hierarchical generalised linear models a synthesis of generalised linear models random effect models and structured dispersions summary hierarchical generalised linear models are developed as a synthesis of generalised linear models mixed linear models and structured dispersions we generalise the restricted maximum likelihood method for the estimation of dispersion to the wider class and show how the joint fitting of models for mean and dispersion can be expressed by two interconnected generalised linear models the method allows models with i any combination of a generalised linear model distribution for the response with any conjugate distribution for the random effects ii structured dispersion components iii different link and variance functions for the fixed and random effects and iv the use of quasilikelihoods in place of likelihoods for either or both of the mean and dispersion models inferences can be made by applying standard procedures in particular those for model checking to components of either generalised linear model we also show by numerical studies that the new method gives an efficient estimation procedure for substantial class of models of practical importance likelihood type inference is extended to this wide class of models in a unified way

doa estimation by exploiting the symmetric configuration of uniform linear array a new direction of arrival doa estimation method is proposed for uniform linear array in this paper when both uncorrelated and coherent sources are present the uncorrelated and coherent sources are estimated at two different stages the uncorrelated sources are first estimated using conventional subspace methods and then they are eliminated by exploiting the symmetric configuration of the array finally the remaining coherent sources are estimated by reconstructing a non toeplitz matrix the number of sources resolved by our method can exceed the number of array elements simulation results demonstrate the effectiveness and efficiency of our proposed method

estimation of the negative binomial parameter κ by maximum quasi likelihood we investigate estimation of the parameter k of the negative binomial distribution for small samples using a method of moments estimate mme and a maximum quasi likelihood estimate mqle previous work is reviewed the importance of indirect estimation of k through its reciprocal a and of allowance for negative estimates of k or a are discussed samples of size 50 are simulated 10 000 times for each of several parameter combinations to examine the properties of the estimates samples of sizes 10 20 30 and 50 are simulated 1 000 times to investigate the effect of sample size both estimators perform reasonably well except when the mean is small and the sample size does not exceed 20 three examples are given one of a designed experiment for which the mqle is especially suited confidence limits are derived for the mqle further work along these lines is required for adequate assessment of the usual maximum likelihood estimate

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

tests of hypotheses in overdispersed poisson regression and other quasi likelihood models abstract test statistics for evaluating the significance of added variables in a regression equation are developed for mixed poisson models where the structural parameter that determines the mean variance relationship var 2 is estimated by the method of moments and the regression coefficients are estimated by quasi likelihood the formulas presented for test statistics and related estimating equations are applicable generally to quasi likelihood models specified by an arbitrary mean value function x together with a variance function v that contains one or more unknown parameters two versions of the wald and score tests are investigated one calculated from the usual model based covariance matrix whose validity depends on correct specification of the variance function and another using an empirical covariance matrix that has a more general asymptotic justification monte carlo simulations demonstrate that the quasi likelihood method of moments ql m procedures yield ap

analysis of joint angle frequency estimation using esprit high resolution parameter estimation techniques have been applied to jointly estimate multiple signal parameters we consider the problem of determining the directions and center frequencies of a number of narrowband sources in a band of interest we present a joint angle frequency estimation method based on the multidimensional esprit algorithm a perturbation error analysis gives bounds on the parameter estimates and provides optimal values for the temporal and spatial smoothing parameters the analysis is shown to be consistent with simulation results

sparse spatial spectral estimation a covariance fitting algorithm performance and regularization in this paper the sparse spectrum fitting spsf algorithm for the estimation of directions of arrival doas of multiple sources is introduced and its asymptotic consistency and effective regularization under both asymptotic and finite sample cases are studied specifically through the analysis of the optimality conditions of the method we prove the asymptotic in the number of snapshots consistency of spsf estimators of the doas and the received powers of uncorrelated sources in a sparse spatial spectra model along with this result an explicit formula of the best regularization parameter of spsf estimator with infinitely many snapshots is obtained we then build on these results to investigate the problem of selecting an appropriate regularization parameter for spsf with finite snapshots an automatic selector of such regularization parameter is presented based on the formulation of an upper bound on the probability of correct support recovery of spsf which can be efficiently evaluated by monte carlo simulations simulation results illustrating the effectiveness and performance of this selector are provided and the application of spsf to direction finding for correlated sources is discussed

a support vector machine music algorithm this paper introduces a new support vector machine svm formulation for the direction of arrival doa estimation problem we establish a theoretical relationship between the minimum variance distortionless response mvdr and the multiple signal characterization music methods this leads naturally to the derivation of an svm music algorithm which combines the benefits of subspace methods with those of svm spatially smoothed versions and a recursive form of the algorithms exhibit good performance against coherent signals we test the method s performance in scenarios with noncoherent and coherent signals and in small sample size situations obtaining an improved performance in comparison with existing standard approaches

on the number of signals resolvable by a uniform linear array an algebraic limitation on the maximum number of directions of arrival of plane waves that can be resolved by a uniform linear sensor array is studied achievable lower and upper bounds are derived on that number as a function of the number of elements in the array number of snapshots and the rank of the source sample correlation matrix the signals are assumed narrow band and of identical and known center frequency the results are also applicable in the coherent signal case and when directions of arrival are estimated from few snapshots while in the multiple snapshot case the lower bounds coincide with known asymptotic results the upper bounds indicate the potential for resolving more signals than by present methods of array processing

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

decorrelation performance of deese and spatial smoothing techniques for direction of arrival problems second order spatial analysis methods for array signal processing have been shown to yield high resolution by exploiting specific eigenstructure properties of the array output covariance matrix however when some of the signals are coherent these covariance based methods face serious difficulties produced by smaller rank in this correspondence a theoretical expression is derived for the effective correlation coefficient between sources after processing when using spatial smoothing and a new scheme of space diversity called deese decomposition de l espace source estime monte carlo simulations have been used to compare deese and spatial smoothing and to show the advantages of using deese when noise is present

sensitivity to basis mismatch in compressed sensing the theory of compressed sensing suggests that successful inversion of an image of the physical world broadly defined to include speech signals radar sonar returns vibration records sensor array snapshot vectors 2 d images and so on for its source modes and amplitudes can be achieved at measurement dimensions far lower than what might be expected from the classical theories of spectrum or modal analysis provided that the image is sparse in an apriori known basis for imaging problems in spectrum analysis and passive and active radar sonar this basis is usually taken to be a dft basis however in reality no physical field is sparse in the dft basis or in any apriori known basis no matter how finely we grid the parameter space the sources may not lie in the center of the grid cells and consequently there is mismatch between the assumed and the actual bases for sparsity in this paper we study the sensitivity of compressed sensing to mismatch between the assumed and the actual sparsity bases we start by analyzing the effect of basis mismatch on the best k term approximation error which is central to providing exact sparse recovery guarantees we establish achievable bounds for the l1 error of the best k term approximation and show that these bounds grow linearly with the image or grid dimension and the mismatch level between the assumed and actual bases for sparsity we then derive bounds with similar growth behavior for the basis pursuit l1 recovery error indicating that the sparse recovery may suffer large errors in the presence of basis mismatch although we present our results in the context of basis pursuit our analysis applies to any sparse recovery principle that relies on the accuracy of best k term approximations for its performance guarantees we particularly highlight the problematic nature of basis mismatch in fourier imaging where spillage from off grid dft components turns a sparse representation into an incompressible one we substantiate our mathematical analysis by numerical examples that demonstrate a considerable performance degradation for image inversion from compressed sensing measurements in the presence of basis mismatch for problem sizes common to radar and sonar

detection of coherent signals using weighted subspace smoothing a new approach to detecting the number of coherent signals incident upon a uniformly spaced linear array is presented the approach combines a modified spatial smoothing scheme and a modified mdl criterion the modified spatial smoothing scheme referred to as weighted subspace smoothing is actually a generalization of the post smoothing approach proposed by krim and proakis in 1994 it is shown that the noise eigenvalues obtained with weighted subspace smoothing are more accurate than those obtained with the original spatial smoothing we thus attempt to improve the detection performance using these more accurate eigenvalues a novel modification of the minimum description length mdl criterion is proposed to accomplish this computer simulations are presented to study the performance improvement of this new approach

on linear and quadratic estimating functions summary in some cases maximum quasi likelihood estimation which is at the core of glim can fail to give reasonable results a more general class of estimating functions is investigated which avoids such failure and also is not restricted to the particular forms of mean and variance function of glim

doa estimation for mixed signals in the presence of mutual coupling in this paper a new direction of arrival doa estimation method is proposed in the presence of unknown mutual coupling the impinging signals are a mixture of signals in different correlation degrees which are uncorrelated partially correlated or coherent with each other the method proceeds in three steps the noncoherent uncorrelated or partially correlated signals are firstly estimated with unknown mutual coupling then these estimates are utilized to get the mutual coupling coefficients finally by eliminating the contributions of the noncoherent signals and compensating the mutual coupling effect only coherent signals remain to be estimated this method is simple but effective and does not need iterative processing simulation results demonstrate the effectiveness and performance of the proposed method

analysis of two way layout of count data involving multiple counts in each cell abstract multiple counts may occur in each cell of an a b two way layout balanced or unbalanced of two fixed factors a and b standard log linear model analysis based on a poisson distribution assumption of the cell counts is not applicable here because of the unbalanced nature of the table or because the poisson distribution assumption is not valid we develop c tests for interaction and main effects assuming data to be poisson distributed and also assuming that data within the cells have extra over under dispersion beyond that explained by a poisson distribution for this we consider an extended negative binominal distribution and a semiparametric model using the quasi likelihood we show that in all situations the c tests for interaction are of very simple forms for c tests for the main effect in presence of no interaction such simplification is possible only under certain conditions a score test for detecting extra dispersion in presence of interaction is also obtained and is of sim

a conditional likelihood approach to residual maximum likelihood estimation in generalized linear models summary residual maximum likelihood reml estimation is often preferred to maximum likelihood estimation as a method of estimating covariance parameters in linear models because it takes account of the loss of degrees of freedom in estimating the mean and produces unbiased estimating equations for the variance parameters in this paper it is shown that reml has an exact conditional likelihood interpretation where the conditioning is on an appropriate sufficient statistic to remove dependence on the nuisance parameters this interpretation clarifies the motivation for reml and generalizes directly to non normal models in which there is a low dimensional sufficient statistic for the fitted values the conditional likelihood is shown to be well defined and to satisfy the properties of a likelihood function even though this is not generally true when conditioning on statistics which depend on parameters of interest using the conditional likelihood representation the concept of reml is extended to generalized linear models with varying dispersion and canonical link explicit calculation of the conditional likelihood is given for the one way lay out a saddlepoint approximation for the conditional likelihood is also derived

forward backward spatial smoothing techniques for coherent signal identification a spatial smoothing scheme is further investigated in the context of coherent signal classification it is shown that by making use of a set of forward and complex conjugated backward subarrays simultaneously it is always possible to estimate any k directions of arrival using at most 3k 2 sensor elements this is achieved by creating a smoothed array output covariance matrix that is structurally identical to a covariance matrix in some noncoherent situation by incorporating eigenstructure based techniques on this smoothed covariance matrix it then becomes possible to correctly identify all directions of arrival irrespective of their correlation

efficient direction finding methods employing forward backward averaging in this paper we develop a general approach for reducing the computational complexity of any direction finding method implemented with forward backward fb averaging we develop simplified fb data matrices in a manner paralleling previous work related to centrohermitian correlation matrices based on these simplified data matrices efficient construction and updating of the fb correlation matrix is developed in addition efficient fb fft fb beamspace fb evd updating fb svd and fb svd updating methods are derived in most cases fb based direction finding methods can be simplified so that the computational complexity is reduced below that of an analogous forward only implementation thus effectively twice the amount of data is processed with less total computation

a tree structure one dimensional based algorithm for estimating the two dimensional direction of arrivals and its performance analysis a tree structure algorithm using one dimensional 1d multiple signal classification music algorithm is proposed to estimate the two dimensional direction of arrivals 2d doas of coherent signals impinging on a uniform rectangular array the basic idea of the proposed algorithm is to successively apply several times of the 1d spatial smoothing music algorithm in tree structure to estimate the azimuth and the elevation angles independently to optimally separate the receive signal constrained spatial beamformers with adjustable null width are exploited in conjunction with the 1d spatial smoothing music algorithm to decompose the received signal into several signals each lead by its own 2d doa performance analysis is provided to investigate the estimation bias caused by the residue signal propagating in the tree structure

on the zeros of the linear prediction error filter for deterministic signals the zeros of a linear prediction error filter polynomial for a class of deterministic signals that are a sum of samples of m exponentially damped undamped sinusoids is studied it is assumed that n samples are available for processing and that they are uncorrupted by noise it is shown that the exponent parameters of the m signals can be determined from m zeros called signal zeros of an lth degree prediction error filter polynomial l m if l lies in between m and n m n m 2 in a special case the rest of the l m zeros of the filter polynomial switch are called extraneous zeros are shown to be approximately uniformly distributed with in the unit circle regardless of the type of exponentials in the signal if the prediction filter coefficients are chosen to have minimum euclidean length the results obtained provide insight into the estimation problem with noisy data

performance analysis for finite sample mvdr beamformer with forward backward processing the employment of forward backward fb processing to both batch and adaptive beamformers provides a superior performance than the forward only fo algorithm based on the finite sample minimum variance distortionless response mvdr beamformer a set of closed form expressions for the variance of the weight vector the output signal to interference plus noise ratio sinr and the mean square error mse is derived for both fb and fo algorithms as shown in our analysis all errors of the fb algorithm are only approximately half of the fo case

interval estimation of the over dispersion parameter in the analysis of one way layout of count data the over dispersion parameter is an important and versatile measure in the analysis of one way layout of count data in biological studies for example it is commonly used as an inverse measure of aggregation in biological count data its estimation from finite data sets is a recognized challenge many simulation studies have examined the bias and efficiency of different estimators of the over dispersion parameter for finite data sets see for example clark and perry biometrics 1989 45 309 316 and piegorsch biometrics 1990 46 863 867 but little attention has been paid to the accuracy of the confidence intervals cis of it in this paper we first derive asymptotic procedures for the construction of confidence limits for the over dispersion parameter using four estimators that are specified by only the first two moments of the counts we also obtain closed form asymptotic variance formulae for these four estimators in addition we consider the asymptotic ci based on the maximum likelihood ml estimator using the negative binomial model it appears from the simulation results that the asymptotic cis based on these five estimators have coverage below the nominal coverage probability to remedy this we also study the properties of the asymptotic cis based on the restricted estimates of ml extended quasi likelihood and double extended quasi likelihood by eliminating the nuisance parameter effect using their adjusted profile likelihood and quasi likelihoods it is shown that these cis outperform the competitors by providing coverage levels close to nominal over a wide range of parameter combinations two examples to biological count data are presented copyright 2010 john wiley sons ltd

simple and efficient nonparametric method for estimating the number of signals without eigendecomposition inspired by the computational simplicity and numerical stability of qr decomposition a nonparametric method for estimating the number of signals without eigendecomposition mense is proposed for the coherent narrowband signals impinging on a uniform linear array ula by exploiting the array geometry and its shift invariance property to decorrelate the coherency of signals through subarray averaging the number of signals is revealed in the rank of the qr upper trapezoidal factor of the autoproduct of a combined hankel matrix formed from the cross correlations between some sensor data since the infection of additive noise is defused signal detection capability is improved a new detection criterion is then formulated in terms of the row elements of the qr upper triangular factor when finite array data are available and the number of signals is determined as a value of the running index for which this ratio criterion is maximized where the qr decomposition with column pivoting is also used to improve detection performance the statistical analysis clarifies that the mense detection criterion is asymptotically consistent furthermore the proposed mense algorithm is robust against the array uncertainties including sensor gain and phase errors and mutual coupling and against the deviations from the spatial homogeneity of noise model the effectiveness of the mense is verified through numerical examples and the simulation results show that the mense is superior in detecting closely spaced signals with a small number of snapshots and or at relatively low signal to noise ratio snr

bias corrected maximum likelihood estimator of the negative binomial dispersion parameter nous decrivons un estimateur du maximum de vraisemblance avec correction du premier ordre pour le biais sur le parametre de dispersion d une distribution binomiale negative cet estimateur est compare en terme debiais et d efficacite avec l estimateur du maximum de vraisemblance etudie par piegorsch 1990 biometrics 46 863 867 les estimateurs de moment et du maximum de quasi vraisemblance etendue de clark et perry 1989 biometrics 45 309 316 et un estimateur de double quasi vraisemblance etendue l estimateur du maximum de vraisemblance avec correction du biais a des proprietes de biais et d efficacite superieures dans la plupart des cas pour faciliter la comparaison nous donnons les resultats pour le modele binomial negatif a deux parametres cependant un exemple impliquant la regression binomiale negative est donne

testing for overdispersion in poisson and binomial regression models abstract in this article a method for obtaining tests for overdispersion with respect to a natural exponential family is derived the tests are designed to be powerful against arbitrary alternative mixture models where only the first two moments of the mixed distribution are specified various tests for extra poisson and extra binomial variation are obtained as special cases the use of a particular test may be motivated by a consideration of the mechanism through which the overdispersion may arise the common occurrence of extra poisson and extra binomial variation has been noted by several authors however the poisson and binomial models remain valid in many instances and because of their simplicity and appeal it is of real interest to ascertain when they apply this paper develops a unifying theory for testing for overdispersion and generalizes tests previously derived including those by fisher 1950 collings and margolin 1985 and prentice 1986 it also shows the pearson statistic to be a sc

a modified cumulant matrix for doa estimation presents a modification of the fourth order cumulant matrix c sub g proposed by one source the modification consists of taking certain submatrices of c sub g and using them to apply the esprit principle with general arrays which may not be composed of matched sensor doublets or to perform spatial smoothing to deal with the coherent sources in the cumulant domain computer simulations are carried out to illustrate the effectiveness of the modified cumulant matrix

enhanced puma for direction of arrival estimation and its performance analysis direction of arrival doa estimation is a problem of significance in many applications in practice due to the occurrence of coherent signals and or when the number of available snapshots is small it is a challenge to find doas accurately this problem is revisited here through a new enhanced principal singular vector utilization for modal analysis epuma doa estimation approach which improves the threshold performance by first generating p k doa candidates for k sources where p geq k and then judiciously selecting k of them the asymptotic variance of epuma is theoretically derived and numerical results are provided to validate the asymptotic analysis and illustrate the practical merits of epuma

an extended quasi likelihood function summary wedderburn s original definition of quasi likelihood for generalized linear models is extended to allow the comparison of variance functions as well as those of linear predictors and link functions the relationship between generalized linear models and the use of transformations of the response variable is explored and the ideas are illustrated by three examples generalized linear models by allowing the full distributional assumption about the random component in the model to be replaced by a much weaker assumption in which only the first and second moments were defined in making this extension wedderburn widened the scope of generalized linear models in a way very similar to that of gauss when he replaced the assumption of normality in classical linear models by that of equal variance for generalized linear models with distributions in the exponential family likelihood ratio and score tests are used for testing hypotheses concerning nested subsets of covariates in the linear predictor and for assessing hypothesized link functions these methods are also applicable with wedderburn s form of quasi likelihood however neither of these methods is suitable for the comparison of different variance functions in this paper we introduce an extended quasi likelihood function which allows for the comparison of various forms of all the components of a generalized linear model i e the linear predictor the link function and the variance function we then apply the ideas to the analysis of several sets of data

two dimensional direction estimation for a mixture of noncoherent and coherent signals this paper deals with the two dimensional 2 d direction of arrival doa estimation of a mixture of noncoherent including uncorrelated and partially correlated and coherent i e fully correlated narrowband signals impinging on a planar sensor array composed of two parallel uniform linear arrays ulas an oblique projection based approach for 2 d direction estimation opade is proposed by using some cross correlations between the received array data in the proposed opade the oblique projection is utilized to isolate the coherent signals from the noncoherent ones and the effect of additive noise is alleviated while the computationally intensive eigendecomposition is avoided and the estimated elevation and azimuth angles are paired automatically further an iterative alternating scheme is presented to improve the estimation accuracy of the oblique projector and hence that of the doas of coherent signals the cramer rao lower bound crb for the mixture of noncoherent and coherent signals is also derived explicitly where the prior knowledge of the signal correlation is incorporated into the 2 d doa estimation of noncoherent signals finally the effectiveness of the opade and the theoretical analysis are substantiated through numerical examples

diagnostics for overdispersion abstract diagnostic tools are proposed for assessing the dependence of extrabinomial or extra poisson variation on explanatory variables and for comparing several common models for overdispersion these tools are based on tests for regression terms in the dispersion parameter of a generalized linear model using double exponential family and pseudolikelihood formulations score tests do not require the full fitting of models for variation and lead to easy graphical and numerical procedures based on squared residuals deviance or pearson robust modifications of these are motivated by levene s test in linear models the diagnostic tools are intended primarily to ensure prudent modeling of the variance to make correct inferences about parameters in the mean

spatial spectrum estimation in a coherent signal environment using an array in motion spatial spectrum estimation utilizing an array in motion is here investigated for dealing with coherent arrivals in a multiple signal environment the effect of estimating the spatial correlations while the array is moving is studied in terms of the decorrelation it produces the change it causes in the eigenvalues of the correlation matrix and the improvements obtained in the measured spectrum cases of both fixed and varying angle of arrival are investigated the former arises with distant sources and will with a sufficiently long estimation interval emulate uncorrelated sources and given correspondingly sharp spectra the latter arises with nearby sources and will allow them to be distinguished but will be attended by spectral shift and broadening and loss of resolution it is shown that meaningful estimates of the arrival angles can nevertheless be made specific illustrations are worked out using a seven element sparse nonuniformly spaced linear array utilizing the well known superresolution spectral estimators the maximum likelihood ml method the method of linear prediction lp and the method of multiple signal classification music

a unitary transformation method for angle of arrival estimation eigenstructure methods for estimating angles of arrival of radiation sources generally require complex computations in computing eigencomponents of the covariance matrix and calculating the search function a unitary transformation method that transforms the complex covariance matrix of an equally spaced linear array which is hermitian persymmetric and the complex search vector into a real symmetric matrix and a real vector respectively is presented both tasks can be accomplished by real computations the sampled covariance matrix available is not persymmetric to suit the unitary transformation method a persymmetrized estimator of the sampled covariance matrix which is optimal in the sense of euclidean distance is proposed

unitary esprit how to obtain increased estimation accuracy with a reduced computational burden esprit is a high resolution signal parameter estimation technique based on the translational invariance structure of a sensor array previous esprit algorithms do not use the fact that the operator representing the phase delays between the two subarrays is unitary the authors present a simple and efficient method to constrain the estimated phase factors to the unit circle if centro symmetric array configurations are used unitary esprit the resulting closed form algorithm has an esprit like structure except for the fact that it is formulated in terms of real valued computations throughout since the dimension of the matrices is not increased this completely real valued algorithm achieves a substantial reduction of the computational complexity furthermore unitary esprit incorporates forward backward averaging leading to an improved performance compared to the standard esprit algorithm especially for correlated source signals like standard esprit unitary esprit offers an inexpensive possibility to reconstruct the impinging wavefronts signal copy these signal estimates are more accurate since unitary esprit improves the underlying signal subspace estimates simulations confirm that even for uncorrelated signals the standard esprit algorithm needs twice the number of snapshots to achieve a precision comparable to that of unitary esprit thus unitary esprit provides increased estimation accuracy with a reduced computational burden

estimation of fading coefficients in the presence of multipath propagation in order to get the information about multipath propagation this communication presents two estimation methods for slowly varying fading coefficients with known numbers of the far field sources and multipaths from each far field source the fading coefficients in multipath propagation can be well estimated the methods not only have low complexity but also have high performance and the fading coefficients can be resolved directly without a searching procedure afterwards we make an extension to further improve the estimation accuracy of both direction of arrival doa and fading coefficients after obtaining their estimations the cramer rao bound crb for this problem is also deduced simulation results demonstrate the effectiveness and efficiency of the proposed methods

maximum likelihood estimation for the negative binomial dispersion parameter a 2 this yf y k for k 0 u 0 anscombe 1950 here u e y and k 1 a also var y u a2 k a aa2 this distribution has numerous applications in the biological sciences see e g breslow 1984 margolin kim and risko 1989 and the references in clark and perry 1989 anscombe 1950 observed that strictly speaking the maximum likelihood ml estimator of k k does not have a distribution since there exists a finite probability of observing a data set from which k may not be calculated this occurs when the sample mean exceeds the sample variance a more useful parameterization involves a 1 k giving

performance analysis of spatial smoothing with interpolated arrays the interpolated spatial smoothing algorithm is a computationally efficient method for estimating the directions of arrival doas of signals some of which may be perfectly correlated it extends the spatial smoothing method to arbitrary array geometries a statistical performance analysis of the algorithm is presented closed form expressions for the covariance matrix of the doa estimation errors are derived using a perturbation analysis evaluating these expressions for specific cases and comparing them to the cramer rao lower bound for the doa estimates provides insight into the statistical efficiency of this algorithm the formulas for the error covariance are quite general and can be specialized to provide results for other doa estimation algorithms as well

uniqueness nonuniqueness for nonnegative solutions of second order parabolic equations of the form ut lu vu γup in rn in this paper we investigate uniqueness and nonuniqueness for solutions of the equation ns ut lu vu upinrn 0 u x 0 f x x rn u 0 where 0 p 1 v c rn 0 f c rn and l i j 1nai j x 2 xi xj i 1nbi x xi with ai j bi c rn

positive solutions of reaction diffusion equations with super linear absorption universal bounds uniqueness for the cauchy problem boundedness of stationary solutions abstract consider classical solutions u c 2 r n 0 c r n 0 to the parabolic reaction diffusion equation u t lu f x u x t r n 0 u x 0 g x 0 x r n u 0 where l i j 1 n a i j x 2 x i x j i 1 n b i x x i is a nondegenerate elliptic operator g c r n and the reaction term f converges to at a super linear rate as u the first result in this paper is a parabolic osserman keller type estimate we give a sharp minimal growth condition on f independent of l in order that there exist a universal a priori upper bound for all solutions to the above cauchy problem that is in order that there exist a finite function m x t on r n 0 such that u x t m x t for all solutions to the cauchy problem assuming now in addition that f x 0 0 so that u 0 is a solution to the cauchy problem we show that under a similar growth condition an intimate relationship exists between two seemingly disparate phenomena namely uniqueness for the cauchy problem with initial data g 0 and the nonexistence of unbounded stationary solutions to the corresponding elliptic problem we also give a generic sufficient condition guaranteeing uniqueness for the cauchy problem

computationally efficient subspace based method for direction of arrival estimation without eigendecomposition a computationally simple direction of arrival doa estimation method with good statistical performance is attractive in many practical applications of array processing in this paper we propose a new computationally efficient subspace based method without eigendecomposition sumwe for the coherent narrowband signals impinging on a uniform linear array ula by exploiting the array geometry and its shift invariance property the coherency of incident signals is decorrelated through subarray averaging and the null space is obtained through a linear operation of a matrix formed from the cross correlations between some sensor data where the effect of additive noise is eliminated consequently the doas can be estimated without performing eigendecomposition and there is no need to evaluate all correlations of the array data furthermore the sumwe is also suitable for the case of partly coherent or incoherent signals and it can be extended to the spatially correlated noise by choosing appropriate subarrays the statistical analysis of the sumwe is studied and the asymptotic mean squared error mse expression of the estimation error is derived the performance of the sumwe is demonstrated and the theoretical analysis is substantiated through numerical examples it is shown that the sumwe is superior in resolving closely spaced coherent signals with a small number of snapshots and at low signal to noise ratio snr and offers good estimation performance for both uncorrelated and correlated incident signals

liouville type results for a class of quasilinear parabolic problems the aim of this paper is to study the properties of positive solutions to the nonlinear diffusion equation with a nonlinear bistable source we show that there exists a universal a priori upper bound for all positive solutions moreover under some assumptions we prove the convergence of these solutions to a constant if t

nested arrays in two dimensions part ii application in two dimensional array processing this paper explores the practical application of a new class of two dimensional arrays namely the two dimensional nested arrays in array processing problems like two dimensional direction of arrival estimation nested arrays constitute a class of two dimensional arrays with physical sensors on lattice s whose difference co array gives rise to a virtual two dimensional array with o mn elements although the number of physical sensors used is m n the structure of the two dimensional nested array was proposed in a companion paper and several issues related to the geometrical orientation of the difference co array in the two dimensional space were addressed in this paper the practical aspects of the application of the nested array in two dimensional array processing are considered which can enable us to exploit the increased degrees of freedom offered by the co array under the constraint of a fixed total number of physical sensors the optimal structure of the 2d nested array is solved which maximizes the number of elements in the virtual co array this provides closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors it is shown that one can obtain o n2 virtual elements in the co array using only n physical sensors to exploit the increased degrees of freedom large number of virtual sensors offered by the virtual array for two dimensional doa estimation of more sources than sensors a novel algorithm based on the concept of two dimensional spatial smoothing is proposed and several issues related to identifiability in two dimensional doa estimation problem which is a fundamental issue in two dimensions are addressed the validity of the proposed methods is verified through several numerical examples

theory and application of covariance matrix tapers for robust adaptive beamforming we unify several seemingly disparate approaches to robust adaptive beamforming through the introduction of the concept of a covariance matrix taper cmt this is accomplished by recognizing that an important class of adapted pattern modification techniques are realized by the application of a conformal matrix taper to the original sample covariance matrix from the schur product theorem for positive semi definite matrices and kolmogorov s existence theorem we further establish that cmts are in fact the solution to a minimum variance optimum beamformer associated with an auxiliary stochastic process that is related to the original by a hadamard schur product this allows us to gain deeper insight into the design of both existing pattern modification techniques and new cmts that can for example simultaneously address several different design constraints such as pattern distortion due to insufficient sample support and weights mismatch due to nonstationary interference a new two dimensional 2 d cmt for space time adaptive radar applications designed to provide more robust clutter cancellation is also introduced since the cmt approach only involves a single matrix haddamard product it is also inherently low complexity the practical utility of the cmt approach is illustrated through its application to both spatial and spatio temporal adaptive beamforming examples

performance analysis of root music the authors analyze the performance of root music a variation of the music algorithm for estimating the direction of arrival doa of plane waves in white noise in the case of a linear equispaced sensor array the performance of the method is analyzed by examining the perturbation in the roots of the polynomial formed in the intermediate step of root music in particular asymptotic results for the mean squared error in the estimates of the direction of arrival are derived simplified expressions are presented for the one and two source case and compared to those obtained for least squares esprit computer simulations are also presented and they are in close agreement with the theory an important outcome of this analysis is the fact that the error in the signal zeros has a largely radial component this provides an explanation as to why the root music is superior to the spectral music algorithm

grid free compressive beamforming the direction of arrival doa estimation problem involves the localization of a few sources from a limited number of observations on an array of sensors thus it can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing cs to achieve high resolution imaging on a discrete angular grid the cs reconstruction degrades due to basis mismatch when the doas do not coincide with the angular directions on the grid to overcome this limitation a continuous formulation of the doa problem is employed and an optimization procedure is introduced which promotes sparsity on a continuous optimization variable the doa estimation problem with infinitely many unknowns i e source locations and amplitudes is solved over a few optimization variables with semidefinite programming the grid free cs reconstruction provides high resolution imaging even with non uniform arrays single snapshot data and under noisy conditions as demonstrated on experimental towed array data

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

two dimensional grid free compressive beamforming compressive beamforming realizes the direction of arrival doa estimation and strength quantification of acoustic sources by solving an underdetermined system of equations relating microphone pressures to a source distribution via compressive sensing the conventional method assumes doas of sources to lie on a grid its performance degrades due to basis mismatch when the assumption is not satisfied to overcome this limitation for the measurement with plane microphone arrays a two dimensional grid free compressive beamforming is developed first a continuum based atomic norm minimization is defined to denoise the measured pressure and thus obtain the pressure from sources next a positive semidefinite programming is formulated to approximate the atomic norm minimization subsequently a reasonably fast algorithm based on alternating direction method of multipliers is presented to solve the positive semidefinite programming finally the matrix enhancement and matrix pencil method is introduced to process the obtained pressure and reconstruct the source distribution both simulations and experiments demonstrate that under certain conditions the grid free compressive beamforming can provide high resolution and low contamination imaging allowing accurate and fast estimation of two dimensional doas and quantification of source strengths even with non uniform arrays and noisy measurements

doa estimation with enhanced dofs by exploiting cyclostationarity many modulated signals exhibit a cyclostationarity property which has been applied in direction of arrival estimation due to its immunity to interference and noise in this paper we focus on how this cyclostationarity can be effectively integrated with the spatial dimension to enhance both the degrees of freedom and the accuracy of doa estimation first for narrowband signal case by vectorizing the second order cyclic correlation matrix instead of the conventional zero lag covariance matrix one can directly generate an augmented virtual array with sensors at positions defined by the difference coarray of the physical array then for wideband signal case two additional fractional factors are introduced so that the vectorized cyclic correlation matrix can be viewed as a single snapshot received signal from an array with sensors at positions defined by the fractional weighted difference coarray due to the fact that cyclic correlation matrices as special second order statistics allow us to obtain more degrees of freedom the proposed two virtual array models can resolve o n 2 sources by using a sparse linear array consisting of only n physical sensors e g nested coprime array furthermore a scheme of multipseudosampling is proposed in order to reduce the sensitivity to noise and parameter the proposed models can be considered as an extension of difference coarray perspective via the combination of cyclic frequency and temporal lag in the end numerical simulation results validate the effectiveness of the proposed models

forward backward averaging in the presence of array manifold errors we investigate the use of forward backward f b averaging for estimating the covariance matrix used for adaptive beamforming and space time adaptive processing stap we demonstrate that the estimation loss is reduced by the use of f b averaging and for some stap cases f b averaging can even quadruple the available sample support we also show that unknown array manifold errors have little effect on the effectiveness of f b averaging the gain from f b averaging is demonstrated on data from the mountaintop database

subspace based direction of arrival estimation using nonparametric statistics the problem of subspace estimation using multivariate nonparametric statistics is addressed we introduce new high resolution direction of arrival doa estimation methods that have almost optimal performance in nominal conditions and are robust in the face of heavy tailed noise the extensions of the techniques for the case of coherent sources are considered as well the proposed techniques are based on spatial sign and rank concepts we show that spatial sign and rank covariance matrices can be used to obtain convergent estimates of the signal and noise subspaces in the proofs the noise is assumed to be spherically symmetric moreover we illustrate how the number of signals may be determined using the proposed covariance matrix estimates and a robust estimator of variance the performance of the algorithms is studied using simulations in a variety of noise conditions including noise that is not spherically symmetric the results show that the algorithms perform near optimally in the case of gaussian noise and highly reliably if the noise is non gaussian

the forward backward averaging technique applied to tls esprit processing certain array geometries greatly simplify and enhance high resolution array processing two techniques are used the esprit algorithm which employs two shifted but otherwise identical subarrays and forward backward averaging which can be applied to axis symmetrical arrays the former has been shown to provide an efficient solution to bearing estimation while the latter incorporates the a priori knowledge about the symmetry effectively increasing the number of data vectors available and decorrelating coherent or highly correlated signals a combination of the two techniques implies a special array geometry that includes uniformly spaced linear arrays the resulting algorithm yields parameter estimates that are constrained on the unit circle satisfying the postulated data model provided merely that the arguments of these estimates are distinct however if the arguments of some parameter estimates coincide in a given scenario the esprit algorithm does not yield different results for distinct signals and these estimates can be rejected perhaps the most significant advantage of combining forward backward averaging with esprit parameter estimation is the substantial reduction in computational complexity that can be achieved based on the centro hermitian property of the data and noise covariance matrices the computational complexity of the esprit solution is reduced almost by a factor of four and the algorithm can be formulated entirely over the field of real numbers

block sparse beamforming for spatially extended sources in a bayesian formulation direction of arrival doa estimation refers to the localization of sound sources on an angular grid from noisy measurements of the associated wavefield with an array of sensors for accurate localization the number of angular look directions is much larger than the number of sensors hence the problem is underdetermined and requires regularization traditional methods use an l2 norm regularizer which promotes minimum power smooth solutions while regularizing with l1 norm promotes sparsity sparse signal reconstruction improves the resolution in doa estimation in the presence of a few point sources but cannot capture spatially extended sources the doa estimation problem is formulated in a bayesian framework where regularization is imposed through prior information on the source spatial distribution which is then reconstructed as the maximum a posteriori estimate a composite prior is introduced which simultaneously promotes a piecewise constant profile and sparsity in the solution simulations and experimental measurements show that this choice of regularization provides high resolution doa estimation in a general framework i e in the presence of spatially extended sources

compressed sensing off the grid this paper investigates the problem of estimating the frequency components of a mixture of s complex sinusoids from a random subset of n regularly spaced samples unlike previous work in compressed sensing the frequencies are not assumed to lie on a grid but can assume any values in the normalized frequency domain 0 1 an atomic norm minimization approach is proposed to exactly recover the unobserved samples and identify the unknown frequencies which is then reformulated as an exact semidefinite program even with this continuous dictionary it is shown that o slog s log n random samples are sufficient to guarantee exact frequency localization with high probability provided the frequencies are well separated extensive numerical experiments are performed to illustrate the effectiveness of the proposed method

on the structure of the signal subspace in a correlated signal environment this correspondence considers the problem of signal enumeration and direction finding with a uniform linear array in the presence of correlated wavefronts the principal contribution is to present the relationships between the physical model the array steering vectors the computational model the signal eigenvectors and the processed data the covariance matrices in a common mathematical framework

adaptive beamforming with conjugate symmetric weights the hermitian persymmetric maximum likelihood estimator mle is better than the conventional mle in estimating the covariance matrix of a symmetrically distributed antenna array though using the hermitian persymmetric mle improves the performance of adaptive beamforming it increases the computational load due to the forward backward averaging of array input sample data by observing that the weight vector obtained from the hermitian persymmetric mle is conjugate symmetric if the phase origin is chosen at the array geometry center methods are developed to reduce the computational load of the direct form beamformer and the generalized sidelobe canceler gsc the weights of both beamformers can be adapted with real computations with significant savings in computation time

generalized forward backward subaperture smoothing techniques for sample starved stap a major issue in space time adaptive processing stap for moving target indicator mti radar is the so called sample support problem often the available sample support for estimating the requisite interference covariance matrix is inadequate thereby precluding stap beamforming utilizing many adaptive degrees of freedom dofs although deterministic rank reduction methods can reduce sample support requirements they are invariably suboptimal from a signal to interference plus noise ratio sinr standpoint a new generalized subspatial and subtemporal aperture smoothing method employing forward and backward data vectors is introduced to overcome the data deficiency problem it is shown that multiplicative improvement in data samples can be obtained at the expense of negligible loss in space time aperture of the steering vector

a new index of aggregation for animal counts a new index is described that is especially appropriate for measuring the aggregation of entomological data in the form of counts per sample unit and that can make use of spatial information when it is available calculation of the index is based on a comparison of the effort required of individuals in a sample to achieve complete crowding with that to achieve complete randomness the power of tests of randomness based on this index is found to be greater than those based on the index of dispersion especially when spatial information is available

towards a mathematical theory of super resolution this paper develops a mathematical theory of super resolution broadly speaking super resolution is the problem of recovering the fine details of an object the high end of its spectrum from coarse scale information only from samples at the low end of the spectrum suppose we have many point sources at unknown locations in 0 1 and with unknown complex valued amplitudes we only observe fourier samples of this object up to a frequency cutoff fc we show that one can super resolve these point sources with infinite precision i e recover the exact locations and amplitudes by solving a simple convex optimization problem which can essentially be reformulated as a semidefinite program this holds provided that the distance between sources is at least 2 fc this result extends to higher dimensions and other models in one dimension for instance it is possible to recover a piecewise smooth function by resolving the discontinuity points with infinite precision as well we also show that the theory and methods are robust to noise in particular in the discrete setting we develop some theoretical results explaining how the accuracy of the super resolved signal is expected to degrade when both the noise level and the super resolution factor vary 2014 wiley periodicals inc

improved spatial smoothing techniques for doa estimation of coherent signals in the context of coherent signal classification spatial smoothing is necessary for the application of the eigen based direction of arrival doa estimation methods however the currently known spatial smoothing algorithms not only reduce the effective aperture of the array but also do not consider the cross correlations of the subarray outputs an improved spatial smoothing algorithm which can fully utilize the correlations of the array outputs and produce a more stable estimate of the covariance matrix is presented simulation results are provided to verify the theoretical prediction the superiority of this method over the conventional methods is obvious especially when the sosr subarray to overall size ratio is small

tests for detecting overdispersion in poisson regression models abstract poisson regression models are widely used in analyzing count data this article develops tests for detecting extra poisson variation in such situations the tests can be obtained as score tests against arbitrary mixed poisson alternatives and are generalizations of tests of fisher 1950 and collings and margolin 1985 accurate approximations for computing significance levels are given and the power of the tests against negative binomial alternatives is compared with those of the pearson and deviance statistics one way to test for extra poisson variation is to fit models that parametrically incorporate and then test for the absence of such variation within the models for example negative binomial models can be used in this way cameron and trivedi 1986 lawless 1987a the tests in this article require only the poisson model to be fitted two test statistics are developed that are motivated partly by a desire to have good distributional approximations for computing significance levels simu

nested arrays a novel approach to array processing with enhanced degrees of freedom a new array geometry which is capable of significantly increasing the degrees of freedom of linear arrays is proposed this structure is obtained by systematically nesting two or more uniform linear arrays and can provide o n2 degrees of freedom using only n physical sensors when the second order statistics of the received data is used the concept of nesting is shown to be easily extensible to multiple stages and the structure of the optimally nested array is found analytically it is possible to provide closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors this cannot be done for existing classes of arrays like minimum redundancy arrays which have been used earlier for detecting more sources than the number of physical sensors in minimum input minimum output mimo radar the degrees of freedom are increased by constructing a longer virtual array through active sensing the method proposed here however does not require active sensing and is capable of providing increased degrees of freedom in a completely passive setting to utilize the degrees of freedom of the nested co array a novel spatial smoothing based approach to doa estimation is also proposed which does not require the inherent assumptions of the traditional techniques based on fourth order cumulants or quasi stationary signals as another potential application of the nested array a new approach to beamforming based on a nonlinear preprocessing is also introduced which can effectively utilize the degrees of freedom offered by the nested arrays the usefulness of all the proposed methods is verified through extensive computer simulations

linear prediction approach to direction estimation of cyclostationary signals in multipath environment we investigate the estimation of the directions of arrival doa of closely spaced narrowband cyclostationary signals in the presence of multipath propagation by exploiting the spatial and temporal properties of most communication signals we propose a new cyclic forward backward linear prediction fblp approach for coherent signals impinging on a uniform linear array ula in the proposed algorithm the evaluation of the cyclic array covariance matrix is avoided and the difficulty of choosing the optimal time lag parameter is alleviated as a result the proposed approach has two advantages 1 the computational load is relatively reduced and 2 the robustness of estimation is significantly improved the performance of the proposed approach is confirmed through numerical examples and it is shown that this approach is superior in resolving the closely spaced coherent signals with a small length of array data and at relatively low signal to noise ratio snr

sequential bayesian sparse signal reconstruction using array data in this paper the sequential reconstruction of source waveforms under a sparsity constraint is considered from a bayesian perspective let the wave field which is observed by a sensor array be caused by a spatially sparse set of sources a spatially weighted laplace like prior is assumed for the source field and the corresponding weighted least absolute shrinkage and selection operator lasso cost function is derived after the weighted lasso solution has been calculated as the maximum a posteriori estimate at time step k the posterior distribution of the source amplitudes is analytically approximated the weighting of the laplace like prior for time step k 1 is then fitted to the approximated posterior distribution this results in a sequential update for the lasso weights thus a sequence of weighted lasso problems is solved for estimating the temporal evolution of a sparse source field the method is evaluated numerically using a uniform linear array in simulations and applied to data which were acquired from a towed horizontal array during the long range acoustic communications experiment

subspace leakage analysis and improved doa estimation with small sample size classical methods of doa estimation such as the music algorithm are based on estimating the signal and noise subspaces from the sample covariance matrix for a small number of samples such methods are exposed to performance breakdown as the sample covariance matrix can largely deviate from the true covariance matrix in this paper the problem of doa estimation performance breakdown is investigated we consider the structure of the sample covariance matrix and the dynamics of the root music algorithm the performance breakdown in the threshold region is associated with the subspace leakage where some portion of the true signal subspace resides in the estimated noise subspace in this paper the subspace leakage is theoretically derived we also propose a two step method that improves the performance by modifying the sample covariance matrix such that the amount of the subspace leakage is reduced furthermore we introduce a phenomenon named as root swap which occurs in the root music algorithm in the low sample size region and degrades the performance of the doa estimation a new method is then proposed to alleviate this problem numerical examples and simulation results are given for uncorrelated and correlated sources to illustrate the improvement achieved by the proposed methods moreover the proposed algorithms are combined with the pseudo noise resampling method to further improve the performance