Shaping filter representation of nonstationary colored noise

The problem of determining a shaping filter for nonstationary colored noise is considered. The shaping filter transforms white noise into a possibly nonstationary random process (having no white noise component) with a specified covariance function. A set of conditions to be satisfied by the covariance function leads to the determination of a shaping filter. The shaping filter coefficients are simply related to the solution of a matrix Riccati equation. In order to formulate the Riccati equation, basic results concerning the mean-square differentiability of a random process are developed. If the Riccati equation can not be defined, an autonomous (zero-input) shaping filter may be easily determined.     

Asymptotic expressions for the Fredholm determinant for state-variable covariance functions (Corresp.)

A new asymptotic expression for the Fredholm determinant is derived for stationary separable covariance functions. Solutions are given for the cases of known state-variable model and known separable covariance. The expression is obtained from the solution of a Riccati equation.     

On discrete-time H/sub /spl infin// fixed-lag smoothing

The H/sub /spl infin// fixed-lag smoothing problem for discrete-time linear systems is considered. It is well known that such a problem can be reformulated as a filtering problem for a suitable augmented system. However, in order to check the solvability of the smoothing problem and compute the relevant gains, one must solve a Riccati equation involving the augmented system matrices, which is an approach that may be inefficient, especially for long lags. In this paper, efficient algorithms are worked out that permit checking of solvability and implementation of the smoother, relying only on the solution of the H/sub /spl infin// filtering Riccati equation. In particular, this provides a fast method to compute the minimum lag guaranteeing a desired attenuation level.     

An iterative solution of fredholm integral equations of the first kind

A formal solution is obtained for the Fredholm integral equation of the first kind. The unknown function is represented by a completely general Fourier series, and the Fourier coefficients are obtained by an iterative process. The formulation also yields an easily obtained approximate solution, as well as the estimate of its accuracy.     

One-dimensional profile inversion of a half-space over a two-partimpedance ground

A method which permits one to reveal the one-dimensional (1-D) electromagnetic profile of a half-space bounded by a two-part impedance ground is established. The method reduces the problem to the solution of two functional equations. One of these equations is solved exactly by reducing it to a Riemann-Hilbert problem while the other is reduced under the Born approximation to a Fredholm equation of the first kind whose kernel involves the solution to the first equation. Since this latter constitutes an ill-posed problem, its regularized solution, in the sense of Tikhonov, is given. An illustrative application shows the applicability and the accuracy of the theory. The functional equations are valid also when the impedance of the ground varies in an arbitrary manner. The theory can be applied to a quick determination of the constitutive electromagnetic parameters of the atmosphere over a nonhomogeneous impedance ground     

电磁逆散射非相关照射法的普遍公式

由第一类Fredholm积分方程所描述的电磁逆散射问题是非适定问题。通过一系列非相关照射,有可能获得散射体的更多信息,从而改善解的非适定性。本文基于求解逆散射问题的非相关原理,推导了适于散射体在各种正交基下展开,求解电磁逆散射的普遍公式,并对所建立的参数反演公式解的唯一性进行了证明。     

One-sided recursive filters for two-dimensional random fields (Corresp.)

The one-sided (or line-by-line) recursive filtering problem for a two-parameter Gaussian random signal in additive white Gaussian noise is considered. For a reasonably large class of models for the signal dynamics, both the filtering equation and the generalized Riccati equation explicitly obtained. As an example, the Riccati equation is solved to give the filter gain in a time-in-variant case and is compared with the infinite-time limiting solution to the Wiener filter solution obtained by spectral factorization techniques.     

Efficient method of solving the discrete Riccati equation when the plant matrix contains a noise-shaping filter

The solution of the optimal linear discrete control problem can, in many practical cases, be computed with increased efficiency by decomposition of the discrete Riccati equation.     

Solution stability of iterative schemes utilizing the discreteFourier transform [EM scattering]

The Fredholm integral equation of the first kind can be solved numerically using iterative schemes which minimize the integral square error. When the kernal is of the convolution type, the discrete Fourier transform (DFT) can be used when evaluating the operator equation in the iterative schemes. However, the DFT imposes an artificial periodicity, thus changing the nature of the problem. The effect of this on the solution has been studied and convergence investigated by comparison with a method of moments solution. A proposed method of avoiding the periodicity problem has been studied. The effect of introducing losses in the medium surrounding the scatterer has been investigated; provided losses are low, there is little effect on the solution     

A new well-conditioned Integral formulation for Maxwell equations in three dimensions

We present a new boundary integral equation dedicated to the solution of the boundary problem of a perfectly electrically conducting surface for the harmonic Maxwell equations in unbounded domains. Any solution of the harmonic Maxwell equations is represented as the electromagnetic field generated by a combination of electric and magnetic potentials. These potentials are those appearing in the classical combined field integral equation (CFIE), but their coupling is realized by an operator Y/spl tilde//sup +/ instead of a coefficient. Therefore, the integral equation obtained can be viewed as a generalization of the CFIE. In this paper, we propose an explicit construction of the coupling operator Y/spl tilde//sup +/ which is designed to approximate the exterior admittance operator of the scattering obstacle. A local approximation by the admittance operator of the tangential plane seems to be relevant thanks to the localization effects related to high-frequency phenomena. The provided numerical simulations show that this formulation leads to linear systems that are better conditioned compared to more classical integral equations, which speeds up the resolution when solved with iterative techniques.     

Analysis of finite arrays-a new approach

A novel method for the analysis of finite arrays is presented. The method is based on a global array concept where the array problem (for single-mode elements) is reduced to a solution of a single Fredholm integral equation of the second kind. This formulation offers several types of solutions (not all explored yet) with illuminating results. The approximate solution of this integral equation, for example, yields finite array characteristics in terms of equivalent infinite array scattering parameters and mutual admittances. The method is general, i.e., applicable to any element-type and periodic array geometry. Presently, the method applies to single-mode elements (one unknown per element), however, it can be extended to a multimode analysis     

On the Scattering of Electromagnetic Waves by Periodic Rough Dielectric Surfaces: A BOA Solution

A new approach for the scattering of electromagnetic (EM) waves from periodic dielectric rough surfaces is addressed. The method is an extension of the buried object approach (BOA), which is developed for rough surfaces of infinite extend, to the present problem. The BOA allows to model the original problem as the scattering of EM waves from cylindrical objects located in a two-half-space medium with planar interface. Then, the problem is reduced to the solution of a Fredholm integral equation of second kind through the periodic Green's function of two-half-space medium. The periodic Green's function of two-half-space medium is calculated via the Floquet mode expansion, whose numerical evaluation can be accelerated by using effective methods. The method can also be used to solve the scattering problems of rough surfaces of infinite extend and having a localized roughness. Numerical simulations show that the method yields effective and accurate results for surfaces of arbitrary variation.      

The variational method and the method of moments in the problem of plane wave scattering by a rectangular cavity in an impedance screen

The problem of electromagnetic plane wave diffraction by a rectangular cavity in an impedance screen is solved. The problem is reduced to solution of a Fredholm integral equation for the field function in the aperture. The equation has a symmetric kernel. Expressions for the angular distribution of the scattered far-field are obtained by the method of moments and the variational method. Numerical results are analyzed and compared.     

Approximate Kalman filtering for multiply perturbed systems

An approximate Kalman filtering algorithm for multiply perturbed systems is proposed based on an approximate solution to the Riccati equation. This new algorithm not only greatly reduces the computational complexity, but also lends itself to solving a parameter optimization problem.     

A spectral domain method for remotely probing stratified media

The problem of remotely probing a stratified, lossless, dielectric medium is formulated using the spectral domain method of probing. The response of the medium to a spectrum of plane waves incident at various angles is used to invert the unknown profile. For TE polarization, the electric field satisfies a Helmholtz equation. The inverse problem is solved by means of a new representation for the wave function. The principal step in this inversion is solving a second kind Fredholm equation which is very amenable to numerical computations. Several examples are presented including some which indicate that the method can be used with experimentally obtained data. When the fields exhibit a surface wave behavior, a unique inversion can be obtained only if information about the magnetic field is also available. In this case, the inversion is accomplished by a two-step procedure which employs a formula of Jost and Kohn. Some examples are presented, and an approach which greatly shortens the computations without greatly deteriorating the results is discussed.     

H∞ filtering of 2-D discrete systems

This paper deals with H_∞ filtering of two-dimensional (2-D) linear discrete systems described by a 2-D local state-space (LSS) Fornasini-Marchesini (1978) second model. Several versions of the bounded real lemma of the 2-D discrete systems are established. The 2-D bounded real lemma allows us to solve the finite horizon and infinite horizon H_∞ filtering problems using a Riccati difference equation or a Riccati inequality approach. Further a solution to the infinite horizon H_∞ filtering problem based on a linear matrix inequality (LMI) approach is developed. Our results extend existing work for one-dimensional (1-D) systems to the 2-D case and give a state-space solution to the bounded realness of 2-D discrete systems as well as 2-D H_∞ filtering for the first time. Numerical examples are given to demonstrate the Riccati difference equation approach to the 2-D finite horizon H_∞ filtering problem and the LMI approach to the 2-D infinite horizon H_∞ filtering problem     

On the effects of boundary conditions at the cathode on the equations of steady space-charge flow

The steady, zero-temperature, space-charge flow problem has a unique solution if formulated in the differential equation form. However, if the differential equations are approximated by a difference equation formulation, it is shown that the solution is no longer unique. The effect is demonstrated by the example of the Langmuir planar diode. It is proved theoretically for the planar diode, and demonstrated numerically for a two-dimensional example, that the ambiguity in the perveance of a gun due to this effect is of orderh/d; herehis the mesh size of the difference mesh, anddis the mean length of the particle trajectories.