Direct solution for fixed source location using well-posed TDOA and FDOA measurements

Based on the time differences of arrival(TDOA) and frequency differences of arrival(FDOA) measurements of the given planar stationary radiation source, the joint TDOA/FDOA location algorithm which solves the location of the target directly is proposed. Compared with weighted least squares(WLS) methods,the proposed algorithm is also suitable for well-posed conditions,and gets rid of the dependence on the constraints of Earth's surface. First of all, the solution formulas are expressed by the radial range. Then substitute it into the equation of the radial range to figure out the radial range between the target and the reference station. Finally use the solution expression of the target location to estimate the location of the target accurately. The proposed algorithm solves the problem that WLS methods have a large positioning error when the number of observation stations is not over-determined. Simulation results show the effectiveness of the proposed algorithm, including effectively increasing the positioning accuracy and reducing the number of observatories.

Well-posed analysis for a class of Helmholtz equation with periodic coefficients

The scattering theory in periodic structures has many applications in modern microoptics and industry. Periodic structures are often referred to as diffraction gratings. In this paper we consider a planar dielectric-layer modulated grating problem. The diffraction problem may be modeled by a Helmholtz equation with periodic coefficients. Results on existence and uniqueness of the solution for the diffraction problem are obtained by variational method and integral equation method, respectively. At the end of the paper, we also discuss the Born approximation to the solution of an equivalent integral equation.

The Well-Posed Operators with Their Spectra in Lpw-Spaces

In this paper, we have considered the general ordinary quasi-differential operators generated by a general quasi-differential expression τp,q in Lpw-spaces of order n with complex coefficients and its formal adjoint τ+q',p' in Lpw-spaces for arbitrary p,q∈[1,∞). We have proved in the case of one singular end-point that all well-posed extensions of the minimal operator T0 (τp,q) generated by such expression τp,q and their formal adjoint on the interval [a,b) with maximal deficiency indices have resolvents which are Hilbert-Schmidt integral operators and consequently have a wholly discrete spectrum. This implies that all the regularly solvable operators have all the standard essential spectra to be empty. Also, a number of results concerning the location of the point spectra and regularity fields of the operators generated by such expressions can be obtained. Some of these results are extensions or generalizations of those in the symmetric case, while others are new.

THE SEMI-DISCREIXTE METHOD FOR SOLVING HIGH-DIMENSION WAVE EQUATION

The article gives a semi-discrete method for solving high-dimension wave equationBy the method, high-dimension wave equation is converted by, means of diseretizationinto I-D wave equation system which is well-posed. The convergence of the semidijcrete method is given. The numerical calculating resulis show that the speed of convergence is high.

THE STUDY OF RETRIEVAL THEORY AND METHODS FROM SATELLITE REMOTE SENSING FOR METEOROLOGICAL PARAMETERS OVER EASTERN ASIA-PARTI:ISPRM AND SRRM

A review of ten-year's practice in developing the improved simultaneous physical retrieval method(ISPRM)is given in the hope that some creative ideas can be drawn from it.The improvement upon the SPRM is associated with the under-determinedness of this ill-posed inverse problem.In our experiment,the precondition is observed that prior information must be independent of the satellite measurements.The well-posed retrieval theory has told us that the forward process is fundamental for the retrieval,and it is the bridge between the input of satellite radiance and the output of retrievals.In order to obtain a better result from the forward process. the full advantage of every prior information available must be taken.It is necessary to turn the ill- posed inverse problem into the well-posed one.Then by using the Ridge regression or Bayes algorithm to find the optimal combination among the first guess,the theoretical analogue information and the satellite observations,the impact of the under-determinedness of this inverse problem on the numerical solution is minimized.

NONHOMOGENEOUS BOUNDARY VALUE PROBLEMS FOR THE KORTEWEG-DE VRIES EQUATION ON A BOUNDED DOMAIN

This paper studies an initial-boundary-value problem (IBVP) of the Korteweg-de Vriesequation posed on a finite interval with general nonhomogeneous boundary conditions.Using thestrong Kato smoothing property of the associated linear problem,the IBVP is shown to be locallywell-posed in the space H^s(0,1) for any s≥0 via the contraction mapping principle.

Some problems of linear differential equations on abstract spaces and unbounded perturbations of linear operator semigroup

This paper is a survey for development of linear distributed parameter system.At first we point out some questions existing in current study of control theory for the L^(p)linear system with an unbounded control operator and an unbounded observation operator,such as stabilization problem and observer theory that are closely relevant to state feedback operator.After then we survey briefly some results on relevant problems that are related to solvability of linear differential equations in general Banach space and semigroup perturbations.As a principle,we propose a concept of admissible state feedback operator for system(A,B).Finally we give an existence result of admissible state feedback operators,including semigroup generation and the equivalent conditions of admissibility of state feedback operators,for an L^(p)well-posed system.

An Energy Regularization Method for the Backward Diffusion Problem and its Applications to Image Deblurring

For the backward diffusion equation,a stable discrete energy regularization algorithm is proposed.Existence and uniqueness of the numerical solution are given.Moreover,the error between the solution of the given backward diffusion equation and the numerical solution via the regularization method can be estimated.Some numerical experiments illustrate the efficiency of the method,and its application in image deblurring.

Local Solvability of Cauchy Problem for Kaup-Kupershmidt Equation

This paper deals with the local solvability of initial value problem for Kaup-Kupershmidt equations. Indeed, using Bourgain method, we prove that the Cauchy problem of Kaup-Kupershmidt equation is local well-posed in H8 whenever s 〉 9/8, which improves the former results in [5].