on a class of degenerate parabolic equations with dynamic boundary conditions we consider a quasi linear parabolic possibly degenerate equation with nonlinear dynamic boundary conditions the corresponding class of initial and boundary value problems has already been studied previously proving well posedness of weak solutions and the existence of the global attractor assuming that the nonlinearities are subcritical to a given exponent the goal of this article is to show that the previous analysis can be redone for supercritical nonlinearities by proving an additional l estimate on the solutions in particular we derive new conditions which reflect an exact balance between the internal and the boundary mechanisms involved even when both the nonlinear sources contribute in opposite directions then we show how to construct a trajectory attractor for the weak solutions of the associated parabolic system and prove that any solution belonging to the attractor is bounded which implies uniqueness finally we also prove for the semilinear reaction diffusion equation with nonlinear dynamic boundary conditions that the fractal dimension of the global attractor is of the order n 1 as diffusion 0 in any space dimension n 2 improving some recent results in gal 2012 23

a posteriori error analysis for stabilised finite element approximations of transport problems we develop the a posteriori error analysis of stabilised finite element approximations to linear transport problems via duality arguments two alternative dual problems are considered one is based on the formal adjoint of the hyperbolic differential operator the other on the transposition of the bilinear form for the stabilised finite element method we show both analytically and through numerical experiments that the second approach is superior in the sense that it leads to sharper a posteriori error bounds and more economical adaptively refined meshes

error estimation and adaptation for functional outputs in time dependent flow problems the paper presents an adjoint based approach for determining global error in the time domain that is relevant to functional outputs from unsteady flow simulations the algorithm is derived for the unsteady euler equations that are discretized for second order accuracy in both space and time and takes into account the effect of dynamic meshes in addition to error due to temporal resolution the formulation also takes into account algebraic error arising from partial convergence of the governing equations at each implicit time step the resulting error distributions are then used to drive adaptation of the temporal resolution and the convergence tolerances for the governing equations at each time step the method is demonstrated in the context of both time integrated and instantaneous functionals and the results are compared against traditional adaptation methods

on the accuracy and resolvability of vector parameter estimates in this paper we address the problem of fundamental limitations on resolution in deterministic parameters estimation we introduce a definition of resolvability based on probability and incorporating a requirement for accuracy unlike most existing definitions indeed in many application the key problem is to obtain distributions of estimates that are not only distinguishable but also accurate and compliant with a required precision we exemplify the proposed definition with estimators that produce normal estimates as in the conditional model for which the gaussianity and efficiency of maximum likelihood estimators mles in the asymptotic region of operation in terms of signal to noise ratio and or in large number of snapshots is well established even for a single snapshot in order to measure the convergence in distribution we derive a simple test allowing to check whether the conditional mles operate in the asymptotic region of operation last we discuss the resolution of two complex exponentials with closely spaced frequencies and compare the results obtained with the ones provided by the various statistical resolution limit released in the open literature

a parametric estimation approach to instantaneous spectral imaging spectral imaging the simultaneous imaging and spectroscopy of a radiating scene is a fundamental diagnostic technique in the physical sciences with widespread application due to the intrinsic limitation of two dimensional 2d detectors in capturing inherently three dimensional 3d data spectral imaging techniques conventionally rely on a spatial or spectral scanning process which renders them unsuitable for dynamic scenes in this paper we present a nonscanning instantaneous spectral imaging technique that estimates the physical parameters of interest by combining measurements with a parametric model and solving the resultant inverse problem computationally the associated inverse problem which can be viewed as a multiframe semiblind deblurring problem with shift variant blur is formulated as a maximum a posteriori map estimation problem since in many such experiments prior statistical knowledge of the physical parameters can be well estimated subsequently an efficient dynamic programming algorithm is developed to find the global optimum of the nonconvex map problem finally the algorithm and the effectiveness of the spectral imaging technique are illustrated for an application in solar spectral imaging numerical simulation results indicate that the physical parameters can be estimated with the same order of accuracy as state of the art slit spectroscopy but with the added benefit of an instantaneous 2d field of view this technique will be particularly useful for studying the spectra of dynamic scenes encountered in space remote sensing

upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation abstract for a smooth bounded domain r n n 3 and e a real parameter consider the hyperbolic equation eu tt u t u u g in with dirichlet boundary conditions under certain conditions on this equation has a compact attractor a e in h 0 1 l 2 for e 0 the parabolic equation also has a compact attractor which can be naturally embedded into a compact set a 0 in h 0 1 l 2 it is shown that for any neighborhood u of a 0 the set a e u for e small

nonmatrix cramer rao bound expressions for high resolution frequency estimators analytical expressions are derived for the cramer rao cr lower bound on the variance of frequency estimates for the two signal time series data models consisting of either one real sinusoid or two complex sinusoids in white gaussian noise the expressions give the bound in terms of the signal to noise ratio snr the number n of data samples and a function dependent on the frequency separation and the initial phase difference between the two signal components of each model the bounds are examined as the phase difference is varied and the largest and smallest bound expressions and the corresponding critical values of the phase difference are obtained the exact expressions are analyzed for the case of small frequency separations spl delta spl omega it is found that the largest bound is proportional to n spl middot spl delta spl omega sup 4 n sup 3 spl middot snr and that the smallest bound is proportional to n spl middot spl delta spl omega sup 2 n sup 3 spl middot snr for small spl delta spl omega examples indicate that the small spl delta spl omega results closely approximate the exact ones whenever the frequency separation is smaller than the fourier resolution limit based on the asymptotic results it is found that the threshold snr at which an unbiased estimator can resolve the two signal frequencies is at least proportional to n spl middot spl delta spl omega sup 6 n for the worst phase difference case and to n spl middot spl delta spl omega sup 4 n for the best phase difference case for small spl delta spl omega the results are applicable to the general case of sampling where the samples are taken at arbitrary instants

on the resolvability of normally distributed vector parameter estimates this paper presents a metric useful in analyzing the resolution of multidimensional vector parameter estimators that produce normal estimates this metric is based on the distance between ellipsoidal confidence regions about each of the parameters when the ellipsoids are disjoint the parameters are deemed resolvable this paper presents a method for finding the noise level at which all of the ellipsoids are disjoint but at least two are tangent this is deemed the resolution threshold noise level the underlying mathematical result treats the problem of finding a dilation noise level at which two coupled quadratic equations have a unique solution

compact cramer rao bound expressions on directional covariance for df of sources with unknown constant polarizations the cramer rao bound b sub c on directional covariance routinely is used as a yardstick for assessing the performance of candidate direction finding df algorithms stoica and nehorai 1989 1990 and yau and bresler see ibid vol 40 no 5 p 1226 1992 introduced compact formulae for b sub c applicable to df scenarios in which sources transmit signals having known polarizations these formulae have proven quite useful in that they facilitate identification of performance limitations that otherwise would be difficult or impossible to obtain this article presents compact formulae for b sub c for df scenarios in which n uncorrelated sources transmit signals having constant but unknown polarizations also it is shown that these formulae elucidate achievable df performance for scenarios involving partially correlated sources

pde constrained optimization with error estimation and control the paper describes an algorithm for pde constrained optimization that controls numerical errors using error estimates and grid adaptation during the optimization process a key aspect of the algorithm is the use of adjoint variables to estimate errors in the first order optimality conditions multilevel optimization is used to drive the optimality conditions and their estimated errors below a specified tolerance the error estimate requires two additional adjoint solutions but only at the beginning and end of each optimization cycle moreover the adjoint systems can be formed and solved with limited additional infrastructure beyond that found in typical pde constrained optimization algorithms the approach is general and can accommodate both reduced space and full space formulations of the optimization problem the algorithm is illustrated using the inverse design of a nozzle constrained by the quasi one dimensional euler equations

on lower bounds for nonstandard deterministic estimation we consider deterministic parameter estimation and the situation where the probability density function p d f parameterized by unknown deterministic parameters results from the marginalization of a joint p d f depending on random variables as well unfortunately in the general case this marginalization is mathematically intractable which prevents from using the known standard deterministic lower bounds lbs on the mean squared error mse actually the general case can be tackled by embedding the initial observation space in a hybrid one where any standard lb can be transformed into a modified one fitted to nonstandard deterministic estimation at the expense of tightness however furthermore these modified lbs mlbs appears to include the submatrix of hybrid lbs which is an lb for the deterministic parameters moreover since in the nonstandard estimation maximum likelihood estimators mles can be no longer derived suboptimal nonstandard mles nsmles are proposed as being a substitute we show that any standard lb on the mse of mles has a nonstandard version lower bounding the mse of nsmles we provide an analysis of the relative performance of the nsmles as well as a comparison with the mlbs for a large class of estimation problems last the general approach introduced is exemplified among other things with a new look at the well known gaussian complex observation models

performance analysis of the approximate dynamic programming algorithm for parameter estimation of superimposed signals we consider the classical problem of fitting a model composed of multiple superimposed signals to noisy data using the criteria of maximum likelihood ml or subspace fitting jointly termed generalized subspace fitting gsf we analyze a previously proposed approximate dynamic programming algorithm adp which provides a computationally efficient solution to the associated multidimensional multimodal optimization problem we quantify the error introduced by the approximations in adp and deviations from the key local interaction signal model lismo modeling assumption in two ways first we upper bound the difference between the exact minimum of the gsf criterion and its value at the adp estimate and compare the adp with gsf estimates obtained by exhaustive multidimensional search on a fine lattice second motivated by the similar accuracy bounds we use perturbation analysis to derive approximate expressions for the mse of the adp estimates these various results provide for the first time an effective tool to predict the performance of the adp algorithm for various signal models at nonasymptotic conditions of interest in practical applications in particular they demonstrate that for the classical problems of sinusoid retrieval and array processing adp performs comparably to exact but expensive maximum likelihood ml over a wide range of signal to noise ratios snrs and is therefore an attractive algorithm

optimum shape design for unsteady flows with time accurate continuous and discrete adjoint methods this paper presents an adjoint method for the optimal control of unsteady flows the goal is to develop the continuous and discrete unsteady adjoint equations and their corresponding boundary conditions for the time accurate method first this paper presents the complete formulation of the time dependent optimal design problem second we present the time accurate unsteady continuous and discrete adjoint equations third we present results that demonstrate the application of the theory to a two dimensional oscillating airfoil the results are compared with a multipoint approach to illustrate the added benefit of performing full unsteady optimization

a compact cramer rao bound expression for parametric estimation of superimposed signals the problem of parameter estimation of superimposed signals in white gaussian noise is considered closed form expressions of the cramer rao bound for real or complex signals with vector parameters are derived extending recent results by p stoica and a nehorai 1989

maximum likelihood parameter estimation of superimposed signals by dynamic programming the problem of fitting a model composed of a number of superimposed signals to noisy data using the maximum likelihood criterion is considered it is shown using the cramer rao bound for the estimation accuracy that in many instances useful models for the composite signal can be restricted without loss of generality to component signals that directly interact only with one or two of their closest neighbors in parameter space it is shown that for such models the global extremum of the criterion can be found efficiently by dynamic programming the computation requirements are linear in the number of signals rather than exponential as in the case of exhaustive search the technique applies for arbitrary sampling of the signals the dynamic programming method is easily adapted to determining the number of signals as well as is demonstrated using the minimum description length principle computer simulation results are given for several examples

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

efficient mixed spectrum estimation with applications to target feature extraction we present a decoupled parameter estimation dpe algorithm for estimating sinusoidal parameters from both 1 d and 2 d data sequences corrupted by autoregressive ar noise in the first step of the dpe algorithm we use a relaxation relax algorithm that requires simple fast fourier transforms ffts to obtain the estimates of the sinusoidal parameters we describe how the relax algorithm may be used to extract radar target features from both 1 d and 2 d data sequences in the second step of the dpe algorithm a linear least squares approach is used to estimate the ar noise parameters the dpe algorithm is both conceptually and computationally simple the algorithm not only provides excellent estimation performance under the model assumptions in which case the estimates obtained with the dpe algorithm are asymptotically statistically efficient but is also robust to mismodeling errors

joint estimation and correction of geometric distortions for epi functional mri using harmonic retrieval magnetic resonance imaging mri uses applied spatial variations in the magnetic field to encode spatial position therefore nonuniformities in the main magnetic field can cause image distortions in order to correct the image distortions it is desirable to simultaneously acquire data with a field map in registration we propose a joint estimation je framework with a fast noniterative approach using harmonic retrieval hr methods combined with a multi echo echo planar imaging epi acquisition the connection with hr establishes an elegant framework to solve the je problem through a sequence of 1 d hr problems in which efficient solutions are available we also derive the condition on the smoothness of the field map in order for hr techniques to recover the image with high signal to noise ratio compared to other dynamic field mapping methods this method is not constrained by the absolute level of the field inhomogeneity over the slice but relies on a generous pixel to pixel smoothness moreover this method can recover image field map and t2 map simultaneously

global attractors for singular perturbations of the cahn hilliard equations abstract we consider the singular perturbations of two boundary value problems concerning respectively the viscous and the nonviscous cahn hilliard equations in one dimension of space we show that the dynamical systems generated by these two problems admit global attractors in the phase space h 0 1 0 h 1 0 and that these global attractors are at least upper semicontinuous with respect to the vanishing of the perturbation parameter

continuous families of exponential attractors for singularly perturbed equations with memory for a family of semigroups s epsilon t h epsilon h epsilon depending on a perturbation parameter epsilon is an element of 0 1 where the perturbation is allowed to become singular at epsilon 0 we establish a general theorem on the existence of exponential attractors epsilon epsilon satisfying a suitable holder continuity property with respect to the symmetric hausdorff distance at every epsilon is an element of 0 1 the result is applied to the abstract evolution equations with memorypartial derivative t x t integral infinity 0 k epsilon s b 0 x t s ds b1 x t 0 epsilon is an element of 0 1 where k epsilon s 1 epsilon k s epsilon is the resulting of a convex summable kernel k with unit mass such a family can be viewed as a memory perturbation of the equationpartial derivative t x t b 0 x t b 1 x t 0 formally obtained in the singular limit epsilon 0

statistical resolution limits and the complexified crame spl acute r rao bound array resolution limits and accuracy bounds on the multitude of signal parameters e g azimuth elevation doppler range cross range depth frequency chirp polarization amplitude phase etc estimated by array processing algorithms are essential tools in the evaluation of system performance the case in which the complex amplitudes of the signals are unknown is of particular practical interest a computationally efficient formulation of these bounds from the perspective of derivations and analysis is presented for the case of deterministic and unknown signal amplitudes a new derivation is given using the unknown complex signal parameters and their complex conjugates the new formula is readily applicable to obtaining either symbolic or numerical solutions to estimation bounds for a very wide class of problems encountered in adaptive sensor array processing this formula is shown to yield several of the standard crame spl acute r rao results for array processing along with new results of fundamental interest specifically a new closed form expression for the statistical resolution limit of an aperture for any asymptotically unbiased superresolution algorithm e g music esprit is provided the statistical resolution limit is defined as the source separation that equals its own crame spl acute r rao bound providing an algorithm independent bound on the resolution of any high resolution method it is shown that the statistical resolution limit of an array or coherent integration window is about 1 2 spl middot snr sup 1 4 relative to the fourier resolution limit of 2 spl pi n radians large number n of array elements that is the highest achievable resolution is proportional to the reciprocal of the fourth root of the signal to noise ratio snr in contrast to the square root snr sup 1 2 dependence of standard accuracy bounds these theoretical results are consistent with previously published bounds for specific superresolution algorithms derived by other methods it is also shown that the potential resolution improvement obtained by separating two collinear arrays synthetic ultra wideband each with a fixed aperture b wavelengths by m wavelengths assumed large is approximately m b sup 1 2 in contrast to the resolution improvement of m b for a full aperture exact closed form results for these problems with their asymptotic approximations are presented

a posteriori error bounds and global error control for approximation of ordinary differential equations the author analyzes a finite element method for the integration of initial value problems in ordinary differential equations general and contractive problems are treated and quasi optimal a priori and a posteriori error bounds obtained in each case in particular good results are obtained for a class of stiff dissipative problems these results are used to construct a rigorous and robust theory of global error control the author also derives an asymptotic error estimate that is used in a discussion of the behavior of the error in conclusion the properties of the error control are exhibited in a series of numerical experiments

superconvergent functional output for time dependent problems using finite differences on summation by parts form finite difference operators satisfying the summation by parts sbp rules can be used to obtain high order accurate energy stable schemes for time dependent partial differential equations when the boundary conditions are imposed weakly by the simultaneous approximation term sat in general an sbp sat discretization is accurate of order p 1 with an internal accuracy of 2p and a boundary accuracy of p despite this it is shown in this paper that any linear functional computed from the time dependent solution will be accurate of order 2p when the boundary terms are imposed in a stable and dual consistent way the method does not involve the solution of the dual equations and superconvergent functionals are obtained at no extra computational cost four representative model problems are analyzed in terms of convergence and errors and it is shown in a systematic way how to derive schemes which gives superconvergent functional outputs

a gtd based parametric model for radar scattering this paper presents a new approach to scattering center extraction based on a scattering model derived from the geometrical theory of diffraction gtd for stepped frequency measurements at high frequencies the model is better matched to the physical scattering process than the damped exponential model and conventional fourier analysis in addition to determining downrange distance energy and polarization the gtd based model extracts frequency dependent scattering information allowing partial identification of scattering center geometry we derive expressions for the cramer rao bound of this model using these expressions we analyze the behavior of the new model as a function of scatterer separation bandwidth number of data points and noise level additionally a maximum likelihood algorithm is developed for estimation of the model parameters we present estimation results using data measured on a compact range to validate the proposed modeling procedure

the stability of nonlinear least squares problems and the cramer rao bound a number of problems of interest in signal processing can be reduced to nonlinear parameter estimation problems the traditional approach to studying the stability of these estimation problems is to demonstrate finiteness of the cramer rao bound crb for a given noise distribution we review an alternate deterministic notion of stability for the associated nonlinear least squares nls problem from the realm of nonlinear programming i e that the global minimizer of the least squares problem exists and varies smoothly with the noise furthermore we show that under mild conditions identifiability of the parameters along with a finite crb for the case of gaussian noise is equivalent to the deterministic stability of the nls problem finally we demonstrate the application of our result which is general to the problems of multichannel blind deconvolution and sinusoid retrieval to generate new stability results for these problems with little additional effort

ziv zakai bounds on time delay estimation in unknown convolutive random channels using the ziv zakai bound zzb methodology we develop a bayesian mean square error bound on time delay estimation tde in convolutive random channels and compare it with time delay estimator performance and a crame r rao bound the channel is modeled as a tapped delay line whose taps are gaussian random variables that may be nonzero mean and correlated a model widely adopted in many applications such as wideband fading in a multipath channel the time delay has a uniform prior distribution a zzb is developed that incorporates the prior on the random time delay as well as the convolutive random gaussian channel and does not assume the receiver has knowledge of the channel realization the zzb provides good performance prediction for maximum a posteriori map time delay estimation tracking the low medium and high signal to noise ratio snr regimes the convolutive channel model includes important special cases such as narrowband gaussian channels corresponding to rayleigh rician fading wideband multipath channels with a power decay profile such as exponential decay and known channels we show that the associated crame r rao bound is tight only at high snr whereas the zzb predicts threshold behavior and tde breakdown as the snr decreases when compared to a zzb that assumes knowledge of the channel realization the zzb developed here provides a more realistic and tighter bound revealing the performance loss due to lack of channel knowledge the map estimator incorporates knowledge of the channel statistics and so performs much better than a maximum likelihood estimator that minimizes mean square error but does not use knowledge of the random channel statistics several examples illustrate the estimator and bound behaviors

adjoint sensitivity analysis for time dependent partial differential equations with adaptive mesh refinement a new adjoint sensitivity analysis approach is presented for time dependent partial differential equations with adaptive mesh refinement the new approach called adda combines the best features of both the adjoint of the discretization ad and discretization of the adjoint da approaches it removes the obstacles of applying ad to adaptive methods and in contrast to da requires for its use only a minimal amount of knowledge about the formulation of adjoint pdes and their boundary conditions the effectiveness and efficiency of adda are demonstrated for several numerical examples

a robust approach for high resolution frequency estimation a robust estimation method for frequencies of received signals is considered the influence function of a robust estimate is derived for the sinusoidal signals the variance of the robust estimate is also derived using the influence function it is found that the robust estimate attains the cramer rao lower bound crlb for the contaminated gaussian distribution it is of order o n sup 3 and is close to the crlb for the perfect gaussian distribution the authors introduce some basic definitions for the high resolution frequency estimation method and prove that the robust estimate has the high resolution property this property is also confirmed by numerical simulations

cramer rao bounds for 2 d target shape estimation in nonlinear inverse scattering problems with application to passive radar we present new methods for computing fundamental performance limits for two dimensional 2 d parametric shape estimation in nonlinear inverse scattering problems with an application to passive radar imaging we evaluate cramer rao lower bounds crb on shape estimation accuracy using the domain derivative technique from nonlinear inverse scattering theory the crb provides an unbeatable performance limit for any unbiased estimator and under fairly mild regularity conditions is asymptotically achieved by the maximum likelihood estimator mle the resultant crbs are used to define an asymptotic global confidence region centered around the true boundary in which the boundary estimate lies with a prescribed probability these global confidence regions conveniently display the uncertainty in various geometric parameters such as shape size orientation and position of the estimated target and facilitate geometric inferences numerical simulations are performed using the layer approach and the nystrom method for computation of domain derivatives and using fourier descriptors for target shape parameterization this analysis demonstrates the accuracy and generality of the proposed methods

adjoint sensitivity formulation for discontinuous galerkin discretizations in unsteady inviscid flow problems this paper presents an unsteady discrete adjoint algorithm for high order implicit discontinuous galerkin discretizations in time dependent inviscid flow problems the major function of the adjoint approach is to obtain the sensitivity information in a time dependent functional output which in turn is used to drive an unsteady shape optimization process to deliver a minimum of the objective functional a gradient based optimization strategy is investigated in which the sensitivity derivatives of the objective functional with respect to input variables are formulated in the context of high order discontinuous galerkin discretizations while special emphasis is given to the variations and linearizations of curvilinear boundary elements implicit temporal discretizations consisting of a second order backward euler scheme and a fourth order implicit runge kutta scheme are considered exclusively in this work where the corresponding adjoint problem is required to be solved in a backward time integration manner due to the associated transpose operation two numerical examples for the unsteady shape design techniques are presented to verify the derived sensitivity formulations and to demonstrate the performance of the adjoint approach the first involves an inverse shape optimization case by matching a time dependent target pressure profile for a two dimensional periodic vortical gust impinging on a rae 2822 airfoil and the second considers minimization of the acoustic noise produced by subsonic flow over a naca0012 airfoil with a 0 03c thick blunt trailing edge

goal oriented a posteriori error estimation for finite volume methods a general framework for goal oriented a posteriori error estimation for finite volume methods is developed the framework does not rely on recasting finite volume methods as special cases of finite element methods but instead directly determines error estimators from the discretized finite volume equations thus the framework can be applied to arbitrary finite volume methods it also provides the proper functional settings to address well posedness issues for the primal and adjoint problems numerical results are presented to illustrate the validity and effectiveness of the a posteriori error estimates and their applicability to adaptive mesh refinement

attractors for damped semilinear wave equations with a robin acoustic boundary perturbation abstract under consideration is the damped semilinear wave equation u t t u t u u f u 0 on a bounded domain in r 3 with a perturbation parameter e 0 occurring in an acoustic boundary condition limiting e 0 to a robin boundary condition with minimal assumptions on the nonlinear term f the existence and uniqueness of global weak solutions is shown for each e 0 1 also the existence of a family of global attractors is shown to exist after proving a general result concerning the upper semicontinuity of a one parameter family of sets the result is applied to the family of global attractors because of the complicated boundary conditions for the perturbed problem fractional powers of the laplacian are not well defined moreover because of the restrictive growth assumptions on f the family of global attractors is obtained from the asymptotic compactness method developed by j ball for generalized semiflows with more relaxed assumptions on the nonlinear term f we are able to show the global attractors possess optimal regularity and prove the existence of an exponential attractor for each e 0 1 this result insures that the corresponding global attractor inherits finite fractal dimension however the dimension is not necessarily uniform in e

sensor array calibration using a maximum likelihood approach high resolution array processing algorithms for source localization are known to be sensitive to errors in the model for the sensor array spatial response in particular unknown gain phase and mutual coupling as well as errors in the sensor positions can seriously degrade the performances of array processing algorithms this paper describes a calibration algorithm that estimates the calibration matrix consisting of the unknown gain phase and mutual coupling coefficients as well as the sensor positions using a set of calibration sources in known locations the estimation of the various parameters is based on a maximum likelihood approach cramer rao lower bound crb expressions for the sensor positions and the calibration matrix parameters are also derived numerical results are shown to illustrate the potential usefulness of the proposed calibration algorithm toward better accuracy and resolution in parametric array processing algorithms

performance predictions for parameter estimators that minimize cost functions using wirtinger calculus with application to cm blind equalization we present calculations of the first order bias and first order variance of parameters which are estimated batch wise from the global minimum of a cost function of complex valued signals embedded in zero mean gaussian noise the derivation involves the calculation of the multidimensional taylor series of the non analytic cost function up to third order using the elegant wirtinger calculus whereas closed form expressions for the variance can be obtained straightforwardly from a second order taylor series and have been presented in various other contexts an exact expression for the bias cannot be derived in general in this paper we propose approximate expressions for the first order bias and confirm them in a comparison of results from extensive analytical calculations with results from monte carlo mc simulations for the statistical efficiency of a batch processing blind equalizer using the constant modulus cm criterion we study the equalization of independent and identically distributed i i d random symbols and obtain asymptotic for large batch size expressions for the averages of the bias and variance over zero mean random real valued signals of binary phase shift keying bpsk and complex valued signals of m ary psk modulation m 2 finally we compare the statistical efficiency of the cm estimator with the one of the maximum likelihood ml blind estimation of the path parameters and equalized symbols with cm constraint

grid adaptation for functional outputs application to two dimensional inviscid flows this paper presents an error estimation and grid adaptive strategy for estimating and reducing simulation errors in integral outputs functionals of partial differential equations adaptive criteria are derived using an adjoint based error correction technique that relates the local residual errors of both the primal and adjoint solutions to the global error in the prescribed functional this relationship allows local error contributions to be used as indicators in a grid adaptive strategy designed to produce specially tuned grids for accurately estimating the chosen functional in this paper attention is limited to two dimensional inviscid flows using a standard finite volume discretization although the procedure may be readily applied to other types of multidimensional problems and discretizations numerical examples demonstrate that the proposed adaptive procedure compares favorably in terms of accuracy efficiency and robustness relative to a commonly used gradient based adaptive method

on the hyperbolic relaxation of the one dimensional cahn hilliard equation abstract we consider the one dimensional cahn hilliard equation with an inertial term u t t for 0 this equation endowed with proper boundary conditions generates a strongly continuous semigroup s t which acts on a suitable phase space and possesses a global attractor our main result is the construction of a robust family of exponential attractors m whose common basins of attraction are the whole phase space

worst case cramer rao bounds for parametric estimation of superimposed signals with applications the problem of parameter estimation of superimposed signals in white gaussian noise is considered the effect of the correlation structure of the signals on the cramer rao bounds is studied for both the single and multiple experiment cases the best and worst conditions are found using various criteria the results are applied to the example of parameter estimation of superimposed sinusoids or plane wave direction finding in white gaussian noise and best and worst conditions on the correlation structure and relative phase of the sinusoids are found this provides useful information on the limits of the resolvability of sinusoid signals in time series analysis or of plane waves in array processing the conditions are also useful for designing worst case simulation studies of estimation algorithms and for the design of minimax signal acquisition and estimation procedures as demonstrated by an example

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

higher order time integration schemes for aeroelastic applications on unstructured meshes efficient techniques for computational aeroelasticity on unstructured meshes are investigated these include the formulation of a fourth order implicit runge kutta time integration scheme a third order backward difference time integration scheme and a second order backward difference time integration scheme for the coupled system of flow and structural equations strong coupling between the flow solution and structural equations is maintained by fully converging the fully coupled system at each time step or stage the time integration schemes are constructed such that discrete conservation is maintained in the flow solution in the presence of dynamically deforming meshes by verifying the discrete geometric conservation law efficient multigrid solution techniques are devised for solving both the governing flow equations and the mesh motion equations using the same agglomerated coarse levels for both problems the flutter boundary prediction of the agard 445 6 wing is used to demonstrate the accuracy and efficiency of these techniques as well as the sensitivity of flutter boundary prediction to time step size and temporal errors

error estimates and adaptive time step control for a class of one step methods for stiff ordinary differential equations we prove new optimal a priori error estimates for a class of implicit one step methods for stiff ordinary differential equations obtained by using the discontinuous galerkin method with piecewise polynomials of degree zero and one starting from these estimates we propose a new algorithm for automatic time step control and we discuss the relation between this algorithm and earlier algorithms implemented in packages for the numerical solution of stiff ordinary differential equations

doa estimation of wideband sources using a harmonic source model and uniform linear array we consider the problem of estimation of the doas of multiple wideband sources incident on a uniform linear array ula in the presence of spatially and temporally white gaussian noise wgn the approach presented builds up on the iqml algorithm suggested by bresler and macovski 1986 for the case of narrowband doa estimation it is shown that the concept of an arma model for the observed data vector for the narrowband case can be generalized to model an appropriately stacked space time data vector obtained by combining the space time samples the coefficients of the corresponding 2 d predictor polynomial can be used to represent the null subspace of the wideband array steering matrix and rooting of the polynomial at each frequency separately gives the doa estimates these separate estimates at multiple frequencies are combined into a single doa estimate in a least squares sense this leads to the formulation of an iqml like procedure for the spatial parameter estimation of wideband sources like its narrowband counterpart the proposed approach is applicable to both noncoherent and coherent sources the performance of the proposed method is studied via extensive computer simulations and by comparison with the cramer rao bounds

new results on deterministic cramer rao bounds for real and complex parameters the cramer rao bounds crb is a lower bound of great interest for system analysis and design in the asymptotic region high signal to noise ratio snr and or large number of snapshots as it is simple to calculate and it is usually possible to obtain closed form expressions the first part of the paper is a generalization to complex parameters of the barankin rationale for deriving mse lower bounds that is the minimization of a norm under a set of linear constraints with the norm minimization approach the study of fisher information matrix fim singularity constrained crb and regularity conditions become straightforward corollaries of the derivation the second part provides new results useful for system analysis and design a general reparameterization inequality the equivalence between reparameterization and equality constraints and an explicit relationship between parameters unidentifiability and fim singularity

multigrid solution of the discrete adjoint for optimization problems on unstructured meshes techniques for the efficient formulation and solution of the discrete adjoint problem for the reynolds averaged navier stokes equations and for the mesh deformation equations are developed for use on unstructured grids in two dimensions an explicit two pass approach is used to construct the second order accurate flow adjoint equations and a defect correction scheme is used to solve the flow adjoint equations employing a line implicit agglomeration multigrid strategy to drive the defect correction scheme a similar line implicit multigrid approach is used to solve the mesh deformation equations as well as the adjoint system of these equations for the flow sensitivity and mesh motion equations the multigrid solver is constructed to be duality preserving delivering similar convergence rates for the primal and dual adjoint problems in both cases these techniques are demonstrated for a viscous turbulent airfoil shape optimization problem

cramer rao bounds for parametric shape estimation in inverse problems we address the problem of computing fundamental performance bounds for estimation of object boundaries from noisy measurements in inverse problems when the boundaries are parameterized by a finite number of unknown variables our model applies to multiple unknown objects each with its own unknown gray level or color and boundary parameterization on an arbitrary known background while such fundamental bounds on the performance of shape estimation algorithms can in principle be derived from the cramer rao lower bounds very few results have been reported due to the difficulty of computing the derivatives of a functional with respect to shape deformation we provide a general formula for computing cramer rao lower bounds in inverse problems where the observations are related to the object by a general linear transform followed by a possibly nonlinear and noisy measurement system as an illustration we derive explicit formulas for computed tomography fourier imaging and deconvolution problems the bounds reveal that highly accurate parametric reconstructions are possible in these examples using severely limited and noisy data