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Long-time Asymptotics for the Reverse Space-time Nonlocal Hirota Equation with Decaying Initial Value Problem:without Solitons
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作者 Wei-qi PENG Yong CHEN 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2024年第3期708-727,共20页
In this work,we mainly consider the Cauchy problem for the reverse space-time nonlocal Hirota equation with the initial data rapidly decaying in the solitonless sector.Start from the Lax pair,we first construct the ba... In this work,we mainly consider the Cauchy problem for the reverse space-time nonlocal Hirota equation with the initial data rapidly decaying in the solitonless sector.Start from the Lax pair,we first construct the basis Riemann-Hilbert problem for the reverse space-time nonlocal Hirota equation.Furthermore,using the approach of Deift-Zhou nonlinear steepest descent,the explicit long-time asymptotics for the reverse space-time nonlocal Hirota is derived.For the reverse space-time nonlocal Hirota equation,since the symmetries of its scattering matrix are different with the local Hirota equation,the v(λ_(i))(i=0,1)would like to be imaginary,which results in theδ_(λi)^(0)contains an increasing t(±Imv(λ_(i)))/2,and then the asymptotic behavior for nonlocal Hirota equation becomes differently. 展开更多
关键词 Riemann-Hilbert problem reverse space-time nonlocal Hirota equation long-time asymptotics nonlinear steepest descent method
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Spectral Analysis and Long-time Asymptotics for the Coherently-coupled Nonlinear Schrödinger System
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作者 Ming Ming CHEN Xian Guo GENG Ke Dong WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2022年第11期2090-2114,共25页
On the basis of the spectral analysis of the 4×4 matrix Lax pair,the initial value problem of the coherently-coupled nonlinear Schrödinger system is transformed into a 4×4 matrix Riemann–Hilbert proble... On the basis of the spectral analysis of the 4×4 matrix Lax pair,the initial value problem of the coherently-coupled nonlinear Schrödinger system is transformed into a 4×4 matrix Riemann–Hilbert problem.By using the nonlinear steepest decent method,the long-time asymptotics of the solution of the initial value problem for the coherently-coupled nonlinear Schrödinger system is obtained through deforming the Riemann–Hilbert problem into a solvable model one. 展开更多
关键词 Coherently-coupled nonlinear Schrödinger system nonlinear steepest descent method long-time asymptotics
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Long-time asymptotics for the initial-boundary value problem of coupled Hirota equation on the half-line
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作者 Nan Liu Boling Guo 《Science China Mathematics》 SCIE CSCD 2021年第1期81-110,共30页
The object of this work is to investigate the initial-boundary value problem for coupled Hirota equation on the half-line.We show that the solution of the coupled Hirota equation can be expressed in terms of the solut... The object of this work is to investigate the initial-boundary value problem for coupled Hirota equation on the half-line.We show that the solution of the coupled Hirota equation can be expressed in terms of the solution of a 3×3 matrix Riemann-Hilbert problem formulated in the complex k-plane.The relevant jump matrices are explicitly given in terms of the matrix-valued spectral functions s(k)and S(k)that depend on the initial data and boundary values,respectively.Then,applying nonlinear steepest descent techniques to the associated 3×3 matrix-valued Riemann-Hilbert problem,we can give the precise leading-order asymptotic formulas and uniform error estimates for the solution of the coupled Hirota equation. 展开更多
关键词 coupled Hirota equation initial-boundary value problem long-time asymptotics
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Multiple Soliton Asymptotics in a Spin-1 Bose–Einstein Condensate
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作者 Zhong-Zhou Lan 《Chinese Physics Letters》 SCIE EI CAS CSCD 2024年第9期15-22,共8页
Spinor Bose–Einstein condensates(BECs)are formed when atoms in the multi-component BECs possess single hyperfine spin states but retain internal spin degrees of freedom.This study concentrates on a(1+1)-dimensional t... Spinor Bose–Einstein condensates(BECs)are formed when atoms in the multi-component BECs possess single hyperfine spin states but retain internal spin degrees of freedom.This study concentrates on a(1+1)-dimensional three-couple Gross–Pitaevskii system to depict the macroscopic spinor BEC waves within the meanfield approximation.Regarding the distribution of the atoms corresponding to the three vertical spin projections,a known binary Darboux transformation is utilized to derive the𝑁matter-wave soliton solutions and triple-pole matter-wave soliton solutions on the zero background,where𝑁is a positive integer.For those multiple matterwave solitons,the asymptotic analysis is performed to obtain the algebraic expressions of the soliton components in the𝑁matter-wave solitons and triple-pole matter-wave solitons.The asymptotic results indicate that the matter-wave solitons in the spinor BECs possess the property of maintaining their energy content and coherence during the propagation and interactions.Particularly,in the𝑁matter-wave solitons,each soliton component contributes to the phase shifts of the other soliton components;and in the triple-pole matter-wave solitons,stable attractive forces exist between the different matter-wave soliton components.Those multiple matter-wave solitons are graphically illustrated through three-dimensional plots,density plot and contour plot,which are consistent with the asymptotic analysis results.The present analysis may provide the explanations for the complex natural mechanisms of the matter waves in the spinor BECs,and may have potential applications in designs of atom lasers,atom interferometry and coherent atom transport. 展开更多
关键词 SOLITON SOLITONS asymptotIC
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Exact Tail Asymptotics for a Queueing System with a Retrial Orbit and Batch Service
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作者 Huijun Lu 《Applied Mathematics》 2024年第6期406-420,共15页
This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts servi... This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts serving, it serves all customers in the queue in a single batch, which is the so-called batch service. If a new customer or a retrial customer finds all the customers’ rooms are occupied, he will decide whether or not to join the retrial orbit. By using the censoring technique and the matrix analysis method, we first obtain the decay function of the stationary distribution for the quantity of customers in the retrial orbit and the quantity of customers in the queue. Then based on the form of decay rate function and the Karamata Tauberian theorem, we finally get the exact tail asymptotics of the stationary distribution. 展开更多
关键词 Exact Tail asymptotics Batch Service Censoring Technique Matrix Analysis Method Karamata Tauberian Theorem
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Long-Time Asymptotics for the Nonlocal MKdV Equation 被引量:1
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作者 Feng-Jing He En-Gui Fan Jian Xu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2019年第5期475-488,共14页
In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation(nonlocal mKdV) qt(x, t)+qxxx(x, t)-6 q(x, t)q(-x,-t)qx(x, t) = 0, which can be viewed as a gen... In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation(nonlocal mKdV) qt(x, t)+qxxx(x, t)-6 q(x, t)q(-x,-t)qx(x, t) = 0, which can be viewed as a generalization of the local classical mKdV equation. We first formulate the Riemann-Hilbert problem associated with the Cauchy problem of the nonlocal mKdV equation. Then we apply the Deift-Zhou nonlinear steepest-descent method to analyze the long-time asymptotics for the solution of the nonlocal m KdV equation. In contrast with the classical mKdV equation,we find some new and different results on long-time asymptotics for the nonlocal mKdV equation and some additional assumptions about the scattering data are made in our main results. 展开更多
关键词 NONLOCAL MKDV equation RIEMANN-HILBERT problem Deift-Zhou nonlinear steepest-descent long-time asymptotics
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Radar fast long-time coherent integration via TR-SKT and robust sparse FRFT
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作者 CHEN Xiaolong GUAN Jian +2 位作者 ZHENG Jibin ZHANG Yue YU Xiaohan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2023年第5期1116-1129,共14页
Long-time coherent integration(LTCI)is an effective way for radar maneuvering target detection,but it faces the problem of a large number of search parameters and large amount of calculation.Realizing the simultaneous... Long-time coherent integration(LTCI)is an effective way for radar maneuvering target detection,but it faces the problem of a large number of search parameters and large amount of calculation.Realizing the simultaneous compensation of the range and Doppler migrations in complex clutter back-ground,and at the same time improving the calculation efficiency has become an urgent problem to be solved.The sparse transformation theory is introduced to LTCI in this paper,and a non-parametric searching sparse LTCI(SLTCI)based maneuvering target detection method is proposed.This method performs time reversal(TR)and second-order Keystone transform(SKT)in the range frequency&slow-time data to complete high-order range walk compensation,and achieves the coherent integra-tion of maneuvering target across range and Doppler units via the robust sparse fractional Fourier transform(RSFRFT).It can compensate for the nonlinear range migration caused by high-order motion.S-band and X-band radar data measured in sea clutter background are used to verify the detection performance of the proposed method,which can achieve better detection performance of maneuvering targets with less computational burden compared with several popular integration methods. 展开更多
关键词 radar maneuvering target detection sea clutter long-time coherent integration(LTCI) sparse transformation time reversal(TR) second-order Keystone transform(SKT)
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Reinforcement learning based adaptive control for uncertain mechanical systems with asymptotic tracking
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作者 Xiang-long Liang Zhi-kai Yao +1 位作者 Yao-wen Ge Jian-yong Yao 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2024年第4期19-28,共10页
This paper mainly focuses on the development of a learning-based controller for a class of uncertain mechanical systems modeled by the Euler-Lagrange formulation.The considered system can depict the behavior of a larg... This paper mainly focuses on the development of a learning-based controller for a class of uncertain mechanical systems modeled by the Euler-Lagrange formulation.The considered system can depict the behavior of a large class of engineering systems,such as vehicular systems,robot manipulators and satellites.All these systems are often characterized by highly nonlinear characteristics,heavy modeling uncertainties and unknown perturbations,therefore,accurate-model-based nonlinear control approaches become unavailable.Motivated by the challenge,a reinforcement learning(RL)adaptive control methodology based on the actor-critic framework is investigated to compensate the uncertain mechanical dynamics.The approximation inaccuracies caused by RL and the exogenous unknown disturbances are circumvented via a continuous robust integral of the sign of the error(RISE)control approach.Different from a classical RISE control law,a tanh(·)function is utilized instead of a sign(·)function to acquire a more smooth control signal.The developed controller requires very little prior knowledge of the dynamic model,is robust to unknown dynamics and exogenous disturbances,and can achieve asymptotic output tracking.Eventually,co-simulations through ADAMS and MATLAB/Simulink on a three degrees-of-freedom(3-DOF)manipulator and experiments on a real-time electromechanical servo system are performed to verify the performance of the proposed approach. 展开更多
关键词 Adaptive control Reinforcement learning Uncertain mechanical systems asymptotic tracking
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Asymptotic normality of error density estimator in stationary and explosive autoregressive models
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作者 WU Shi-peng YANG Wen-zhi +1 位作者 GAO Min HU Shu-he 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第1期140-158,共19页
In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity... In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors. 展开更多
关键词 explosive autoregressive models residual density estimator asymptotic distribution association sequence
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Modeling Method of C/C-ZrC Composites and Prediction of Equivalent Thermal Conductivity Tensor Based on Asymptotic Homogenization
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作者 Junpeng Lyu Hai Mei +2 位作者 Liping Zu Lisheng Liu Liangliang Chu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第1期391-410,共20页
This article proposes a modeling method for C/C-ZrC composite materials.According to the superposition of Gaussian random field,the original gray model is obtained,and the threshold segmentation method is used to gene... This article proposes a modeling method for C/C-ZrC composite materials.According to the superposition of Gaussian random field,the original gray model is obtained,and the threshold segmentation method is used to generate the C-ZrC inclusion model.Finally,the fiber structure is added to construct the microstructure of the three-phase plain weave composite.The reconstructed inclusions can meet the randomness of the shape and have a uniform distribution.Using an algorithm based on asymptotic homogenization and finite element method,the equivalent thermal conductivity prediction of the microstructure finite element model was carried out,and the influence of component volume fraction on material thermal properties was explored.The sensitivity of model parameters was studied,including the size,mesh sensitivity,Gaussian complexity,and correlation length of the RVE model,and the optimal calculation model was selected.The results indicate that the volume fraction of the inclusion phase has a significant impact on the equivalent thermal conductivity of the material.As the volume fraction of carbon fiber and ZrC increases,the equivalent thermal conductivity tensor gradually decreases.This model can be used to explore the impact of materialmicrostructure on the results,and numerical simulations have studied the relationship between structure and performance,providing the possibility of designing microstructure based on performance. 展开更多
关键词 3D reconstruction randomheterogeneous media microstructure asymptotic homogenization effective properties
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THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE
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作者 东瑜昕 林和子 陆琳根 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期189-194,共6页
In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality... In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature. 展开更多
关键词 asymptotically nonnegative sectional curvature logarithmic Sobolev inequality ABP method
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THE ASYMPTOTIC BEHAVIOR AND OSCILLATION FOR A CLASS OF THIRD-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS
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作者 黄先勇 邓勋环 王其如 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期925-946,共22页
In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existe... In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results. 展开更多
关键词 nonlinear delay dynamic equations NONOSCILLATION asymptotic behavior Philostype oscillation criteria generalized Riccati transformation
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Enhanced Differentiable Architecture Search Based on Asymptotic Regularization
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作者 Cong Jin Jinjie Huang +1 位作者 Yuanjian Chen Yuqing Gong 《Computers, Materials & Continua》 SCIE EI 2024年第2期1547-1568,共22页
In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search spa... In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search space with different complexity according to various operations.Meanwhile rationalizing the search strategies to explore the well-defined search space will further improve the speed and efficiency of architecture search.With this in mind,we propose a faster and more efficient differentiable architecture search method,AllegroNAS.Firstly,we introduce a more efficient search space enriched by the introduction of two redefined convolution modules.Secondly,we utilize a more efficient architectural parameter regularization method,mitigating the overfitting problem during the search process and reducing the error brought about by gradient approximation.Meanwhile,we introduce a natural exponential cosine annealing method to make the learning rate of the neural network training process more suitable for the search procedure.Moreover,group convolution and data augmentation are employed to reduce the computational cost.Finally,through extensive experiments on several public datasets,we demonstrate that our method can more swiftly search for better-performing neural network architectures in a more efficient search space,thus validating the effectiveness of our approach. 展开更多
关键词 Differentiable architecture search allegro search space asymptotic regularization natural exponential cosine annealing
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An Arbitrarily High Order and Asymptotic Preserving Kinetic Scheme in Compressible Fluid Dynamic
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作者 Remi Abgrall Fatemeh Nassajian Mojarrad 《Communications on Applied Mathematics and Computation》 EI 2024年第2期963-991,共29页
We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics,both in time and space,which include the relaxation schemes by Jin and Xin.These methods can use the... We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics,both in time and space,which include the relaxation schemes by Jin and Xin.These methods can use the CFL number larger or equal to unity on regular Cartesian meshes for the multi-dimensional case.These kinetic models depend on a small parameter that can be seen as a"Knudsen"number.The method is asymptotic preserving in this Knudsen number.Also,the computational costs of the method are of the same order of a fully explicit scheme.This work is the extension of Abgrall et al.(2022)[3]to multidimensional systems.We have assessed our method on several problems for two-dimensional scalar problems and Euler equations and the scheme has proven to be robust and to achieve the theoretically predicted high order of accuracy on smooth solutions. 展开更多
关键词 Kinetic scheme Compressible fluid dynamics High order methods Explicit schemes asymptotic preserving Defect correction method
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A general result on precise asymptotics for linear processes of positively associated sequences 被引量:10
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作者 TAN Xi-li YANG Xiao-yun 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第2期190-196,共7页
Let {εt; t ∈ Z^+} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2+1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^+} is a sequence of real numbers s... Let {εt; t ∈ Z^+} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2+1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^+} is a sequence of real numbers satisfying ∑j=0^∞|aj|〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E|ε1|^2+δ′〈 for some δ′〉0 and μ(n)=O(n^-ρ) for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}. 展开更多
关键词 PA sequence linear process general law precise asymptotics.
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PRECISE ASYMPTOTICS IN THE BAUM-KATZ AND DAVIS LAW OF LARGE NUMBERS FOR POSITIVELY ASSOCIATED SEQUENCES 被引量:10
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作者 MiChenjing 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2005年第2期197-204,共8页
Let {X_i;i≥1} be a strictly stationary sequence of associated random variables with mean zero and let σ2=EX2_1+2∞_~j=2 EX_1X_j with 0<σ2<∞.Set S_n=n_~i=1 X_i,the precise asymptotics for _~n≥1 n^rp-2 P(|S_n... Let {X_i;i≥1} be a strictly stationary sequence of associated random variables with mean zero and let σ2=EX2_1+2∞_~j=2 EX_1X_j with 0<σ2<∞.Set S_n=n_~i=1 X_i,the precise asymptotics for _~n≥1 n^rp-2 P(|S_n|≥εn^1p ),_~n≥1 1nP(|S_n|≥εn^1p ) and _~n≥1 (log n)δnP(|S_n|≥εnlogn) as ε0 are established. 展开更多
关键词 complete convergence associated random variables Baum-Katz law precise asymptotics.
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ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS VIA THE RIEMANN-HILBERT APPROACH 被引量:2
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作者 R.Wong 赵育求 《Acta Mathematica Scientia》 SCIE CSCD 2009年第4期1005-1034,共30页
In this survey we give a brief introduction to orthogonal polynomials, including a short review of classical asymptotic methods. Then we turn to a discussion of the Riemann-Hilbert formulation of orthogonal polynomial... In this survey we give a brief introduction to orthogonal polynomials, including a short review of classical asymptotic methods. Then we turn to a discussion of the Riemann-Hilbert formulation of orthogonal polynomials, and the Delft & Zhou method of steepest descent. We illustrate this new approach, and a modified version, with the Hermite polynomials. Other recent progress of this method is also mentioned, including applications to discrete orthogonal polynomials, orthogonal polynomials on curves, multiple orthogonal polynomials, and certain orthogonal polynomials with singular behavior. 展开更多
关键词 orthogonal polynomials asymptotic methods Riemann-Hilbert approach
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PRECISE ASYMPTOTICS IN SELF-NORMALIZED SUMS OF ITERATED LOGARITHM FOR MULTIDIMENSIONALLY INDEXED RANDOM VARIABLES 被引量:3
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作者 Jiang Chaowei Yang Xiaorong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2007年第1期87-94,共8页
In the case of Z+^d(d ≥ 2)-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k∈ Z+^d} i.i.d, random variables with mean 0, Sn =∑k≤nXk and Vn^2 = ∑j≤nXj^2, the precise asymptotics for ∑... In the case of Z+^d(d ≥ 2)-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k∈ Z+^d} i.i.d, random variables with mean 0, Sn =∑k≤nXk and Vn^2 = ∑j≤nXj^2, the precise asymptotics for ∑n1/|n|(log|n|dP(|Sn/Vn|≥ε√log log|n|) and ∑n(logn|)b/|n|(log|n|)^d-1P(|Sn/Vn|≥ε√log n),as ε↓0,is established. 展开更多
关键词 multidimensionally indexed random variable precise asymptotics self-normalized sum Davislaw of large numbers law of iterated logarithm.
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HAZARD REGRESSION WITH PENALIZED SPLINE:THE SMOOTHING PARAMETER CHOICE AND ASYMPTOTICS 被引量:1
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作者 童行伟 胡涛 崔恒建 《Acta Mathematica Scientia》 SCIE CSCD 2010年第5期1759-1768,共10页
In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establi... In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure. 展开更多
关键词 proportional hazards penalized spline smoothing parameter choice asymptotic normality
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A Novel Long-Time Coherent Integration Method for Moving Target Detection 被引量:2
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作者 Xia Bai Yan Wang +1 位作者 Juan Zhao Ran Tao 《Journal of Beijing Institute of Technology》 EI CAS 2021年第4期340-351,共12页
Long-time coherent integration(LTCI)can remarkably improve the detection ability of radar for moving target.To increase the processing efficiency,this paper proposes a novel LTCI method based on segment time reversing... Long-time coherent integration(LTCI)can remarkably improve the detection ability of radar for moving target.To increase the processing efficiency,this paper proposes a novel LTCI method based on segment time reversing transform(STRT)and chirp z-transform(CZT).In this method,STRT operation is first presented to estimate the Doppler ambiguity factor,and keystone transform(KT)is used to correct the whole range migration(RM).Then,CZT and non-uniform fast Fourier transform(NUFFT)are used to estimate the parameters as well as correct the second and third order Doppler frequency migration(DFM).Compared with the existing methods,the proposed method can achieve RM correction and DFM correction without repetitive operation.The effectiveness of the proposed method is validated by both simulated and real data. 展开更多
关键词 long-time coherent integration range migration Doppler frequency migration
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