on the segre weyr characteristics of right left regular matrix pencils the classical segre weyr characteristic theory of the standard eigenvalue eigenvector problem defined on a n n is extended to the case of right left regular pencils sf g f g m n the notions of toeplitz matrices and of the right left f g sequences j r f g j 1 f g respectively are introduced for right left regular pairs it is shown that j r f g j 1 f g are piecewise arithmetic progression sequences paps the singular points of those paps define the possible degrees of the elementary divisors e d at whereas the deviations or gaps from the arithmetic progression sequence define the multiplicity of the corresponding degree e d s the links between the algebraic notion of the segre characteristic and the geometric notion of the weyr characteristic are established for such families of pencils two different procedures for the computation of the segre characteristic are given the first is based on the analysis of singular points of paps and the second is based o

stability of reducing subspaces abstract we characterize the stability of reducing subspaces of a rectangular matrix pencil of complex matrices b a except for the special case in which the pencil has no eigenvalues and only has one row and one column minimal indices and both are different from zero

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

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

linearization of hyperbolic finite time processes abstract we adapt the notion of processes to introduce an abstract framework for dynamics in finite time i e on compact time sets for linear finite time processes a notion of hyperbolicity namely exponential monotonicity dichotomy emd is introduced thereby generalizing and unifying several existing approaches we present a spectral theory for linear processes in a coherent way based only on a logarithmic difference quotient in this abstract setting we introduce a new topology prove robustness of emd and provide exact perturbation bounds we suggest a new intrinsic approach for the investigation of linearizations of finite time processes including finite time analogues of the local un stable manifold theorem and theorem of linearized asymptotic stability as an application we discuss our results for ordinary differential equations on a compact time interval

on the lipschitz stability of a b invariant subspaces abstract let t be the set of triples a b s where s is an a b invariant subspace and let f be the matrix having minimum norm such that a bf s s then if t m m n is the map defined by a b s f and is continuous at a b s a simple necessary and sufficient condition is given for the lipschitz stability of s it is shown that this continuity condition is satisfied in an open and dense subset of t and that the set of triples a b s such that s is lipschitz stable is also open and dense in t

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

an improved algorithm for the computation of structural invariants of a system pencil and related geometric aspects in this paper we propose a new recursive algorithm for computing the staircase form of a matrix pencil and implicitly its kronecker structure the algorithm compares favorably to existing ones in terms of elegance versatility and complexity in particular the algorithm without any modification yields the structural invariants associated with a generalized state space system and its system pencil two related geometric aspects are also discussed we show that an appropriate choice of a set of nested spaces related to the pencil leads directly to the staircase form we extend the notion of deflating subspace to the singular pencil case c 1997 elsevier science b v

direct transcription solution of high index optimal control problems and regular euler lagrange equations direct transcription methods are used to solve optimal control problems in many industrial settings models for physical systems often take the form of differential algebraic equations daes the index of the dae traditionally is viewed as an important factor in deciding whether a particular numerical approach should be used recently it has been observed that what the user thinks is the index of the dae may not be the same as the index available to the optimization software an investigation of this fact is underway in order to develop guidelines to assist users of various numerical optimal control packages this paper develops some theoretical results that will be needed for this development

stable subspaces of matrix pairs abstract let a b c n n c n m and let m be an a b invariant subspace in this paper the following results are presented i if dim m rank b n then m is stable ii if m im b 0 under some additional hypotheses necessary and sufficient conditions for the stability of m are given iii if m contains the controllability subspace of the pair a b sufficient conditions are given in terms of the brunovsky r numbers and the weyr characteristic of the eigenvalues of a quotient endomorphism associated to the noncontrollable part of the subspace m

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

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

a 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

stability of controlled invariant subspaces abstract let a b c n n c n m and m be an a b invariant subspace let c a b be the controllability subspace of the pair a b if m c a b m im b under additional hypotheses necessary and sufficient conditions for the stability of the subspace m are given

geometric characterization and classification of marked subspaces abstract given an endomorphism of a finite dimensional c vector space we obtain geometric conditions in order to characterize and to classify the marked invariant subspaces w e that is to say the invariant subspaces having some jordan basis which can be extended to a jordan basis of e both conditions are expressed in terms of the double family of subspaces ker f h im f d the starting point is a new criterion for extensibility of jordan bases

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

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

efficient subspace based algorithm for adaptive bearing estimation and tracking in some practical applications of array processing the directions of the incident signals should be estimated adaptively and or the time varying directions should be tracked promptly in this paper an adaptive bearing estimation and tracking abest algorithm is investigated for estimating and tracking the uncorrelated and correlated narrow band signals impinging on a uniform linear array ula based on the subspace based method without eigendecomposition sumwe where a linear operator is obtained from the array data to form a basis for the null space by exploiting the array geometry and its shift invariance property specifically the null space is estimated using the least mean square lms or normalized lms nlms algorithm and the directions are updated using the approximate newton method the transient analyses of the lms and nlms algorithms are studied where the weight i e the linear operator is in the form of a matrix and there is a correlation between the additive noise and input data that involve the instantaneous correlations of the received array data in the updating equation and the step size stability conditions are derived explicitly in addition the analytical expressions for the mean square error mse and mean square deviation msd learning curves of the lms algorithm are clarified the effectiveness of the abest algorithm is verified and the theoretical analyses are corroborated through numerical examples simulation results show that the abest algorithm is computationally simple and has good adaptation and tracking abilities

local behavior of sylvester matrix equations related to block similarity topological properties of a matrix equation of sylvester type are considered this equation is related to the block similarity between rectangular matrices and the passage matrices in this equivalence relation are solutions a local criterion for that similarity is exposed the points of continuity of the map that associates with the coefficient matrices the solution space of that equation are determined

spatial analysis using new properties of the cross spectral matrix a novel concept called the propagator based upon a partition of the steering vectors matrix and correlatively of the received signals cross spectral matrix csm is introduced for the characterization of source and noise subspaces without reference to the csm eigenstructure a localization technique can thereby be applied for uncorrelated or partially correlated sources with an arbitrary propagation model which is directly comparable to the music algorithm given the signals produced by one particular source on some of the sensors the propagator permits the extrapolation of the signals received by the remaining sensors various applications of this property can be found an example is given concerning the estimation of the sensors complex gains

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

finite level systems hermitian operators isometries and a novel parametrization of stiefel and grassmann manifolds in this paper we provide an explicit parametrization of arbitrary n dimensional hermitian operators on the hilbert space operators that may be considered either as hamiltonians or density matrices for finite level quantum systems the description of which gives a complete solution to the over parametrization problem it is shown that all the spectral multiplicities are encoded in a flag unitary matrix obtained as an ordered product of special unitary matrices each one generated by a complex n k dimensional unit vector k 0 1 n 2 as a byproduct an alternative and simple parametrization of stiefel and grassmann manifolds is obtained

condensation phenomena with distinguishable particles we study real space condensation phenomena in types of classical stochastic processes site particle system such as zero range processes and urn models we study a stochastic process in the ehrenfest class i e particles in a site are distinguishable in terms of the statistical mechanical analog the ehrenfest class obeys the maxwell boltzmann statistics we analytically clarify conditions for condensation phenomena in disordered cases in the ehrenfest class in addition we discuss the preferential urn model as an example of the disordered urn model it becomes clear that the quenched disorder property plays an important role in the occurrence of the condensation phenomenon in the preferential urn model it is revealed that the preferential urn model shows three types of condensation depending on the disorder parameters

analytic study of the three urn model for separation of sand we present an analytic study of the urn model for separation of sand recently introduced by lipowski and droz phys rev e 65 031307 2002 we solve analytically the master equation and the first passage problem the analytic results confirm the numerical results obtained by lipowski and droz we find that the stationary probability distribution and the shortest one among the characteristic times are governed by the same free energy we also analytically derive the form of the critical probability distribution on the critical line which supports their results obtained by numerically calculating binder cumulants a lipowski and m droz e print cond mat 0201472

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

discontinuous condensation transition and nonequivalence of ensembles in a zero range process we study a zero range process where the jump rates do not only depend on the local particle configuration but also on the size of the system rigorous results on the equivalence of ensembles are presented characterizing the occurrence of a condensation transition in contrast to previous results the phase transition is discontinuous and the system exhibits ergodicity breaking and metastable phases this leads to a richer phase diagram including nonequivalence of ensembles in certain phase regions the paper is motivated by results from granular clustering where these features have been observed experimentally

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

on line structured subspace identification with application to switched linear systems this article is concerned with the identification of switched linear multiple inputs multiple outputs state space systems in a recursive way first a structured subspace identification scheme for linear systems is presented which turns out to have many attractive features more precisely it does not require any singular value decomposition but is derived using orthogonal projection techniques it allows a computationally appealing implementation and it is closely related to input output models identification second it is shown that this method can be implemented on line to track both the range space of the extended observability matrix and its dimension and thereby the system matrices third by making use of an on line switching times detection strategy this method is applied to blindly identify switched systems and to label the obtained submodels simulation results on noisy data illustrate the abilities and the benefits of the proposed approach

the effective calculation of all assignable polynomials to a single input system over a bezout domain the set of all feedback assignable polynomials to a given single input system over a bezout domain is obtained the general case is reduced to the case of weakly reachable systems for these systems a canonical form for the algebraic equivalence is obtained algorithms and examples over a euclidean domain and in particular over the ring z of rational integers are also given the problem of deciding and feedback assignment of a given polynomial to a given non reachable n dimensional linear system is solved effectively up to a cost of o n4 arithmetic operations

miniversal deformations of marked matrices abstract given the set of square matrices m m n m c that keep the subspace w c n x 0 c n m invariant we obtain the implicit form of a miniversal deformation of a matrix a m and we compute it explicitely when this matrix is marked this is if there is a permutation matrix p m n m c such that p 1 ap is a jordan matrix we derive some applications to tackle the classical carlson problem

differentiable structure of the set of controllable a b t invariant subspaces abstract given a b t hom c n c n m observable we prove that the set of a b t invariant subspaces having a fixed brunovsky kronecker structure is a connected manifold and we compute its dimension also we include some applications of these results

dynamics of the breakdown of granular clusters recently van der meer et al studied the breakdown of a granular cluster phys rev lett 88 174302 2002 we reexamine this problem using an urn model which takes into account fluctuations and finite size effects general arguments are given for the absence of a continuous transition when the number of urns compartments is greater than two monte carlo simulations show that the lifetime of a cluster ensuremath tau diverges at the limits of stability as ensuremath tau ensuremath sim n 1 3 where n is the number of balls after the breakdown depending on the dynamical rules of our urn model either normal or anomalous diffusion of the cluster takes place

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

brief paper convergence analysis of instrumental variable recursive subspace identification algorithms the convergence properties of recently developed recursive subspace identification methods are investigated in this paper the algorithms operate on the basis of instrumental variable iv versions of the propagator method for signal subspace estimation it is proved that under suitable conditions on the input signal and the system the considered recursive subspace identification algorithms converge to a consistent estimate of the propagator and by extension to the state space system matrices

occupation probabilities and fluctuations in the asymmetric simple inclusion process the asymmetric simple inclusion process asip a lattice gas model of unidirectional transport and aggregation was recently proposed as an inclusion counterpart of the asymmetric simple exclusion process in this paper we present an exact closed form expression for the probability that a given number of particles occupies a given set of consecutive lattice sites our results are expressed in terms of the entries of catalan s trapezoids number arrays which generalize catalan s numbers and catalan s triangle we further prove that the asip is asymptotically governed by the following i an inverse square root law of occupation ii a square root law of fluctuation and iii a rayleigh law for the distribution of interexit times the universality of these results is discussed

fast and efficient time reversal imaging using space frequency propagator method it is known that the eigenvalue decomposition and singular value decomposition svd of multi static data matrices mdms are the basis of time reversal tr imaging however the computational loads of the svd can be significantly high when the mdms are large the computational cost of the propagator method pm without any svd of mdms is much lower than that of svd based methods in this paper to reduce the computational complexity in tr imaging first a novel space frequency propagator method sf pm for tr imaging in large mdms is proposed the computational complexity of the proposed sf pm is then analyzed moreover the theoretical analysis is presented to show that the sf pm has a significantly lower computational complexity than the conventional svd based approach finally the reasonable imaging results and superior computational efficiency of the sf pm are verified by simulation

global reduction to the kronecker canonical form of a cr family of time invariant linear systems abstract we present an approach to the kronecker equivalence of quadruples of matrices a b c d based on a natural equivalence relation between pairs of linear mappings we apply this approach to smooth families of quadruples of constant kronecker type obtaining smooth families of transformation matrices that pointwise reduce each quadruple to its kronecker canonical form

a real time procedure for affinely dependent parametric model order reduction using interpolation on grassmann manifolds summary model order reduction helps to reduce the computational time in dealing with large dynamical systems for example during simulation control optimization in many cases the considered model depends on parameters model order reduction techniques are therefore preferred to symbolically preserve this dependence or to be adaptive to the change of the model caused by the variation in the values of the parameters in this paper we first present the application of the interpolation technique on grassmann manifolds to this problem we then improve the method for the models whose system matrices depend affinely on parameters by considerably reducing the computational complexity on the basis of analyzing the structure of sums of singular value decompositions and decomposing the whole procedure into offline and online stages a numerical example is shown to illustrate the method as well as to prove its effectiveness copyright 2012 john wiley sons ltd

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

characterization of controllability based on continuity of closed loop eigenvectors application to controller driven sampling stabilization this technical note presents a novel characterization of controllability for linear time invariant finite dimensional systems this characterization relates eigenvalue controllability with the continuity of the map that assigns to each closed loop eigenvalue the smallest subspace containing the set of corresponding closed loop eigenvectors application of the given characterization is illustrated on a specific case of controller driven sampling stabilization where the sampled system is interpreted as a discrete time switched system and stability under arbitrary switching is ensured via simultaneous triangularization lie algebraic solvability

parameterization and identification of multivariable state space systems a canonical approach in this paper the problem of determining a canonical state space representation for multivariable systems is revisited a method is derived to build a canonical state space representation directly from data generated by a linear time invariant system contrary to the classic construction methods of canonical parameterizations the technique developed in this paper does not assume the availability of any observability or controllability indices however it requires the a matrix of any minimal realization of the system to be non derogatory a subspace based identification algorithm is also introduced to estimate such a canonical state space parameterization directly from input output data

factorized steady states in mass transport models on an arbitrary graph we study a general mass transport model on an arbitrary graph consisting of l nodes each carrying a continuous mass the graph also has a set of directed links between pairs of nodes through which a stochastic portion of mass chosen from a site dependent distribution is transported between the nodes at each time step the dynamics conserves the total mass and the system eventually reaches a steady state this general model includes as special cases various previously studied models such as the zero range process and the asymmetric random average process we derive a general condition on the stochastic mass transport rules valid for arbitrary graph and for both parallel and random sequential dynamics that is sufficient to guarantee that the steady state is factorizable we demonstrate how this condition can be achieved in several examples we show that our generalized result contains as a special case the recent results derived by greenblatt and lebowitz for d dimensional hypercubic lattices with random sequential dynamics

analytic study of clustering in shaken granular material using zero range processes abstract we show that models used to describe granular clustering due to vertical shaking belong to the class of zero range processes this correspondence allows us to derive analytically in the large particle number limit in a very easy and straightforward manner a number of properties of the models like particle distribution functions phase diagram and characteristic time of clusterization

similarity of matrices over commutative rings abstract a canonical form is given for nilpotent matrices which have constant rational canonical form on the spectrum of a commutative ring the similarity class of a matrix with constant rational or jordan canonical form is considered

urn model of separation of sand we introduce an urn model that describes spatial separation of sand in this dynamical model in a certain range of parameters spontaneous symmetry breaking takes place and equipartitioning of sand into two compartments is broken the steady state equation for an order parameter a critical line and the tricritical point on the phase diagram are found exactly the master equation and the first passage problem for the model are solved numerically and the results are used to locate first order transitions exponential divergence of a certain characteristic time shows that the model can also exhibit very strong metastability in certain cases characteristic time diverges as n z where n is the number of balls and z frac 1 2 critical line frac 2 3 tricritical point or frac 1 3 limits of stability

simultaneous versal deformations of endomorphisms and invariant subspaces abstract we study the set m of pairs f v defined by an endomorphism f of f n and a d dimensional f invariant subspace v it is shown that this set is a smooth manifold that defines a vector bundle on the grassmann manifold we apply this study to derive conditions for the lipschitz stability of invariant subspaces and determine versal deformations of the elements of m with respect to a natural equivalence relation introduced on it

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

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

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

differentiable families of subspaces abstract we show how the differentiable families of subspaces can be studied from a geometrical point of view by means of their representation as a differentiable mapping from the manifold of parameters m into the grassmann manifold gr k n of all k dimensional subspaces of k n and the consideration of principal bundles over gr k n and m in order to achieve this first we present a survey of the topology the differentiable structure and the bundle structure of gr k n in particular we show that the topology induced by the gap metric is equivalent to the usual quotient topology second we use these structures to prove two local characterizations of the differentiability of a family of subspaces and we state that these characterizations can be globalized if m is contractible finally we apply these properties to study the existence of global jordan basis of class c r

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

a homeomorphism between observable pairs and conditioned invariant subspaces abstract a bijective correspondence between similarity classes of observable systems c a and n codimensional conditioned invariant subspaces of a pair c a is constructed that leads to a homeomorphism of the spaces this is applied to the parametrization of inner functions of fixed mcmillan degree proofs using state space methods as well as using polynomial models are given

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

right left characteristic sequences and column row minimal indices of a singular pencil for a general singular pencil sf g m n s the right left characteristic sequences r f g l f g are defined and they are shown to be of the piecewise arithmetic progression type the sets of column row minimal indices c f g r f g are defined by a singular points analysis of r f g l f g respectively thus c f g r f g emerge as numerical invariants of the ordered pair f g and they may be computed by rank tests on toeplitz matrices defined on f g

quaternion music for vector sensor array processing this paper considers the problem of direction of arrival doa and polarization parameters estimation in the case of multiple polarized sources impinging on a vector sensor array the quaternion model is used and a data covariance model is proposed using quaternion formalism a comparison between long vector orthogonality and quaternion vector orthogonality is also performed and its implications for signal subspace estimation are discussed consequently a music like algorithm is presented allowing estimation of wave s doas and polarization parameters the algorithm is tested in numerical simulations and performance analysis is conducted when compared with other music like algorithms for vector sensor array the newly proposed algorithm results in a reduction by half of memory requirements for representation of data covariance model and reduces the computational effort for equivalent performance this paper also illustrates a compact and elegant way of dealing with multicomponent complex valued data

on similarities of class cp and applications to matrix differential equations abstract this paper deals with similarities of class cp in particular reduction of class cp to jordan form and unitary triangularization of class cp of a matrix function the main result is applied to establish a method to lower the order of nonlinear matrix differential equations belonging to a broad class of equations in particular this method permits one to transform nonlinear equations of the first order into an algebraic equation joint to a linear differential equation of the first order the method is applied to the matrix differential equation xx x x x and a particular solution is easily obtained

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

lipschitz stability of controlled invariant subspaces abstract let a b c n n c n m and m be an a b invariant subspace in this paper the following results are presented i if m im b 0 necessary and sufficient conditions for the lipschitz stability of m are given ii if m contains the controllability subspace of the pair a b sufficient conditions for the lipschitz stability of the subspace m are given

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

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