discrete time techniques for time delay estimation basic aspects of time delay estimation tde based on sampled signals are investigated the direct cross correlation method is analyzed and compared to the average square difference function asdf and the addition only based average magnitude difference function amdf estimators their relative accuracy is theoretically evaluated and previous empirical results are explained it is shown that both the asdf and the amdf based estimators outperform the direct cross correlation based estimator for medium high signal to noise ratios moreover the amdf based estimator which avoids any multiplications significantly reduces the computational complexity of the estimation procedure while offering only a moderate performance loss with respect to the asdf based estimator

estimation of input pulse locations from the response of an all pole transfer system using tapered rank reduction when ordinary rank reduction is used to remove the characteristics of the transfer system and to estimate the multipulse input time series the nonsignificant singular values are sharply cut off by low order truncation if the system q quality factor is high and then a large ripple occurs around each pulse location in order to avoid these difficulties a method is proposed in which the multipulse time series is estimated by a rank reduction using a tapering window in order to suppress the ripple due to the low order sharp truncation and then by applying the pole estimation method to the inverse fourier transform of the resultant time series thus the pulse locations are accurately estimated by using the pulse locations as the initial estimates the maximum likelihood estimates of the pulse locations are obtained from simulation experiments these principles are confirmed

criteria for quasi convexity and pseudo convexity relationships and comparisons a first order criterion for pseudo convexity and second order criteria for quasi convexity and pseudo convexity are given for twice differentiable functions on open convex sets the relationships between these second order criteria and other known criteria are also analysed finally the numbers of operations required to verify these criteria are calculated and compared

lamb wave propagation in inhomogeneous elastic waveguides the problem of lamb wave propagation in an axially multilayered waveguide is treated by a multimodal approach a general formalism is proposed that avoids the numerical divergence due to evanescent

generalized invex monotonicity abstract in this paper the generalized invex monotone functions are defined as an extension of monotone functions a series of sufficient and necessary conditions are also given that relate the generalized invexity of the function with the generalized invex monotonicity of its gradient function this new class of functions will be important in order to characterize the solutions of the variational like inequality problem and mathematical programming problem

matrix theoretic criteria for the quasiconvexity of twice continuously differentiable functions abstract the author examines matrices and bordered matrices having exactly one or at most one negative eigenvalue these results are then used to state matrix theoretic criteria for the quasiconvexity of twice continuously differentiable functions for quadratic functions a new criterion for quasiconvexity is established and its equivalence to the already known criterion 11 23 is also shown

lower bounds on worst case probability of large error for two channel time delay estimation a lower bound on the worst case probability of large error for two channel time delay estimation using random signals is developed the bound is based on the minimum probability of error m ary hypothesis test using a maximum likelihood estimator mle the bound can only be evaluated approximately however it can be determined arbitrarily well via simulation if the mle can be instrumented the bound is evaluated in detail for uniform lowpass signal and noise spectra and large bandwidth time product it is then compared with another lower bound based on a binary hypothesis test with computer simulation results for an approximate mle instrumentation and with an upper bound established via computer simulation for a correlator for a uniform lowpass spectrum the m ary bound is shown to be very nearly a greatest lower bound over the full range of input signal to noise ratio further the correlator is shown to be very nearly an optimal instrumentation in the sense of reaching the minimum probability of large error

robust adapative kalman filtering for systems with unknown step inputs and non gaussian measurement errors target tracking with kalman filters is hampered by target maneuvering and unknown process and measurement noises we show that moving data windows may be used to analyze state and measurement error sequences determining robust estimates of bias and covariance for steps in the system forcing functions and non gaussian measurement errors the robust estimators yield improvements over linear bias and covariance estimators extensive simulations compare conventional linear adaptive and robust adaptive average step responses of a first order system filter quantities examined are state estimate state error process and measurement covariance estimates kalman gain and input step estimate

delay estimation using narrow band processes array processing of narrow band gaussian signals is studied with emphasis on delay estimation the barankin bound is used to examine the effect of ambiguity on mean square measurement error when the bound is plotted as a function of signal to noise ratio one observes a distinct threshold above the critical signal to noise ratio the lower bound on mean square error is given by the cramer rao inequality which is approached by the barankin inequality under these conditions below the threshold the barankin bound can exceed the cramer rao bound by large factors the relative magnitude of the bounds in that region depends critically on the ratio of signal center frequency to signal bandwidth

estimating the gap of finite metric spaces of strict p negative type abstract let x d be a finite metric space this paper first discusses the spectrum of the p distance matrix of a finite metric space of p negative type and then gives upper and lower bounds for the so called gap x p of a finite metric space of strict p negative type furthermore estimations for x p under a certain gluing construction for finite metric spaces are given and finally be applied to finite ultrametric spaces

hadamard inverses square roots and products of almost semidefinite matrices abstract let a aij be an n n symmetric matrix with all positive entries and just one positive eigenvalue bapat proved then that the hadamard inverse of a given by a 1 1 a ij is positive semidefinite we show that if moreover a is invertible then a 1 is positive definite we use this result to obtain a simple proof that with the same hypotheses on a except that all the diagonal entries of a are zero the hadamard square root of a given by a 1 2 a ij 1 2 has just one positive eigenvalue and is invertible finally we show that if a is any positive semidefinite matrix and b is almost positive definite and invertible then a b 1 e t b 1 e a

on euclidean distance matrices abstract if a is a real symmetric matrix and p is an orthogonal projection onto a hyperplane then we derive a formula for the moore penrose inverse of pap as an application we obtain a formula for the moore penrose inverse of an euclidean distance matrix edm which generalizes formulae for the inverse of a edm in the literature to an invertible spherical edm we associate a laplacian matrix which we define as a positive semidefinite n n matrix of rank n 1 and with zero row sums and prove some properties known results for distance matrices of trees are derived as special cases in particular we obtain a formula due to graham and lovasz for the inverse of the distance matrix of a tree it is shown that if d is a nonsingular edm and l is the associated laplacian then d 1 l is nonsingular and has a nonnegative inverse finally infinitely divisible matrices are constructed using edms

invariant monotone vector fields on riemannian manifolds abstract various concepts of invariant monotone vector fields on riemannian manifolds are introduced some examples of invariant monotone vector fields are given several notions of invexities for functions on riemannian manifolds are defined and their relations with invariant monotone vector fields are studied

definiteness and semidefiniteness of quadratic forms revisited abstract it is shown how the schur complement theory can be used for the derivation of criteria for the definiteness or semidefiniteness of the restriction of a quadratic form to the null space of a matrix

closed loop least mean square time delay estimator an lms closed loop time delay estimator is presented it uses the error between two samples of the incoming signal the difference between the delayed signal and the reference signal passed through a known delay as a performance index for the estimator the lms algorithm adaptively controls the delay so as to minimize the mean square of this error the controlled delay is implemented using surface acoustic wave devices certain design conditions are applied resulting in a unique minimum for the performance surface it is shown that the proposed estimator is unbiased and has a small variance if the input signal occupies most of the system bandwidth in fact the variance depends on the input noise power and the generalized noise to signal power ratio r n 0 r s 0 as well as on the loop gain the analysis performed also gives a bound on the loop gain required for convergence of the estimator and predicts its rate of convergence computer simulation results show good agreement with the theory

algorithms for ambiguity function processing calculation of the complex ambiguity function is viewed as the basis for joint estimation of the differential delay and differential frequency offset between two waveforms that contain a common component plus additive noise in many applications the required accuracy leads to a need for integration over long data sets that can become a challenge for near real time digital processing the nature of the ambiguity processing is interpreted and an algorithm approach is shown that minimizes the processing burden over a broad category of applications without affecting performance

a unified approach to closed loop time delay estimation systems two generalized configurations for a closed loop delay estimation system cldes are discussed the indirect correlation ic configuration is compared to the conventional cldes the direct correlation dc configuration it is shown that the baseband equivalents of the two configurations differ only by the input noise however the noise power in the ic configuration is far less than that of the dc configuration using the known procedure for calculation of the variance of the time delay estimator it is shown that the two configurations result in the same variance however this procedure is known to be incorrect since for the direct correlation configuration which is known to have an intrinsic noise that persists even when the input signals are ideal the variance is nonzero for zero input signal to noise ratio snr thus another procedure is suggested for variance calculation that overcomes this problem it is shown using this expression that the variance of the time delay estimator is smaller for the ic configuration provided the input snr is not less than 0 db

a first order characterization of generalized monotonicity it is shown that pseudomonotone and quasimonotone maps can be characterized by a first order property provided they are regular this result extends the well known characterization of nonvanishing generalized monotone maps to an essentially larger class the paper supplements a recent contribution by crouzeix and ferland 1996 and solves a related open problem concerning homogeneous excess demand functions which occur in general equilibrium theory

modelling of electromagnetic waves in periodic media with finite elements edge elements have been previously used to study electromagnetic waves conically propagating through a finite stack of arrays of fibres ieee trans magn 38 2 2002 this paper presents a new extension of this technique to the analysis of the propagation of such waves in a doubly periodic array of fibres in the proposed approach only the unit cell of the periodic material has to be meshed thanks to floquet bloch theory

a new generalized cross correlator a new generalized cross correlator gcc for the passive time delay estimation problem is presented the interpretation of this gcc is that of estimating the cross correlation function by cross correlating the least mean square estimates of the signal component in each of the observed waveforms the implementation is simply a gcc with the weighting filter equal to the magnitude coherency squared numerical evaluation of the performance of this processor and a robust version indicate that they compare favorably to some of the well known gcc procedures

error analysis and bounds in time delay estimation we have analyzed the error propagation in the classical delay estimation based on the identification of the maximum of the cross correlation between the input signals the resulting error propagation model has the form of a linear combination of the errors additional to the signal samples these errors are weighted by the derivative of the input signals at the sampling instants based on the error propagation model we have further found an upper bound to the square of the estimation error the use of the model is demonstrated by two simple examples

eigenvalue problems for doubly periodic elastic structures and phononic band gaps we consider the problem of elastic waves propagating in a two dimensional array of circular cavities taking rigorous account of coupling between shear and dilational waves a technique originally due to rayleigh is derived that involves an elegant identity between the singular and non singular components of the stress fields in the array this leads to an infinite linear system which can be truncated and solved in order to determine the complete structure of the propagating modes of particular interest is the possibility of exhibiting phononic band gaps i e domains of frequency for which all propagating vibration in the material is suppressed

criteria for differentiable generalized monotone maps first order criteria for pseudomonotonicity and quasimonotonicity are given for differentiable maps on open convex sets these criteria are proved stronger than those introduced earlier

improved multimodal method for the acoustic propagation in waveguides with a wall impedance and a uniform flow we present an efficient multimodal method to describe the acoustic propagation in the presence of a uniform flow in a waveguide with locally a wall impedance treatment the method relies on a variational formulation of the problem which allows to derive a multimodal formulation within a rigorous mathematical framework notably to properly account for the boundary conditions on the walls being locally the myers condition and the neumann condition otherwise also the method uses an enriched basis with respect to the usual cosine basis able to absorb the less converging part of the modal series and thus to improve the convergence of the method using the cosine basis the modal method has a low convergence 1 n with n the order of truncation using the enriched basis the improvement in the convergence is shown to depend on the mach number from 1 n5 to roughly 1 n1 5 for m 0 to m close to unity the case of a continuously varying wall impedance is considered and we discuss the limiting case of piecewise constant impedance which defines pressure edge conditions at the impedance discontinuities

time delay estimation via cross correlation in the presence of large estimation errors the estimate of the difference in time of arrival of a common random signal received at two sensors each of which also receives uncorrelated noise is examined for both small and large estimation errors it is shown that as the post integration signal to noise ratio decreases the correlator exhibits a thresholding effect that is the probability of a large error an anomalous estimate increases rapidly approximate theoretical results for the probability of an anomaly are presented and are verified experimentally the variance of the time delay estimate is examined for both a gated mode in which the time delay corresponding to the correlation peak closest to the true time delay is used as the estimate of time delay and an ungated mode in which the time delay corresponding to the largest peak over the full range of the correlator delay times is used as the estimate the observed variance for both modes is compared with the theoretical variance based on a small error analysis for the gated modes the signal to noise ratio below which the observed variance begins to differ significantly from the small error theory can be reliably predicted from a linearity criterion it is shown however that the expected variance for the ungated mode can depart from the small error theory at a higher signal to noise ratio than for the gated modes thus the variance due to anomalies can be the most important factor in determining the region of applicability of the small error analysis

multiple scattering of waves in random media a transfer matrix approach transfer matrices address multiple scattering of waves in dense media by relating properties of a thick slice of medium to the corresponding properties of a slice thin enough for multiple scattering to be absent hence scattering properties can easily be calculated we present a new method for deriving a whole hierarchy of transfer matrices which can be applied to studying statistics of waves in random media under conditions of extreme multiple scattering the new method based on matrix power series expansions confirms early results and carries them forward into new areas allowing us to study density of states fluctuations and transport phenomena

noncommuting limits in electromagnetic scattering asymptotic analysis for an array of highly conducting inclusions we consider formulations for the helmholtz operator for periodic media containing high contrast inclusions in the limit when the wavelength outside the inclusions tends to infinity applications are to problems of electromagnetism the main focus is on the analysis of the effect of noncommuting limits an effect which indicates that linear boundary value problems of electromagnetism give formally different results for the long wavelength limits in cases where highly conducting inclusions have refractive indices of different orders of magnitude specifically the effective moduli of the homogenized material will depend on the path used to approach the origin in the coordinate space wave number normalized refractive index of the inclusions 1 this mathematical observation gives a physical subtlety which is studied in this paper the dispersion relation for the lowest frequency or acoustic mode is investigated as are the conditions for existence of an acoustic mode cases of both nondispersive and di

np hardness of deciding convexity of quartic polynomials and related problems we show that unless p np there exists no polynomial time or even pseudo polynomial time algorithm that can decide whether a multivariate polynomial of degree four or higher even degree is globally convex this solves a problem that has been open since 1992 when n z shor asked for the complexity of deciding convexity for quartic polynomials we also prove that deciding strict convexity strong convexity quasiconvexity and pseudoconvexity of polynomials of even degree four or higher is strongly np hard by contrast we show that quasiconvexity and pseudoconvexity of odd degree polynomials can be decided in polynomial time

bloch waves in periodic multi layered acoustic waveguides the band spectrum and associated floquet bloch eigensolutions arising in acoustic and electromagnetic waveguides which have periodic structure along the guide while remaining of finite width are found homogeneous dirichlet or neumann conditions along the guide walls or an alternation of them are taken importantly in some cases a total stop band at zero frequency is identified providing space for low frequency localized modes geometric defects in the structured waveguide also create these modes numerical and asymptotic techniques identify dispersion curves and trapped modes some cases demonstrate maxima and minima of the spectral edges within the brillouin zone and also allow for ultraslow light or sound imaging applications using anomalous dispersion to generate subwavelength resolution are possible and are demonstrated

generalized convexity on affine subspaces with an application to potential functions second order conditions for the pseudo convexity of a function restricted to an affine subspace are obtained by extending those already known for functions on n these results are then used to analyse the pseudo convexity of potential functions of the type introduced by karmarkar

robust recursive estimation in the presence of heavy tailed observation noise a first order approximation is derived for the conditional prior distribution of the state of a discrete time stochastic linear dynamic system in the presence of contaminated normal observation noise this distribution is then used to derive a first order approximation of the conditional mean minimum variance estimator if the observation noise distribution can be represented as a member of the e contaminated normal neighborhood then the conditional prior is also to first order an analogous perturbation from a normal distribution whose first two moments are given by the kalman filter moreover the perturbation is itself of a special form combining distributions whose parameters are given by banks of parallel kalman filters and optimal smoothers

oblique propagation of electromagnetic and elastic waves for an array of cylindrical fibres this paper presents analysis of electromagnetic and elastodynamic waves propagating through a doubly periodic array of cylindrical channels in oblique incidence a new method based on a multipole scattering approach has been proposed to reduce these spectral problems for partial differential equations to certain algebraic problems of the rayleigh type we obtain a formulation in terms of an eigenvalue problem that enables us to construct the high order dispersion curves and to study both photonic and phononic band gap structures in oblique incidence we also address the question of a singular perturbation induced by the conical incidence and discuss some effective properties for ferromagnetic photonic crystal fibres in the long wavelength limit

time delay estimation by combining efficient algorithms and generalized cross correlation methods this paper analyzes the performance of the two efficient algorithms presented by stein and cabot for time delay of arrival estimation tde between two signals it is shown that these estimators are unbiased and explicit expressions for the tde mean square error mse are presented it is also shown how to improve the performance of these algorithms by combining them with generalized cross correlation gcc methods in the analysis we only assume stationary signals which are not necessarily gaussian the first algorithm stein is indirect and uses the symmetry of the cross correlation function between the two signals it is shown here that the tde mse depends on the unknown delay the performance of this algorithm can be improved by combining it with the gcc method and the pertinent tde mse expressions are presented the second algorithm cabot is based on finding the zero of the cross correlation function between one signal and the hilbert transform of the other signal here too the pertinent tde mse expressions are presented this algorithm is also combined with the gcc method and the optimal weight function for which the tde mse expression coincides with the cramer rao lower bound is found

on the simulation of a class of time delay estimation algorithms the time delay between signals received at two or more sensors has proven to be a useful parameter in passive sonar for estimating the location of an acoustic source this paper presents the results of a simulation comparing the smoothed coherence transform and maximum likelihood estimation methods to the basic cross correlation technique for time delay estimation band limited random signals which are corrupted by white noise and received at two sensors are considered at various signal to noise ratios the variance of the time delay estimates are compared to the minimum variance obtainable in theory as given by the cramer rao lower bound

additively decomposed quasiconvex funtions in a recently published paper with the same title debreu and koopmans have studied conditions which imply the quasiconvexity of the function f x mathop sum limits i 1 n f i x i x i in x i wherex x1 x2 xn and fori 1 2 n x1 is a finite dimensional open convex set andfi a real valued nonconstant function onx1 these conditions involve the convexity indices of functionsfi a concept introduced in the debreu and koopmans paper first we give a new definition of the convexity index equivalent to that of debreu and koopmans then by means of this definition we can simplify the proofs given by debreu and koopmans and extend some of their results

the structure and performance of estimators for real time estimation of randomly varying time delay structures for time delay estimation are described which are deduced using the maximum likelihood technique the performance of estimators designed for time invariant delays is discussed for the case of signals with a time variable delay a two step algorithm for the estimation of a randomly varying time delay between two stochastic signals is developed in the first step the maximum likelihood estimate is computed over an observation interval small enough to consider the delay to be approximately constant due to the short averaging interval the probability of ambiguous peaks in the estimation function and the variance of the estimate are greatly increased therefore in the second step a decision directed adaptive postfiltering algorithm is presented that effectively suppresses outliers and reduces the variance

matrix criteria for the pseudo p convexity of a quadratic form abstract except for the family of quasiconvex quadratic functions no characterization of generalized convex quadratic forms on convex sets in r k exists we characterize pseudo p convex quadratic functions i e bi pseudoconvex quadratics for which every stationary point is a global minimum on solid convex sets in r n r m

robust eckart filters for time delay estimation minimax or robust filters which optimize worst case performance have been considered previously for matched and wiener filtering in this paper we show how similar ideas can be applied to obtain robust versions of one particular filter the eckart filter for time delay estimation the use of a robust filter can eliminate the requirement of estimation of the signal and noise power spectral densities psd s and cross psd s robust filters being less sensitive in their performance to variations of the input psd s within specified classes of psd s explicit solutions for specific classes of psd s are derived and several numerical examples and simulation results are given similar formulations for robust filters should also be possible for other types of filters used in time delay estimation

alignment blur in coherently averaged images blurring of coherently averaged images due to imperfect alignment is studied and two restoration methods are proposed and evaluated it is shown that iterative realignment is more powerful than post filtering in reducing blur the value of averaging and restoration is illustrated on human subjects in noisy video sequences

semidefiniteness without real symmetry abstract let a be an n by n matrix with real entries we show that a necessary and sufficient condition for a to have positive semidefinite or negative semidefinite symmetric part h a 1 2 a a t is that rank h a x rank x t ax for all x m n r further if a has positive semidefinite or negative semidefinite symmetric part and a 2 has positive semidefinite symmetric part then rank ax rank x t ax for all x m n r this result implies the usual row and column inclusion property for positive semidefinite matrices finally we show that if a a 2 a k k 2 all have positive semidefinite symmetric part then rank ax rank x t ax rank x t a k 1 x for all x m n r

exact maximum likelihood time delay estimation for short observation intervals an exact solution is presented to the problem of maximum likelihood time delay estimation for a gaussian source signal observed at two different locations in the presence of additive spatially uncorrelated gaussian white noise the solution is valid for arbitrarily small observation intervals that is the assumption t tau sub c mod d mod made in the derivation of the conventional asymptotic maximum likelihood aml time delay estimator where tau sub c is the correlation time of the various random processes involved and d is the differential time delay is relaxed the resulting exact maximum likelihood eml instrumentation is shown to consist of a finite time delay and sum beamformer followed by a quadratic postprocessor based on the eigenvalues and eigenfunctions of a one dimensional integral equation with nonconstant weight the solution of this integral equation is obtained for the case of stationary signals with rational power spectral densities finally the performance of the eml and aml estimators is compared by means of computer simulations

large and small error performance limits for multipath time delay estimation the cramer rao lower bound crlb and a lower bound on the probability of large errors for multipath time delay estimation for a single resolvable multipath are developed these theoretical results are compared to the performance of the maximum likelihood estimator mle and an autocorrelator via computer simulation for small errors and large snr the mle reaches the crlb the variance of the time delay estimate for the autocorrelator is much larger than the crlb if the reflection coefficient for the delayed path is near unity for small errors and small snr the mle reduces to an autocorrelator hence their performance is identical for large errors and bandwidth time products greater than 500 the error probability for the autocorrelator is within 1 db in input snr of the lower bound on large error probability thus the autocorrelator is nearly an optimal instrumentation from the point of view of large errors at least for large bandwidth time products and the flat low pass spectrum considered here

on occurrence of spectral edges for periodic operators inside the brillouin zone the paper discusses the following frequently arising question on the spectral structure of periodic operators of mathematical physics e g schrodinger maxwell waveguide operators etc is it true that one can obtain the correct spectrum by using the values of the quasimomentum running over the boundary of the reduced brillouin zone only rather than the whole zone or do the edges of the spectrum occur necessarily at the set of corner high symmetry points this is known to be true in 1d while no apparent reasons exist for this to be happening in higher dimensions in many practical cases though this appears to be correct which sometimes leads to the claims that this is always true there seems to be no definite answer in the literature and one encounters different opinions about this problem in the community in this paper starting with simple discrete graph operators we construct a variety of convincing multiply periodic examples showing that the spectral edges might occur deeply inside the brillouin zone on the other hand it is also shown that in a generic case the situation of spectral edges appearing at high symmetry points is stable under small perturbations this explains to some degree why in many maybe even most practical cases the statement still holds

blind identification of simo systems and simultaneous estimation of multiple time delays from hos based inverse filter criteria higher order statistics based inverse filter criteria ifc have been effectively used for blind equalization of single input multiple output simo systems recently chi and chen reported a relationship between the unknown simo system and the optimum equalizer designed by the ifc for finite signal to noise ratio snr in this paper based on this relationship an iterative fast fourier transform fft based nonparametric blind system identification bsi algorithm and an fft based multiple time delay estimation mtde algorithm are proposed with a given set of non gaussian measurements the proposed bsi algorithm allows the unknown simo system to have common subchannel zeros and its performance estimation accuracy is superior to that of the conventional ifc based methods the proposed mtde algorithm can simultaneously estimate all the p 1 time delays with respect to a reference sensor with space diversity of sensors exploited therefore its performance estimation accuracy is robust to the nonuniform distribution of snrs of p spl ges 2 sensors due to channel fading some simulation results are presented to support the efficacy of the proposed bsi algorithm and mtde algorithm