l shape 2 dimensional arrival angle estimation with propagator method it is known that computational loads of the propagator method pm can be significantly smaller e g one or two order than those of music and esprit because the pm does not require any eigenvalue decomposition evd of the cross correlation matrix and singular value decomposition svd of the received data however the pm of the parallel shape array has nonnegligible drawbacks such as 1 requirement of pair matching between the 2 d azimuth and elevation angle estimation which is an exhaustive search and 2 estimation failure problems when elevation angles are between 70 spl deg and 90 spl deg the purpose of this paper is to show a way to remove these problems in the pm without additional computational loads this paper will employ one or two l shape arrays because the parallel shape used in the pm may cause the aforesaid problems simulation results verify that the pm with one or two l shape configurations can remove these problems and improve the performance of the pm significantly e g almost 5 db in signal to noise ratio for the parameters used in this paper

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

moishezon s theorem and degeneration abstract let l be a tensor product of two very ample line bundles on the smooth projective complex threefold x under the hypothesis that h 0 x k x l 0 we show that the restriction map r pic x pic y is an isomorphism for very general y in the linear system l for such l this result recovers the noether lefschetz theorem of moishezon who extended the original topological and hodge theoretic arguments of lefschetz we give a degeneration argument which is almost completely algebraic in nature

on the geometry of isotropic arrays we consider array geometries whose direction of arrival doa estimation performance is isotropic an isotropic array is one whose cramer rao bound crb on the doa of a single source is uniform for all angles for both planar arrays and volume arrays we derive necessary and sufficient conditions on array element locations so that the array is isotropic we also present several designs of isotropic planar and volume arrays the results apply to both narrowband and wideband scenarios we analyze the special case where a planar array is used to estimate the doa of three dimensional 3 d source finally we compare isotropic array performance to the best possible array performance

solution and analysis of tdoa localization of a near or distant source in closed form point positioning and direction of arrival doa localization require separate estimators depending on whether the source is near or distant from the sensors the use of modified polar representation mpr for the source location enables the integration of the two estimators together and eliminates the knowledge needed if the source is in the near field or far field the previous work on mpr only provides an iterative implementation of the maximum likelihood estimator mle initialized by a coarse semidefinite relaxation sdr solution this paper proposes a formulation for time difference of arrival tdoa localization of a 2 d or 3 d source in mpr that would lead to a closed form solution through the minimization of a quadratic function with a quadratic constraint two techniques the successive unconstrained minimization sum and the generalized trust region subproblem gtrs are applied to solve the optimization detailed analysis in the first order for mean square and in the second order for estimation bias is performed for both methods the theoretical results illustrate that the closed form solution from each of the methods provides the cramer rao lower bound performance for gaussian noise the gtrs solution has better accuracy than the sum solution when the source signal is arriving at an azimuth or elevation angle close to zero 90 circ or 180 circ or when the measurement noise level is large they yield comparable performance with the mle albeit having less complexity and avoiding possible divergence behavior they outperform the closed form solutions from the literature in angle estimation and have smaller bias

joint 2 d doa estimation via sparse l shaped array in this paper we address the problem of estimating the two dimensional 2 d directions of arrival doa of multiple signals by means of a sparse l shaped array the array consists of one uniform linear array ula and one sparse linear array sla the shift invariance property of the ula is used to estimate the elevation angles with low computational burden the signal subspace is constructed by the cross covariance matrix ccm of the received data without implementing eigendecomposition the source waveforms are then obtained by the estimated elevation angles which together with each sensor of the sla considered as a linear regression model is used to estimate the azimuth angle by the modified total least squares mtls technique our new algorithm yields correct parameter pairs without requiring the computationally expensive pairing operation and therefore has at least two advantages over the previous l shaped array based algorithms less computational load and better performance due to the use of sla and ccm expressions for the asymptotic mean squared error mse of the 2 d doa estimates are derived simulation results show that our method provides accurate and consistent 2 d doa estimation results that could not be obtained by the existing methods with comparable computational complexity

on the noether lefschetz theorem and some remarks on codimension two cycles here of general moduli means that there is a countable union v of subvarieties of the space pn of surfaces of degree d in p3 such that the statement pie s z holds for s p n v noether it would seem stated this theorem but never completely proved it instead he gave a plausibility argument based on the following construction 1 let g be the hilbert scheme of curves of degree n and genus 9 in p3 l gr3 d l ip n the space of surfaces of degree d in p3 and zc t the incidence correspondence s o a c s c z s

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

joint elevation and azimuth direction finding using l shaped array for two dimensional 2 d directions of arrival doa estimation problem the l shaped array seems to have higher accuracy than other structured arrays see an l shaped array for estimating 2 d directions of wave arrival by hua for details and has received much attention to estimate elevation and azimuth angles two correctly matched electric angles functions of elevation and azimuth angles are estimated in advance so that elevation and azimuth angles are obtained from the two correctly matched electric angles however the failure in pairing will cause severe performance degradation in this communication a novel algorithm which doesn t require match procedure is proposed to estimate 2 d doa in the l shaped array geometry the key points of this communication are i by introducing a novel electric angle the steering vector is separated into two parts ii the two parts can be obtained in turn by generalized esprit approach and eigenvalue decomposition evd of one particular matrix respectively iii elevation and azimuth angles can be obtained from the recovered steering vector the resultant algorithm avoids match operation and requires one dimensional search once simulation results are presented to validate the performance of the proposed method

optimum ambiguity free directional and omnidirectional planar antenna arrays for doa estimation this paper studies the antenna array geometry impact on both direction of arrival doa estimation accuracy and array rank ambiguity some restrictions are imposed on the array geometry that guarantee first order ambiguity free arrays and at the same time reduce the cost of a global systematic optimization the subsequently derived cramer rao bound crb on the doa estimates shows to be attractive for numerical evaluation depending on whether the doa estimation accuracy is desired to be uniform in all possible directions or is to be enhanced in a given aperture around some privileged direction two optimization problems are formulated and solved by exhaustive search to compute the optimal array geometries the obtained optimal arrays significantly outperform their circular counterparts and tend to have a form close to the v shape we study in details v shaped arrays and derive asymptotic performance measures that apply for large sized arrays where exhaustive search is unaffordable

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

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

the noether lefschetz theorem for the divisor class group let x be a normal projective threefold over a field of characteristic zero and vertical bar l vertical bar be a base point free ample linear system on x under suitable hypotheses on x vertical bar l vertical bar we prove that for a very general member y is an element of vertical bar l vertical bar the restriction map on divisor class groups cl x cl y is an isomorphism in particular we are able to recover the classical noether lefschetz theorem that a very general hypersurface x subset of p c 3 of degree 4 has pic x congruent to z

an algorithm for pole zero modeling and spectral analysis an explicit connection between fitting exponential models and pole zero models to observed data is made the fitting problem is formulated as a constrained nonlinear minimization problem this problem is then solved using a simplified iterative algorithm the algorithm is applied to simulated data and the performance of the algorithm is compared to previous results

direction finding antenna arrays for the randomly located source we consider the problem of sensor placement for estimating the direction of arrival of a narrow band source randomly located in the far field of a planar antenna array performance is evaluated by means of the expectation of the conditional cramer rao bound normalized to that of the uniform circular array two cost functions are obtained relative to azimuth and elevation respectively they depend on the array geometry as well as the distribution of the source azimuth a class of uniform antenna arrays is investigated it is adapted to the particular probabilistic distribution of the azimuth while ensuring protection against array ambiguities using an exhaustive search procedure we either seek the same reduction of both cost functions or rather focus on one in particular in the first approach we achieve a reduction of almost 36 of both regardless of the source azimuth distribution in the second approach we can obtain larger reductions for the targeted parameter in both cases optimal arrays are close to the v shape for which performance analysis is conducted and closed form expressions are obtained

decoupled estimation of 2 d angles of arrival using two parallel uniform linear arrays a new polynomial root finding based method for two dimensional 2 d angles of arrival aoas estimation is proposed which uses two parallel uniform linear arrays the method takes the special structure of the array that enables decoupling the 2 d aoa estimation problem into two successive one dimensional 1 d aoa estimation problems thereby increases the array aperture to estimate more sources than those of 2 d esprit and doa matrix methods the computation complexity of the proposed method is evaluated and a relevant cramer rao bound of the proposed method is derived numerical examples are presented to show the effectiveness of the proposed method

cramer rao bounds for antenna array design we study the impact of the geometry of the planar antenna array on the accuracy of the estimated direction s of arrivals of an emitting source we develop explicit cramer rao bounds crbs of the azimuth and elevation angles that show a simple structure in particular for a fixed elevation angle the crbs are cosine functions of the source azimuth and so regardless of the array geometry the amplitude and extremes of these functions depend on the array geometry hence the array configuration can be chosen in order to ensure a desired an isotropic behavior to do so we propose a pragmatic methodology that also takes into account the array ambiguity problem the array design problem is simplified by limiting the array search within a family of v shaped arrays that are advantageously characterized by a single parameter the angle between the two branches a performance measure is proposed then analytically expressed to assess the array directivity and gain with respect to the more standardly used uniform circular array

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

a generalization of kharitonov s theorem robust stability of interval plants the robust stability problem is considered for interval plants in the case of single input multioutput or single output multi input systems a necessary and sufficient condition for the robust stabilization of such plants is developed using a generalization of v l kharitonov s theorem 1978 the generalization given provides necessary and sufficient conditions for the stability of a family of polynomials delta s q sub 1 s p sub 1 s q sub m s p sub m s where the q sub i are fixed and the p sub i are interval polynomials the coefficients of which are regarded as a point in parameter space which varies within a prescribed box this generalization called the box theorem reduces the question of the stability of the box in parameter space to the equivalent problem of the stability of a prescribed set of line segments it is shown that for special classes of polynomials q sub i s the set of line segments collapses to a set of points and this version of the box theorem in turn reduces to kharitonov s original theorem

parameter estimation of superimposed signals using the em algorithm a computationally efficient algorithm for parameter estimation of superimposed signals based on the two step iterative em estimate and maximize with an e step and an m step algorithm is developed the idea is to decompose the observed data into their signal components and then to estimate the parameters of each signal component separately the algorithm iterates back and forth using the current parameter estimates to decompose the observed data better and thus increase the likelihood of the next parameter estimates the application of the algorithm to the multipath time delay and multiple source location estimation problems is considered

a bayesian approach to array geometry design in this paper we consider the design of planar arrays that optimize direction of arrival doa estimation performance we assume that the single source doa is a random variable with a known prior probability distribution and the sensors of the array are constrained to lie in a region with an arbitrary boundary the crame spl acute r rao bound crb and the fisher information matrix fim for single source doa constitute the basis of the optimality criteria we relate the design criteria to a bayesian crb criterion and to array beamwidth we also derive closed form expressions for the design criteria when the doa prior is uniform on a sector of angles we show that optimal arrays have elements on the constraint boundary thus providing a reduced dimension iterative solution procedure finally we present example designs

computationally efficient subspace based method for two dimensional direction estimation with l shaped array in order to mitigate the effect of additive noises and reduce the computational burden we propose a new computationally efficient cross correlation based two dimensional 2 d direction of arrivals doas estimation code method for noncoherent narrowband signals impinging on the l shaped sensor array structured by two uniform linear arrays ulas by estimating the azimuth and elevation angles independently with a one dimensional 1 d subspace based estimation technique without eigendecomposition where the null spaces are obtained through a linear operation of the matrices formed from the cross correlation matrix between the received data of two ulas then the pair matching of estimated azimuth and elevation angles is accomplished by searching the minimums of a cost function of the azimuth and elevation angles where the computationally intensive and time consuming eigendecomposition process is avoided further the asymptotic mean square error mse expressions of the azimuth and elevation estimates are derived the effectiveness of proposed method and the theoretical analysis are verified through numerical examples and it is shown that the proposed code method performs well at low signal to noise ratio snr and with a small number of snapshots

eigenstructure techniques for 2 d angle estimation with uniform circular arrays the problem of 2d angle estimation azimuth and elevation of multiple plane waves incident on a uniform circular array uca of antennas is considered two eigenstructure based estimation algorithms that operate in beamspace and employ phase mode excitation based beamformers have been developed the first uca rb music is a beamspace version of music that offers numerous advantages over element space operation including reduced computation as subspace estimates are obtained via real valued eigendecompositions enhanced performance in correlated source scenarios due to the attendant forward backward averaging effect and the applicability of root music the second uca esprit represents a significant advance in the area of 2d angle estimation it is a novel closed form algorithm that provides automatically paired source azimuth and elevation estimates with uca esprit the eigenvalues of a matrix have the form spl mu sub i sin spl theta sub i e sup j spl phi i where spl theta sub i and spl phi sub i are the elevation and azimuth angles respectively expensive search procedures being thus avoided uca esprit is superior to existing 2d angle estimation algorithms with respect to computational complexity finally asymptotic expressions for the variances of the element space music and uca rb music estimators for the 2d scenario have been derived results of simulations that compare uca rb music and uca esprit and also validate the theoretical performance expressions are presented

robust stability of multivariable interval control systems in this paper we will give necessary and sufficient conditions for the hurwitz stability of mimo interval systems as a consequence of this result we will give a precise bound on the h norm of unstructured perturbations that can be tolerated by mimo interval systems connected in feedback with these perturbations we will also consider the robust version of the popov problem that considers interval mimo systems subject to nonlinear time invariant sector bounded perturbations and in turn obtain a robust stability condition of the popov problem with mixed perturbations

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

robust stability under structured and unstructured perturbations the problem of robust stability for linear time invariant single output control systems subject to both structured parametric and unstructured h sub infinity perturbations is studied a generalization of the small gain theorem which yields necessary and sufficient conditions for robust stability of a linear time invariant dynamic system under perturbations of mixed type is presented the solution involves calculating the h sub infinity norm of a finite number of extremal plants the problem of calculating the exact structured and unstructured stability margins is then constructively solved a feedback control system containing a linear time invariant plant which is subject to both structured and unstructured perturbations is considered the case where the system to be controlled is interval is treated and a nonconservative easily verifiable necessary and sufficient condition for robust stability is given the solution is based on the extremal of a finite number of line segments in the plant parameter property of a finite number of line segments in the plant parameter space along which the points closest to instability are encountered

oblique projection based enumeration of mixed noncoherent and coherent narrowband signals in many application scenarios the signals impinging on the array of sensors comprise the noncoherent uncorrelated and or partially correlated signals and the coherent signals with several groups due to multipath propagation in this paper we consider the problem of estimating the number of noncoherent narrowband signals and that of coherent narrowband signals with multiple groups impinging on a planar sensor array composed of two parallel uniform linear arrays ulas and an oblique projection based enumerator for the mixed signals opems is proposed by utilizing the qr decomposition based ratio criterion qrrc for rank determination of a matrix in the opems the number of noncoherent signals and that of coherent signals in each group are estimated separately where only the elevation angles of noncoherent signals are estimated to isolate the coherent signals from the noncoherent ones and the computationally intensive and time consuming eigendecomposition procedure is avoided the consistency of the proposed opems is analyzed and its effectiveness is verified through numerical examples

a kharitonov like theorem for interval polynomial matrices abstract as an extension of kharitonov s theorem robust stability of interval polynomial matrices is studied here a polynomial matrix is said to be stable if its determinant has all roots with negative real parts the present paper shows that the robust stability of interval polynomial matrices is equivalent to that of the subclasses where each row column has only one element that involves kharitonov edge polynomials and all the other elements take on one of the four kharitonov vertex polynomials

crb based design of linear antenna arrays for near field source localization this paper is devoted to the cramer rao bound crb on the angle and range of a narrow band near field source localized by means of an arbitrary linear array using the exact expression of the time delay parameter first we prove that the conditional and unconditional crbs are proportional for an arbitrary parametrization of the steering vector that may include but is not limited to the source doa range or polarization then a taylor expansion of the crb is conducted to obtain accurate nonmatrix closed form expressions of the crb on angle and range in contrast to the existing expressions our expressions are simple interpretable and more general because the sensors are only constrained to be placed along some axis our analysis leads to the characterization and design of a class of centro symmetric linear arrays with improved near field angle and range estimation capabilities

an l shaped array for estimating 2 d directions of wave arrival a simple structured 2 d array the l shaped array is presented the l shaped array consists of two uniform linear arrays ula connected orthogonally at one end of each ula it is shown that the cramer rao bounds crb of the estimated wave directions based on the l shaped array are about 37 smaller than those for the cross array the crb indicates the accuracy potential because it is the reachable lower bound on the variance of any unbiased estimate an efficient maximum likelihood algorithm is developed utilizing the ula structure inherent in the l shaped array

an elementary proof of kharitonov s stability theorem with extensions gives an elementary proof of kharitonov s theorem using simple complex plane geometry without invoking the hermite bieler theorem kharitonov s theorem is a stability result for classes of polynomials defined by letting each coefficient vary independently in an arbitrary interval the result states that the whole class is hurwitz if and only if four special well defined polynomials are hurwitz the paper also gives elementary proofs of two previously known extensions for polynomials of degree less than six the requirement is reduced to fewer than four polynomials and the theorem is generalized to polynomials with complex coefficients