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

reply to comments on l shape two dimensional arrival angle estimation with propagator method in this reply to the paper by shu liu and lu see ibid p 1502 3 2008 a novel method with low complexity but showing neither estimation failure nor the pair matching problems is described for the two dimensional doa estimation the authors in the previous papers kikuchi et al 2006 gu et al 2008 also proposed two methods different from that in van der veen et a 1992 to achieve the automatic pair matching by employing the l shaped array configuration the method in this reply is also different from the ones in kikuchi et al 2006 gu et al 2008 in this reply an independently developed algorithm is presented by using the unitary root music and unitary music and changing the l shape to a cross shaped array configuration

indirect dominant mode rejection a solution to low sample support beamforming under conditions of low sample support a low rank solution of the minimum variance distortionless response mvdr equations can yield a higher output signal to interference plus noise ratio sinr than the full rank mvdr beamformer in this paper we investigate several low rank beam forming techniques and we also propose a new beamformer that we refer to as the indirect dominant mode rejection idmr we analyze the degradation in the output sinr caused by residual cross correlations embedded in the sampled covariance matrix due to low sample support the idmr beamformer is based on a parametric estimate of the covariance matrix in which any cross correlation is canceled out simulations reveal that the idmr beamformer yields a dramatic improvement in output sinr relative to the conjugate gradient cg principal component inverse pci and dominant mode rejection dmr beamformers in our investigation of the low rank cg beamformer we address the issue of whether the unity gain constraint in the look direction should be enforced a priori via the use of a blocking matrix or effected a posteriori through simple scaling of the beamforming vector remarkably it is proven that the two methods yield exactly the same low rank beamformer at each and every rank

modified subspace algorithms for doa estimation with large arrays this paper proposes the use of a new generalized asymptotic paradigm in order to analyze the performance of subspace based direction of arrival doa estimation in array signal processing applications instead of assuming that the number of samples is high whereas the number of sensors antennas remains fixed the asymptotic situation analyzed herein assumes that both quantities tend to infinity at the same rate this asymptotic situation provides a more accurate description of a potential situation where these two quantities are finite and hence comparable in magnitude it is first shown that both music and ssmusic are inconsistent when the number of antennas sensors increases without bound at the same rate as the sample size this is done by analyzing and deriving closed form expressions for the two corresponding asymptotic cost functions by examining these asymptotic cost functions one can establish the minimum number of samples per antenna needed to resolve closely spaced sources in this asymptotic regime next two alternative estimators are constructed that are strongly consistent in the new asymptotic situation i e they provide consistent doa estimates not only when the number of snapshots goes to infinity but also when the number of sensors antennas increases without bound at the same rate these estimators are inspired by the theory of g estimation and are therefore referred to as g music and g ssmusic respectively simulations show that the proposed algorithms outperform their traditional counterparts in finite sample size situations although they still present certain limitations

on the virtual array concept for higher order array processing for about two decades many fourth order fo array processing methods have been developed for both direction finding and blind identification of non gaussian signals one of the main interests in using fo cumulants only instead of second order so ones in array processing applications relies on the increase of both the effective aperture and the number of sensors of the considered array which eventually introduces the fo virtual array concept presented elsewhere and allows in particular a better resolution and the processing of more sources than sensors to still increase the resolution and the number of sources to be processed from a given array of sensors new families of blind identification source separation and direction finding methods at an order m 2q q spl ges 2 only have been developed recently in this context the purpose of this paper is to provide some important insights into the mechanisms and more particularly to both the resolution and the maximal processing capacity of numerous 2qth order array processing methods whose previous methods are part of by extending the virtual array concept to an arbitrary even order for several arrangements of the data statistics and for arrays with space angular and or polarization diversity

subspace fitting approaches for frequency estimation using real valued data a novel data covariance model has recently been proposed for the subspace based estimation of multiple real valued sine wave frequencies in this paper we develop weighted subspace fitting approaches using this new data model a new parameterization of the noise subspace is proposed this parameterization is used to solve the subspace fitting problem analytically an expression for the residual covariance matrix is derived this covariance matrix is further used to obtain an optimally weighted gauss markov estimator a computationally efficient suboptimal weighting is also proposed and the associated estimator is close to the gauss markov estimator in performance the suboptimal weighting strategy is quite general and can be used in other related applications the performance of the algorithms are illustrated using numerical simulations the proposed subspace fitting approach shows improved resolution performance it is also robust to additive noise

complex elliptically symmetric distributions survey new results and applications complex elliptically symmetric ces distributions have been widely used in various engineering applications for which non gaussian models are needed in this overview circular ces distributions are surveyed some new results are derived and their applications e g in radar and array signal processing are discussed and illustrated with theoretical examples simulations and analysis of real radar data the maximum likelihood ml estimator of the scatter matrix parameter is derived and general conditions for its existence and uniqueness and for convergence of the iterative fixed point algorithm are established specific ml estimators for several ces distributions that are widely used in the signal processing literature are discussed in depth including the complex t distribution k distribution the generalized gaussian distribution and the closely related angular central gaussian distribution a generalization of ml estimators the m estimators of the scatter matrix are also discussed and asymptotic analysis is provided applications of ces distributions and the adaptive signal processors based on ml and m estimators of the scatter matrix are illustrated in radar detection problems and in array signal processing applications for direction of arrival doa estimation and beamforming furthermore experimental validation of the usefulness of ces distributions for modelling real radar data is given

direction finding with partly calibrated uniform linear arrays a new method for direction finding with partly calibrated uniform linear arrays ulas is presented it is based on the conventional estimation of signal parameters via rotational invariance techniques esprit by modeling the imperfections of the ulas as gain and phase uncertainties for a fully calibrated array it reduces to the conventional esprit algorithm moreover the direction of arrivals doas unknown gains and phases of the uncalibrated sensors can be estimated in closed form without performing a spectral search hence it is computationally very attractive the cramer rao bounds crbs of the partly calibrated ulas are also given simulation results show that the root mean squared error rmse performance of the proposed algorithm is better than the conventional methods when the number of uncalibrated sensors is large it also achieves satisfactory performance even at low signal to noise ratios snrs

orthogonal eigensubspace estimation using neural networks we present a neural network nn approach for simultaneously estimating all or some of the orthogonal eigenvectors of a symmetric nonindefinite matrix corresponding to its repeated minimum in magnitude eigenvalue this problem has its origin in the constrained minimization framework and has extensive applications in signal processing we recast this problem into the nn framework by constructing an appropriate energy function which the nn minimizes the nn is of feedback type with the neurons having sigmoidal activation function the proposed approach is analyzed to characterize the nature of the minimizers of the energy function the main result is that the matrix w is a minimizer of the energy function if and only if the columns of w are the orthogonal eigenvectors with a given norm corresponding to the smallest eigenvalue of the given matrix further all minimizers are global minimizers bounds on the integration time step that is required to numerically solve the system of differential equations which define the dynamics of the nn have also been derived results of computer simulations are presented to support our analysis

rational invariant subspace approximations with applications subspace methods such as music minimum norm and esprit have gained considerable attention due to their superior performance in sinusoidal and direction of arrival doa estimation but they are also known to be of high computational cost in this paper new fast algorithms for approximating signal and noise subspaces and that do not require exact eigendecomposition are presented these algorithms approximate the required subspace using rational and power like methods applied to the direct data or the sample covariance matrix several esprit as well as music type methods are developed based on these approximations a substantial computational saving can be gained comparing with those associated with the eigendecomposition based methods these methods are demonstrated to have performance comparable to that of music yet will require fewer computations to obtain the signal subspace matrix

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

discontinuity of the magnetization in one dimensional 1 x y 2 ising and potts models results from percolation theory are used to study phase transitions in one dimensional ising and q state potts models with couplings of the asymptotic form j sub x y approx const absolute value x y sup 2 for translation invariant systems with well defined lim sub x infinity x sup 2 j sub x j sup possibly o or infinity we establish 1 there is no long range order at inverse temperatures beta with beta j sup less than or equal to1 2 if beta j sup q then by sufficiently increasing j sub 1 the spontaneous magnetization m is made positive 3 in models with 0 j sup infinity the magnetization is discontinuous at the transition point as originally predicted by thouless and obeys m beta sub c less than or equal to 1 beta sub c j sup sup 1 2 4 for ising q 2 models with j sup infinity it is noted that the correlation function decays as beta approx c beta absolute value x y sup 2 whenever beta beta sub c points 1 3 are deduced from previous percolation results by utilizing the fortuin kasteleyn representation which also yields other results of independent interest relating potts models with different values of q

a fast squares power inversion array for tracking nonstationary environments this correspondence presents and investigates a fast algorithm tracking of nonstationary environments in power inversion the algorithm is based on the use of iterative least squares techniques and the introduction of an additional gradient vector in the objective function so that both the optimal weight vector and its rate of change are estimated recursively although the algorithm is computationally more complex than conventional least squares methods it has better performance in moving sources as the velocities of the latter are also being estimated

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

tracking of signal subspace projectors a new subspace tracking approach that directly operates on the projection matrix onto the signal subspace instead of tracking its unitary eigenbasis is proposed therefore the difficulties arising from introducing a calculus on the manifold of projection matrices are overcome by a proper parameterization of the projectors simulation results are presented from the field of angular frequency retrieval in array signal processing

brief robust adaptive compensation of biased sinusoidal disturbances with unknown frequency asymptotically stable observable linear systems of order n which are not required to be minimum phase and are affected by an additive noisy biased sinusoidal disturbance with unknown bias magnitude phase and frequency are considered the problem of designing an output feedback compensator which regulates the output to zero for any initial condition and for any biased sinusoidal disturbance with no noise is addressed under the assumption that the system parameters are known this problem is solved by a 2n 6 order compensator which generates asymptotically convergent estimates of the biased sinusoidal disturbance and of its parameters including frequency the robustness of the closed loop system with respect to sufficiently small additive unmodelled noise is characterized in terms of input to state stability

steady state analysis of the multistage constant modulus array the multistage constant modulus cm array is a cascade adaptive beamforming system that can recover several narrowband cochannel signals without training we examine its steady state properties at convergence using a stochastic analysis and computer simulations based on a wiener model of convergence for the gradient adaptive algorithms closed form expressions are derived for the cm array and canceller weight vectors as well as the effective source direction vectors at all stages along the cascade system the signal capture and direction finding capabilities of the system are also discussed computer simulations for stationary and fading sources are presented to confirm the theoretical results and to illustrate the rapid convergence behavior of the adaptive algorithms

system size dependence of the autocorrelation time for the swendsen wang ising model abstract we present monte carlo simulation results of the autocorrelation time for the swendsen wang method for the simulation of the ising model we have calculated the exponential and the integrated autocorrelation time at the critical point t c of the two dimensional ising model our results indicate that both autocorrelation times depend logarithmically on the linear system size l instead of a power law the simulations were carried out on the parallel computer of the condensed matter theory group at the university of mainz

blind separation of independent sources for virtually any source probability density function the blind source separation bss problem consists of the recovery of a set of statistically independent source signals from a set of measurements that are mixtures of the sources when nothing is known about the sources and the mixture structure in the bss scenario of two noiseless real valued instantaneous linear mixtures of two sources an approximate maximum likelihood ml approach has been suggested in the literature which is only valid under certain constraints on the probability density function pdf of the sources in the present paper the expression for this ml estimator is reviewed and generalized to include virtually any source distribution an intuitive geometrical interpretation of the new estimator is also given in terms of the scatter plots of the signals involved an asymptotic performance analysis is then carried out yielding a closed form expression for the estimator asymptotic pdf simulations illustrate the behavior of the suggested estimator and show the accuracy of the asymptotic analysis in addition an extension of the method to the general bss scenario of more than two sources and two sensors is successfully implemented

a subspace based direction finding algorithm using fractional lower order statistics we propose several classes of fractional lower order moment flom based matrices that can be used with music to estimate the doas of independent circular signals embedded in additive s spl alpha s symmetric spl alpha stable noise e g sea clutter we run simulations with different choices of the flom parameter p for our flom based matrices and conclude that when the noise is s spl alpha s with unknown spl alpha spl ne 2 flom multiple signal classification music with p close to unity yields good performance the performance of flom music and robust covariation based roc music are similar three scenarios that contain circular signals phase modulation pm circularly symmetrical gaussian and quaternary phase shift keying qpsk and one scenario that contains noncircular signals binary phase shift keying bpsk all embedded in the same s spl alpha s noise are tested these simulation results reveal that the scenario containing bpsk signals leads to poor performance indicating that flom music is presently limited to circular signals

fundamental performance limitations in tracking sinusoidal signals this paper attempts to give a thorough treatment of the performance limitation of a linear time invariant multivariable system in tracking a reference signal which is a linear combination of a step signal and several sinusoids with different frequencies the tracking performance is measured by an integral square error between the output of the plant and the reference signal our purpose is to find the fundamental limit for the attainable tracking performance under any control structure and parameters in terms of the characteristics and structural parameters of the given plant as well as those of the reference signal under consideration it is shown that this fundamental limit depends on the interaction between the reference signal and the nonminimum phase zeros of the plant and their frequency dependent directional information

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

doa estimation by exploiting the symmetric configuration of uniform linear array a new direction of arrival doa estimation method is proposed for uniform linear array in this paper when both uncorrelated and coherent sources are present the uncorrelated and coherent sources are estimated at two different stages the uncorrelated sources are first estimated using conventional subspace methods and then they are eliminated by exploiting the symmetric configuration of the array finally the remaining coherent sources are estimated by reconstructing a non toeplitz matrix the number of sources resolved by our method can exceed the number of array elements simulation results demonstrate the effectiveness and efficiency of our proposed method

invaded cluster algorithm for potts models the invaded cluster algorithm a method for simulating phase transitions is described in detail theoretical albeit nonrigorous justification of the method is presented and the algorithm is applied to potts models in two and three dimensions the algorithm is shown to be useful for both first order and continuous transitions and evidently provides an efficient way to distinguish between these possibilities the dynamic properties of the invaded cluster algorithm are studied numerical evidence suggests that the algorithm has no critical slowing for ising models s1063 651x 96 09208 2

robust adaptive observers for nonlinear systems with bounded disturbances since existing adaptive observers for nonlinear systems may generate unbounded parameter estimates in the presence of bounded disturbances robust adaptive observers are presented which prevent parameter estimate drift in addition the input to state stability of the error dynamics with respect to disturbances and parameter time derivatives is guaranteed by generalizing a persistency of excitation result asymptotic convergence of state estimation errors is still achieved for systems in adaptive observer form when disturbances are not present by a suitable extension of barbalat s lemma

regulation of linear systems with unknown exosystems of uncertain order the problem of designing an output feedback control law which exponentially achieves output regulation is considered for known stabilizable and detectable linear systems which are allowed to be non minimum phase output references and or additive disturbances are both generated by a linear exosystem with unknown purely imaginary eigenvalues and uncertain order the novelty of this note is to require only an upper bound on the exosystem order to achieve a global solution which includes exponentially convergent estimates of the exosystem unknown frequencies

analytical performance assessment of multi dimensional matrix and tensor based esprit type algorithms in this paper we present a generic framework for the asymptotic performance analysis of subspace based parameter estimation schemes it is based on earlier results on an explicit first order expansion of the estimation error in the signal subspace obtained via an svd of the noisy observation matrix we extend these results in a number of aspects firstly we demonstrate that an explicit first order expansion of the higher order svd hosvd based subspace estimate can be derived secondly we show how to obtain explicit first order expansions of the estimation error of arbitrary esprit type algorithms and provide the expressions for r d standard esprit r d unitary esprit r d standard tensor esprit as well as r d unitary tensor esprit thirdly we derive closed form expressions for the mean square error mse and show that they only depend on the second order moments of the noise hence to apply this framework we only need the noise to be zero mean and possess finite second order moments additional assumptions such as gaussianity or circular symmetry are not needed

a globally convergent frequency estimator online estimation of the frequency of a sinusoidal signal is a classical problem in systems theory that has many practical applications in this paper the authors provide a solution to the problem of ensuring a globally convergent estimation more specifically they propose a new adaptive notch filter whose dynamic equations exhibit the following remarkable features 1 all signals are globally bounded and the estimated frequency is asymptotically correct for all initial conditions and all frequency values 2 the authors obtain a simple tuning procedure for the estimator design parameters which trades off the adaptation tracking capabilities with noise sensitivity ensuring exponential stability of the desired orbit and 3 transient performance is considerably enhanced even for small or large frequencies as witnessed by extensive simulations to reveal some of the stability instability mechanisms of the existing algorithms and motivate our modifications the authors make appeal to a novel nonlinear state dependent time scaling the main advantage of working in the new time scale is that they remove the coupling between the parameter update law and the filter itself decomposing the system into a feedback form where the required modifications to ensure stability become apparent even though they limit their attention here to the simplest case of a single constant frequency without noise the algorithm is able to track time varying frequencies preserve local stability in the presence of multiple sinusoids and is robust with respect to noise

coprime sensing via chinese remaindering over quadratic fields part i array designs a coprime antenna array consists of two or more sparse subarrays featuring enhanced degrees of freedom dof and reduced mutual coupling this paper introduces a new class of planar coprime arrays based on the theory of ideal lattices in quadratic number fields a splitting prime p can be decomposed into the product of two distinct prime ideals which give rise to the two sparse subarrays their virtual difference coarray enjoys a quadratic gain in dof thanks to the generalized chinese remainder theorem crt to enlarge the contiguous aperture of the coarray we present hole free symmetric crt arrays with simple closed form expressions the ring of gaussian integers and the ring of eisenstein integers are considered as examples to demonstrate the procedure of designing coprime arrays with eisenstein integers our design yields a difference coarray that is a subset of the hexagonal lattice offering a significant gain in dof over the rectangular lattice given the same physical areas maximization of crt arrays in the aspect of essentialness and the superior performance in the context of angle estimation will be presented in the companion paper part ii

disturbance cancellation for linear systems by adaptive internal models abstract the adaptive disturbance cancellation problem is considered for single input single output linear systems when the linear exosystem which generates the disturbances to be rejected and or the reference signals to be tracked is unknown that is both its order 2 r 1 and its parameters 1 r are unknown the proposed regulator makes use of two observers and contains an adaptive internal model which tunes m internal parameters on the basis of the output regulation error it is shown that if m r that is the adaptive internal model can reproduce the required input the regulation error tends exponentially to zero if m r that is the adaptive internal model can only approximate the required input within an approximation error the regulation error tends exponentially into a closed ball whose radius is proportional to provided that is sufficiently small so that singularities are avoided

output regulation for linear minimum phase systems with unknown order exosystem under the assumption that the regulation error is the only feedback signal it is shown how to design a global regulator capable of rejecting and or tracking signals made of at most m sinusoidal terms with unknown frequencies magnitudes and phases for linear observable minimum phase systems the asymptotic convergence of the tracking error to zero is guaranteed provided that an upper bound is known on the number of sinusoidal terms even though the values of the unknown frequencies may not be recovered exponential convergence is achieved if all the exosystem frequencies are excited

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

direction finding for diversely polarized signals using polynomial rooting a direction finding algorithm for diversely polarized arrays that is based on polynomial rooting is presented using polynomial rooting instead of search reduces significantly the computational requirements of the algorithm and enhances resolution the basic method is limited to linear uniformly spaced arrays however using an interpolation technique the algorithm is extended to a larger class of arrays the performance of the proposed algorithm is analyzed computer simulations are used to demonstrate the performance of the new technique and to verify the performance analysis

consistency and mse performance of music based doa of a single source in white noise with randomly missing data music is a popular algorithm for estimating the direction of arrival doa in array signal processing applications in this paper we analyze the performance of the music algorithm for a single source system in the presence of noisy and missing data when only a random subset of the entries in the data matrix are observed we prove consistency of the doa estimate when signal from a single source is impinging on low coherence arrays and derive an analytic expression for the mean squared error mse performance of music for the case of uniform linear arrays in the large array and relatively large sample setting our analysis is mathematically justified in both the sample rich and deficient regimes the expression for the mse is a simple function of array geometry signal to noise ratio snr the fraction of entries observed and the ratio of the number of sensors to number of snapshots we derive a phase transition threshold which separates a regime where music is consistent from a regime where music is inconsistent this threshold depends upon the snr the probability of observing entries in the data matrix and number of sensors and snapshots in a simple manner which we make explicit

dynamic and static properties of the invaded cluster algorithm simulations of the two dimensional ising and three state potts models at their critical points are performed using the invaded cluster ic algorithm it is argued that observables measured on a sublattice of size l should exhibit a crossover to swendsen wang sw behavior for l sufficiently less than the lattice size l and a scaling form is proposed to describe the crossover phenomenon it is found that the energy autocorrelation time t l l for an l3l sublattice attains a maximum in the crossover region and a dynamic exponent z ic for the ic algorithm is defined according to t max l z ic simulation results for the three state model yield z ic 50 34660 002 which is smaller than values of the dynamic exponent found for the sw and wolff algorithms and also less than the li sokal bound the results are less conclusive for the ising model but it appears that z ic 0 21 and possibly that t max ln l so that z ic 50 similar to previous results for the sw and wolff algorithms s1063 651x 99 00902 2

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

comments on l shape 2 dimensional arrival angle estimation with propagator method for original paper see n tayem et al ibid vol 53 no 5 p 1622 30 2005 we indicate that the two dimensional 2 d direction of arrival doa estimation method proposed by n tayem has an error in the pair matching between the azimuth and elevation angle estimates a feasible solution for pair matching is proposed

generalized and extended subspace algorithms for error correction with quantized dft codes discrete fourier transform dft codes have been used to provide robustness against errors and erasures in various applications this paper focuses on improving error localization of the bose chaudhuri hocquenghem bch dft codes first we analyze how the subspace based error localization outperforms the coding theoretic one then we propose an extension of the subspace based error localization based on additional syndrome that improves the existing one and is naturally suitable for rate adaptive distributed source coding dsc further we propose a new generic subspace based algorithm to decode bch dft codes the proposed approach generalizes the encoding and decoding of this important class of dft codes it introduces many different decoding matrices for a dft code this diversity is then used to diminish the effect of the quantization noise and thus to improve the decoding finally the extended and generalized approaches are combined to maximize the decoding gain simulation results demonstrate the capability of the proposed algorithms to perform significantly better than the existing subspace based error localization in the presence of quantization noise

global adaptive observers for nonlinear systems via filtered transformations the problem of determining global adaptive observers for a class of single output nonlinear systems which are linear with respect to an unknown constant parameter vector is addressed sufficient conditions are given to observe asymptotically an equivalent state without persistency of excitation under additional geometric conditions the original state can be observed as well the results obtained are based on a nonlinear change of coordinates driven by auxiliary filters filtered transformations

waveform preserving blind estimation of multiple independent sources the problem of blind estimation of source signals is to estimate the source signals without knowing the characteristics of the transmission channel it is shown that the minimum variance unbiased estimates can be obtained if and only if the transmission channel can be identified blindly it is shown that the channel can be blindly identified if and only if there is not more than one gaussian source this condition suggests that waveform preserving blind estimation can be achieved over a wide range of signal processing applications including those cases in which the source signals have identical nongaussian distributions the constructive proof of the necessary and sufficient condition serves as a foundation for the development of waveform preserving blind signal estimation algorithms examples are presented to demonstrate the applications of the theoretical results

a two stage method for inverse medium scattering we present a novel numerical method to the time harmonic inverse medium scattering problem of recovering the refractive index from noisy near field scattered data the approach consists of two stages one pruning step of detecting the scatterer support and one resolution enhancing step with nonsmooth mixed regularization the first step is strictly direct and of sampling type and it faithfully detects the scatterer support the second step is an innovative application of nonsmooth mixed regularization and it accurately resolves the scatterer size as well as intensities the nonsmooth model can be efficiently solved by a semi smooth newton type method numerical results for two and three dimensional examples indicate that the new approach is accurate computationally efficient and robust with respect to data noise

multiple source location the signal subspace approach the multiple source location problem is solved for a general array geometry using the principal of least squares modeling the incident wavefields may be a mixture of coherent and noncoherent sources that are broadband and or narrowband furthermore the wavefields may be plane waves and or spherical waves an effective algorithmic approach is developed for solving the multiple source location problem in the signal and covariance domains in each domain it is necessary to represent a set of vectors as a linear combination of array steering vectors using this property a generic descent algorithmic approach is developed for estimating the wavefield directions of arrival the success of such iterative approaches is critically dependent on the generation of good estimates to initialize the algorithm an effective initialization procedure is developed for this purpose direction of arrival estimates which arise from the proposed procedure are empirically found to be unbiased and low variance

on the smallest singular value of multivariate vandermonde matrices with clustered nodes abstract we prove lower bounds for the smallest singular value of rectangular multivariate vandermonde matrices with nodes on the complex unit circle the nodes are off the grid groups of nodes cluster and the studied minimal singular value is bounded below by the product of inverted distances of a node to all other nodes in the specific cluster by using known and new upper bounds for the smallest singular value this completely settles the univariate case and pairs of nodes in the multivariate case both including reasonable sharp constants for larger clusters we show that the smallest singular value depends also on the geometric configuration within a cluster

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

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

direction of arrival estimation using rank revealing qr factorization the authors describe a novel technique for direction of arrival estimation based on computing a permutation matrix e and a qr factorization re hb of the permuted covariance matrix r such that a possible rank deficiency of r is revealed in the triangular factor b having a minimum norm lower right block a subset of the columns of the orthogonal matrix h is shown to be orthogonal to the direction vectors of sources and hence can be used to estimate their bearings the cost of this algorithm is only slightly more than that of one qr factorization but is much lower than that of an eigen decomposition simulation results are included to show that the proposed method performs nearly as well as music in terms of signal resolution bias and variance of the estimated bearings

performance analysis of spatial smoothing with interpolated arrays the interpolated spatial smoothing algorithm is a computationally efficient method for estimating the directions of arrival doas of signals some of which may be perfectly correlated it extends the spatial smoothing method to arbitrary array geometries a statistical performance analysis of the algorithm is presented closed form expressions for the covariance matrix of the doa estimation errors are derived using a perturbation analysis evaluating these expressions for specific cases and comparing them to the cramer rao lower bound for the doa estimates provides insight into the statistical efficiency of this algorithm the formulas for the error covariance are quite general and can be specialized to provide results for other doa estimation algorithms as well

eigenvalue estimation of parameterized covariance matrices of large dimensional data this article deals with the problem of estimating the covariance matrix of a series of independent multivariate observations in the case where the dimension of each observation is of the same order as the number of observations although such a regime is of interest for many current statistical signal processing and wireless communication issues traditional methods fail to produce consistent estimators and only recently results relying on large random matrix theory have been unveiled in this paper we develop the parametric framework proposed by mestre and consider a model where the covariance matrix to be estimated has a known finite number of eigenvalues each of it with an unknown multiplicity the main contributions of this work are essentially threefold with respect to existing results and in particular to mestre s work to relax the restrictive separability assumption to provide joint consistent estimates for the eigenvalues and their multiplicities and to study the variance error by means of a central limit theorem

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

direction finding for wide band signals using an interpolated array the authors derive a new direction finding algorithm for multiple wideband signals received by an arbitrary array and analyze its performance using an interpolation technique they generate a set of virtual arrays each for a different frequency band having the same array manifold the convergence matrices of these arrays are added to produce a composite covariance matrix direction of arrival doa estimates are obtained by eigendecomposition of this composite covariance matrix using the narrowband music algorithm or its variants closed form expressions for the asymptotic covariance matrix of the doa estimation errors are derived using a perturbation analysis evaluated for specific cases and compared with the cramer rao lower bound special attention is given to correlated and coherent signals the formulas for the error covariance are quite general and can be modified to provide results for other wideband doa estimation algorithms

discrete time adaptive command following and disturbance rejection with unknown exogenous dynamics we present an adaptive controller that requires limited model information for stabilization command following and disturbance rejection for mult input multi output minimum phase discrete time systems specifically the controller requires knowledge of the open loop system s relative degree as well as a bound on the first nonzero markov parameter notably the controller does not require knowledge of the command or the disturbance spectrum as long as the command and disturbance signals are generated by a lyapunov stable linear system thus the command and disturbance signals are combinations of discrete time sinusoids and steps in addition the markov parameter based adaptive controller uses feedback action only and thus does not require a direct measurement of the command or disturbance signals using a logarithmic lyapunov function we prove global asymptotic convergence for command following and disturbance rejection as well as lyapunov stability of the adaptive system when the open loop system is asymptotically stable

grid free compressive beamforming the direction of arrival doa estimation problem involves the localization of a few sources from a limited number of observations on an array of sensors thus it can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing cs to achieve high resolution imaging on a discrete angular grid the cs reconstruction degrades due to basis mismatch when the doas do not coincide with the angular directions on the grid to overcome this limitation a continuous formulation of the doa problem is employed and an optimization procedure is introduced which promotes sparsity on a continuous optimization variable the doa estimation problem with infinitely many unknowns i e source locations and amplitudes is solved over a few optimization variables with semidefinite programming the grid free cs reconstruction provides high resolution imaging even with non uniform arrays single snapshot data and under noisy conditions as demonstrated on experimental towed array data

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 statistical resolution theory of the ar method of spectral analysis the autoregressive ar method of spectral analysis is widely used in diverse areas for its solid theoretical foundation interesting physical interpretation computational efficiency and more importantly high resolution capability various aspects of its statistical performance have been investigated however the resolution probability that provides the most rigorous description of the spectrum resolution capability is still not available in the literature in this paper by formulating the resolution event in the framework of statistical decision theory and directly determining its probability from its characteristic function we obtain an exact asymptotic formula for the probability of resolution on this basis we determine the limiting resolving behavior of the sample ar spectrum and develop the corresponding geometrical insight in the parametric space simulation and numerical results are also presented to confirm and illustrate the theory

doa estimation with enhanced dofs by exploiting cyclostationarity many modulated signals exhibit a cyclostationarity property which has been applied in direction of arrival estimation due to its immunity to interference and noise in this paper we focus on how this cyclostationarity can be effectively integrated with the spatial dimension to enhance both the degrees of freedom and the accuracy of doa estimation first for narrowband signal case by vectorizing the second order cyclic correlation matrix instead of the conventional zero lag covariance matrix one can directly generate an augmented virtual array with sensors at positions defined by the difference coarray of the physical array then for wideband signal case two additional fractional factors are introduced so that the vectorized cyclic correlation matrix can be viewed as a single snapshot received signal from an array with sensors at positions defined by the fractional weighted difference coarray due to the fact that cyclic correlation matrices as special second order statistics allow us to obtain more degrees of freedom the proposed two virtual array models can resolve o n 2 sources by using a sparse linear array consisting of only n physical sensors e g nested coprime array furthermore a scheme of multipseudosampling is proposed in order to reduce the sensitivity to noise and parameter the proposed models can be considered as an extension of difference coarray perspective via the combination of cyclic frequency and temporal lag in the end numerical simulation results validate the effectiveness of the proposed models

matrix based higher order spectral analysis for three wave coupling processes composite linear and quadratic systems produce three wave coupling when stimulated by random phase input sinusoids due to the nonlinearity of the system the output frequencies are arithmetically related to the input using third order cumulant statistics and their associated bispectrum techniques are devised based on phase insensitive matrix structures for detection and frequency estimation of coupling frequencies the separation of the third order cumulant series into symmetric and skew symmetric portions allows one to exploit their characteristic eigendecompositions for frequency estimation after symmetrization biphases can be easily extracted as coefficients of the cumulant sequence using a generalized eigenvector representation one can relate symmetric and skew symmetric bases by a subspace rotation algorithm biphases can be estimated directly from generalized eigenvalues of the matrix pencil formed by symmetric and skew symmetric matrices the dimensionality of the matrices can be reduced through the use of cumulant projections that yield a slice of the bispectrum the radon transform procedure is related to bispectral processing through an isotropic radial slice volterra filter the compact third order kronecker product matrix formulation and algorithms for coupling frequency estimation can also be converted for use in biphase estimation simulations showing the performance of the above procedures are also presented for both synthetic and biomedical time series

performance analysis of the enhanced minimum variance spatial spectrum estimator the performance of the enhanced minimum variance emv spatial spectrum estimator is studied expressions are presented fur the variance and bias of direction of arrival estimators based on general functions of the covariance matrix and these expressions are then used to study the emv estimator finite data effects and random perturbations on the ideal modeling assumptions are studied separately

brief paper an adaptive learning regulator for uncertain minimum phase systems with undermodeled unknown exosystems the design of an adaptive learning regulator is addressed for uncertain minimum phase linear systems with known bounds known upper bound on system order known relative degree known high frequency gain sign and for unknown exosystems with unknown order uncertain frequencies on the basis of a known bound on system uncertainties and a known bound on the modeled exosystem frequencies a new adaptive output error feedback control algorithm is proposed which guarantees exponential convergence of both the output and the control input errors into residual bounds which decrease as the exosystem modeling error decreases exponential convergence of both errors to zero is obtained when the regulator exactly models all exosystem excited frequencies while asymptotic convergence of both errors to zero is achieved when the actual exosystem is overmodeled by the regulator the new algorithm generalizes existing learning controllers since in the case of periodic references and or disturbances the knowledge of the period is not required

markov based eigenanalysis method for frequency estimation this paper proposes an eigenanalysis based method for estimating the frequencies of complex valued sine waves the basic idea behind this method consists of using a set of linearly independent vectors that are orthogonal to the signal subspace spanned by the principal eigenvectors of the data covariance matrix exploiting that orthogonality condition gives an overdetermined system of linear equations the unknown parameters of which are uniquely related to the frequencies analytical expressions are derived for the covariances of the equation errors in the sample version of the aforementioned linear system of equations based on these expressions a markov like estimate of the unknown parameters is introduced which asymptotically with respect to either the number of data samples or the signal to noise ratio provides the minimum variance frequency estimates in a fairly large class of consistent estimators the paper includes monte carlo simulations that support the theoretical analysis results and show that those results may apply to scenarios with rather low values of the number of data samples and the signal to noise ratio

ramanujan sums in the context of signal processing part ii fir representations and applications the mathematician ramanujan introduced a summation in 1918 now known as the ramanujan sum c q n in a companion paper part i properties of ramanujan sums were reviewed and ramanujan subspaces s q introduced of which the ramanujan sum is a member in this paper the problem of representing finite duration fir signals based on ramanujan sums and spaces is considered first it is shown that the traditional way to solve for the expansion coefficients in the ramanujan sum expansion does not work in the fir case two solutions are then developed the first one is based on a linear combination of the first n ramanujan sums with n being the length of the signal the second solution is based on ramanujan subspaces with q 1 q 2 q k denoting the divisors of n it is shown that x n can be written as a sum of k signals x qi n s qi furthermore the i th signal x qi n has period q i and any pair of these periodic components is orthogonal the components x qi n can be calculated as orthogonal projections of x n onto ramanujan spaces s qi then the ramanujan periodic transform rpt is defined based on this and is useful to identify hidden periodicities it is shown that the projection matrices which compute x qi n from x n are integer matrices except for an overall scale factor the calculation of projections is therefore rendered easy to estimate internal periods n n of x n one only needs to know which projection energies are nonzero

global exponential regulation of discrete time linear systems with unknown neutrally stable exosystems discrete time linear stabilizable and detectable systems with known parameters are considered the regulation problem is addressed when the reference output and or the disturbances contain sinusoidal terms generated by a linear exosystem with unknown parameters only an upper bound on the number of unknown sinusoids is supposed to be known a constructive algorithm is proposed to drive the regulation error exponentially to zero on the basis of its measurement only under the same necessary and sufficient conditions which are required when the exosystem is known the control strategy includes an online detector for the number of excited frequencies and exponentially converging global estimates of the exosystem unknown parameters an illustrative example containing a variable number of frequencies is worked out and simulated

direction of arrival estimation in time modulated linear arrays with unidirectional phase center motion a novel approach for estimating the direction of arrivals doas in time modulated linear arrays tmlas with unidirectional phase center motion upcm scheme is proposed in this paper based on the fact that the main beams of the patterns at different sidebands can be directed at different directions the corresponding received signals can be used to compose a received data space thus the spatial locations of the far field sources can be estimated by using multiple signal classification music algorithm simulation results of the doa estimation in an 8 element tmla with the upcm scheme validate the proposed approach where the performance such as the accuracy and resolution of the doa estimation is obtained through monte carlo simulations as compared to the doa estimation based on conventional uniform linear arrays ulas a much better resolution performance is obtained

combining sparsity and rotational invariance in eeg meg source reconstruction we introduce focal vector field reconstruction fvr a novel technique for the inverse imaging of vector fields the method was designed to simultaneously achieve two goals a invariance with respect to the orientation of the coordinate system and b a preference for sparsity of the solutions and their spatial derivatives this was achieved by defining the regulating penalty function which renders the solutions unique as a global l 1 norm of local l 2 norms we show that the method can be successfully used for solving the eeg inverse problem in the joint localization of 2 3 simulated dipoles fvr always reliably recovers the true sources the competing methods have limitations in distinguishing close sources because their estimates are either too smooth loreta minimum l 1 norm or too scattered minimum l 2 norm in both noiseless and noisy simulations fvr has the smallest localization error according to the earth mover s distance emd which is introduced here as a meaningful measure to compare arbitrary source distributions we also apply the method to the simultaneous localization of left and right somatosensory n20 generators from real eeg recordings compared to its peers fvr was the only method that delivered correct location of the source in the somatosensory area of each hemisphere in accordance with neurophysiological prior knowledge

invaded cluster algorithm for critical properties of periodic and aperiodic planar ising models we demonstrate that the invaded cluster algorithm introduced by machta et al 1995 phys rev lett 75 2792 5 is a fast and reliable tool for determining the critical temperature and the magnetic critical exponent of periodic and aperiodic ferromagnetic ising models in two dimensions the algorithm is shown to reproduce the known values of the critical temperature on various periodic and quasiperiodic graphs with an accuracy of more than three significant digits but only modest computational effort on two quasiperiodic graphs which were not investigated in this respect before the 12 fold symmetric square triangle tiling and the 10 fold symmetric tubingen triangle tiling we determine the critical temperature furthermore a generalization of the algorithm to non identical coupling strengths is presented and applied to a class of ising models on the labyrinth tiling for generic cases in which the heuristic harris luck criterion predicts deviations from the onsager universality class we find a magnetic critical exponent different from the onsager value but notable exceptions to the criterion are found which consist not only of the exactly solvable cases in agreement with a recent exact result but also of the self dual ones and maybe more

a new optimization technique for adaptive antenna arrays an adaptive nulling algorithm for adjusting the array weights under the soft constraint of the weight norm being very much less than 1 or equal to 1 based on the measured correlations between the array and element outputs is described the algorithm can be regarded as an extension of the constrained least mean square algorithm it is derived from the same concept of signal and noise subspaces defined in the multiple signal classification music algorithm one of the unique features of the present algorithm is that the number of the iterations required to adapt the array weights to form nulls is exactly equal to the number of interferers

adaptive algorithms for the rejection of sinusoidal disturbances with unknown frequency abstract two algorithms are presented for the rejection of sinusoidal disturbances with unknown frequency the first is an indirect algorithm where the frequency of the disturbance is estimated and the estimate is used in another adaptive algorithm that adjusts the magnitude and phase of the input needed to cancel the effect of the disturbance a direct algorithm that uses the concept of a phase locked loop is also presented in which frequency estimation and disturbance cancellation are performed simultaneously approximate analyses are presented for both schemes and the results are found useful for the selection of the design parameters simulations are given which demonstrate the validity of the analytical results and the ability of the algorithms to reject sinusoidal disturbances with unknown frequency the indirect algorithm is found to have a larger capture region for the parameter estimates whereas the direct algorithm has superior convergence properties locally about the optimum parameter estimates

kalman based estimator for doa estimations we introduce a new kalman based noise subspace estimator combined with the root music for direction of arrival doa estimation of uncorrelated narrow band plane waves impinging on an array of sensors without both a priori knowledge of the number of sources and the inflation method presented by yang and kaveh 1988 we show that the kalman based estimator can approximately estimate the complete noise subspace with small bias for high input signal to noise ratio snr scenario the proposed algorithm needs slightly more computation operations per adaptive cycle than yang and kaveh s lms based algorithm but with much more rapid convergence simulations demonstrate the effectiveness of the proposed algorithm

first order perturbation analysis of singular vectors in singular value decomposition singular value decomposition svd is an important technique in signal processing in the literature the perturbation analysis of svd has been well documented in the context of subspace decomposition the contribution of the signal subspace to the perturbation of the singular vectors that span the signal subspace is often ignored as it is treated as second and higher order terms and thus the first order perturbation is typically given as the column span of the noise subspace in this correspondence we show that not only the noise subspace but also the signal subspace contribute to the first order perturbation of the singular vectors we further show that the contribution of the signal subspace does not impact on the performance analysis of algorithms that rely on the signal subspace for parameter estimation but it affects the analysis of algorithms that depends on the individual basis vectors for the latter we also give a condition under which the contribution of the signal subspace to the perturbation of singular vectors may be ignored in the statistical sense numerical examples are provided to validate our theoretic claims

source localization in a waveguide using polynomial rooting source localization in acoustic waveguides involves a multidimensional search procedure we propose a new algorithm in which the search in the depth direction is replaced by polynomial rooting using the proposed algorithm range and depth estimation by a vertical array requires a 1 d search procedure for a 3 d localization problem i e range depth and direction of arrival doa estimation the algorithm involves a 2 d search procedure consequently the proposed algorithm requires significantly less computation than other methods that are based on a brute force search procedure over the source location parameters in order to evaluate the performance of the algorithm an error analysis is carried out and monte carlo simulations are performed the results are compared with the cramer rao bound crb and to the maximum likelihood ml simulation performance the algorithm is shown to be efficient while being computationally simpler than the ml or the bartlett processors the disadvantage of the algorithm is that its snr threshold occurs in lower snr than in the ml algorithm

reduced complexity maximum likelihood direction of arrival estimation based on spatial aliasing spatial aliasing is an undesirable phenomenon that prevents the unique determination of the direction of arrival doa of impinging signals in array signal processing however the characteristics of spatial aliasing that generates ambiguous doas can be also used to reduce the computational complexity in maximum likelihood ml doa estimation this paper proposes a structural method to dramatically reduce the computational complexity of the ml doa estimation using the spatial aliasing generated by a nested array structure with a doubly scaled aper ture an ml full grid search is computationally simplified by the highly compressed searching range and the small number of candidate values to be searched which are derived based on spatial aliasing performance analyses based on the theoretical bounds and computational complexity with computer simulations show that the proposed method requires an extremely reduced computational load compared to the conventional ml doa estimation with a uniform linear array ula while achieving the performance enhancement in the estimation accuracy due to the enlarged array aperture

perturbation analysis of subspace based methods in estimating a damped complex exponential we present a study of mode variance statistics for three svd based estimation methods in the case of a single mode damped exponential the methods considered are namely kumaresan tufts matrix pencil and kung s direct data approximation through first order perturbation analysis we derive closed form expressions of the variance of the complex mode frequency and damping factor estimates these expressions are used to compare the different methods and to determine the optimal prediction order for matrix pencil and direct data approximation methods application to the undamped case shows the coherence of the results with those already stated in the literature it is also found that the variances converge linearly towards the cramer rao bound finally the theoretical results are verified using monte carlo simulations

output regulation for linear systems via adaptive internal model given a stabilizable and detectable linear system with additive disturbances and output references generated by a linear stable exosystem with unknown parameters and known order the problem of designing a global output feedback regulator which asymptotically achieves output regulation and disturbance rejection is considered the system is assumed to be known while the frequencies of the exosystem are unknown all exosystem oscillatory modes are assumed to be excited by the initial condition a global solution is proposed consisting of a dynamic output feedback controller which includes exponentially convergent estimates of the unknown frequencies

subspace leakage analysis and improved doa estimation with small sample size classical methods of doa estimation such as the music algorithm are based on estimating the signal and noise subspaces from the sample covariance matrix for a small number of samples such methods are exposed to performance breakdown as the sample covariance matrix can largely deviate from the true covariance matrix in this paper the problem of doa estimation performance breakdown is investigated we consider the structure of the sample covariance matrix and the dynamics of the root music algorithm the performance breakdown in the threshold region is associated with the subspace leakage where some portion of the true signal subspace resides in the estimated noise subspace in this paper the subspace leakage is theoretically derived we also propose a two step method that improves the performance by modifying the sample covariance matrix such that the amount of the subspace leakage is reduced furthermore we introduce a phenomenon named as root swap which occurs in the root music algorithm in the low sample size region and degrades the performance of the doa estimation a new method is then proposed to alleviate this problem numerical examples and simulation results are given for uncorrelated and correlated sources to illustrate the improvement achieved by the proposed methods moreover the proposed algorithms are combined with the pseudo noise resampling method to further improve the performance