Cramer-rao Study of One-dimensional Scattering Systems: Part I: Formulation
نویسندگان
چکیده
A Cramer-Rao bound (CRB) study is developed in onedimensional (1D) space which sheds fundamental insight onto the information about multiply scattering point-like scatterers that is contained in scattering field data corresponding to transmissive, reflective, and combined transmissive plus reflective sensing geometries, and singleand multi-frequency measurements.
منابع مشابه
Cramer-rao Study of One-dimensional Scattering Systems: Part Ii: Computer Simulations
This paper is the second of a two-part paper aimed at studying fundamental limits in estimation in 1D scattering systems via the Cramer-Rao bound. In this paper we provide and discuss computer simulation results illustrating the theory in the first paper.
متن کاملCramer-rao Study of Scattering Systems in One-dimensional Space
A Cramer-Rao bound (CRB) study is developed to characterize the information content about scattering parameters that is contained in reflective (R), transmissive (T), and combined R plus T wave scattering data. The analysis is developed for scalar wave scattering systems in onedimensional space, paying particular attention to elastic scatterers, which simplifies the signal model (relative to mo...
متن کاملImproved Cramer-Rao Inequality for Randomly Censored Data
As an application of the improved Cauchy-Schwartz inequality due to Walker (Statist. Probab. Lett. (2017) 122:86-90), we obtain an improved version of the Cramer-Rao inequality for randomly censored data derived by Abdushukurov and Kim (J. Soviet. Math. (1987) pp. 2171-2185). We derive a lower bound of Bhattacharya type for the mean square error of a parametric function based on randomly censor...
متن کاملConvolution Representation in Practice
The convolution theorem (Hájek [8]) characterizes the weak limit of any regular estimator as a convolution of two independent components. One is an optimal achievable part and another is a noise. Therefore, the optimal estimator is one without the noise part in its weak limit, which is a deeper characterization than the Cramer-Rao bound. However, this result is derived under the assumption that...
متن کاملNote for Cramer-Rao Bounds
• (z)r and (z)i denote the real and imaginary part of z. II. CONSTRAINED CRAMER-RAO BOUND A. Problem Statement Problem statement and notation are based on [1]. • a: a K × 1 non-random vector which are to be estimated. • r: an observation of a random vector . • â (R): an estimate of a basing on the observed vector r . It is required that â (R) satisfies M nonlinear equality constraints (M < K), ...
متن کامل