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

direction of arrival estimation for nonuniform sensor arrays from manifold separation to fourier domain music methods in this paper the problem of spectral search free direction of arrival doa estimation in arbitrary nonuniform sensor arrays is addressed in the first part of the paper we present a finite sample performance analysis of the well known manifold separation ms based root music technique then we propose a new class of search free doa estimation methods applicable to arrays of arbitrary geometry and establish their relationship to the ms approach our first technique is referred to as fourier domain fd root music and is based on the fact that the spectral music function is periodic in angle it uses the fourier series to expand this function and reformulate the underlying doa estimation problem as an equivalent polynomial rooting problem our second approach applies the zero padded inverse fourier transform to the fd root music polynomial to avoid the polynomial rooting step and replace it with a simple line search our third technique refines the fd root music approach by using weighted least squares approximation to compute the polynomial coefficients the proposed techniques are shown to offer substantially improved performance to complexity tradeoffs as compared to the ms technique

exact and operator rational approximate solutions of the helmholtz weyl composition equation in underwater acoustics the quadratic profile the application of phase space and path integral methods to both mathematical and computational direct and inverse wave propagation modeling at the level of the scalar one way helmholtz equation is briefly reviewed the role of operator symbols is stressed and their properties briefly discussed the construction of the operator symbol requires the exact or approximate solution of the helmholtz weyl composition equation in the weyl pseudodifferential operator calculus the exact symbols for several quadratic profiles are presented and briefly analyzed the symbols exactly corresponding to a family of operator rational approximations are also presented for the quadratic case these results are used to illustrate several points pertinent to wide angle propagation modeling and the refractive index profile reconstruction problem in underwater acoustics

point set lattice theoretic topology this essay attempts to survey in a coherent way certain aspects of point set lattice theoretic or poslat topology by which we mean fuzzy topology grounded in notions of sets functions powersets and powerset operators the latter two being lattice theoretic in nature and examined from a lattice theoretic point of view using methods of category theory connections with other related issues and developments are frequently given

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

signal enhancement a composite property mapping algorithm a signal enhancement algorithm is developed that seeks to recover a signal from noise contaminated distorted measurements made on that signal this object is achieved by utilizing a set of properties which the signal is known or is hypothesized as possessing the measured signal is modified to the smallest degree necessary to sequentially possess each of the individual properties conditions for the algorithm s convergence are established in which the primary requirement is that a composite property mapping be closed this is a relatively unrestricted condition in comparison to that required of most existing signal enhancement algorithms

on almost compactness in the fuzzy setting net theoretic and filter theoretic characterizations of almost n compactness are provided corrected version of a result of meng han and meng guangwu fuzzy sets and systems 91 1997 115 is provided almost fuzzy compactness is introduced and its characterization is provided by using fuzzy nets and fuzzy filters

lowen s compactness in l fuzzy topological spaces abstract r lowen has introducedin 1976 a fuzzy compactness for fuzzy topological spaces wang has generalized it in 1988 to l fuzzy topological spaces and given it a characterization by means of nets in this paper we obtain some new characterization for lowen s compactness in l fuzzy topological spaces means of remote neighborhood families r covers filters and the family of closed l fuzzy subsets which has the finite intersection property in addition we have proved that lowen s compactness is an l good extension of usual compactness in general topological spaces

exact constructions of square root helmholtz operator symbols the focusing quadratic profile operator symbols play a pivotal role in both the exact well posed one way reformulation of solving the elliptic helmholtz equation and the construction of the generalized bremmer coupling series the inverse square root and square root helmholtz operator symbols are the initial quantities of interest in both formulations in addition to providing the theoretical framework for the development and implementation of the parabolic equation pe method in wave propagation modeling exact standard left and weyl symbol constructions are presented for both the inverse square root and square root helmholtz operators in the case of the focusing quadratic profile in one transverse spatial dimension extending and ultimately unifying the previously published corresponding results for the defocusing quadratic case j math phys 33 1887 1914 1992 both i spectral modal summation representations and ii contour integral representations exploiting the underlying periodicity of the associated quantum mechanical harmonic oscillator problem are derived and ultimately related through the propagating and nonpropagating contributions to the operator symbol high and low frequency asymptotic operator symbol expansions are given along with the exact symbol representations for the corresponding operator rational approximations which provide the basis for the practical computational realization of the pe method moreover while the focusing quadratic profile is in some respects nonphysical the corresponding helmholtz operator symbols nevertheless establish canonical symbol features for more general profiles containing locally quadratic wells

phase space methods and path integration the analysis and computation of scalar wave equations abstract the scalar helmholtz equation plays a significant role in studies of electromagnetic seismic and acoustic direct wave propagation phase space or microscopic methods and path functional integral representations provide the appropriate framework to extend homogeneous fourier methods to inhomogeneous environments the two complementary approaches to this analysis and computation of the n dimensional helmholtz propagator are reviewed for the factorization one way path integration invariant imbedding approach the exact solution of the helmholtz composition equation for the weyl square root operator symbol is presented in the quadratic case the filtered one way phase space marching algorithm is examined in detail and compared numerically with wide angle one way partial differential wave equations formally derived from approximation theory for the second approach which directly constructs approximate two way path functionals the feasibility of a monte carlo statistical evaluation of the feynman garrod propagator is discussed

on the asymptotic performance analysis of subspace doa estimation in the presence of modeling errors case of music this paper provides a new analytic expression of the bias and rms error root mean square error of the estimated direction of arrival doa in the presence of modeling errors in first order approximations of the rms error are derived which are accurate for small enough perturbations however the previously available expressions are not able to capture the behavior of the estimation algorithm into the threshold region in order to fill this gap we provide a second order performance analysis which is valid in a larger interval of modeling errors to this end it is shown that the doa estimation error for each signal source can be expressed as a ratio of hermitian forms with a stochastic vector containing the modeling error then an analytic expression for the moments of such a hermitian forms ratio is provided finally a closed form expression for the performance bias and rms error is derived simulation results indicate that the new result is accurate into the region where the algorithm breaks down

the statistical performance of the music and the minimum norm algorithms in resolving plane waves in noise this paper presents an asymptotic statistical analysis of the null spectra of two eigen assisted methods music 1 and minimum norm 2 for resolving independent closely spaced plane waves in noise particular attention is paid to the average deviation of the null spectra from zero at the true angles of arrival for the plane waves these deviations are expressed as functions of signal to noise ratios number of array elements angular separation of emitters and the number of snapshots in the case of music an approximate expression is derived for the resolution threshold of two plane waves with equal power in noise this result is validated by monte carlo simulations

almost n compact sets in l fuzzy topological spaces abstract in this paper the concept of almost n compactness in l fuzzy topological spaces is introduced the characterizations of almost n compact sets are systematically discussed it is showed that the fuzzy almost continuous image of an almost n compact set is an almost n compact set it is proved that the almost n compactness is a good extension

single antenna power measurements based direction finding in this paper the problem of estimating direction of arrival doa of multiple uncorrelated sources from single antenna power measurements is addressed utilizing the fact that the antenna pattern is bandlimited and can be modeled as a finite sum of complex exponentials we first show that the problem can be transformed into a frequency estimation problem then we explain how the annihilating filter method can be used to solve for the doa in the noiseless case in the presence of noise we propose to use cadzow denoising that is formulated as an iterative algorithm derived from exploiting the matrix rank and linear structure properties furthermore we have also derived the cramer rao bound crb and reviewed several alternative approaches that can be used as a comparison to the proposed approach from the simulation and experimental results we demonstrate that the proposed approach significantly outperforms other approaches it is also evident from the monte carlo analysis that the proposed approach converges to the crb

factorization and path integration of the helmholtz equation numerical algorithms the propagator for the reduced scalar helmholtz equation plays a significant role in both analytical and computational studies of acoustic direct wave propagation path functional integrals are taken to provide the principal representation of the propagator and are computed directly the path integral is the primary tool in extending the classical fourier methods so appropriate for wave propagation in homogeneous media to inhomogeneous media for transversely inhomogeneous environments the n dimensional helmholtz equation can be exactly factored into separate forward and backward one way wave equations a parabolic based one way phase space path integral construction provides the generalization of the tappert hardin split step fft algorithm to the full one way factored helmholtz wave equation these extended marching algorithms can readily accommodate density profiles and range updating and further in conjunction with imbedding methods provide the basis for incorporating backscatter effects in a complementary manner for general range dependent environments elliptic based two way path integral constructions lead to an approximate representation of the propagator feynman garrod and a natural statistical monte carlo means of evaluation taken together the path integrals provide the basis for a global analysis in addition to providing a unifying framework for dynamical approximations resolution of the square root operator and the concept of an underlying stochastic process the one way marching algorithms are applied to ocean acoustic environments seismological environments and extreme model environments designed to establish their range of validity and manner of breakdown

sampling signals with finite rate of innovation the authors consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation examples of signals with a finite rate of innovation include streams of diracs e g the poisson process nonuniform splines and piecewise polynomials even though these signals are not bandlimited we show that they can be sampled uniformly at or above the rate of innovation using an appropriate kernel and then be perfectly reconstructed thus we prove sampling theorems for classes of signals and kernels that generalize the classic bandlimited and sinc kernel case in particular we show how to sample and reconstruct periodic and finite length streams of diracs nonuniform splines and piecewise polynomials using sinc and gaussian kernels for infinite length signals with finite local rate of innovation we show local sampling and reconstruction based on spline kernels the key in all constructions is to identify the innovative part of a signal e g time instants and weights of diracs using an annihilating or locator filter a device well known in spectral analysis and error correction coding this leads to standard computational procedures for solving the sampling problem which we show through experimental results applications of these new sampling results can be found in signal processing communications systems and biological systems

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

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

music maximum likelihood and cramer rao bound further results and comparisons the problem of determining the direction of arrival of narrowband plane waves using sensor arrays and the related problem of estimating the parameters of superimposed signals from noisy measurements are studied a number of results have been recently presented by the authors on the statistical performance of the multiple signal characterization music and the maximum likelihood ml estimators for the above problems this work extends those results in several directions first it establishes that in the class of weighted music estimators the unweighted music achieves the best performance i e the minimum variance of estimation errors in large samples next it derives the covariance matrix of the ml estimator and presents detailed analytic studies of the statistical efficiency of music and ml estimators these studies include performance comparisons of music and mle with each other as well as with the ultimate performance corresponding to the cramer rao bound finally some numerical examples are given which provide a more quantitative study of performance for the problem of finding two directions with uniform linear sensor arrays

derivation and application of extended parabolic wave theories ii path integral representations the n dimensional reduced scalar helmholtz equation for a transversely inhomogeneous medium is naturally related to parabolic propagation models through 1 the n dimensional extended parabolic weyl pseudodifferential equation and 2 an imbedding in an n 1 dimensional parabolic schrodinger equation the first relationship provides the basis for the parabolic based hamiltonian phase space path integral representation of the half space propagator the second relationship provides the basis for the elliptic based path integral representations associated with feynman and fradkin feynman and garrod and feynman and dewitt morette exact and approximate path integral constructions are derived for the homogeneous and transversely inhomogeneous cases corresponding to both narrow and wide angle extended parabolic wave theories the path integrals allow for a global perspective of the transition from elliptic to parabolic wave theory in addition to providing a unifying framework for dynamical approximations resolution of the square root operator and the concept of an underlying stochastic process

direction finding with fewer receivers via time varying preprocessing we present a new technique for localizing multiple narrowband sources by a passive sensor array based on dimensionality reducing time varying preprocessing of the sensor outputs the technique allows a significant reduction in the number of receivers required for the implementation with only two receivers sufficing in the extreme case the estimation method we use is based on approximating the corresponding maximum likelihood estimator by a computationally simpler generalized least squares gls estimator that is proved to be both consistent and asymptotically efficient simulation results confirming the theoretical results are included

generalization of the bremmer coupling series an operator formalism is developed to expand the acoustic wave field in a multi dimensionally smoothly varying medium generated by a source localized in space and time into a sum of constituents each of which can be interpreted as a wave that has traveled up and down with respect to a direction of preference a definite number of times this expansion is a generalization of the bremmer coupling series the condition of smoothness of the medium relates to the width of the signature of the source in the configuration both the existence and the convergence in the weak sense of the expansion are discussed the operator calculus involved leads to a natural generalization of the concept of slowness surface to multi dimensionally smoothly varying media the operator associated with the corresponding generalized vertical slowness induces the full one way wave operator in the type of media under consideration in addition a wavefield decomposition operator as well as an interaction operator that couples the decomposed constituents are derived

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

propagation modelling based on wave field factorization and invariant imbedding the proposed propagation models address the propagation of cw acoustic fields through a transition region separating two different range independent oceans wave field factorization refers to the conceptual decoupling of the radiation fields in the two range independent oceans into positive and negative propagating components invariant imbedding refers to the reformulation of the propagation problem from a two point boundary value problem to an initial value problem in the reformulation the extent of the transition region is an independent variable the formulation is expressed in terms of reflection and transmission operators which apply to the transition region the proposed models are generalizations of existent models in reflection seismology these latter models allow for no cross range variability of wave speed in either the two now homogeneous oceans nor in the transition region the seismology models do accommodate p s coupling which is neglected in the acoustic application the incorporat

computation of the exact information matrix of gaussian time series with stationary random components the paper presents an algorithm for efficient recursive computation of the fisher information matrix of gaussian time series whose random components are stationary and whose means and covariances are functions of a parameter vector the algorithm is first developed in a general framework and then specialized to the case of autoregressive moving average processes with possible additive white noise the asymptotic behavior of the algorithm is explored and a termination criterion is derived finally the algorithm is used to demonstrate the behavior of the exact cramer rao bound for unbiased estimates for some arma processes as a function of the number of data points it is shown that for processes with zeros near the unit circle and short data records the exact cramer rao bound differs dramatically from its common approximation based on asymptotic theory

wavefield modeling and array processing iii resolution capacity for pt ii see ibid vol 42 no 10 p 2560 1994 we use here the wavefield modeling formalism in order to derive some fundamental limitations on the performance of passive arrays we first derive upper bounds on both the ideal and effective resolution capacities and show that the effective resolution capacity is bounded by the effective rank of the relevant sampling matrix i e is determined by the array structure we then study how the resolution capacity is affected when the sources are constrained to lie within an angular sector we also look at the case where the source spectra are known a priori to be flat and show that contrary to the common opinion if the array satisfies the spectral sampling condition the effective wideband resolution capacity is bounded by the same bound as the narrowband one we conclude by examining the interesting phenomenon of resonance in arrays we show that these resonances far from being mathematical artifacts can manifest quite dramatically in the performance of arrays

wide angle one way wave equations a one way wave equation also known as a paraxial or parabolic wave equation is a differential equation that permits wave propagation in certain directions only such equations are used regularly in underwater acoustics in geophysics and as energy absorbing numerical boundary conditions the design of a one way wave equation is connected with the approximation of 1 s2 1 2 on 1 1 by a rational function which has usually been carried out by pade approximation this article presents coefficients for l2 l and other alternative classes of approximants that have better wide angle behavior for theoretical results establishing the well posedness of these wide angle equations see the work of trefethen and halpern well posedness of one way wave equations and absorbing boundary conditions math comput 47 421 435 1986

doa estimation via manifold separation for arbitrary array structures in this paper we consider the manifold separation technique mst which stems from the wavefield modeling formalism developed for array processing mst is a method for modeling the steering vector of antenna arrays of practical interest with arbitrary 2 d or 3 d geometry it is the product of a sampling matrix dependent on the antenna array only and a vandermonde structured coefficients vector depending on the wavefield only this allows fast direction of arrival doa algorithms designed for linear arrays to be used on arrays with arbitrary configuration in real world applications the calibration measurements used to determine the sampling matrix are corrupted by noise this impairs the performance of mst based algorithms in particular we study the effect of noisy calibration measurements on subspace based doa algorithms using mst expressions describing the error in the doa estimates due to calibration noise and truncation are derived this allows predicting the performance of mst based algorithms in real world applications the analysis is verified by simulations we established a link between the optimal number of selected modes and the statistics of calibration noise we analyze the modeling error when mst is used for 1 d azimuth doa estimation

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

wavefield modeling and array processing i spatial sampling we introduce the concept of wavefield modeling and study its relationship to array professing and direction finding we show how the output of an array can be written as the product of a wavefield independent sampling matrix and an array independent coefficient vector using this decomposition we derive the conditions under which the array output may be linearly interpolated to give the array output of a different array within a desired accuracy we proceed to show under what conditions the array output may be linearly interpolated to give the value of the wavefield over a continuous manifold as a result we also derive conditions under which the array manifold may be linearly transformed between frequencies finally we treat the case where the sources are known to be limited to specific possibly disjoint angular sectors of arbitrary shape and show how the sampling matrix can in this case be replaced by a modified sampling matrix of lower rank this result yields a straightforward extension of the formalism presented in this paper to the ease of limited angular sectors in two companion papers we use wavefield modeling to derive practical algorithms and bounds on the performance of arrays

wavefield modeling and array processing ii algorithms for pt i see ibid vol 42 no 10 p 2549 1994 we present several novel algorithms for array processing as well as extensions of existing methods based on this approach we first consider the problem of localization of wideband sources via coherent processing and show how wavefield modeling enables us to derive expressions for the frequency transformation focusing matrices this method is extended to three dimensions and to sector processing we then develop computationally efficient implementations of music and root music for the narrowband and the coherent and incoherent wideband cases as well as a natural extension of root music to any 2 d array in addition wavefield modeling allows us for the first time to extend root music to 3 d arrays and wavefields we also present a low complexity variant of root music for direction finding within a limited angular sector finally we derive a low dimensional sufficient statistic and reduced rank processing schemes for the case of oversampled arrays and or limited angular sector scenarios

derivation and application of extended parabolic wave theories i the factorized helmholtz equation the reduced scalar helmholtz equation for a transversely inhomogeneous half space supplemented with an outgoing radiation condition and an appropriate boundary condition on the initial value plane defines a direct acoustic propagation model this elliptic formulation admits a factorization and is subsequently equivalent to a first order weyl pseudodifferential equation which is recognized as an extended parabolic propagation model perturbation treatments of the appropriate weyl composition equation result in a systematic development of approximate wave theories which extend the narrow angle weak inhomogeneity and weak gradient ordinary parabolic schrodinger approximation the analysis further provides for the formulation and exact solution of a multidimensional nonlinear inverse problem appropriate for ocean acoustic and seismic studies the wave theories foreshadow computational algorithms the inclusion of range dependent effects and the extension to 1 the vector formulation appropriate for elas