scholarly journals Estimation of Atmospheric Duct Structure Using Radar Sea Clutter

2012 ◽  
Vol 69 (9) ◽  
pp. 2808-2818 ◽  
Author(s):  
Xiaofeng Zhao ◽  
Sixun Huang
Keyword(s):  
Approximate Solutions ◽  
Propagation Loss ◽  
Sea Surface ◽  
Model Parameters ◽  
Sea Clutter ◽  
Radar Clutter ◽  
Atmospheric Duct ◽  
Analytical Transformation ◽  
Ill Posed ◽  
Adjoint Approach

Abstract Retrieving atmospheric refractivity profiles from the sea surface backscattered radar clutter is known as the refractivity-from-clutter (RFC) technique. Because the relationship between refractivity and radar sea clutter is clearly nonlinear and ill posed, it is difficult to get analytical solutions according to current theories. Previous works treat this problem as a model parameter estimation issue and some optimization algorithms are selected to get approximate solutions. Two main factors that limit the accuracy of the estimation are that 1) the refractive environments are described by using some idealized refractivity parameter models that cannot describe the exact information of the refractivity profile, and 2) accurate modeling of the sea surface radar cross section (RCS) is very difficult. Rather than estimating a few model parameters, this paper puts forward possibilities of using the variational adjoint approach to jointly retrieve the every-height refractivity values and sea surface RCS using radar clutter data. The derivation of the adjoint model is accomplished by an analytical transformation of the parabolic equation (PE) in the continuous domain. Numerical simulations including range-independent and range-dependent RCS cases are presented to demonstrate the ability of this method for RFC estimations. Making use of the refractivity retrievals, propagation loss predictions are also presented.

scholarly journals Atmospheric Duct Estimation Using Radar Sea Clutter Returns by the Adjoint Method with Regularization Technique

2014 ◽  
Vol 31 (6) ◽  
pp. 1250-1262 ◽  
Author(s):  
Xiaofeng Zhao ◽  
Sixun Huang
Keyword(s):  
Genetic Algorithm ◽  
Parabolic Equation ◽  
Adjoint Method ◽  
Regularization Parameter ◽  
Background Field ◽  
Sea Clutter ◽  
Regularization Technique ◽  
Atmospheric Duct ◽  
Adjoint Approach ◽  
Space Range

Abstract This paper focuses on retrieving the atmospheric duct structure from radar sea clutter returns by the adjoint approach with the regularization technique. The adjoint is derived from the split-step Fourier parabolic equation method, and the regularization term is constructed by the background refractivity field. To ensure successful implementations of the regularization, the L-curve criterion is used to find the optimal regularization parameter. The feasibility of the proposed method is validated by the numerical simulations of different noise-level clutter returns, as well as a real clutter profile measured by the S-Band Space Range Radar located in Wallops Island. In the process of inversions, the refractivity profile is first obtained by genetic algorithm, and then it is used as the background field for the adjoint method. The retrieved results indicate that, with an appropriate regularization parameter, the structure of the background refractivity profile can be improved by the proposed method.

scholarly journals Using particle filter to track horizontal variations of atmospheric duct structure from radar sea clutter

2012 ◽  
Vol 5 (4) ◽  
pp. 6059-6082
Author(s):  
X. F. Zhao ◽  
S. X. Huang
Keyword(s):  
Particle Filter ◽  
Real Data ◽  
Forward Simulation ◽  
Sea Clutter ◽  
Radar Clutter ◽  
Atmospheric Duct ◽  
Basic Ideas ◽  
Recursive Bayesian Filter ◽  
Horizontal Variations ◽  
Recursive Bayesian

Abstract. This paper addresses the problem of estimating range-varying parameters of the height-dependent refractivity over the sea surface from radar sea clutter. In the forward simulation, the split-step Fourier parabolic equation (PE) is used to compute the radar clutter power in the complex refractive environments. Making use of the inherent Markovian structure of the split-step Fourier PE solution, the refractivity from clutter (RFC) problem is formulated within a nonlinear recursive Bayesian state estimation framework. Particle filter (PF) that is a technique for implementing a recursive Bayesian filter by Monte Carlo simulations is used to track range-varying characteristics of the refractivity profiles. Basic ideas of employing PF to solve RFC problem are introduced. Both simulation and real data results are presented to check up the feasibility of PF-RFC performances.

scholarly journals Using particle filter to track horizontal variations of atmospheric duct structure from radar sea clutter

2012 ◽  
Vol 5 (11) ◽  
pp. 2859-2866 ◽  
Author(s):  
X. F. Zhao ◽  
S. X. Huang ◽  
D. X. Wang
Keyword(s):  
Particle Filter ◽  
Real Data ◽  
Forward Simulation ◽  
Sea Clutter ◽  
Radar Clutter ◽  
Atmospheric Duct ◽  
Basic Ideas ◽  
Recursive Bayesian Filter ◽  
Horizontal Variations ◽  
Recursive Bayesian

Abstract. This paper addresses the problem of estimating range-varying parameters of the height-dependent refractivity over the sea surface from radar sea clutter. In the forward simulation, the split-step Fourier parabolic equation (PE) is used to compute the radar clutter power in the complex refractive environments. Making use of the inherent Markovian structure of the split-step Fourier PE solution, the refractivity from clutter (RFC) problem is formulated within a nonlinear recursive Bayesian state estimation framework. Particle filter (PF), which is a technique for implementing a recursive Bayesian filter by Monte Carlo simulations, is used to track range-varying characteristics of the refractivity profiles. Basic ideas of employing PF to solve RFC problem are introduced. Both simulation and real data results are presented to confirm the feasibility of PF-RFC performances.

scholarly journals Bayesian Reconstruction through Adaptive Image Notion

Proceedings ◽  
2019 ◽  
Vol 33 (1) ◽  
pp. 21
Author(s):  
Fabrizia Guglielmetti ◽  
Eric Villard ◽  
Ed Fomalont
Keyword(s):  
Inverse Problem ◽  
Image Plane ◽  
Source Distribution ◽  
Bayesian Probability ◽  
Model Parameters ◽  
Uncertain Information ◽  
Source Detection ◽  
Component Mixture ◽  
Ill Posed ◽  
Image Planes

A stable and unique solution to the ill-posed inverse problem in radio synthesis image analysis is sought employing Bayesian probability theory combined with a probabilistic two-component mixture model. The solution of the ill-posed inverse problem is given by inferring the values of model parameters defined to describe completely the physical system arised by the data. The analysed data are calibrated visibilities, Fourier transformed from the ( u , v ) to image planes. Adaptive splines are explored to model the cumbersome background model corrupted by the largely varying dirty beam in the image plane. The de-convolution process of the dirty image from the dirty beam is tackled in probability space. Probability maps in source detection at several resolution values quantify the acquired knowledge on the celestial source distribution from a given state of information. The information available are data constrains, prior knowledge and uncertain information. The novel algorithm has the aim to provide an alternative imaging task for the use of the Atacama Large Millimeter/Submillimeter Array (ALMA) in support of the widely used Common Astronomy Software Applications (CASA) enhancing the capabilities in source detection.

A Deterministic Sea-Clutter Space–Time Model Based on Physical Sea Surface

2016 ◽  
Vol 54 (11) ◽  
pp. 6659-6673 ◽  
Author(s):  
Zhihui Xin ◽  
Guisheng Liao ◽  
Zhiwei Yang ◽  
Yuhong Zhang ◽  
Hongxing Dang
Keyword(s):  
Space Time ◽  
Sea Surface ◽  
Sea Clutter ◽  
Time Model ◽  
Model Based ◽  
Space Time Model

scholarly journals Range-relaxed criteria for choosing the Lagrange multipliers in nonstationary iterated Tikhonov method

2018 ◽  
Vol 40 (1) ◽  
pp. 606-627 ◽  
Author(s):  
R Boiger ◽  
A Leitão ◽  
B F Svaiter
Keyword(s):  
Lagrange Multipliers ◽  
Approximate Solutions ◽  
Identification Problem ◽  
Linear Operators ◽  
Type Method ◽  
Geometrical Properties ◽  
Regularization Parameters ◽  
New Strategy ◽  
Parameter Identification Problem ◽  
Ill Posed

Abstract In this article we propose a novel nonstationary iterated Tikhonov (NIT)-type method for obtaining stable approximate solutions to ill-posed operator equations modeled by linear operators acting between Hilbert spaces. Geometrical properties of the problem are used to derive a new strategy for choosing the sequence of regularization parameters (Lagrange multipliers) for the NIT iteration. Convergence analysis for this new method is provided. Numerical experiments are presented for two distinct applications: (I) a two-dimensional elliptic parameter identification problem (inverse potential problem); and (II) an image-deblurring problem. The results obtained validate the efficiency of our method compared with standard implementations of the NIT method (where a geometrical choice is typically used for the sequence of Lagrange multipliers).

Upper and Lower Bounds for the Parameters of One-Dimensional Theories for Sandwich Fracture Specimens

2020 ◽  
Vol 88 (3) ◽  
Author(s):  
Roberta Massabò
Keyword(s):  
Crack Length ◽  
Lower Bounds ◽  
Beam Theory ◽  
Approximate Solutions ◽  
Upper And Lower Bounds ◽  
Model Parameters ◽  
One Dimensional ◽  
Limit Value ◽  
Elastic Mismatch ◽  
Fracture Specimens

Abstract Upper and lower bounds for the parameters of one-dimensional theories used in the analysis of sandwich fracture specimens are derived by matching the energy release rate with two-dimensional elasticity solutions. The theory of a beam on an elastic foundation and modified beam theory are considered. Bounds are derived analytically for foundation modulus and crack length correction in single cantilever beam (SCB) sandwich specimens and verified using accurate finite element results and experimental data from the literature. Foundation modulus and crack length correction depend on the elastic mismatch between face sheets and core and are independent of the core thickness if this is above a limit value, which also depends on the elastic mismatch. The results in this paper clarify conflicting results in the literature, explain the approximate solutions, and highlight their limitations. The bounds of the model parameters can be applied directly to specimens satisfying specific geometrical/material ratios, which are given in the paper, or used to support and validate numerical calculations and define asymptotic limits.

scholarly journals Optimal order yielding discrepancy principle for simplified regularization in Hilbert scales: finite-dimensional realizations

2004 ◽  
Vol 2004 (37) ◽  
pp. 1973-1996 ◽  
Author(s):  
Santhosh George ◽  
M. Thamban Nair
Keyword(s):  
Wide Class ◽  
Noise Level ◽  
A Priori ◽  
Approximate Solutions ◽  
Optimal Order ◽  
Discrepancy Principle ◽  
A Posteriori ◽  
Operator Equations ◽  
Finite Dimensional ◽  
Ill Posed

Simplified regularization using finite-dimensional approximations in the setting of Hilbert scales has been considered for obtaining stable approximate solutions to ill-posed operator equations. The derived error estimates using an a priori and a posteriori choice of parameters in relation to the noise level are shown to be of optimal order with respect to certain natural assumptions on the ill posedness of the equation. The results are shown to be applicable to a wide class of spline approximations in the setting of Sobolev scales.

Full waveform inversion with sparse structure constrained regularization

2018 ◽  
Vol 26 (2) ◽  
pp. 243-257 ◽  
Author(s):  
Zichao Yan ◽  
Yanfei Wang
Keyword(s):  
Large Scale ◽  
Regularization Parameter ◽  
Waveform Inversion ◽  
Difference Operators ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Structure Information ◽  
Full Waveform ◽  
Ill Posed ◽  
Scale Optimization

AbstractFull waveform inversion is a large-scale nonlinear and ill-posed problem. We consider applying the regularization technique for full waveform inversion with structure constraints. The structure information was extracted with difference operators with respect to model parameters. And then we establish an {l_{p}}-{l_{q}}-norm constrained minimization model for different choices of parameters p and q. To solve this large-scale optimization problem, a fast gradient method with projection onto convex set and a multiscale inversion strategy are addressed. The regularization parameter is estimated adaptively with respect to the frequency range of the data. Numerical experiments on a layered model and a benchmark SEG/EAGE overthrust model are performed to testify the validity of this proposed regularization scheme.

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