sensitivity analysis for antenna near field imaging although imaging and inverse scattering problems have been thoroughly studied during the last century there is only a partial understanding of these complex problems most of the efforts have been placed on the development of efficient inversion algorithms and mathematical uniqueness results in comparison there are very few results and a limited knowledge about the information content in the inversion data in this paper we provide a mathematical framework for sensitivity analysis of antenna near field imaging problems based on the multipole expansion of the electromagnetic field and the fisher information to quantify the quality of data by exploiting this framework a fundamental relation for accuracy and resolution is formulated based on the crameacuter rao bound crb the sensitivity analysis is illustrated using a relevant example with cylindrical measurement data

vibration analysis by discrete singular convolution this paper explores the utility of a discrete singular convolution algorithm for vibration analysis a number of different realizations of singular convolution kernels are selected to illustrate the present algorithm vibration analysis of strings rods beams diatomic molecules membranes waveguides and thin plates are utilized to test numerical accuracy and speed of convergence of the present approach numerical experiments indicate that the discrete singular convolution is a simple and reliable algorithm for vibration analysis

a cfar adaptive subspace detector based on a single observation in system dependent clutter background in this paper the problem of detecting target in system dependent clutter sdc background with a single observation from the test cell is researched classical detectors such as the generalized likelihood ratio detectors glrds and the adaptive matched filters amfs etc usually deal with the clutter and the noise as a whole the low rank detectors lrds make use of the low rank property of the clutter to improve the detection performance however the performance of lrds degrades when the signal is not orthogonal with respect to w r t the clutter in this paper an adaptive subspace detector for sdc sdc asd background which deals with the clutter and the noise separately is proposed the sdc asd designs the test statistic by replacing the signal and the clutter covariance matrix with their maximum likelihood estimations mles its theoretical false alarm probability and detection probability are analytically deduced analytical results show that the test statistic has the form of non central distribution besides it is shown that the sdc asd has constant false alarm rate cfar performance w r t the clutter and the noise numerical experiments are provided to validate the detection performance of the sdc asd in dealing with the target detection in sdc background less

transverse vibration of a rectangular plate with bidirectional thickness variation abstract the transverse vibrations of a rectangular plate of variable thickness have been investigated with different combinations of boundary conditions at the four edges the thickness variation is bidrectional and is the cartesian product of linear variations along two concurrent edges of the plate successive approximations have been worked out by the rayleigh ritz method using basis functions satisfying essential boundary conditions convergence is ensured by taking a sufficient number of approximations extensive numerical work has been carried out to obtain the first three frequencies for some selected cases the mode shapes have also been plotted comparison is made with results available in the literature for speacial cases

joint estimation of porosity and saturation using stochastic rock physics modeling sediment porosity and saturation affect bulk modulus shearmodulus anddensity consequently estimatinghydrocarbon saturation and reservoir porosity from seismic data is a joint estimation problem uncertainty in porosity will lead toerrorsinsaturationprediction andviceversa porosityand saturation can be jointly estimated using stochastic rockphysicsmodelingandformalbayesianestimationmethodology knowledge of shear impedance reduces the uncertainty inporosityandthusalsoreducesuncertaintyinsaturationestimation this study investigates joint estimation of porosity and saturation by using rock physics stochastic modeling and bayesian estimation theory to derive saturation and porosity maps of expected pay sands in the field example the uncertainty in porosity quantified by the standard deviation stdassociatedwiththeposteriorprobabilitydensityfunctionpdf derivedfrominversionofseismicdataismuchless than the uncertainty in the derived saturation for a typical case the std associated with saturation is 24 while porositystdisabout1 34porosityunitsgivenseismic derived inversionattributeswithreasonableaccuracy comparisonof these numbers with prior estimates showed that inversion of seismic data decreased the uncertainty in porosity to 15 of the prior uncertainty while saturation uncertainty was only reduced to 92 of the prior uncertainty although these resultsmayvaryfromonelocationtoanother themethodology isgeneralandcanbeappliedtootherlocations

the beta model maximum likelihood cramer rao bounds and hypothesis testing we study the maximum likelihood estimator in a setting where the dependent variable is a random graph and covariates are available on a graph level the model generalizes the well known beta model for random graphs by replacing the constant model parameters with regression functions cramer rao bounds are derived for special cases of the undirected beta model the directed beta model and the covariate based beta model the corresponding maximum likelihood estimators are compared with the bounds by means of simulations moreover examples are given on how to use the presented maximum likelihood estimators to test for directionality and significance finally the applicability of the model is demonstrated using temporal social network data describing communication among healthcare workers

limits of sensing temporal concentration changes by single cells berg and purcell biophys j 20 193 1977 calculated how the accuracy of concentration sensing by single celled organisms is limited by noise from the small number of counted molecules here we generalize their results to the sensing of concentration ramps which is often the biologically relevant situation e g during bacterial chemotaxis we calculate lower bounds on the uncertainty of ramp sensing by three measurement devices a single receptor an absorbing sphere and a monitoring sphere we contrast two strategies simple linear regression of the input signal versus maximum likelihood estimation and show that the latter can be twice as accurate as the former finally we consider biological implementations of these two strategies and identify possible signatures that maximum likelihood estimation is implemented by real biological systems

dsc ritz method for the free vibration analysis of mindlin plates this paper introduces a novel method for the free vibration analysis of mindlin plates the proposed method takes the advantage of both the local bases of the discrete singular convolution dsc algorithm and the pb 2 ritz boundary functions to arrive at a new approach called dsc ritz method two basis functions are constructed by using dsc delta sequence kernels of the positive type the energy functional of the mindlin plate is represented by the newly constructed basis functions and is minimized under the ritz variational principle extensive numerical experiments are considered by different combinations of boundary conditions of mindlin plates of rectangular and triangular shapes the performance of the proposed method is carefully validated by convergence analysis the frequency parameters agree very well with those in the literature numerical experiments indicate that the proposed dsc ritz method is a very promising new method for vibration analysis of mindlin plates copyright 2004 john wiley sons ltd

a generalized approach for implementing general boundary conditions in the gdq free vibration analysis of plates abstract a new approach for implementing general boundary conditions in the gdq free vibration analysis of rectangular plates is presented in this paper the proposed approach directly couples the boundary conditions with the governing equations and is referred to as the cbcge approach it can be applied to any combination of simply supported clamped and free boundary conditions the generality and accuracy of the cbcge approach are demonstrated through its application to the vibration analysis of a rectangular plate with various combinations of free edges and corners in particular the effect of grid point distribution on the numerical results for plates with free boundary conditions is discussed and a new grid point distribution is suggested

robust linear channel estimation methods for per subcarrier transmit antenna selection the linear minimum mean squared error mse channel estimator for systems employing per subcarrier transmit antenna selection is developed frequency domain correlations after the selection process are shown to be approximated well using a simple function which makes near optimal channel estimation practically possible however the resultant estimators are not robust to errors in the assumed model in terms of the antenna to subcarrier assignment used at transmission as we motivate both analytically and via simulations this is an issue when the channels for conveying this information to the receiver are severely constrained we present windowed channel estimations and new robust estimation algorithms either individually or in combination as solutions to counter this sensitivity the robust estimators are developed based on the principles of 1 minimising the worst case mse over the set of possible models and 2 minimising the expected mse over the set of possible models the latter estimator is preferred due to the lower implementation complexity and better mse performance we also prove theoretical asymptotic in signal to noise ratio performances of the two estimators used with the proposed correlation model simulation results illustrate the performance gains and improved robustness offered by the developed estimators

active learning applied to rcs computations with nonuniform sampling using different objective functions an active learning framework is introduced to reduce the number of frequencies and angles one must consider for wideband monostatic scattering computations or measurements this method is used to optimally select those frequencies and angles that would be most informative resulting in nonuniform sampling and often a reduced number of points vis agrave vis uniform sampling in this paper we focus on jointly two dimensional optimal sampling in frequency and incident angle thetas for monostatic scattering the method consists of two basic steps one step involves estimation of model parameters using a least square ls algorithm the next step is to optimally choose the next point frequency and thetas for analysis by the computational model or experiment this new point is selected with the goal of reducing uncertainty in the parametric model quantified via the fisher information matrix iterating these two steps a sequence of numerical computations or measurements are performed each at the most informative point for learning the parameters of the associated simpler parametric model this idea is demonstrated here in the context of reducing the number of points frequencies and orientations at which a computational model must be employed and in order to avoid repeatedly gathering samplings at the edge of the input space an alternative objective function is applied which makes the actively selected points closer to a region of interest

vibration of thick skew plates based on mindlin shear deformation plate theory the free flexural vibration of thick skew plates is considered the total energy functional is derived based on the first order shear deformation plate theory by mindlin the newly developed pb 2 rayleigh ritz method is applied to obtain the solution the method features the versatile pb 2 ritz functions for approximating the deflection and rotation functions which comprise the product of 1 a two dimensional polynomial function p 2 and 2 a basic function b the basic function is the key to ensure the automatic satisfaction of the geometric boundary conditions at the outset since it is formed from the product of the boundary equations raised to appropriate powers natural frequency parameters for skew mindlin plates with different combinations of boundary conditions are presented the solutions where possible are verified by comparisons with those available in the open literature the effect of the poisson ratio on vibration frequencies of plates with free edges is also investigated

the performance of a matched subspace detector that uses subspaces estimated from finite noisy training data we analyze the performance of a matched subspace detector msd where the test signal vector is assumed to reside in an unknown low rank k subspace that must be estimated from finite noisy signal bearing training data under both a stochastic and deterministic model for the test vector subspace estimation errors due to limited training data degrade the performance of the standard plug in detector relative to that of an oracle detector to avoid some of this performance loss we utilize and extend recent results from random matrix theory rmt that precisely quantify the quality of the subspace estimate as a function of the eigen snr dimensionality of the system and the number of training samples we exploit this knowledge of the subspace estimation accuracy to derive from first principles a new rmt detector and to characterize the associated roc performance curves of the rmt and plug in detectors using more than the a critical number of informative components which depends on the training sample size and eigen snr parameters of training data will result in a performance loss that our analysis quantifies in the large system limit we validate our asymptotic predictions with simulations on moderately sized systems

locally optimum detection of signals in a generalized observation model the random signal case locally optimum detectors for weak random signals are derived for a generalized observation model incorporating signal dependent and multiplicative noise it is shown that the locally optimum random signal detectors in the generalized observation model are interesting generalizations of those that would be obtained in the purely additive noisy signal model examples of explicit results for the locally optimum detector test statistics are given for some typical cases both asymptotic and finite sample size performances of the locally optimum detectors are considered and compared with those of other standard detector structures

calculation of the fisher information matrix for multidimensional data sets data sets that are acquired in many practical systems can be described as the output of a multidimensional linear separable denominator system with gaussian measurement noise an important example is nuclear magnetic resonance nmr spectroscopy in nmr spectroscopy high accuracy parameter estimation is of central importance a classical result on the crame spl acute r rao lower bound states that the inverse of the fisher information matrix fim provides a lower bound for the covariance of any unbiased estimator of the parameter vector the calculation of the fim is therefore of central importance for an assessment of the accuracy with which parameters can be estimated it is shown how the fim can be expressed using the matrices that determine the system that generates the data set for uniformly sampled data it is shown how the fim can be expressed through the solutions of lyapunov equations the novel techniques are demonstrated with an example arising from nmr spectroscopy

a robust matched detector we address the matched detector problem in the case the signal to be detected is imperfectly known while in the standard detector the signal is known to lie along a particular direction we consider the case where this direction is known up to additive white gaussian noise this somehow amounts to assuming that the signal lies in a cone the aperture of which depends upon the level of uncertainty we build the associated generalized likelihood ratio glr analyze its statistical properties indicate how to set the threshold to achieve a given false alarm rate and how to predict the associated probability of detection the so obtained detector reduces to the conventional one when the uncertainty vanishes and we analyze its behavior when the level of uncertainty which has to be known a priori is mis evaluated it appears that the sensitivity of the detector is quite low with respect to this kind of errors more importantly several realistic examples are presented that indicate that the proposed detector remains quite efficient when the true signals are far from being of the assumed model and whatever the model of the uncertainty actually is it is this robustness that makes the detector valuable

analyzing the free vibrations of a plate using finite difference and differential transformation method this paper analyses the free vibrations of clamped and simply supported rectangular thin plates a hybrid method which combines the finite difference method and the differential transformation method is employed to reduce the partial differential equations of the plate to a set of algebraic equations the investigative parameters include the order of the differential transformation the number of sub domain spaces the variable conditions and the type of initial condition the numerical simulation results indicate that the solution of the natural frequency is more accurate when calculated using a higher number of sub domains the effect of the difference transformation order value k on the solution of the natural frequency is not significant when the combined t spectra method and differential transformation method is applied the initial mode shape of the plate has a significant influence on the solution of the natural frequency the current modeling results confirm the viability of using the hybrid method proposed in this paper to solve the free vibrations and natural frequency of clamped and simply supported plates

retinal vessel centerline extraction using multiscale matched filters confidence and edge measures motivated by the goals of improving detection of low contrast and narrow vessels and eliminating false detections at nonvascular structures a new technique is presented for extracting vessels in retinal images the core of the technique is a new likelihood ratio test that combines matched filter responses confidence measures and vessel boundary measures matched filter responses are derived in scale space to extract vessels of widely varying widths a vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile vessel boundary measures and associated confidences are computed at potential vessel boundaries combined these responses form a six dimensional measurement vector at each pixel a training technique is used to develop a mapping of this vector to a likelihood ratio that measures the vesselness at each pixel results comparing this vesselness measure to matched filters alone and to measures based on the hessian of intensities show substantial improvements both qualitatively and quantitatively the hessian can be used in place of the matched filter to obtain similar but less substantial improvements or to steer the matched filter by preselecting kernel orientations finally the new vesselness likelihood ratio is embedded into a vessel tracing framework resulting in an efficient and effective vessel centerline extraction algorithm

matched subspace detection with hypothesis dependent noise power we consider the problem of detecting a subspace signal in white gaussian noise when the noise power may be different under the null hypothesis where it is assumed to be known and the alternative hypothesis this situation occurs when the presence of the signal of interest soi triggers an increase in the noise power accordingly it may be relevant in the case of a mismatch between the actual soi subspace and its presumed value resulting in a modelling error we derive the generalized likelihood ratio test glrt for the problem at hand and contrast it with the glrt which assumes known and equal noise power under the two hypotheses a performance analysis is carried out and the distributions of the two test statistics are derived from this analysis we discuss the differences between the two detectors and provide explanations for the improved performance of the new detector numerical simulations attest to the validity of the analysis

on the use of orthogonal polynomials in the rayleigh ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates series composed of recently proposed orthogonal polynomial functions are used in the rayleigh ritz method to generate results for a number of flexural vibration and buckling problems for rectangular isotropic and orthotropic plates it is demonstrated that the approach yields excellent results not only for natural frequencies and buckling loads but also for the more sensitive mode shape bending moment and shear force distribution problem

free vibration analysis of beams and rectangular plates with free edges by the discrete singular convolution in this paper free vibration of beams annular plates and rectangular plates with free boundaries are analyzed by using the discrete singular convolution dsc a novel method to apply the free boundary conditions is proposed detailed derivations are given to validate the proposed method eight examples including the free vibrations of beams annular plates and rectangular plates with free boundaries are analyzed two kernels the regularized shannon s kernel and the non regularized lagrange s delta sequence kernel are tested dsc results are compared with either analytical solutions or and differential quadrature dq data it is demonstrated that the proposed method to incorporate the free boundary conditions is simple to use and can yield accurate frequency data for beams with a free end and plates with free edges thus the proposed method for applying the boundary conditions extends the application range of the dsc

iterative cdma multiuser receiver with soft decision directed channel estimation we develop an iterative code division multiple access cdma receiver for multipath block fading channels in the uplink the mean square error mse of the channel estimates is reduced iteratively by using soft data estimates as additional pilots the multiuser detector performs parallel interference cancellation pic with subsequent linear filtering we consider a single user matched filter sumf and develop a low complexity linear minimum mse lmmse filter for intersymbol interference isi channels that allows for 33 more users than the sumf we investigate two choices of training sequences for initial channel estimation the first is a random pilot symbol sequence modulated by a short spreading sequence rand and the second is a perfect root of unity sequence prus used as long sounding chip sequence we observe that the rand scheme approaches the single user bound up to 2 db and in case of prus up to 1 db at a target bit error rate ber of 10 3 further several channel estimators are developed that use various combinations of soft decision symbols and statistical a priori knowledge about the channel these are the approximated least squares als approximated linear mmse almmse and linear mmse lmmse estimators the iterative estimators show an improvement of 2 5 and 5 db with prus and rand pilots respectively over estimators that do not exploit soft feedback symbols at a ber of 10 3 the als is sacrificing less than 0 6 db to obtain a ber of 10 3 in a system at load 1 5 when compared with the almmse and lmmse schemes the load is understood as the ratio of the number of users to the spreading factor this paper shows that significant improvements in system capacity can be achieved in multipath scenarios with low complexity choices of multiuser detectors and channel estimators

em based recursive estimation of channel parameters recursive online expectation maximization em algorithm along with stochastic approximation is employed in this paper to estimate unknown time invariant variant parameters the impulse response of a linear system channel is modeled as an unknown deterministic vector process and as a gaussian vector process with unknown stochastic characteristics using these models which are embedded in white or colored gaussian noise different types of recursive least squares rls kalman filtering and smoothing and combined rls and kalman type algorithms are derived directly from the recursive em algorithm the estimation of unknown parameters also generates new recursive algorithms for situations such as additive colored noise modeled by an autoregressive process the recursive em algorithm is shown as a powerful tool which unifies the derivations of many adaptive estimation methods

on minimum variance unbiased estimation of clock offset in a two way message exchange mechanism for many applications distributed networks require the local clocks of the constituent nodes to run close to an agreed upon notion of time most of the widely used clock synchronization algorithms in such systems employ the sender receiver protocol based on a two way timing message exchange paradigm maximum likelihood estimator mle of the clock offset based on the timing message exchanges between two clocks was derived in d r jeske on maximum likelihood estimation of clock offset ieee trans commun vol 53 pp 53 54 jan 2005 when the fixed delays are symmetric and the variable delays in each direction assume an exponential distribution with an unknown mean herein the best linear unbiased estimate using order statistics blue os of the clock offset between two nodes is derived assuming both symmetric and asymmetric exponential network delays respectively the rao blackwell lehmann scheffe theorem is then exploited to obtain the minimum variance unbiased estimate mvue for the clock offset which it is shown to coincide with the blue os in addition it is found that the mvue of the clock offset in the presence of symmetric network delays also coincides with the mle finally in the presence of asymmetric network delays although the mle is biased it is shown to achieve lesser mean square error mse than the mvue in the region around the point where the bidirectional network link delays are symmetric and hence its merit as the most versatile estimator is fairly justified

the fourth moment of ζ ρ discrete moments of the riemann zeta function were studied by gonek 3 4 and hejhal 8 in the 1980s they independently formulated a conjecture concerning the size of these moments in 1999 hughes keating and o connell 9 by employing a random matrix model made this conjecture more precise subject to the riemann hypothesis we establish upper and lower bounds of the correct order of magnitude in the case of the fourth moment

representation of mutual information via input estimates a relationship between information theory and estimation theory was recently shown for the gaussian channel relating the derivative of mutual information with the minimum mean square error this paper generalizes the link between information theory and estimation theory to arbitrary channels giving representations of the derivative of mutual information as a function of the conditional marginal input distributions given the outputs we illustrate the use of this representation in the efficient numerical computation of the mutual information achieved by inputs such as specific codes or natural language

improvement of tdoa position fixing using the likelihood curvature a conventional multilateration is a two step process where in the first step the time difference of arrivals tdoa of a signal at multiple sensors are estimated and in the second step these tdoas are used in some position fixing technique to estimate the location of an emitter several estimators have been proposed over the years for the estimation of the tdoas many techniques have been proposed for position fixing as well much of the research on position fixing has been focused on obtaining a simplified closed form solution for the unknown deterministic signal model stein had derived the maximum likelihood estimator mle for the tdoa between two sensors which is the peak location of the cross correlation function since the asymptotic variance of an mle approaches the cramer rao lower bound crlb which is the inverse of the negative of the expected value of the curvature of the log likelihood function using this as a motivation we propose a weighted least squares type position fixing technique where the weights are computed from the curvature of the log likelihood function

the risk unbiased cramer rao bound for non bayesian multivariate parameter estimation how accurately can one estimate a deterministic parameter subject to other unknown deterministic model nuisance parameters the most popular answer to this question is given by the cramer rao bound crb the main assumption behind the derivation of the crb is local unbiased estimation of all model parameters the foundations of this paper rely on doubting this assumption generally in multivariate parameter estimation each parameter in its turn can be treated as a single parameter of interest whereas the other model parameters are treated as nuisance as their misknowledge interferes with the estimation of the parameter of interest this approach is utilized in this paper to provide a fresh look at deterministic parameter estimation a new cramer rao cr type bound is derived without assuming unbiased estimation of the nuisance parameters rather than that we apply lehmann s concept of unbiasedness for a risk that measures the distance between the estimator and the locally best unbiased estimator which assumes perfect knowledge of the nuisance parameters the proposed risk unbiased crb rucrb is proven to be asymptotically attainable by the maximum likelihood estimator while being tighter than the conventional crb furthermore simulations verify the asymptotic achievability of the rucrb by the maximum likelihood estimator for an array processing problem

robust detection of signals a large deviations approach robust detection of a signal is considered for the case of independent and identically distributed observations following an asymptotic but nonlocal approach the exponential rates of decrease of the error probabilities are considered as measure of performance under this measure a robust detection structure for the symmetric density case is derived this detection structure is a generalization of an existing result for the local case and is reduced to it when the signal magnitude tends to zero

flexural vibration of skew plates using boundary characteristic orthogonal polynomials in two variables abstract the first five frequencies have been determined for the transverse vibration of a rectangular or a skew plate under different boundary conditions by using boundary characteristic orthogonal polynomials in two variables the given plate is first mapped into a square plate over which a set of orthonormal polynomials satisfying the essential boundary conditions is generated by using the gram schmidt process the rayleigh ritz method is then used to determine the frequencies for all possible combination of the boundary conditions and with different skew angles comparison has been made with known results

free vibration analysis of tapered rectangular plates by differential quadrature method a semi analytical approach abstract the particular type of thin rectangular plate configurations considered in the present work are the ones having two opposite edges simply supported and are of varying thickness between the other two edges the boundary conditions at these two edges may be quite general the plates may isotropic or specially orthotropic for the numerical solution to evaluate the free vibration characteristics of such plates a semi analytical approach is adopted first by using the trigonometric sine functions for the mode shape between the simply supported edges the eigenvalue partial differential equation is reduced to an ordinary differential equation the solution of the reduced equation is then carried out by the differential quadrature method on the basis of comparison with the available results in the published literature it is believed that this solution method is capable of yielding highly accurate results moreover the very small computation times required for the evaluation of the vibration characteristics demonstrate the high computational efficiency of the method and point to its possible use in the real time analysis and design of vibrating plate systems

an efficient mixed methodology for free vibration and buckling analysis of orthotropic rectangular plates abstract in this paper a simple and efficient mixed ritz differential quadrature dq method is presented for free vibration and buckling analysis of orthotropic rectangular plates the mixed scheme combines the simplicity of the ritz method and high accuracy and efficiency of the dq method the accuracy of the proposed method is demonstrated by comparing the calculated results with those available in the literature it is shown that highly accurate results can be obtained using a small number of ritz terms and dq sample points the proposed method is suitable for the problem considered due to its simplicity and potential for further development

differential quadrature for static and free vibration analyses of anisotropic plates abstract the differential quadrature method is used to analyse the deflection buckling and free vibration behavior of anisotropic rectangular plates under various boundary conditions the roots of chebyshev polynomials are used to obtain grid point locations and a new approach is used to apply boundary conditions results compare very well with existing numerical data and less computational effort is required for the problems considered

high accuracy mixed finite element ritz formulation for free vibration analysis of plates with general boundary conditions abstract a high order accurate mixed finite element ritz method is introduced and developed to study the vibration problem of plates with general boundary conditions the finite element method fem with higher order interpolation functions is first used to discretize the spatial partial derivatives with respect to a co ordinate direction of the plate the ritz method is then employed to analogize the resulting system of ordinary differential equations a novel technique is also presented to exactly satisfy the mixed natural boundary conditions the proposed method is applied here to solve some benchmark vibration problems of plates including isotropic and anisotropic rectangular plates variable thickness rectangular plates multi span rectangular plates and skew plates comparisons with existing numerical and analytical solutions show that the proposed mixed method can yield highly accurate results for vibration problem of plates involving free edges free corners and irregular boundaries using a small number of finite elements and ritz terms

robust rls in the presence of correlated noise using outlier sparsity relative to batch alternatives the recursive least squares rls algorithm has well appreciated merits of reduced complexity and storage requirements for online processing of stationary signals and also for tracking slowly varying nonstationary signals however rls is challenged when in addition to noise outliers are also present in the data due to e g impulsive disturbances existing robust rls approaches are resilient to outliers but require the nominal noise to be white an assumption that may not hold in e g sensor networks where neighboring sensors are affected by correlated ambient noise prewhitening with the known noise covariance is not a viable option because it spreads the outliers to noncontaminated measurements which leads to inefficient utilization of the available data and unsatisfactory performance in this correspondence a robust rls algorithm is developed capable of handling outliers and correlated noise simultaneously in the proposed method outliers are treated as nuisance variables and estimated jointly with the wanted parameters identifiability is ensured by exploiting the sparsity of outliers which is effected via regularizing the least squares ls criterion with the l1 norm of the outlier vectors this leads to an optimization problem whose solution yields the robust rls estimates for low complexity real time operation a suboptimal online algorithm is proposed which entails closed form updates per time step in the spirit of rls simulations demonstrate the effectiveness and improved performance of the proposed method in comparison with the nonrobust rls and its state of the art robust renditions

comparison of discrete singular convolution and generalized differential quadrature for the vibration analysis of rectangular plates this paper presents a comprehensive comparison study between the discrete singular convolution dsc and the well known global method of generalized differential quadrature gdq for vibration analysis so as to enhance the understanding of the dsc algorithm the dsc method is implemented through lagrange s delta sequence kernel dsc lk which utilizes local lagrange polynomials to calculate weighting coefficients whereas the gdq requires global ones moreover it is shown that the treatments of boundary conditions and the use of grid systems are different in the two methods comparison study is carried out on 21 rectangular plates of different combinations of simply supported s clamped c and transversely supported with nonuniform elastic rotational restraint e edges and five rectangular plates of mixed supporting edges some of which with a range of aspect ratios and rotational spring coefficients all the results of the dsc lk agree very well with both those in the literature and newly computed gdq results furthermore it is observed that the dsc lk performs much better for plates vibrating at higher order eigenfrequencies unlike the gdq the dsc lk is numerically stable for problems which require a large number of grid points

random matrix theory and ζ 1 2 it we study the characteristic polynomials z u of matrices u in the circular unitary ensemble cue of random matrix theory exact expressions for any matrix size n are derived for the moments of z and z z and from these we obtain the asymptotics of the value distributions and cumulants of the real and imaginary parts of log z as n in the limit we show that these two distributions are independent and gaussian costin and lebowitz 15 previously found the gaussian limit distribution for im log z using a different approach and our result for the cumulants proves a conjecture made by them in this case we also calculate the leading order n asymptotics of the moments of z and z z these cue results are then compared with what is known about the riemann zeta function s on its critical line re s 1 2 assuming the riemann hypothesis equating the mean density of the non trivial zeros of the zeta function at a height t up the critical line with the mean density of the matrix eigenvalues gives a connection between n and t invoking this connection our cue results coincide with a theorem of selberg for the value distribution of log 1 2 it in the limit t they are also in close agreement with numerical data computed by odlyzko 29 for large but finite t this leads us to a conjecture for the moments of 1 2 it finally we generalize our random matrix results to the circular orthogonal coe and circular symplectic cse ensembles

a semi analytical dqem for free vibration analysis of thick plates with two opposite edges simply supported this paper is introducing a semi analytical differential quadrature element method dqem based on first order shear deformation theory for free vibration analysis of thick plates by decomposing the plate into a series of sub domains or elements any discontinuity in geometry material properties and elastic foundations in one direction can be handled conveniently classical as well as non classical boundary conditions can be imposed one benefits of this semi analytical dqem is reducing the storage requirements and the computational efforts needed to assemble the global equations the method would also increase the computational efficiency in comparison with the finite element method fem or differential quadrature method dqm analysis of such problems the accuracy versatility stability and convergence of the algorithm are certified

matched subspace detectors we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise we derive the generalized likelihood ratio glr for each problem in the class we then establish the invariances for the glr and argue that these are the natural invariances for the problem in each case the glr is a maximal invariant statistic and the distribution of the maximal invariant statistic is monotone this means that the glr test glrt is the uniformly most powerful invariant detector we illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise in each case we give the distribution for the detector and compute performance curves

auditory motivated level crossing approach to instantaneous frequency estimation we address the problem of estimating the instantaneous frequency if of a phase signal using its level crossing lc information based on front end auditory processing motivation we show that the problem of if estimation using lc information can be cast in the framework of estimation from irregularly sampled data the formulation has the generality of estimating different types of if without the need for a quasistationary assumption we consider two types of if polynomial and bandlimited we use polynomial interpolating functions for the former and for the latter we propose a novel line plus sum of sines model the model parameters are estimated by linear regression considering the noisy case lc data for different levels is analyzed and methods for combining different estimators from lcs are discussed theoretical and extensive simulation results show that the performance of the zero crossing zc based if estimator and the level crossing based if estimator with smaller level values is better than those obtained with higher level values or their combinations the new technique reaches the crame spl acute r rao bound crb roughly above 4 db signal to noise ratio snr and its performance does not deteriorate rapidly with mismatch in the if order compared with the other techniques in the literature

subspace partitioning for target detection and identification detection of a given target or set of targets from observed data is a problem countered in many applications regardless of the algorithm selected detection performance can be severely degraded when the subspace defined by the target data set is singular or ill conditioned high correlations between target components and their linear combinations lead to false positives and misidentifications especially for subspace based detectors in this paper we propose a subspace partitioning scheme that allows for detection to be performed in a number of better conditioned subspaces instead of the original subspace the proposed technique is applied to raman spectroscopic data analysis through both simulation and experimental results we demonstrate the improvement in the overall detection performance when using the proposed subspace partitioning scheme in conjunction with several subspace detection methods that are commonly used in practice

vibration analysis of multi span plates having orthogonal straight edges abstract an accurate numerical technique is developed for flexural vibration of rectangular and l shaped plates continuous over rigid supports with arbitrary number of spans a set of orthogonally generated two dimensional plates function is used in the rayleigh ritz method to determine the natural frequencies of the plate systems several numerical examples are presented and the results obtained where possible are compared with the known solutions in the literature the present method is proven to be extremely versatile in solving a broad class of the aforementioned problems

low complexity lmmse based mimo ofdm channel estimation via angle domain processing in many situations multiple input multiple output with orthogonal frequency division multiplexing mimo ofdm channels tend to be spatially correlated due for example to limited scattering prior knowledge of this channel spatial correlation and the channel frequency correlation can be exploited by using the linear minimum mean square error lmmse technique however the complexity of the 2 d lmmse technique which fully utilizes both the channel spatial and frequency correlation is quite high to solve this problem this paper presents and analyzes several low complexity suboptimal approximated lmmse channel estimation techniques in the angle domain where the channel model lends itself to a physical interpretation the choice of angle domain techniques is largely dependent on the extent of channel stochastic information e g channel correlation or power that is available to the receiver nevertheless all the proposed angle domain techniques have much lower complexity compared to the 2 d lmmse technique further all the angle domain techniques improve over the conventional least square ls technique for all the typical mimo ofdm models under consideration more importantly our simulation results show that the angle domain quasi 1 d ql d lmmse technique can achieve similar performance compared to the 2 d lmmse technique for all typical mimo ofdm models with significantly lower complexity

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

imposition of boundary conditions by modifying the weighting coefficient matrices in the differential quadrature method one of the important issues in the implementation of the differential quadrature method is the imposition of the given boundary conditions there may be multiple boundary conditions involving higher order derivatives at the boundary points the boundary conditions can be imposed by modifying the weighting coefficient matrices directly however the existing method is not robust and is known to have many limitations in this paper a systematic procedure is proposed to construct the modified weighting coefficient matrices to overcome these limitations the given boundary conditions are imposed exactly furthermore it is found that the numerical results depend only on those sampling grid points where the differential quadrature analogous equations of the governing differential equations are established the other sampling grid points with no associated boundary conditions are not essential copyright 2002 john wiley sons ltd

a novel approach for the analysis of high frequency vibrations abstract despite much effort in the past few decades the numerical prediction of high frequency vibrations remains a challenging task to the engineering and scientific communities due to the numerical instability of existing computational methods however such prediction is of crucial importance to certain problems of pressing practical concern as pointed out by langley and bardell 1998 the aeronautical journal102 287 297 this paper introduces the discrete singular convolution dsc algorithm for the prediction and analysis of high frequency vibration of structures both a beam and two span plates are employed as test examples to demonstrate the capability of the dsc algorithm for high frequency vibration analysis a completely independent approach the levy method is employed to provide exact solutions for a cross validation of the proposed method the reliability of the dsc results is also validated by convergence studies remarkably extremely accurate and stable results are obtained in this work e g the relative dsc errors for the first 7100 modes of the beam and the first 4500 modes of the two span plates are all

fundamental limits of linear equalizers diversity capacity and complexity linear equalizers les have been widely adopted for practical systems due to their low computational complexity however it is also well known that les provide inferior performance relative to a maximum likelihood equalizer mle or other near mles because les usually cannot collect the diversity order enabled by the transmitter and at the same time they lose mutual information more importantly unlike mle or near mles the performance of les has not been well quantified this hinders more general applications of les in wireless systems in this paper we reveal a fundamental link between a channel parameter orthogonality deficiency od of the channel matrix and the diversity and capacity of les we identify that when the od of channel matrix has an upper bound strictly less than 1 the same diversity order as that of mles is collected by les and the outage capacity loss relative to mles is also a constant over signal to noise ratio snr these results can be applied to designing a framework for hybrid equalizers furthermore by studying the statistical properties of the od and comparing the complexity of different equalizers we show that hybrid equalizers can trade off between performance and complexity by tuning the channel matrix od the theoretical analysis is corroborated by computer simulations

accurate calculation methods for natural frequencies of plates with special attention to the higher modes various computational methods have been studied with respect to their suitability for obtaining very accurate solutions of plate vibration problems especially for the higher modes because of the interest in the higher modes also higher order effects such as transverse shear deformation and rotational inertia are considered the rayleigh ritz method with global trial functions appeared to be a suitable choice to reach a high convergence rate in order to obtain accurate solutions the complementary boundary conditions formulated by baruh and tadikonda should be satisfied this can be accomplished when polynomials are used as trial functions when the polynomials are not properly chosen the algorithm is not numerically stable it is shown that orthogonalization of the polynomials by means of the gram schmidt process results in a numerical stable process for free free boundary conditions these orthogonal polynomials are the well known legendre polynomials for other boundary conditions the resulting polynomials are very similar to the legendre polynomials because of the very high convergence rates these methods are suitable for obtaining accurate solutions the numerical stability guarantees that also the higher modes can be calculated

application of differential quadrature to static analysis of structural components the numerical technique of differential quadrature for the solution of linear and non linear partial differential equations first introduced by bellman and his associates is applied to the equations governing the deflection and buckling behaviour of one and two dimensional structural components separate transformations are used for higher order derivatives as suggested by mingle thus extending the method to treat fourth order equations and to include multiple boundary conditions in the respective co ordinate directions results are obtained for various boundary and loading conditions and are compared with existing exact and numerical solutions by other methods the application of differential quadrature to this class of problems is seen to lead to accurate results with relatively small computational effort

on posterior distributions for signals in gaussian noise with unknown covariance matrix a bayesian approach to estimate parameters of signals embedded in complex gaussian noise with unknown color is presented the study specifically focuses on a bayesian treatment of the unknown noise covariance matrix making up a nuisance parameter in such problems by integrating out uncertainties regarding the noise color an enhanced ability to estimate both the signal parameters as well as properties of the error is exploited several noninformative priors for the covariance matrix such as the reference prior the jeffreys prior and modifications to this are considered some of the priors result in analytical solutions whereas others demand numerical approximations in the linear signal model connections are made between the standard adaptive maximum likelihood aml estimate and a bayesian solution using the jeffreys prior with adjustments to the jeffreys prior correspondence to the regularized solution is also established this in turn enables a formal treatment of the regularization parameter simulations indicate that significant improvements compared to the aml estimator can be obtained by considering both the derived regularized solutions as well as the one obtained using the reference prior the simulations also indicate the possibility of enhancing the predictions of properties of the error as uncertainties in the noise color are acknowledged

ccd noise removal in digital images in this work we propose a denoising scheme to restore images degraded by ccd noise the ccd noise model measured in the space of incident light values light space is a combination of signal independent and signal dependent noise terms this model becomes more complex in image brightness space normal camera output due to the nonlinearity of the camera response function that transforms incoming data from light space to image space we develop two adaptive restoration techniques both accounting for this nonlinearity one operates in light space where the relationship between the incident light and light space values is linear while the second method uses the transformed noise model to operate in image space both techniques apply multiple adaptive filters and merge their outputs to give the final restored image experimental results suggest that light space denoising is more efficient since it enables the design of a simpler filter implementation results are given for real images with synthetic noise added and for images with real noise

fundamental frequencies of rectangular plates with linearly varying thickness rectangular plates with two opposite simply supported edges and linearly varying thickness only in one direction are studied and the natural frequencies of the transverse vibrations are investigated

estimation of flows in flow networks abstract let g be a directed graph with an unknown flow on each edge such that the following flow conservation constraint is maintained except for sources and sinks the sum of flows into a node equals the sum of flows going out of a node given a noisy measurement of the flow on each edge the problem we address which we call the m ost p robable f low e stimation problem mpfe is to estimate the most probable assignment of flow for every edge such that the flow conservation constraint is maintained we provide an algorithm called y mpfe for solving the mpfe problem when the measurement error is gaussian g aussian mpfe the algorithm works in o e v 2 when the underlying undirected graph of g is a 2 connected planar graph and in o e v when it is a 2 connected serial parallel graph or a tree this result is applicable to any m inimum c ost f low problem for which the cost function is e x e e 2 for edge e where e and e are constants and x e is the flow on edge e we show that for all topologies the g aussian mpfe s precision for each edge is analogous to the equivalent resistance measured in series to this edge in an electrical network built by replacing every edge with a resistor reflecting the measurement s precision on that edge

random matrix theory and the derivative of the riemann zeta function random matrix theory is used to model the asymptotics of the discrete moments of the derivative of the riemann zeta function s evaluated at the complex zeros i n we also discuss the probability distribution of ln 1 2 i n proving the central limit theorem for the corresponding random matrix distribution and analysing its large deviations

hybrid fm polynomial phase signal modeling parameter estimation and cramer rao bounds parameter estimation for a class of nonstationary signal models is addressed the class contains combination of a polynomial phase signal pps and a frequency modulated fm component of the sinusoidal or hyperbolic type such signals appear in radar and sonar applications involving moving targets with vibrating or rotating components a novel approach is proposed that allows us to decouple estimation of the fm parameters from those of the pps relying on properties of the multilag high order ambiguity function ml haf the accuracy achievable by any unbiased estimator of the hybrid fm pps parameters is investigated by means of the cramer rao lower bounds crlbs both exact and large sample approximate expressions of the bounds are derived and compared with the performance of the proposed methods based on monte carlo simulations

semianalytical differential quadrature solution for free vibration analysis of rectangular plates in this paper the analysis of the titled problem is based on classical thin plate theory and its numerical solution is carried out by a semianalytical differential quadrature method the thin rectangular plates considered herein are simply supported on two opposite edges the boundary conditions at the other two edges may be quite general and between these two edges the plates may have varying thickness however the results contained in this paper are for plates that are elastically restrained against rotation at these edges and have linearly tapered thickness on the basis of comparison with the available results in the published literature it is believed that this solution method guarantees high numerical accuracy for the problem moreover the computation times involved in the evaluation of free vibration characteristics are sufficiently small indicating that the solution method may possibly be further developed for the real time analysis and design of vibrating plate systems

quasi ml period estimation from incomplete timing data given a noisy sequence of possibly shifted integer multiples of a certain period it is often of interest to accurately estimate the period with known integer regressors the problem is classical linear regression in many applications however the regressors are unknown integers and only loose bounds on the period are available examples include hop period and timing estimation wherein hops may be missed at the output of the frequency discriminator or the emitter may hop out of band pulse repetition interval pri analysis and passive rotating beam radio scanning we study several pertinent period estimators our emphasis is on a quasi maximum likelihood approach developed herein and an earlier method based on the fourier transform of a dirac delta train representation of the data surprisingly both are capable of attaining the clairvoyant crame spl acute r rao bound at moderate signal to noise ratios snrs even for short e g 10 samples we carefully address parameter identifiability issues and corroborate our findings with extensive simulations

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

corner stress singularity effects on the vibration of rhombic plates with combinations of clamped and simply supported edges abstract an accurate method is presented for flexural vibrations of rhombic plates having all combinations of clamped and simply supported edge conditions a specific feature here is that the analysis explicitly considers the bending stress singularities that occur in the two opposite clamped hingedand orhinged hinged corners having obtuse angles in rhombic plates the strength of these singularities increases significantly as the obtuse angles at the clamped hinged and or hinged hinged corners increases stationary condition of single field classical thin plate lagrangian functional are derived using the ritz method assumed transverse displacements are constructed from a hybrid set of i admissible and mathematically complete algebraic polynomials and ii comparison functions termed here corner functions which account for both the kinematic boundary condition and the bending stress singularities at the obtuse clamped hinged and or hinged hinged corners extensive convergence studies demonstrate that the corner functions accelerate the convergence of solutions and that these function are required if accurate solutions are to be obtained for highly skewed plates accurate non dimensional frequencies and normalized contours of the vibratory transverse displacement are presented for rhombic plates having a large enough skew angle of 75 i e obtuse corner angles of 165 so that the significant influence of the corner stress singularities may be clearly understood accurate solutions for isosceles triangular plates with various combinations of clamped hinged edges are also available from the frequency and mode shape data presented the upper bound frequency solutions derived from the presented the upper bound frequency solutions derived from the present analysis are shown to improve upon the existing upper bound results in the published literature

static and free vibration analyses of rectangular plates by the new version of the differential quadrature element method a new version of the differential quadrature method is presented in this paper to overcome the difficulty existing in the ordinary differential quadrature method for applying multi boundary conditions in two dimensional problems since the weighting coefficients of the first derivative are the same as for the ordinary differential quadrature method even with the introduction of multi degree of freedom at the boundary points the method is easier to extend to two or three dimensional problems a new version of the differential quadrature plate element has been established for demonstration the essential difference from the existing old version of the differential quadrature plate element is the way the weighting coefficients are determined the methodology is worked out in detail and some numerical examples are given to show the efficiency of the present method