
have been submitted initially, we have purposely omitted
identifying the journals. The volume is intended to be informative,
but not a bibliography