on the existence and multiplicity of positive periodic solutions for first order vector differential equation abstract in this paper we consider the existence and multiplicity of positive periodic solutions for first order vector differential equation x t f t x t 0 a e t 0 under the periodic boundary value condition x 0 x here is a positive constant and f 0 r n r n is a caratheodory function some existence and multiplicity results of positive periodic solutions are derived by using a fixed point theorem in cones

fisher information for a complex gaussian random variable beamforming applications for wave propagation in a random medium we derive a general expression for the fisher information for a special class of complex gaussian random variables whose mean and covariance may be expressed in terms of a specific parameterized linear transformation the deterministic unknown parameter case is considered this class is descriptive of signals that propagate in a homogeneous or inhomogeneous medium and also occurs in numerous beamforming applications the fisher information derived here encompasses a wide range of previously derived well known results for complex gaussian signals propagating in a homogeneous medium and is also applicable to more recent models for signals propagating in an inhomogenous medium the conditions for the estimates of the azimuth and elevation to decouple from the estimates of the nuisance parameters are studied for monochromatic plane wave and spherical wave propagation in a random medium for propagation in an anisotropic medium it is found that in general the cramer rao lower bounds crlbs of the entire unknown parameter set will be coupled for special cases of propagation in an isotropic medium it is found that for plane waves the crlbs of the angles of arrival will be approximately decoupled from the crlbs of the other unknowns and for spherical waves the crlbs of the angles of arrival will be always be coupled to the crlbs of all other unknowns although the couplings may be minimized under certain conditions

remarks on first and second order periodic boundary value problems on etudie les problemes aux valeurs limites periodiques d ordre 1 et 2 suivants u f t u u 0 u 2 et u f t u u 0 u 2 u 0 u 2 on obtient l existence de solutions extremales comme limites d iterees monotones

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

operator approach to performance analysis of root music and root min norm the authors carry out a performance analysis of two eigenstructure based direction of arrival estimation algorithms using a series expansion of projection operators or projectors on the signal and noise subspaces in the interest of algebraic simplicity an operator formalism is utilized a perturbation analysis is performed on the projectors the results of which are used to determine the effect on the estimated parameters the approach makes it possible to carry out the analysis to any chosen order of expansion of the projectors by using an original recurrence formula developed for the higher order terms in the series expansion of the projectors this method is used to study the root music and root min norm algorithms and establish the superiority of root music in all cases the analysis has also resulted in insightful asymptotic expressions that describe the statistical behavior of the estimated angles and radii of the signal zeros

rater agreement and the generalized rudas clogg lindsay index of fit rudas clogg and lindsay proposed a new index of fit for contingency table analysis using the two component mixture where the first component with weight 1 w represents the model to be tested and the second component with weight w is unstructured the rcl index of lack of fit was defined to be the smallest mixing weight w being compatible with the two component mixture to be saturated this index of fit which is not sensitive to sample size is applied to the problem of assessing agreement between two raters whereby three hypotheses pure agreement quasi independence independence are considered as quasi independence comprises the two other hypotheses a natural generalization of the rcl index of fit results from assuming the model itself to be composed of two submodels pure agreement independence while the third component remains unstructured two examples demonstrate the application of this generalized rcl index of fit with the first 3 x 3 contingency table having no empty cells and the second 4 x 4 table having five of them in both cases estimating the parameters and determining w was possible without problems within the linear logistic framework for latent class analysis a further analysis of the 4 x 4 table assumes the model to be the two class latent class model that certainly does not belong to the family of standard models for contingency table analysis thus in contrast to the recommendations given originally the following conclusions seem to be justified i the number of components representing the model may exceed one generalized rcl index ii the application of the original rcl index of fit may be extended to more complex models and iii empty cells bear no problems so that this approach may be recommended in the case of both large and small sample sizes

maximum likelihood direction of arrival estimation in unknown noise fields using sparse sensor arrays we address the problem of maximum likelihood ml direction of arrival doa estimation in unknown spatially correlated noise fields using sparse sensor arrays composed of multiple widely separated subarrays in such arrays intersubarray spacings are substantially larger than the signal wavelength and therefore sensor noises can be assumed to be uncorrelated between different subarrays this leads to a block diagonal structure of the noise covariance matrix which enables a substantial reduction of the number of nuisance noise parameters and ensures the identifiability of the underlying doa estimation problem a new deterministic ml doa estimator is derived for this class of sparse sensor arrays the proposed approach concentrates the ml estimation problem with respect to all nuisance parameters in contrast to the analytic concentration used in conventional ml techniques the implementation of the proposed estimator is based on an iterative procedure which includes a stepwise concentration of the log likelihood ll function the proposed algorithm is shown to have a straightforward extension to the case of uncalibrated arrays with unknown sensor gains and phases it is free of any further structural constraints or parametric model restrictions that are usually imposed on the noise covariance matrix and received signals in most existing ml based approaches to doa estimation in spatially correlated noise

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

computationally efficient maximum likelihood estimation of structured covariance matrices by invoking the extended invariance principle exip we present herein a computationally efficient method that provides asymptotic for large samples maximum likelihood aml estimation for structured covariance matrices and is referred to as the aml algorithm a closed form formula for estimating the hermitian toeplitz covariance matrices that makes aml computationally simpler than most existing hermitian toeplitz matrix estimation algorithms is derived although the aml covariance matrix estimator can be used in a variety of applications we focus on array processing our simulation study shows that aml enhances the performance of angle estimation algorithms such as music by making them very close to the corresponding cramer rao bound crb for uncorrelated signals numerical comparisons with several structured and unstructured covariance matrix estimators are also presented

positive solution for system of nonlinear first order pbvps on time scales abstract in this paper we are concerned with the following system of nonlinear first order periodic boundary value problems on time scale t x i t f i t x 1 t x 2 t x n t 0 t 0 t x i 0 x i t i 1 2 n where f i 0 t 0 n r is continuous and there exists a constant m i 0 such that m i x i f i t x 1 x 2 x n 0 for x 1 x 2 x n 0 n t 0 t some existence criteria of positive solution are established by using a fixed point theorem for operators on cone

inherent limitations in data aided time synchronization of continuous phase modulation signals over time selective fading channels time synchronization of continuous phase modulation cpm signals over time selective rayleigh fading channels is considered the cramer rao lower bound crlb for this problem is studied for data aided da synchronization i e known symbol sequence transmission over a time selective rayleigh fading i e gaussian multiplicative noise channel exact expressions for the bound are derived as well as simplified approximate forms that enable derivation of a number of properties that describe the bound s dependence on key parameters such as signal to noise ratio snr channel correlation sampling rate sequence length and sequence choice comparison with the well known slow fading i e constant channel bound is emphasized further simplifications are obtained for the special case of minimum phase keying msk wherein it is shown how the bound may be used as a sequence design tool to optimize synchronization performance

eigenvalues of schrodinger operators with definite and indefinite weights in this paper computational algorithms are presented to compute the eigenvalues of schrodinger operators with definite and indefinite weights the algorithms are based on titchmarsh weyl s theory and can be applied to solve a wide class of problems in quantum mechanics explicit examples are presented some of which recover the known exact solutions finally some analytical bounds have been reviewed for definite and indefinite singular problems weyl s spectral bisection algorithm has been proposed to solve definite problems as algebraic problems open problems have been presented based on the results of the presented algorithms

a covariance fitting approach to parametric localization of multiple incoherently distributed sources in this paper a new algorithm for parametric localization of multiple incoherently distributed sources is presented this algorithm is based on an approximation of the array covariance matrix using central and noncentral moments of the source angular power densities based on this approximation a new computationally simple covariance fitting based technique is proposed to estimate these moments then the source parameters are obtained from the moment estimates compared with earlier algorithms our technique has lower computational cost and obtains the parameter estimates in a closed form in addition it can be applied to scenarios with multiple sources that may have different angular power densities while other known methods are not applicable to such scenarios

waveform relaxation methods for periodic differential functional systems the convergence of waveform relaxation methods applied to a periodic differential functional system is studied the continuous dependence is also discussed

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

pseudo randomly generated estimator banks a new tool for improving the threshold performance of direction finding a new powerful tool for improving the threshold performance of direction finding is considered the main idea of our approach is to reduce the number of outliers in the doa estimates using a previously proposed joint estimation strategy jes for this purpose multiple different doa estimators are calculated in a parallel manner for the same batch of data i e for a single data record employing these estimators simultaneously the jes improves the threshold performance because it removes outliers and exploits only successful estimators that are sorted out using a hypothesis testing procedure we consider an efficient modification of the jes with application to the pseudo randomly generated eigenstructure estimator banks based on secondand higher order statistics weighted music estimators based on the covariance and contracted quadricovariance matrices are chosen as appropriate underlying techniques for the second and fourth order estimator banks respectively computer simulations with uncorrelated sources verify the dramatic improvements of threshold performance as compared with the conventional second and fourth order music algorithms simulations also show that in the second order case the threshold performance of our technique is close to that of the wsf method and stochastic deterministic ml methods which are known today as the most powerful in the sense of estimation performance and at the same time as the most computationally expensive doa estimation techniques the computational cost of our algorithm is much lower than that of the wsf and ml techniques because no multidimensional optimization is required

broad band signal subspace spatial spectrum bass ale estimation an approach to spatial spectrum estimation of broadband sources is described the approach termed broadband signal subspace spatial spectrum bass ale estimation is based on the eigenstructure of a broadband spatial temporal covariance matrix and is justified by identifying the low rank character of spatial temporal observations of broadband sources bass ale estimators are described which incorporate source focusing spatial temporal noise decorrelating a signal or noise only subspace generated from the eigenstructure of the transformed spatial temporal covariance matrix and broadband source models through discussion and simulation bass ale estimators are compared to the coherent signal subspace processor a similar subspace method and relative advantages of the two are identified

bounds on maximum likelihood ratio part ii application to antenna array detection estimation with imperfect wavefront coherence the multiple hypothesis testing problem of the detection estimation of an unknown number of independent gaussian point sources is adequately addressed by likelihood ratio lr maximization over the set of admissible covariance matrix models we introduce nonasymptotic lower and upper bounds for the maximum lr since lr optimization is generally a nonconvex multiextremal problem any practical solution could now be tested against these bounds enabling a high probability of recognizing nonoptimal solutions we demonstrate that in many applications the lower bound is quite tight with approximate maximum likelihood ml techniques often unable to approach this bound the introduced lower bound analysis is shown to be very efficient in determining whether or not performance breakdown has occurred for subspace based direction of arrival doa estimation techniques we also demonstrate that by proper lr maximization we can extend the range of signal to noise ratio snr values and or number of data samples wherein accurate parameter estimates are produced yet when the snr and or sample size falls below a certain limit for a given scenario we show that ml estimation suffers from a discontinuity in the parameter estimates a phenomenon that cannot be eliminated within the ml paradigm

simple and accurate direction of arrival estimator in the case of imperfect spatial coherence we consider the direction finding problem in the imperfect spatial coherence case i e when the amplitude and phase of the wavefront vary randomly along the array aperture this phenomenon can originate from propagation through an inhomogeneous medium it is also encountered in the case of spatially dispersed sources we derive a fast and accurate estimator for the direction of arrival of a single source using a uniform linear array ula of sensors the estimator is based on a reduced statistic obtained from the subdiagonals of the covariance matrix of the array output it only entails computing the fourier transform of an m 1 length sequence where m is the number of array sensors a theoretical analysis is carried out and an expression for the asymptotic variance of the estimator is derived numerical simulations validate the theoretical results and show that the estimator has an accuracy very close to the cramer rao bound

matrix fitting approach to direction of arrival estimation with imperfect spatial coherence of wavefronts the performance of high resolution direction of arrival doa estimation methods significantly degrades in several practical situations where the wavefronts have imperfect spatial coherence the original solution to this problem was proposed by paulraj and kailath 1988 but their technique requires a priori knowledge of the matrix characterizing the loss of wavefront coherence along the array aperture a novel solution to this problem is proposed which does not require a priori knowledge of the spatial coherence matrix

multi point boundary value problems for second order functional differential equations this paper is concerned with the existence of extreme solutions of multi point boundary value problem for a class of second order functional differential equations we introduce a new concept of lower and upper solutions by using the method of upper and lower solutions and monotone iterative technique we obtain the existence of extreme solutions

periodic solutions to functional differential equations on considere un systeme d equations differentielles fonctionnelles x g t x t ou g r b r n est t periodiquement et b est un espace de phase de fonctions continues qui appliquent 0 dans r n on introduit les concepts de limitation b uniforme et de limitation ultime b uniforme on donne des conditions suffisantes a l existence d une solution t periodique

bearing estimation for a distributed source of nonconstant modulus ounds and analysis the paper considers the problem of estimating the bearing of a single far field source surrounded by local scatterers using passive sensor array measurements an associated source bearing estimation problem is formulated and the crame spl acute r rao lower bound is evaluated in addition a comprehensive analysis is performed of the maximum likelihood estimates that due to mismodeling assume a constant modulus source and the degradation in performance is quantified as a function of the source s empirical variance it is shown that for a limited price in terms of mean square error the constant modulus maximum likelihood estimator can replace the optimal nonconstant modulus estimator

linear logistic latent class analysis for polytomous data abstract for latent class analysis a widely known statistical method for the unmixing of an observed frequency table into several unobservable ones a flexible model is presented in order to restrain the unknown class sizes mixing weights and the unknown latent response probabilities two systems of basic equations are stated such that they simultaneously allow parameter fixations the equality of certain parameters as well as linear logistic constraints of each of the original parameters the maximum likelihood equations for the parameters of this linear logistic latent class analysis are given and their estimation by means of the em algorithm is described further the criteria for their local identifiability and statistical tests pearson and likelihood ratio 2 for goodness of fit are outlined the practical applicability of linear logistic latent class analysis is demonstrated by three examples mixed logistic regression a mixed bradley terry model for paired comparisons with ties and a lo

training based mimo channel estimation a study of estimator tradeoffs and optimal training signals in this paper we study the performance of multiple input multiple output channel estimation methods using training sequences we consider the popular linear least squares ls and minimum mean square error mmse approaches and propose new scaled ls sls and relaxed mmse techniques which require less knowledge of the channel second order statistics and or have better performance than the conventional ls and mmse channel estimators the optimal choice of training signals is investigated for the aforementioned techniques in the case of multiple ls channel estimates the best linear unbiased estimation blue scheme for their linear combining is developed and studied

an efficient approximation of spatial correlation based on gauss hermite quadrature an efficient spatial correlation approximation for clustered multiple input multiple output channels based on a hierarchical angle structure is presented to avoid complicated numerical integrations different approximations have been proposed in the literature one approximation is expressed in a high order series expansion of bessel functions while the other suffers low accuracy for large angle spread an approximation based on gauss hermite quadrature ghq is proposed whose values are shown to match well with theoretical results when the antenna spacing is within a critical range by exploring the properties of the abscissas and the weights of the ghq the proposed approximation can be effectively computed with only a few expansion terms and its validity can be maintained over a large range of angle spread the approximation errors of the proposed and existing methods are analyzed simulation results verify the accuracy of the analysis and the efficiency of the proposed approximation

linear estimation for measurement delay systems with periodic coefficients and multiplicative noise this technical note is concerned with the remote estimation problem for measurement delay systems with multiplicative noise and periodic coefficients the multiplicative noise in every communication channel is described by an independent and identically distributed i i d bernoulli process the quality of the estimation achieved by an admissible filter is measured by a performance criterion described by the cesaro limit of the mean square of the deviation between the remote signal and the estimated signal the filter is designed in terms of the unique periodic solution of a lyapunov equation together with the periodic stabilizing solution of a riccati equation in the end we supply a numerical example to show the effectiveness of our proposed estimation approach

an iterative method for functional differential equations a suitable periodic boundary conditions for a functional differential equations email protected t f t x x t are conditions of the form x 0 q x 2 p q in this paper we use the notion of upper and lower solutions coupled with monotone iterative method to prove the existence of solutions of this periodic boundary value problem

existence and approximation of solutions for discontinuous functional differential equations in this paper existence of solutions of initial value problems for discontinuous functional differential equations is investigated firstly by applying the method of upper and lower solutions which may be discontinuous some existence results of extremal solutions are obtained furthermore we also develop a monotone iterative technique for obtaining extremal solutions which are obtained as limits of monotone sequences

stochastic maximum likelihood method for mimo propagation parameter estimation in this paper we derive a stochastic maximum likelihood ml method for estimating spatio temporal parameters for multiple input multiple output mimo channels such estimators are needed in propagation studies where extensive channel measurements and sounding are required these are seminal tasks in the process of developing advanced channel models the proposed method employs an angular von mises distribution model which is appropriate for angular data observed in channel measurement campaigns the signal model is stochastic and consequentially the method is particularly useful for estimation of the diffuse scattering component this approach leads to lower complexity and faster convergence in comparison to deterministic models these benefits are due to lower dimensionality of the model leading to a simpler optimization problem the statistical performance of the estimator is studied by establishing the crameacuter rao lower bound crlb and comparing the variances the simulations show that the variance of the proposed estimation technique reaches the crlb for relatively small sample size the estimator is robust in the sense that meaningful results are obtained when applied to data generated by channel models other than the one used in its derivation

parameter estimation from quantized observations in multiplicative noise environments the problem of distributed parameter estimation from binary quantized observations is studied when the unquantized observations are corrupted by combined multiplicative and additive gaussian noise these results are applicable to sensor networks where the sensors observe a parameter in combined additive and nonadditive noise and to a case where dispersed receivers are employed with analog communication over fading channels where the receivers employ binary quantization before noise free digital communications to a fusion center we first discuss the case in which all the quantizers use an identical threshold the parameter identifiability condition is given and surprisingly it is shown that unless the common threshold is chosen properly and the parameter lies in an open interval the parameter will not generally be identifiable in contrast to the additive noise case the best achievable mean square error mse performance is characterized by deriving the corresponding cramer rao lower bound crlb a closed form expression describing the corresponding maximum likelihood ml estimator is presented the stability of the performance of the ml estimators is improved when a nonidentical threshold strategy is utilized to estimate the unknown parameter the thresholds are designed by maximizing the minimum asymptotic relative efficiency are between quantized and unquantized ml estimators although the ml estimation problem is nonconvex it is shown that one can relax the optimization to make it convex the solution to the relaxed problem is used as an initial solution in a gradient algorithm to solve the original problem next the case where both the variances of the additive noise and multiplicative noise are unknown is studied the corresponding crlb is obtained and the ml estimation problem is transformed to a convex optimization which can be solved efficiently finally numerical simulations are performed to substantiate the theoretical analysis

a performance analysis of subspace based methods in the presence of model errors i the music algorithm application of subspace based algorithms to narrowband direction of arrival doa estimation requires that both the array response in all directions of interest and the spatial covariance of the noise must be known in practice however neither of these quantities is known precisely depending on the degree to which they deviate from their nominal values serious performance degradation can result the performance of the music algorithm is examined for situations in which the noise covariance and array response are perturbed from their assumed values theoretical expressions for the error in the music doa estimates are derived and compared with simulations performed for several representative cases and with the appropriate cramer rao bound an optimally weighted version of music is proposed for a particular class of array errors

on low complexity robust beamforming with positive semidefinite constraints this paper addresses the problem of robust beamforming for general rank signal models with norm bounded uncertainties in the desired and received signal covariance matrices as well as positive semidefinite constraints on the covariance matrices two novel minimum variance robust beamformers are derived in closed form the first one basically is the closed form version of an existing iterative algorithm while the second one offers even better performance with respect to the first one both of them have the advantage of low complexity the effectiveness and performance improvement of the proposed beamformers are verified by simulation results

efficient quadratic detection in perturbed arrays via fourier transform techniques matched field beamforming used in combination with a generalized likelihood ratio test is the most common detector structure in array processing situations unfortunately various array perturbations caused by phase calibration propagation effects or modeling errors can cause the sensor observations to become only partially correlated limiting the performance of traditional matched field beamformers that assume perfect coherence of the signal wavefronts quadratic array processing is optimal for many perturbed array problems however direct implementation poses a significant computational burden we show that under certain conditions the optimal quadratic detector for dealing with perturbed arrays can be approximately realized efficiently and robustly employing only discrete fourier transforms to deal with spatial processing in addition we show that the proposed spatial processing allows for convenient integration of conventional frequency domain methods for angle of arrival searches our proposed array detection structure provides the robustness and performance benefits of complicated quadratic processing at a computational cost comparable with that of traditional matched field beamforming

positive solutions for first order periodic boundary value problem this paper discusses the existence and multiplicity of positive solutions for the following first order periodic boundary value problemx t f t x t 0 0

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

inversion of seismoacoustic data using genetic algorithms and a posteriori probability distributions the goal of many underwater acoustic modeling problems is to find the physical parameters of the environment with the increase in computer power and the development of advanced numerical models it is now feasible to carry out multiparameter inversion the inversion is posed as an optimization problem which is solved by a directed monte carlo search using genetic algorithms the genetic algorithm presented in this paper is formulated by steady state reproduction without duplicates for the selection of parents the object function is scaled according to a boltzmann distribution with a temperature equal to the fitness of one of the members in the population the inversion would be incomplete if not followed by an analysis of the uncertainties of the result when using genetic algorithms the response from many environmental parameter sets has to be computed in order to estimate the solution the many samples of the models are used to estimate the a posteriori probabilities of the model parameters t

calculation of eigenvector derivatives for structures with repeated eigenvalues in structural optimization and system identification eigenvector derivatives provide important information for updating design model parameters when the current parameter values yield repeated eigenvalues it has not been possible previously to calculate unique eigenvector derivatives recent work has provided a method for determining unique eigenvalue derivatives for this case but methods for calculating the eigenvector sensitivities have been incomplete in this work a complete method for calculation of repeated root eigenvector derivatives is shown for the real symmetric structural eigenproblem the derivation is completed by using information from the second derivative of the eigen problem and is limited to the case of distinct eigenvalue sensitivities as an example the repeated root eigenvector sensitivities are calculated for a simple three degree of freedom beam grillage comparisons of linear approximations using these derivatives to the calculated eigenvectors support the accuracy of the formulation

on doa estimation for rotating arrays using stochastic maximum likelihood approach the flexibility needed to construct doa estimators that can be used with rotating arrays subject to rapid variations of the signal frequency is offered by the stochastic maximum likelihood approach using a combination of analytic methods and monte carlo simulations we show that for low and moderate source correlations the stochastic maximum likelihood estimator that assumes noncorrelated sources has accuracy comparable to the estimator that includes the correlation coefficient as one of the parameters we propose several fast approximations of the stochastic maximum likelihood estimator and compare their accuracy with the cramer rao lower bound we also discuss the model order selection problem for the binary and multiple hypotheses cases

a new index of fit based on mixture methods for the analysis of contingency tables summary a framework based on mixture methods is proposed for evaluating goodness of fit in the analysis of contingency tables for a given model h applied to a contingency table p we consider the two point mixture p 1 r i1 ri2 with 7r the mixing proportion o r 1 and hi and i2 the tables of probabilities for each latent class or component in the unstructured approach recommended here the mixture model applies h to hi but does not impose any restrictions on i2 a contingency table p can generally be represented as such a two point mixture for an interval of 7r values we define our index of lack of fit ir to be the smallest such 7r i e 7r is the fraction of the population that cannot be described by model h this approach can be contrasted with the structured approach that applies model h to both h and i2 and leads to conventional latent class models when h is the hypothesis of independence the case where h is the hypothesis of row column independence and p is a two way contingency table is covered in detail but the procedure is quite general

low complexity estimators for distributed sources in antenna array applications the propagation environment is often more complicated than the ordinarily assumed model of plane wavefronts here a low complexity algorithm is suggested for estimating both the doa and the spread angle of a source subject to local scattering using a uniform linear array the parameters are calculated from the estimates obtained using a standard algorithm such as root music to fit a two ray model to the data the algorithm is shown to give consistent estimates and the statistical performance is studied analytically and through simulations

direction finding for an extended target with possibly non symmetric spatial spectrum we consider the problem of estimating the direction of arrival doa of an extended target in radar array processing two algorithms are proposed that do not assume that the power azimuthal distribution of the scatterers is symmetric with respect to the mass center of the target the first one is based on spectral moments which are easily related to the target s doa the second method stems from a previous paper by the present authors and consists of a least squares fit on the elements of the covariance matrix both methods are simple and are shown to provide accurate estimates furthermore they extend the range of unambiguous doas that can be estimated compared with the same previous paper

in variance of subspace based estimators subspace based estimates i e estimates obtained by exploiting the orthogonality between a sample subspace and a parameter dependent subspace have proved useful in many applications including array processing and system identification the purpose of this paper is to complement the already available theoretical results generally obtained in specific contexts we discuss the generalization of the optimal weighted subspace fitting approach introduced by viberg 1989 in the doa estimation context we exhibit some invariance properties of optimally weighted estimate and we show the equivalence between subspace fitting and subspace matching

a generalization of weighted subspace fitting to full rank models the idea of subspace fitting provides a popular framework for different applications of parameter estimation and system identification previously some algorithms have been suggested based on similar ideas for a sensor array processing problem where the underlying data model is not low rank we show that two of these algorithms dspe and dispare fail to give consistent estimates and introduce a general class of subspace fitting like algorithms for consistent estimation of parameters from a possibly full rank data model the asymptotic performance is analyzed and an optimally weighted algorithm is derived the result gives a lower bound on the estimation performance for any estimator based on a low rank approximation of the linear space spanned by the sample data we show that in general for full rank data models no subspace based method can reach the cramer rao lower bound crb

correlation matching approach for spectrum sensing in open spectrum communications in the new paradigm of open spectrum access the envisioned radio agility calls for fast and accurate spectrum sensing this challenges traditional spectral estimation in this study we propose three new procedures that are able to sense the known spectrum of the candidate or primary user fulfilling the requirements of open spectrum scenarios these procedures are developed by following the framework of correlation matching changing the traditional single frequency scan to a spectral scan with a particular shape and generalizing filter bank designs the proposed techniques are called candidate methods because their goal is to react only when the candidate s spectral shape is present first candidate f is proposed as a spectral detection method where this is based on minimizing the frobenius distance between correlation matrices and can be viewed as an extended version of the weighted overlapped spectrum averaging estimate next candidate g is presented which is a new procedure that is based on a geodesic distance and that presents the lowest complexity lastly a third procedure is studied candidate m which provides the most compliant performance with the demanding open spectrum scenario by generalizing the capon spectral estimator by means of the analytical results simulations of receiver operating characteristics and estimation variance this study shows the advantages of candidate m over the existing filter bank or cyclostationary detector methods

eigenvalue beamforming using a multirank mvdr beamformer and subspace selection we derive eigenvalue beamformers to resolve an unknown signal of interest whose spatial signature lies in a known subspace but whose orientation in that subspace is otherwise unknown the unknown orientation may be fixed in which case the signal covariance is rank 1 or it may be random in which case the signal covariance is multirank we present a systematic treatment of such signal models and explain their relevance for modeling signal uncertainties we then present a multirank generalization of the mvdr beamformer the idea is to minimize the power at the output of a matrix beamformer while enforcing a data dependent distortionless constraint in the signal subspace which we design based on the type of signal we wish to resolve we show that the eigenvalues of an error covariance matrix are fundamental for resolving signals of interest signals with rank 1 covariances are resolved by the largest eigenvalues of the error covariance while signals with multirank covariances are resolved by the smallest eigenvalues thus the beamformers we design are eigenvalue beamformers which extract signal information from eigen modes of an error covariance we address the tradeoff between angular resolution of eigenvalue beamformers and the fraction of the signal power they capture

a fast and accurate single frequency estimator a novel frequency estimator for a single complex sinusoid in complex white gaussian noise is proposed the estimator is more computationally efficient that the optimal maximum likelihood estimator yet attains equally good performance at moderately high signal to noise ratios the estimator is shown to be related to the linear prediction estimator this relationship is used to reveal why the linear prediction estimator does not attain the cramer rao bound even at high signal to noise ratios

doubly constrained robust capon beamformer with ellipsoidal uncertainty sets the doubly constrained robust dcr capon beamformer with a spherical uncertainty set was introduced and studied by stoica and wang here we consider the generalized dcr problem gdcr in which the uncertainty set is an ellipsoid rather than a sphere although as noted previously by stoica and wang this problem is nonconvex and appears to be intractable we show that it can be solved efficiently in fact we prove that the gdcr beamformer can be obtained as a solution to a convex optimization problem to this end we first derive a strong duality result for nonconvex quadratic programs with two quadratic constraints over the complex domain specializing the results to our context leads to a semidefinite programming formulation of the gdcr beamformer

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

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

direction of arrival estimation by eigenstructure methods with imperfect spatial coherence of wave fronts eigenstructure subspace methods for direction of arrival estimation are only applicable when each wave front contributes a rank one component to the array covariance this implies that the wave fronts need to have perfect spatial coherence in several practical situations where the wave fronts may only have partial spatial coherence eigenstructure algorithms show poor performance such as overestimation of the number of sources bias and reduced accuracy and resolution in estimating the directions of arrival in this article the performance degradation due to partial spatial coherence is studied and a new approach is proposed that exploits the underlying coherence model to yield asymptotically exact estimates for finite data this method provides improved results only when the number of snapshots exceeds a certain threshold results of computer simulations are also presented

on circularity circularity is an assumption that was originally introduced for the definition of the probability distribution function of complex normal vectors however this concept can be extended in various ways for nonnormal vectors the first purpose of the paper is to introduce and compare some possible definitions of circularity from these definitions it is also possible to introduce the concept of circular signals and to study whether or not the spectral representation of stationary signals introduces circular components therefore the relationships between circularity and stationarity are analyzed in detail finally the theory of linear mean square estimation for complex signals exhibits some connections with circularity and it is shown that without this assumption the estimation theory must be reformulated

robust adaptive beamforming for general rank signal models the performance of adaptive beamforming methods is known to degrade severely in the presence of even small mismatches between the actual and presumed array responses to the desired signal such mismatches may frequently occur in practical situations because of violation of underlying assumptions on the environment sources or sensor array this is especially true when the desired signal components are present in the beamformer training data snapshots because in this case the adaptive array performance is very sensitive to array and model imperfections the similar phenomenon of performance degradation can occur even when the array response to the desired signal is known exactly but the training sample size is small we propose a new powerful approach to robust adaptive beamforming in the presence of unknown arbitrary type mismatches of the desired signal array response our approach is developed for the most general case of an arbitrary dimension of the desired signal subspace and is applicable to both the rank one point source and higher rank scattered source fluctuating wavefront desired signal models the proposed robust adaptive beamformers are based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix as well as worst case performance optimization simple closed form solutions to the considered robust adaptive beamforming problems are derived our new beamformers have a computational complexity comparable with that of the traditional adaptive beamforming algorithms while at the same time offer a significantly improved robustness and faster convergence rates

on monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations abstract in this paper we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions of first and second order periodic boundary value problems and periodic solutions of functional differential equations we obtain some new results relative to the lower solution and upper solution with

eigenvalues and eigenvectors of covariance matrices for signals closely spaced in frequency the eigenstructures of common covariance matrices are identified for the general case of m closely spaced signals it is shown that the largest signal space eigenvalue is relatively insensitive to signal separation by contrast the ith largest eigenvalue is proportional to delta omega sup 2 i 1 or delta omega sup 4 i 1 where delta omega is a measure of signal separation therefore matrix conditioning degrades rapidly as signal separation is reduced it is also shown that the limiting eigenvectors have remarkably simple structures the results are very general and apply to planar far field direction finding problems involving almost arbitrary scenarios and also to time series analysis of sinusoids exponentials and other signals

sensor array processing based on subspace fitting algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem the methods considered are the deterministic maximum likelihood method ml esprit and a recently proposed multidimensional signal subspace method these methods are formulated in a subspace fitting based framework which provides insight into their algebraic and asymptotic relations it is shown that by introducing a specific weighting matrix the multidimensional signal subspace method can achieve the same asymptotic properties as the ml method the asymptotic distribution of the estimation error is derived for a general subspace weighting and the weighting that provides minimum variance estimates is identified the resulting optimal technique is termed the weighted subspace fitting wsf method numerical examples indicate that the asymptotic variance of the wsf estimates coincides with the cramer rao bound the performance improvement compared to the other techniques is found to be most prominent for highly correlated signals

kappa like indices of observer agreement viewed from a latent class perspective it is common practice to assess consistency of diagnostic ratings in terms of agreement beyond chance to explore the interpretation of such a term we consider relevant statistical techniques such as cohen s kappa and log linear models for agreement on nominal ratings we relate these approaches to a special latent class concept that decomposes observed ratings into a class of systematically consistent and a class of fortuitous ratings this decomposition provides a common framework in which the specific premises of cohen s kappa and of log linear models can be identified and put into perspective as a result it is shown that cohen s kappa may be an inadequate and biased index of chance corrected agreement in studies of intra observer as well as inter observer consistency we suggest a more critical use and interpretation of measures gauging observer reliability by the amount of agreement beyond chance 1998 john wiley sons ltd

an angular parameter estimation method for incoherently distributed sources via generalized shift invariance this paper proposes a new algorithm to estimate the nominal direction of arrival doa and the angular spread of multiple incoherently distributed id sources with the general array manifold gam model the nominal doas are first separated from the original array manifold then a generalized shift invariance property inside the array manifold is identified based on which the nominal doas are obtained when the rank of a trickily formulated matrix drops next the angular spreads are estimated from the central moments of the angular distribution we also derive a polynomial rooting based search free method for nominal doa estimation this method can greatly reduce the computational complexity as compared with the popular esprit id algorithm the proposed algorithm can achieve higher accuracy can handle more sources and applies to a more general array structure extensive simulations are provided to demonstrate the superior performance of the proposed algorithm over the existing works

approximate maximum likelihood estimators for array processing in multiplicative noise environments we consider the problem of localizing a source by means of a sensor array when the received signal is corrupted by multiplicative noise this scenario is encountered for example in communications owing to the presence of local scatterers in the vicinity of the mobile or due to wavefronts that propagate through random inhomogeneous media since the exact maximum likelihood ml estimator is computationally intensive two approximate solutions are proposed originating from the analysis of the high and low signal to noise ratio snr cases respectively first starting with the no additive noise case a very simple approximate ml aml sub 1 estimator is derived the performance of the aml sub 1 estimator in the presence of additive noise is studied and a theoretical expression for its asymptotic variance is derived its performance is shown to be close to the cramer rao bound crb for moderate to high snr next the low snr case is considered and the corresponding aml sub 2 solution is derived it is shown that the approximate ml criterion can be concentrated with respect to both the multiplicative and additive noise powers leaving out a two dimensional 2 d minimization problem instead of a four dimensional 4 d problem required by the exact ml numerical results illustrate the performance of the estimators and confirm the validity of the theoretical analysis

estimating the frequency of a noisy sinusoid by linear regression corresp the estimation of the parameters of a sinusoid from observations of signal samples corrupted by additive noise is investigated at high signal to noise ratios the additive noise is viewed as an equivalent phase noise suggesting frequency and phase estimation by linear regression on the signal phase the variances of the regression estimates are shown to achieve the cramer rao bounds a formula for the variance of the regression frequency estimator is derived in terms of the noise power spectrum a simple formula for the variance with 1 f 2 phase noise is presented

performance study of conditional and unconditional direction of arrival estimation a numerical and analytical study of conditional and unconditional direction of arrival doa estimation is presented explicit expressions for the unconditional cramer rao bounds on the doa estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given it is shown that many doa estimation methods have the same asymptotic statistical properties under conditional and unconditional models the situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed

estimation of directions of arrival of multiple scattered sources we consider the problem of estimating the directions of arrival doa of multiple sources in the presence of local scattering this problem is encountered in wireless communications due to the presence of scatterers in the vicinity of the mobile or when the signals propagate through a random inhomogeneous medium assuming a uniform linear array ula we develop doa estimation algorithms based on covariance matching applied to a reduced size statistic obtained from the sample covariance matrix after redundancy averaging next a computationally efficient estimator based on ar modelling of the coherence loss function is derived a theoretical expression for the asymptotic covariance matrix of this estimator is derived finally the corresponding cramer rao bounds crbs are derived despite its simplicity the ar based estimator is shown to possess performance that is nearly as good as that of the covariance matching method

general asymptotic analysis of the generalized likelihood ratio test for a gaussian point source under statistical or spatial mismodeling this paper investigates the robustness of the generalized likelihood ratio test glrt for a far field gaussian point source given measurements from an array of sensors the performance of the glrt under two types of common modeling errors is investigated the first type is spatial mismodeling which relates to errors due to multipath effects or errors in the assumed number of sources i e deviation from the single point source assumption the second type is statistical mismodeling which relates to errors due to non gaussianity in either the noise or the signal i e deviation from the gaussian assumption it is shown that for some types of modeling errors the detector s performance improves and general conditions for such an improvement are found moreover for both types of errors the change in performance is analyzed and quantified this analysis shows that for a distributed source with small spatial spreading the degradation in performance is significant whereas for a constant modulus point source the performance improves simulations of various cases are shown to verify the analytical results

performance degradation of doa estimators due to unknown noise fields a statistical performance analysis of subspace based directions of arrival doa estimation algorithms in the presence of correlated observation noise with unknown covariance is presented the analysis of five different estimation algorithms is unified by a single expression for the mean squared doa estimation error which is derived using a subspace perturbation expansion the analysis assumes that only a finite amount of array data is available

chirp parameter estimation from a sample covariance matrix this paper considers the problem of estimating the bandwidth and the center frequency of a linear chirp signal the nonstationarity property of chirp signals implies that the signal has high rank and reduces the applicability of subspace based algorithms significantly however the special structure of the sample covariance matrix invites the use of regular frequency estimation algorithms herein we show how subspace type algorithms may be modified to provide accurate signal parameter estimates for linear chirp signals at reasonable complexity the root music algorithm is used as an example

maximum likelihood methods for direction of arrival estimation five methods of direction of arrival doa estimation which can be derived from the maximum likelihood ml principle are considered the ml method mlm results from the application of the ml principle to the statistics of the observed raw data the standard multiple signal classification music procedure called music 1 is obtained as a brute force approximation of the mlm an improved music procedure named music 2 is obtained by applying the ml principle to the statistics of certain linear combinations of the sample noise space eigenvectors a procedure which compromises between the good performance of the mlm and the computational simplicity of music is a method of direction estimation mode 1 which is derived as a large sample realization of the mlm a fifth method called mode 2 is obtained by using the ml principle on the statistics of certain linear combinations of the sample eigenvectors mode 2 is computationally less demanding than the mlm it is of the same complexity as mode 1 and statistically more efficient a numerical comparison of these five doa estimation methods is presented it confirms the analytic results on their theoretical performance levels

joint angular and delay domain mimo propagation parameter estimation using approximate ml method in this paper we derive an estimation method that jointly estimates the parameters of the concentrated propagation paths and the distributed scattering component that are frequently observed in multiple input multiple output mimo channel sounding measurements the joint angular delay domain model leads to a correlation matrix with high dimensionality which makes direct implementation of a maximum likelihood ml estimator unfeasible we derive low complexity methods for computing approximate ml estimates that exploit the structure of the covariance matrices we propose an iterative two step procedure that alternates between the estimation of the parameters of the concentrated propagation paths and the parameters of the distributed scattering for the distributed scattering the estimator first optimizes the parameters describing their time delay structure then using the estimated time delay parameters the parameters of the angular distributions are optimized we present simulation results and compare the estimated time delay and angular distributions to the actual distributions demonstrating that high quality estimates are obtained the large sample performance of the estimator is studied by establishing the cramer rao lower bound crlb and comparing it to the variances of the estimates the simulations show that the variance of the proposed estimation technique reaches the crlb for relatively small sample size for most parameters and no bias is observed

on the expectation of the product of four matrix valued gaussian random variables the formula for the expectation of the product of four scalar real gaussian random variables is generalized to matrix valued real or complex gaussian random variables as an application of the extended formula a simple derivation is presented of the covariance matrix of instrumental variable estimates of parameters in multivariable regression models

efficient subspace based estimator for localization of multiple incoherently distributed sources in this paper a new subspace based algorithm for parametric estimation of angular parameters of multiple incoherently distributed sources is proposed this approach consists of using the subspace principle without any eigendecomposition of the covariance matrix so that it does not require the knowledge of the effective dimension of the pseudosignal subspace and therefore the main difficulty of the existing subspace estimators can be avoided the proposed idea relies on the use of the property of the inverse of the covariance matrix to exploit approximately the orthogonality property between column vectors of the noise free covariance matrix and the sample pseudonoise subspace the resulting estimator can be considered as a generalization of the pisarenko s extended version of capon s estimator from the case of point sources to the case of incoherently distributed sources theoretical expressions are derived for the variance and the bias of the proposed estimator due to finite sample effect compared with other known methods with comparable complexity the proposed algorithm exhibits a better estimation performance especially for close source separation for large angular spread and for low signal to noise ratio

intrinsic limits of dimensionality and richness in random multipath fields we study the dimensions or degrees of freedom of farfield multipath that is observed in a limited source free region of space the multipath fields are studied as solutions to the wave equation in an infinite dimensional vector space we prove two universal upper bounds on the truncation error of fixed and random multipath fields a direct consequence of the derived bounds is that both fixed and random multipath fields have an effective finite dimension for circular and spherical spatial regions we show that this finite dimension is proportional to the radius and area of the region respectively we use the karhunen loegraveve kl expansion of random multipath fields to quantify the notion of multipath richness the multipath richness is defined as the number of significant eigenvalues in the kl expansion that achieve 99 of the total multipath energy we establish a lower bound on the largest eigenvalue this lower bound quantifies to some extent the well known reduction of multipath richness with reducing the angular power spread of multipath angular power spectrum

direction of arrival estimation of an amplitude distorted wavefront in a number of array signal processing applications such as underwater source localization the propagation medium is not homogeneous which causes a distortion of the wavefront received by the array there has been some interest in the direction of arrival doa estimation of such distorted wavefronts most works on this problem considered the so called multiplicative noise scenario based on the rather strong assumption that the distortion is random and can be parameterized by a small number of parameters to gain robustness against mismodeling we assume a scenario in which the wavefront amplitude is distorted in a completely arbitrary way our main contribution consists of showing how to eliminate all nuisance distortion parameters from the likelihood function corresponding to such a scenario and obtain a robust maximum likelihood doa estimate by means of a simple one dimensional 1 d search despite its simplicity it is shown that the estimator has a performance close to the cramer rao bound crb for which we derive a closed form expression moreover its accuracy is comparable with that of estimators that require knowledge of the form of amplitude distortions

parametric localization of distributed sources most array processing algorithms are based on the assumption that the signals are generated by point sources this is a mathematical constraint that is not satisfied in many applications in this paper we consider situations where the sources are distributed in space with a parametric angular cross correlation kernel we propose an algorithm that estimates the parameters of this model using a generalization of the music algorithm the method involves maximizing a cost function that depends on a matrix array manifold and the noise eigenvectors we study two particular cases coherent and incoherent spatial source distributions the spatial correlation function for a uniformly distributed signal is derived from this we find the array gain and show that in contrast to point sources it does not increase linearly with the number of sources we compare our method to the conventional point source music algorithm the simulation studies show that the new method outperforms the music algorithm by reducing the estimation bias and the standard deviation for scenarios with distributed sources it is also shown that the threshold signal to noise ratio required for resolving two closely spaced distributed sources is considerably smaller for the new method

derivation of linear estimation algorithms from measurements affected by multiplicative and additive noises this paper addresses the problem of estimating signals from observation models with multiplicative and additive noises assuming that the state space model is unknown the multiplicative noise is non white and the signal and additive noise are correlated recursive algorithms are derived for the least squares linear filter and fixed point smoother the proposed algorithms are obtained using an innovation approach and taking into account the information provided by the covariance functions of the process involved