system structure and singular control the general continuous time linear quadratic control problem is considered it is shown that recently developed linear system theoretic properties and algorithms play an important role in solving this singular control problem

minimal nonsquare spectral factors we consider the problem of parametrizing the set of all nonsquare minimal spectral factors of a rational matrix function taking positive semidefinite values on the imaginary axis

existence of minimal nonsquare j symmetric factorizations for self adjoint rational matrix functions in this paper we show that any rational matrix function having hermitian values on the imaginary axis and with constant signature and constant pole signature admits a minimal symmetric factorization with possibly nonsquare factors our proof is based on a construction which shows that any such function can be extended preserving its mcmillan degree to a function that admits j symmetric factorization with square factors also we consider other properties of the factors in j symmetric factorizations particular attention is given to the study of the common invariant zero structure of these factors

asymptotic memoryless discrete time detection of phi mixing signals in phi mixing noise corresp in this correspondence we consider the design of memoryless discrete time detectors for a phi mixing signal in phi mixing noise where a large degree of dependency may exist between the signal and the noise the fidelity criterion is taken to be the asymptotic relative efficiency and it is shown that with this fidelity criterion the nonlinearity in the optimal detector can be found as the solution of an integral equation in which knowledge of only the second order statistics of the random processes involved is required

nonsquare spectral factors via factorizations of a unitary function abstract we consider the problem of parametrizing the set of nonsquare minimal spectral factors of a rational matrix function taking positive semidefinite values on the imaginary axis the tool here is the use of factorizations of a certain type of the function w 1w where w resp w is the minimal square spectral factor that has all its poles and zeros in the right resp left halfplane

indecomposable higher chow cycles on jacobians we construct some natural indecomposable elements of ch g j c 1 with trivial regulator and in particular prove that ch g ind j c 1 mb q is uncountable for c a generic curve or a generic hyperelliptic curve of genus g geq 3

parameter estimation and glrt detection in colored non gaussian autoregressive processes the problem of estimating signal and noise parameters from a mixture of nongaussian autoregressive noise with partially known deterministic signal is discussed two models are considered in order to examine different kinds of additive mixing the cramer rao bounds to the joint estimation of the signal amplitude and the noise parameters are presented a computationally simple estimator which was previously proposed for estimation in the absence of signal is extended for the two models under consideration the proposed method essentially consists of two stages of least squares estimation which is motivated by the maximum likelihood estimation the technique is applied to the problem of detecting a signal known except for amplitude in colored nongaussian noise two slightly different mixing models are used and a generalized likelihood ratio test glrt coupled with the proposed estimation scheme is used to solve the problems the results of computer simulations are presented as evidence of the validity of the theoretical productions of performance

minimal realization and dynamic properties of optimal smoothers smoothing algorithms of various kinds have been around for several decades however some basic issues regarding the dynamical structure and the minimal dimension of the steady state algorithm are still poorly understood in this paper we derive a realization of minimal dimension of the optimal smoother for a signal admitting a state space description of dimension n it is shown that the dimension of the smoothing algorithm can vary from n to 2n depending on the zero structure of the signal model the dynamics pole structure of the steady state smoother is also characterized explicitly and is related to the zero structure of the model we use several recent ideas from stochastic realization theory in particular a minimal markovian representation of the smoother is derived which requires solving a nonsymmetric wiener hopf factorization problem in this way the smoother is naturally expressed as the cascade of a whitening filter and a linear filter of least possible dimension whose state space is a minimal markovian subspace containing the smoothed estimate x spl i cap this among other aspects affords a very simple calculation of the error covariance matrix of the smoother a reduced order two filter implementation of the type due to mayne 1966 and fraser 1967 is obtained by solving a riccati equation of reduced dimension which is in general smaller than the dimension of the riccati equations considered in the literature

the solution set of the algebraic riccati equation and the algebraic riccati inequality abstract we present a parametrization of the solution set of the algebraic riccati equation and the algebraic riccati inequality of optimal control where we assume only sign controllability of the underlying system furthermore we characterize the existence of maximal and minimal solutions of both the equation and the inequality by checkable conditions

deconvolution and estimation of transfer function phase and coefficients for nongaussian linear processes nongaussian linear processes are considered it is shown that the phase of the transfer function can be estimated under broad conditions this is not true of gaussian linear processes and in this sense gaussian linear processes are atypical the asymptotic behavior of a phase estimate is determined the phase estimates make use of bispectral estimates these ideas are applied to a problem of deconvolution which is effective even when the transfer function is not minimum phase a number of computational illustrations are given

strongly consistent identification algorithms and noise insensitive mse criteria windowed cumulant projections of nongaussian linear processes yield autocorrelation estimators which are immune to additive gaussian noise of unknown covariance by establishing strong consistency of these estimators strongly consistent and noise insensitive recursive algorithms are developed for parameter estimation these computationally attractive schemes are shown to be optimal with respect to a modified mean square error mse criterion which implicitly exploits the high signal to noise ratio domain of cumulant statistics the novel mse objective function is expressed in terms of the noisy process but it is shown to be a scalar multiple of the standard mse criterion as if the latter was computed in the absence of noise simulations illustrate the performance of the proposed algorithms and compare them with the conventional algorithms

separating function estimation tests a new perspective on binary composite hypothesis testing in this paper we study some relationships between the detection and estimation theories for a binary composite hypothesis test h0 against h1 and a related estimation problem we start with a one dimensional 1d space for the unknown parameter space and one sided hypothesis problems and then extend out results into more general cases for one sided tests we show that the uniformly most powerful ump test is achieved by comparing the minimum variance and unbiased estimator mvue of the unknown parameter with a threshold thus for the case where the ump test does not exist the mvue of the unknown parameter does not exist either therefore for such cases a good estimator of the unknown parameter is deemed as a good decision statistic for the test for a more general class of composite testing with multiple unknown parameters we prove that the mvue of a separating function sf can serve as the optimal decision statistic for the ump unbiased test where the sf is continuous differentiable positive for all parameters under h1 and is negative for the parameters under h0 we then prove that the ump unbiased statistic is equal to the mvue of an sf in many problems with multiple unknown parameters the ump test does not exist for such cases we show that if one detector between two detectors has a better receiver operating characteristic roc curve then using its decision statistic we can estimate the sf more e accurately in probability for example the sf is the signal to noise ratio snr in some problems these results motivate us to introduce new suboptimal sf estimator tests sfets which are easy to derive for many problems finally we provide some practical examples to study the relationship between the decision statistic of a test and the estimator of its corresponding sf

a unifying maximum likelihood view of cumulant and polyspectral measures for non gaussian signal classification and estimation classification and estimation of non gaussian signals observed in additive gaussian noise of unknown covariance are addressed using cumulants or polyspectra by integrating ideas from pattern recognition and model identification asymptotically optimum maximum likelihood classifiers and arma autoregressive moving average parameter estimators are derived without knowledge of the data distribution identifiability of noncausal and nonminimum phase arma models is established using a finite number of cumulant or polyspectral lags of any order greater than two a unifying view of cumulant and polyspectral discriminant measures utilizes these lags and provides a common framework for development and performance analysis of novel and existing estimation and classification algorithms tentative order determination and model validation tests for non gaussian arma processes are described briefly illustrative simulations are also presented

constructive solutions to spectral and inner outer factorizations with respect to the disk we use state space realizations to solve the spectral and inner outer factorization problems with respect to the unit disk formulated for a completely general rational matrix the algorithm is based on orthogonal transformations and standard reliable procedures for solving stein and riccati equations the formulas apply in particular to general descriptor systems or polynomial matrices the main novelty is that we allow for arbitrary rank poles and zeros on the unit circle or at infinity

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

a functional link network with higher order statistics for signal enhancement a functional link network with higher order statistics is introduced for signal enhancement the proposed scheme uses the mean square error mse between higher order statistics of desired signals and filtered output as the learning criterion for training weights in the functional link network this is motivated by the fact that higher order statistics have a natural tolerance to gaussian and symmetrically distributed non gaussian noises results show that the performance of functional link network with higher order statistics is less sensitive to the selection of learning rates than the conventional functional link network and adaptive line enhancement it is also demonstrated that it can enhance signal more effectively under different noise levels for stationary and nonstationary gaussian noises

minimal square spectral factors abstract recently there has been renewed interest in the problem of spectral factorization and in particular the problem of parametrizing all square minimal spectral factors of a given spectrum for instance let us mention two recent papers in this journal one of which dealing with more computational aspects of this problem clements 1993 the other giving a parametrization under additional constraints ferrante et al 1993 this paper is motivated in a large part by ferrante et al 1993 in fact we shall show that a parametrization similar to the one given there can be achieved without one of the additional constraints imposed in ferrante et al 1993 a secondary aim of this paper is to give an overview of several parametrizations available in the literature

asymptotic theory of mixed time averages and kth order cyclic moment and cumulant statistics we generalize parzen s 1961 analysis of asymptotically stationary processes to mixtures of deterministic stationary nonstationary and generally complex time series under certain mixing conditions expressed in terms of joint cumulant summability we show that time averages of such mixtures converge in the mean square sense to their ensemble averages we additionally show that sample averages of arbitrary orders are jointly complex normal and provide their covariance expressions these conclusions provide us with statistical tools that treat random and deterministic signals on a common framework and are helpful in defining generalized moments and cumulants of mixed processes as an important consequence we develop consistent and asymptotically normal estimators for time varying and cyclic moments and cumulants of kth order cyclostationary processes and provide computable variance expressions some examples are considered to illustrate the salient features of the analysis

homogeneous riccati equations versus quadratic inequalities it is proved that under certain hypotheses the existence of hermitian solutions of a homogenized algebraic riccati equation of continuous type is guaranteed if the corresponding quadratic inequality admits a hermitian solution both finite dimensional matrices and infinite dimensional hilbert space operators riccati equations are considered

the algebraic riccati inequality parametrization of solutions tightest local frames and generalized feedback matrices abstract extending on previous work by faurre scherer and pavon a parametrization of the symmetric solutions of the algebraic riccati inequality is established this is then applied to derive new results on tightest local frames and on generalized feedback matrices that arise in stochastic realization theory

brief explicit formulas for lmi based h2 filtering and deconvolution this paper is concerned with the h 2 optimal estimation of a linear combination of the state and of the input of a discrete time linear time invariant dynamic system we reformulate such problem in terms of a set of three linear matrix inequalities lmi and we provide explicit formulas to compute a family of solutions for such lmis this family is explicitly parameterized by a real parameter e the h 2 performance of the corresponding filter may be rendered arbitrarily close to the optimum by choosing a sufficiently small e this procedure is shown to be computationally very efficient

balanced stochastic realizations abstract the balanced stochastic realization is introduced as a balanced solution to the continuous time positive real equations and the dual positive real equations the structure of the associated balanced spectral factors is derived the main result being a product decomposition of the spectral factors the properties of the stochastic model reduction technique of balanced stochastic truncation are considered in particular it is shown that balanced stochastic truncation preserves the right half plane zeros of the spectral factors leading to a transformation approach to the approximation of non minimum phase stochastic systems

consistent identification of stochastic linear systems with noisy input output data abstract a novel criterion is introduced for parametric errors in variables identification of stochastic linear systems excited by non gaussian inputs the new criterion is at least theoretically insensitive to a class of input output disturbances because it implicitly involves higher than second order cumulant statistics in addition it is shown to be equivalent to the conventional mean squared error mse as if the latter was computed in the ideal case of noise free input output data the sampled version of the criterion converges to the novel mse and guarantees strongly consistent parameter estimators the asymptotic behavior of the resulting parameter estimators is analyzed and guidelines for minimum variance experiments are discussed briefly informative enough input signals and persistent of excitation conditions are specified computatonally attractive recursive least squares variants are also developed for on line implementation of arma modeling and their potential is illustrated by applying them to time delay estimation in low snr environment the performance of the proposed algorithms and comparisons with conventional methods are corroborated using simulated data

minimal representations of continuous time processes having spectral density with zeros in the extended imaginary axis given a process y with stationary increments and rational incremental spectral density s we parametrize minimal state space representations of dy we consider the case when s may have zeros on the imaginary axis including infinity and we analyze the zero structure of each state space representation

detection of non gaussian signals in non gaussian noise using the bispectrum the problem of detecting a non gaussian time series in the presence of additive gaussian or non gaussian noise is cast into a classical hypothesis testing framework using the sample bispectrum as the test statistic the power of the test is demonstrated as a function of signal to noise ratio the degree of skewness of the signal and processing parameters the results are compared to the power of a classical energy detection test it is concluded that the bispectrum can be used effectively to detect non gaussian signals in the presence of interfering noise and that it may perform better depending on the degree of non gaussianity than energy detection

approaches of fir system identification with noisy data using higher order statistics the problem of estimating the parameters of a moving average model from the cumulant statistics of the noisy observations of the system output is discussed the system is driven by an independently identically distributed nongaussian sequence that is not observed the noise is additive and may be colored and nongaussian following some existing linear parametric approaches to this problem a linear method and a modification to an existing linear method are proposed for consistent parameter estimation in measurement noise under the assumption that the system order is known both recursive closed form and batch least squares versions of the parameter estimators are presented the existing and the proposed linear methods utilize only a partial set of the relevant output statistics this restriction being necessary to obtain a linear estimator whereas there exist nonlinear method that exploit a much larger set of output statistics a simulation example where two existing linear methods and the two new methods are compared to two existing nonlinear methods is presented

optimal linear quadratic systems for detection and estimation the problem of linear quadratic systems for detection has long been solved by assuming the deflection criterion and gaussian noise it is shown here that the gaussian assumption can be removed and a complete solution is presented for an arbitrary probability distribution with finite fourth order moments the optimal solution can always be obtained by solving a linear system of equations some properties of the optimal systems are developed for particular examples of nongaussian noise it is shown that there is a strong relationship between linear quadratic optimal detection and optimal estimation which extends results known for the purely linear case

on a hardy space approach to the analysis of spectral factors the paper presents a study of several problems related to spectral factorizations we assume only a very weak form of coercivity for the p x p spectral function phi and look at the set wm of all rectangular p x m spectral factors the main object is the arithmetization of the geometry of the set of minimal stable spectral factors by employing hardy space techniques and the arithmetic of inner functions particular attention is paid to the study of various partial orders associated with the set of spectral factors

cumulant based approach to harmonic retrieval and related problems a frequently encountered problem in signal processing is that of estimating the frequencies and amplitudes of harmonics observed in additive colored gaussian noise in practice the observed signals are contaminated with spatially and temporally colored noise of unknown power spectral density a cumulant based approach to these problems is proposed the cumulants of complex processes are defined and it is shown that specific 1 d slices of the fourth order cumulant of the noisy signal for the direction of arrival doa and retrieval of harmonics in noise rhn problems are identical to the autocorrelation of a related noiseless signal hence correlation based high resolution methods may be used with fourth order cumulants as well the effectiveness of the proposed methods is demonstrated through standard simulation examples

detection in correlated impulsive noise using fourth order cumulants we consider detection and estimation in correlated impulsive noise the non gaussian impulsive noise is modeled as the sum of two linear processes a nominal part and an impulsive part this model admits correlated impulsive bursts lasting many data samples identifiability of the noise model is established using fourth and second order cumulants under this model the correlated time series can be whitened and an appropriate memoryless nonlinearity applied to attenuate the impulsive events a detection statistic is then formed from the output of the nonlinearity in the threshold detection case the use of cumulants allows identification of the noise in the presence of the signal to be detected obviating the need for noise only training records simulation results with a sample size of 512 show small loss in detector performance versus an ideal detector with no impulsive part present

on the lyapunov equation coinvariant subspaces and some problems related to spectral factorizations a geometric approach to stochastic realization theory and hence to spectral factorization problems has been developed by lindquist and picci 1985 1991 and lindquist et al 1995 most of this work was done abstractly fuhrmann and gombani 1998 adopted an entirely hardy space approach to this set of problems studying the set of rectangular spectral factors of given size for a weakly coercive spectral function the parametrization of spectral factors in terms of factorizations of related inner functions as developed in fuhrmann 1995 had to be generalized this led to a further understanding of the partial order introduced by lindquist and picci in the set of stable spectral factors in the present paper we study the geometry of finite dimensional coinvariant subspaces of a vectorial hardy space h 2 via realization theory emphasizing the role of the lyapunov equation in lifting the hardy space metric to the statespace domain we follow this by deriving state space formulas for rectangular spect

estimation and detection in non gaussian noise using higher order statistics one of the primary applications of higher order statistics has been for detection and estimation of nongaussian signals in gaussian noise of unknown covariance this is motivated by the fact that higher order cumulants of gaussian processes vanish we study the opposite problem namely detection and estimation in nongaussian noise we estimate cumulants of nongaussian processes in the presence of unknown deterministic and or gaussian signals which allows either parametric or nonparametric estimation of the covariance of the nongaussian noise our approach is to augment existing second order detection methods using cumulants we propose solutions for detection of deterministic signals based on matched filters and the generalized likelihood ratio test which incorporate cumulants where the resulting solutions are valid under either detection hypotheses this allows for single record detection and obviates the need for noise only training records the problem of estimating signal strength in the presence of nongaussian noise of unknown covariance is also considered and a cumulant based solution is proposed which uses a single data record examples are used throughout to illustrate our proposed methods

silverman algorithm and the structure of discrete time stochastic systems abstract it is a well known yet poorly understood fact that contrary to the continuous time case the same discrete time process y can be represented by minimal linear models see 1 1a 1 1b below which may either have a non singular or a singular d matrix in fact models with d 0 have been commonly used in the statistical literature on the other hand for models with a singular d matrix the riccati difference equation of kalman filtering involves in general the pseudo inversion of a singular matrix this cheap filtering problem dual to the better known cheap control problem has been studied for several decades in connection with the so called invariant directions of the riccati equation for a singular d a reduction of the order of the riccati equation is in general possible the reasons for such a reduction do not seem to be completely clear either in this paper we provide an explanation of this phenomenon from the classical point of view of zero flipping among minimal spectral factors changing d s occurs whenever zeros are flipped from z to their reciprocals at z 0 it is well known that for finite zeros the zero flipping process takes place by multiplication of the underlying spectral factor by a suitable rational all pass matrix function for infinite zeros zero flipping is implemented by a dual version of the silverman structure algorithm using this interpretation we derive a new algorithm for filtering of non regular processes based on a reduced order riccati equation we also obtain a precise characterization of the reduction of the order of the riccati equation which is afforded by zeros either at z or at the origin this order reduction has traditionally been associated with the study of invariant directions a point of view which as we show does not capture the essence of the phenomenon

on a connection between spectral factorization and geometric control theory we investigate here how the geometric control theory of basile marro and wonham can be obtained in a hilbert space context as the byproduct of the factorization of a spectral density with no zeros on the imaginary axis we show how controlled invariant subspaces can be obtained as images of orthogonal projections of co invariant subspaces onto a semi invariant markovian subspace of the hardy space of square integrable functions analytic in the right half plane output nulling subspaces are then related to a particular spectral factorization problem a similar construction is presented for controllability subspaces and a new algorithm for the computation of these subspaces is presented

realization theory for multivariate stationary gaussian processes this paper collects in one place a comprehensive theory of stochastic realization for continuous time stationary gaussian vector processes which in various pieces has appeared in a number of our earlier papers it begins with an abstract state space theory based on the concept of splitting subspace these results are then carried over to the spectral domain and described in terms of hardy functions finally differential equations type stochastic realizations are constructed the theory is coordinate free and it accommodates infinite dimensional representations minimality and other systems theoretical concepts being defined by subspace inclusion rather than by dimension we have strived for conceptual completeness rather than generality and the same framework can be used for other types of stochastic realization problems

matrix riccati inequality existence of solutions abstract we consider the various criteria including hamiltonian and frequency domain ones for solvability of the matrix riccati inequality arising from control problems some criteria are given in terms of symplectic algebra which is also used as an important technical tool

zeros of spectral factors the geometry of splitting subspaces and the algebraic riccati inequality in this paper it is shown how the zero dynamics of not necessarily square spectral factors relate to the splitting subspace geometry of stationary stochastic models and to the corresponding algebraic riccati inequality the notion of output induced subspace of a minimal markovian splitting subspace which is the stochastic analogue of the supremal output nulling subspace in geometric control theory is introduced through this concept the analysis can be made coordinate free and straightforward geometric methods can be applied it is shown how the zero structure of the family of spectral factors relates to the geometric structure of the family of minimal markovian splitting subspaces in the sense that the relationship between the zeros of different spectral factors is reflected in the partial ordering of minimal splitting subspaces finally the well known characterization of the solutions of the algebraic riccati equation is generalized in terms of lagrangian subspaces invariant under the corresponding hamiltonian to the larger solution set of the algebraic riccati inequality

higher order statistics based radial basis function networks for signal enhancement in this paper a higher order statistics hos based radial basis function rbf network for signal enhancement is introduced in the proposed scheme higher order cumulants of the reference signal were used as the input of hos based rbf an hos based supervised learning algorithm with mean square error obtained from higher order cumulants of the desired input and the system output as the learning criterion was used to adapt weights the motivation is that the hos can effectively suppress gaussian and symmetrically distributed non gaussian noise the influence of a gaussian noise on the input of hos based rbf and the hos based learning algorithm can be mitigated simulated results indicate that hos based rbf can provide better performance for signal enhancement under different noise levels and its performance is insensitive to the selection of learning rates moreover the efficiency of hos based rbf under the nonstationary gaussian noise is stable

nonsquare spectral factorization for nonlinear control systems this paper considers nonsquare spectral factorization of nonlinear input affine state space systems in continuous time more specifically we obtain a parametrization of nonsquare spectral factors in terms of invariant lagrangian submanifolds and associated solutions of hamilton jacobi inequalities this inequality is a nonlinear analogue of the bounded real lemma and the control algebraic riccati inequality by way of an application we discuss an alternative characterization of minimum and maximum phase spectral factors and introduce the notion of a rigid nonlinear system

acausal models and balanced realizations of stationary processes abstract we study acausal realizations of stationary or stationary increment processes in particular we characterize the family of models whose corresponding spectral factors have a fixed zero structure acausal models with a fixed zero structure are related to each other by a certain group of state feedback transformations which is naturally parametrized by the solution set of a homogeneous algebraic riccati equation each feedback transformation reflects some of the eigenvalues of the generator matrix a of the representation to a mirror image with respect to the imaginary axis dually acausal models with a fixed pole structure are parametrized by a dual riccati equation and by a corresponding family of output injection transformations from a general standpoint the results of this study clarify the role played by dual pairs of riccati equations in spectral factorization and may be relevant to other problem areas than stochastic modelling one natural application of the concepts discussed in the paper is to stochastic balancing balancing of models with an essentially arbitrary eigenvalue location can be accomodated very naturally in this framework a balancing algorithm involving the solution of a dual pair of riccati equations is discussed

classification of digital amplitude phase modulated signals in time correlated non gaussian channels in this paper a new algorithm is proposed for the classification of digital amplitude phase modulated signals in flat fading channels with time correlated non gaussian noise the first order statistics of the additive noise is modeled by a gaussian mixture distribution and an autoregressive ar process is used to model the time correlation the proposed classifier involves the use of a whitening filter necessary to reduce the complexity of the classification process and maximum likelihood classification for the estimation of the whitening filter coefficients a new blind technique that is based on the use of a robust h filter is developed after whitening the received signal following a composite hypothesis testing approach the unknown fading and noise distribution parameters are estimated results are presented which show that when the noise process is time correlated non gaussian the proposed classifier outperforms maximum likelihood classifiers developed under the assumption that the noise process is either white non gaussian or white gaussian it is also shown that when the noise process is white gaussian the proposed classifier s performance closely approaches that of the maximum likelihood classifier developed for white gaussian noise channels

properties of zero free spectral matrices in factor analysis which is used for example in econometrics by definition the number of latent variables has to exceed the number of factor variables the associated transfer function matrix has more rows than columns and when the factor variables are independent zero mean white noise sequences and the transfer function matrix is stable then the output spectrum is singular while a related paper focusses on the properties of such a nonsquare transfer function matrix in this paper we explore a number of properties of the spectral matrix and associated covariance sequence in particular a zero free minimum degree spectral factor can be computed with a finite number of rational calculations from the spectrum in contrast to typical spectral factor calculations assuming the spectrum fulfills a generic condition application of the result to kalman filtering is indicated and presentation of the results is also achieved using finite block toeplitz matrices with entries obtained from the covariance of the latent variable vector

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

a cumulant based adaptive technique for coherent radar detection in a mixture of k distributed clutter and gaussian disturbance in this paper we consider the problem of radar signal detection in the presence of disturbance which is assumed to be a mixture of coherent k distributed and gaussian distributed clutter besides thermal noise which is always present in the radar receiver has been considered the optimum detector is determined by thresholding an appropriate likelihood ratio test to properly operate in an interference environment of unknown correlation the optimum detector needs to adaptively estimate from the data the statistical properties of the interferences second order spectral analysis is unable to separately estimate the correlation structure of k distributed and gaussian distributed clutter sources their separate estimation can be accomplished only in higher order spectrum domain to reach this goal an adaptive algorithm based on second and higher order cumulants is proposed that removes these drawbacks and is able to operate in an environment of unknown correlation structure the performance of the adaptive processing scheme has been evaluated by means of monte carlo simulations

noise suppression by removing singularities a method is proposed for suppressing gaussian noise by extracting local singularities the method is based on truncating riemann series decomposition whose components naturally characterize different orders of holder regularity the approach yields a single step filtering technique whose performance is comparable to three step wavelet decomposition and thresholding techniques