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

a parameter estimation scheme for damped sinusoidal signals based on low rank hankel approximation most of the existing algorithms for parameter estimation of damped sinusoidal signals are based only on the low rank approximation of the prediction matrix and ignore the hankel property of the prediction matrix we propose a modified kumaresan tufts mkt algorithm exploiting both rank deficient and hankel properties of the prediction matrix computer simulation results demonstrate that compared with the original kumaresan tufts 1982 algorithm and the matrix pencil algorithm the mkt algorithm has a lower noise threshold and can estimate the parameters of signal with larger damping factors

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

a new perturbation analysis for signal enumeration in rotational invariance techniques the esprit algorithm is a subspace based high resolution method used in source localization and spectral analysis which provides very accurate estimates of the signal parameters however the underlying theory assumes a known model order which is usually not the case in many applications in particular it is well known that underevaluating the model order biases the estimation in this paper we analyze the perturbation induced by an erroneous model order and we present an error bound for the estimated parameters based on this theoretical framework we propose a new method for selecting an appropriate modeling order which consists in minimizing the error bound this approach is applied to both synthetic and musical signals and its performance is compared to that of existing methods such as the information theoretic criteria

the dirichlet problem for nonlinear second order elliptic equations i monge ampegre equation on considere le probleme de dirichlet pour des equations elliptiques non lineaires pour une fonction reelle u definie dans la fermeture d un domaine borne dans r n avec une frontiere c

asymptotic estimate for a perturbed scalar curvature equation abstract we consider the equation u v u n 2 n 2 w u with n n 2 n 2 n 2 and we give some minimal conditions on v and w for having a uniform estimate for their solutions when 0

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

direction finding using beamspace root estimator banks motivated by the superior performance and reduced computational complexity of beamspace and root implementations of eigenstructure techniques a beamspace root modification of the pseudorandom joint estimation strategy pr jes is developed the essence of the pr jes is to generate the eigenstructure based estimator bank for a given sample covariance or data matrix appropriately combining the results of parallel underlying estimators the pr jes removes outliers and improves the threshold performance in the case of a nonuniform array the interpolated array approach is exploited to enable the application of root underlying techniques simulations show that the proposed beamspace root implementation outperforms spectral elementspace pr jes significantly and achieves a performance similar to or better than that of the stochastic maximum likelihood ml method

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

estimating the parameters of exponentially damped sinusoids and pole zero modeling in noise we have presented techniques 1 6 based on linear prediction lp and singular value decomposition svd for accurate estimation of closely spaced frequencies of sinusoidal signals in noise in this note we extend these techniques to estimate the parameters of exponentially damped sinusoidal signals in noise the estimation procedure presented here makes use of backward prediction in addition to svd first the method is applied to data consisting of one and two exponentially damped sinusoids the choice of one and two signal components facilitates the comparison of estimation error in pole damping factors and pole frequencies to the appropriate cramer rao cr bounds and to traditional methods of linear prediction second our method is applied to an example due to steiglitz 8 in which the data consists of noisy values of the impulse response samples composed of many exponentially damped sinusoids of a linear system having both poles and zeros the poles of the system are accurately determined by our method and the zeros are obtained subsequently using shanks method

esprit a subspace rotation approach to estimation of parameters of cisoids in noise the application of a subspace invariance approach esprit to the estimation of parameters frequencies and powers of cisoids in noise is described esprit exploits an underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets the new approach has several advantages including improved resolution over pisarenko s technique for harmonic retrieval

estimates of the conformal scalar curvature equation via the method of moving planes in this paper we derive a local estimate of a positive singular solution u near its singular set z of the conformal equation where k x is a positive continuous function z is a compact subset of and g satisfies that is nonincreasing for t 0 assuming that the order of flatness at critical points of k on z is no less than we prove that through the application of the method of moving planes the inequality holds for any solution of 0 1 with cap z 0 by the same method we also derive a harnack type inequality for smooth positive solutions let u satisfy assume that the order of flatness at critical points of k is no less than n 2 then the inequality holds for r 1 we also show by examples that the assumption about the flatness at critical points is optimal for validity of the inequality 0 4 1997 john wiley sons inc

rooting based harmonic retrieval using multiple shift invariances the complete and the incomplete sample cases in the present paper we propose a novel method for estimating one dimensional damped and undamped harmonics our method utilizes the multiple shift invariance property comprised in the signal model we develop a new rank reduction estimator which is formed as the weighted sum of the individual matrix polynomials obtained from individual shift invariance equations the uniqueness conditions for the proposed rank reduction criteria are derived under the assumption that all samples are available moreover a novel technique for the incomplete data case where some samples are missing is presented in this case the rank reduction estimator may suffer from ambiguities to overcome this problem we propose an extension of the rank reduction estimator that is based on polynomial intersection and the properties of the sylvester matrix the latter algorithm yields unique estimates of the damped harmonics the proposed high resolution techniques are search free and therefore they enjoy moderate computational complexity

sensor array signal processing via a procrustes rotations based eigenanalysis of the esprit data pencil the authors propose the procrustes rotation based esprit algorithm pro esprit for estimating characteristic parameters associated with a scene of radiating sources given data derived from two identical sensor arrays the x and y arrays which are displaced relative to one another pro esprit uses the inherent redundancy built into the esprit array system to compensate for deviations from the ideal array model this redundancy is manifested by two fundamental properties of the noiseless x and y data matrices comprising the esprit data pencil a they have the same row space the signal subspace and 2 they have the same column space the source subspace these properties are utilized by invoking two primary tools 1 the solution to the procrustes problem for optimally approximating an invariant subspace rotation and 2 the total least squares method for perturbing each of two estimates of a common subspace in a minimal fashion until the two perturbed spaces are the same

nonexistence of positive radial solutions of a quasilinear neumann problem with a critical sobolev exponent note that problem 1 1 always admits the constant solution u0 k ny2 4 in adimurthi yadava 3 and budd knaap peletier 6 it has been proved that there exists a constant k0 0 such that for 0 k k0 1 1 admits a nonconstant solution for n 4 5 6 and does not for n 3 in this paper we study problem 1 1 when n 3 7 in this case the method used in 3 and 6 breaks down due to the fact that n 2 ny 2 2 which leads to a drastic change in the behaviour of the associated pohozhaev s functionals in contrast to the case n 4 5 6 we have

a sup inf inequality for some nonlinear elliptic equations involving exponential nonlinearities let u be a solution of the equation u v x eu in a domain r2 where 0 a v b and v is lipschitz continuous we prove that sup u can be controlled in terms of inf u more precisely supku inf u c a b k v l for any compact subset k this extends an earlier result of shafrir who obtained a similar conclusion when v 1

closed form 2 d angle estimation with rectangular arrays in element space or beamspace via unitary esprit the uca esprit is a closed form algorithm developed for use in conjunction with a uniform circular array uca that provides automatically paired source azimuth and elevation angle estimates the 2 d unitary esprit is presented as an algorithm providing the same capabilities for a uniform rectangular array ura in the final stage of the algorithm the real and imaginary parts of the ith eigenvalue of a matrix are one to one related to the respective direction cosines of the ith source relative to the two major array axes the 2 d unitary esprit offers a number of advantages over other proposed esprit based closed form 2 d angle estimation techniques first except for the final eigenvalue decomposition of a dimension equal to the number of sources it is efficiently formulated in terms of real valued computation throughout second it is amenable to efficient beamspace implementations that are presented third it is applicable to array configurations that do not exhibit identical subarrays e g two orthogonal linear arrays finally the 2 d unitary esprit easily handles sources having one member of the spatial frequency coordinate pair in common simulation results are presented verifying the efficacy of the method

sliding window adaptive svd algorithms the singular value decomposition svd is an important tool for subspace estimation in adaptive signal processing we are especially interested in tracking the svd of a recursively updated data matrix this paper introduces a new tracking technique that is designed for rectangular sliding window data matrices this approach which is derived from the classical bi orthogonal iteration svd algorithm shows excellent performance in the context of frequency estimation it proves to be very robust to abrupt signal changes due to the use of a sliding window finally an ultra fast tracking algorithm with comparable performance is proposed

vector sensor array processing for electromagnetic source localization the authors present a new approach for localizing electromagnetic sources using sensors where the output of each is a vector consisting of the complete six electric and magnetic field components two types of source transmissions are considered 1 single signal transmission sst and 2 dual signal transmission dst the model is given in terms of several parameters including the wave direction of arrival doa and state of polarization a compact expression is derived for the cramer rao bound crb on the estimation errors of these parameters for the multi source multi vector sensor model quality measures including mean square angular error msae and covariance of vector angular error cvae are introduced and their lower bounds are derived the advantage of using vector sensors is highlighted by explicit evaluation of the msae and cvae bounds for source localization with a single vector sensor a simple algorithm for estimating the source doa with this sensor is presented along with its statistical performance analysis

simultaneous schur decomposition of several nonsymmetric matrices to achieve automatic pairing in multidimensional harmonic retrieval problems this paper presents a new jacobi type method to calculate a simultaneous schur decomposition ssd of several real valued nonsymmetric matrices by minimizing an appropriate cost function thereby the ssd reveals the average eigenstructure of these nonsymmetric matrices this enables an r dimensional extension of unitary esprit to estimate several undamped r dimensional modes or frequencies along with their correct pairing in multidimensional harmonic retrieval problems unitary esprit is an esprit type high resolution frequency estimation technique that is formulated in terms of real valued computations throughout for each of the r dimensions the corresponding frequency estimates are obtained from the real eigenvalues of a real valued matrix the ssd jointly estimates the eigenvalues of all r matrices and thereby achieves automatic pairing of the estimated r dimensional modes via a closed form procedure that neither requires any search nor any other heuristic pairing strategy moreover we describe how r dimensional harmonic retrieval problems with r spl ges 3 occur in array signal processing and model based object recognition applications

amplitude estimation of sinusoidal signals survey new results and an application this paper considers the problem of amplitude estimation of sinusoidal signals from observations corrupted by colored noise a relatively large number of amplitude estimators which encompass least squares ls and weighted least squares wls methods are described additionally filterbank approaches which are widely used for spectral analysis are extended to amplitude estimation more exactly we consider the matched filterbank mafi approach and show that by appropriately designing the prefilters the mafi approach to amplitude estimation includes the wls approach the amplitude estimation techniques discussed in this paper do not model the observation noise and yet they are all asymptotically statistically efficient it is however their different finite sample properties that are of particular interest to this study numerical examples are provided to illustrate the differences among the various amplitude estimators although amplitude estimation applications are numerous we focus herein on the problem of system identification using sinusoidal probing signals for which we provide a computationally simple and statistically accurate solution

multiple invariance esprit a subspace fitting formulation of the esprit problem is presented that provides a framework for extending the algorithm to exploit arrays with multiple invariances in particular a multiple invariance mi esprit algorithm is developed and the asymptotic distribution of the estimates is obtained simulations are conducted to verify the analysis and to compare the performance of mi esprit with that of several other approaches the excellent quality of the mi esprit estimates is explained by recent results which state that under certain conditions subspace fitting methods of this type are asymptotically efficient

matrix pencil method for estimating parameters of exponentially damped undamped sinusoids in noise a study of a matrix pencil method for estimating frequencies and damping factors of exponentially damped and or undamped sinusoids in noise is presented comparison of this method to a polynomial method svd prony method shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach and that the pencil method is more efficient in computation and less restrictive about signal probes it is found through perturbation analysis and simulation that for signals with unknown damping factors the pencil method is less sensitive to noise than the polynomial method an expression of the cramer rao bound for the exponential signals is presented

approximate subspace based iterative adaptive approach for fast two dimensional spectral estimation in this paper we devise a new approach for fast implementation of two dimensional 2 d iterative adaptive approach iaa using single or multiple snapshots our underlying idea is to apply the subspace methodology in this nonparametric technique by performing the iaa on the dominant singular vectors extracted from the singular value decomposition svd or higher order svd of the multidimensional observations in doing so 2 d iaa is approximately realized by multiple steps of 1 d iaa implying that computational attractiveness is achieved particularly for large data size number of grid points and or snapshot number algorithms based on matrix and tensor operations are developed and their implementation complexities are analyzed computer simulations are also included to compare the proposed approach with the state of the art techniques in terms of resolution probability spectral estimation performance and computational requirement

computing multiple roots of inexact polynomials we present a combination of two algorithms that accurately calculate multiple roots of general polynomials algorithm i transforms the singular root finding into a regular nonlinear least squares problem on a pejorative manifold and it calculates multiple roots simultaneously from a given multiplicity structure and initial root approximations to fulfill the input requirement of algorithm i we develop a numerical gcd finder containing a successive singular value updating and an iterative gcd refinement as the main engine of algorithm ii that calculates the multiplicity structure and the initial root approximation while limitations exist in certain situations the combined method calculates multiple roots with high accuracy and consistency in practice without using multiprecision arithmetic even if the coefficients are inexact this is perhaps the first blackbox type root finder with such capabilities to measure the sensitivity of the multiple roots a structure preserving condition number is proposed and error bounds are established according to our computational experiments and error analysis a polynomial being ill conditioned in the conventional sense can be well conditioned with the multiplicity structure being preserved and its multiple roots can be computed with high accuracy

fast approximated power iteration subspace tracking this paper introduces a fast implementation of the power iteration method for subspace tracking based on an approximation that is less restrictive than the well known projection approximation this algorithm referred to as the fast approximated power iteration api method guarantees the orthonormality of the subspace weighting matrix at each iteration moreover it outperforms many subspace trackers related to the power iteration method such as past nic np3 and opast while having the same computational complexity the api method is designed for both exponential windows and sliding windows our numerical simulations show that sliding windows offer a faster tracking response to abrupt signal variations

optimality of high resolution array processing using the eigensystem approach in the classical approach to underwater passive listening the medium is sampled in a convenient number of look directions from which the signals are estimated in order to build an image of the noise field in contrast a modern trend is to consider the noise field as a global entity depending on few parameters to be estimated simultaneously in a gaussian context it is worthwhile to consider the application of likelihood methods in order to derive a detection test for the number of sources and estimators for their locations and spectral levels this paper aims to compute such estimators when the wavefront shapes are not assumed known a priori this justifies results previously found using the asymptotical properties of the eigenvalue eigenvector decomposition of the estimated spectral density matrix of the sensor signals they have led to a variety of high resolution array processing methods more specifically a covariance matrix test for equality of the smallest eigenvalues is presented for source detection for source localization a best fit method and a test of orthogonality between the smallest eigenvectors and the source vectors are discussed

high resolution spectral analysis of mixtures of complex exponentials modulated by polynomials high resolution methods such as the esprit algorithm are of major interest for estimating discrete spectra since they overcome the resolution limit of the fourier transform and provide very accurate estimates of the signal parameters in signal processing literature most contributions focus on the estimation of exponentially modulated sinusoids in a noisy signal this paper introduces a more general class of signals involving both amplitude and frequency modulations it shows that this polynomial amplitude complex exponentials pace model is the most general model tractable by high resolution methods a generalized esprit algorithm is developed for estimating the signal parameters and it is shown that this model can be characterized by means of a geometrical criterion