analytic approximation onc0 the banach spacec0is shown to possess the analytic approximation property more precisely given any uniformly continuous function on an open setg c0 an analytic map is constructed which uniformly approximates the given function

algebraic approach to system identification a variety of identification procedures exists for estimating the parameters of an autoregressive moving average arma process from noise free excitation and noise contaminated response data in this paper an identification procedure is proposed for the more realistic situation in which both the excitation and response are contaminated by white noises the method is based upon the null space characterization of an associated data matrix some of the more important algebraic properties possessed by this data matrix are first established in the ideal noise free data case in particular it is found that an overordering of the arma model will not impair the identification of the underlying system in the more realistic noise contaminated data case an approximation of the data matrix s null space is affected by using an eigenvalue eigenvector decomposition by incorporating this null space approximation the deleterious effects of the noise are significantly reduced thereby giving rise to improved modeling performance this improvement is demonstrated by means of a standard example in which the proposed identification method is shown to produce a better modeling behavior than does the classical least squares method the corresponding iterative generalized least squares method and a commonly employed instrumental variable method

approximation of biholomorphic mappings by automorphisms of cn in this paper we prove several results on approximation of biholomorphic mappings between domains in c n 2 by holomorphic automorphisms of c recall that the group of holomorphic automorphisms of c denoted aut c consists of those holomorphic mappings c c that have a holomorphic inverse 4 1 c c with the topology of uniform convergence on compact sets aut c is a topological group while the group aut c 1 of automorphisms of the complex plane consists only of the linear mappings az b a b e c a 4 0 the group aut c is very large and complicated when n 2 let us choose a linear coordinate system on c and write the coordinates as z z w where z z1 zn i c c n 1 and w z c then autc n contains mappings of the form

the steiglitz mcbride identification algorithm revisited convergence analysis and accuracy aspects the convergence and accuracy properties of the steiglitz and mcbride identification method are examined the analysis is valid for a sufficiently large number of data it is shown that the method can converge to the true parameter vector only when the additive output noise is white in that case the method is proved to be locally convergent to the true parameters the global convergence properties are also investigated it is pointed out that the method is not always globally convergent some sufficient conditions guaranteeing global convergence are given assuming convergence takes place the estimates are shown to be asymptotically gaussian distributed an explicit expression is given for their asymptotic covariance matrix

noisy input output system identification using cumulants and the steiglitz mcbride algorithm we consider the problem of identifying a linear time invariant system from its noisy input output data the input and output are assumed to be non gaussian while the input and output noises are assumed to be mutually correlated colored and gaussian using third order cross and auto cumulants we extend the well known steiglitz mcbride 1965 identification method to cumulant domains and show that it is consistent under a certain third order persistency of excitation condition by comparison the steiglitz mcbride method is not consistent when either input noise is present or when the output noise is colored for an empirical assessment we provide simulations that demonstrate the proposed method s usefulness

third order cumulants based methods for continuous time errors in variables model identification in this paper the problem of identifying stochastic linear continuous time systems from noisy input output data is addressed the input of the system is assumed to have a skewed probability density function whereas the noises contaminating the data are assumed to be symmetrically distributed the third order cumulants of the input output data are then asymptotically insensitive to the noises that can be coloured and or mutually correlated using this noise cancellation property two computationally simple estimators are proposed the usefulness of the proposed algorithms is assessed through a numerical simulation

real analytic approximation of lipschitz functions on hilbert space and other banach spaces let x be a separable banach space with a separating polynomial we show that there exists c 1 depending only on x such that for every lipschitz function f x r and every epsilon 0 there exists a lipschitz real analytic function g x r such that vertical bar f x g x vertical bar epsilon e and lip g c lip f this result is new even in the case when x is a hilbert space furthermore in the hilbertian case we also show that c can be assumed to be any number greater than i

on fatou bieberbach domains a fatou bieberbach domain is a domain in c2 which is a biholomorphic image of c2 and is not all of c2 the existence of such domains has been known for a long time there are several papers dealing with fatou bieberbach domains bf bs de e fs gl k n1 n2 rr1 rr2 s nevertheless they remain quite misterious objects and there are many open questions about them one of them is the following rr1 q 11 p 79 if is a fatoubieberbach domain and l is a complex line is it possible that a l is connected b l has finitely many components c l is a circular disc let be the open unit disc in c and let p suppose one wants to obtain a fatou bieberbach domain whose intersection with the z axis z 0 z c is approximately the unit disc one would try to find such that

identification of linear systems using input output cumulants a new identification method is proposed for estimating the parameters of a discrete time linear dynamic system excited by non gaussian inputs using kth order k 2 cumulants of input and output signals contaminated by additive possibly coloured gaussian noise the parameter estimates obtained by this method are proved to be consistent under weak conditions this method has an on line algorithm for computing the parameter estimates just like the least squares method a simulation example is included to demonstrate the effectiveness of this method

stochastic system identification with noisy input output measurements using polyspectra two new classes of parametric frequency domain approaches are proposed for estimation of the parameters of scalar linear errors in variables models i e linear systems where measurements of both input and output of the system are noise contaminated the first approach consists of linear estimators where using the bispectrum or the integrated polyspectrum of the input and the cross bispectrum or the integrated cross polyspectrum the system transfer function is first estimated at a number of frequencies exceeding one half the number of unknown parameters the estimated transfer function is then used to estimate the unknown parameters using an overdetermined linear system of equations in the second class of approaches quadratic transfer function matching criteria are optimized by using the results of the linear estimators as initial guesses both classes of the parameter estimators are shown to be consistent in any measurement noise that has symmetric probability density function when the bispectral approaches are used the proposed parameter estimators are shown to be consistent in gaussian measurement noise when trispectral approaches are used

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

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

penalized least squares estimation of volterra filters and higher order statistics volterra filters vfs and higher order statistics hos are important tools for nonlinear analysis processing and modeling despite their highly desirable properties the transfer of vfs and hos to real world signal processing problems has been hindered by the requirement of very large data records needed to obtain reliable estimates the identification of vfs and the estimation of hos both fall into the category of ill posed estimation problems we develop penalized least squares pls estimation methods for vfs and hos it is shown that pls is a very effective way to incorporate prior information of the problem at hand without directly constraining the estimation procedure hence pls produces much more reliable estimates the main contributions of this paper are the development of appropriate penalizing functionals and cross validation procedures for pls based vf identification and hos estimation

asymptotically optimal estimation of ma and arma parameters of non gaussian processes from high order moments a description is given of an asymptotically minimum variance algorithm for estimating the ma moving average and arma autoregressive moving average parameters of non gaussian processes from sample high order moments the algorithm uses the statistical properties covariances and cross covariances of the sample moments explicitly a simpler alternative algorithm that requires only linear operations is also presented the latter algorithm is asymptotically minimum variance in the class of weighted least squares algorithms

on the uniqueness of prediction error models for systems with noisy input output data abstract this paper addresses the uniqueness problem of the prediction error pe identification for a class of linear systems with noisy input and output data necessary and sufficient conditions are derived for the corresponding pe loss function to have asymptotically a unique global minimum the results indicate that a pe algorithm may give very bad parameter estimates for systems not satisfying these conditions such a possibility is illustrated by a numerical example while the pe method is used as a vehicle for illustration the derived conditions for global uniqueness or identifiability apply to any consistent estimation method based on second order data

brief paper unifying some higher order statistic based methods for errors in variables model identification in this paper the problem of identifying linear discrete time systems from noisy input and output data is addressed several existing methods based on higher order statistics are presented it is shown that they stem from the same set of equations and can thus be united from the viewpoint of extended instrumental variable methods a numerical example is presented which confirms the theoretical results some possible extensions of the methods are then given

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

identification of multivariable stochastic linear systems via polyspectral analysis given noisy input output time domain data the paper considers the problem of identification of unknown parameters of multivariable linear errors invariables models attention is focused on frequency domain approaches where the integrated polyspectrum bispectrum or trispectrum of the input and the integrated cross polyspectrum respectively of the given time domain input output data are exploited two new classes of parametric frequency domain approaches are proposed and analyzed an integrated polyspectrum based persistence of excitation condition on system input is defined both classes of the parameter estimators are shown to be strongly consistent in any measurement noise sequences with vanishing bispectra when integrated bispectrum based approaches are used the proposed parameter estimators are shown to be strongly consistent in gaussian measurement noise when integrated trispectrum based approaches are used the input to the system need not be a linear process but must have nonvanishing bispectrum or trispectrum

a new simultaneous estimation of directions of arrival and channel parameters in a multipath environment we present two new blind techniques for simultaneous estimation of the direction of arrival doa and the channel parameters for a uniform linear array in a multipath environment the first method is based on the sum of weighted complex exponentials and pade spl acute approximation and the second method determines the transfer function of a linear time invariant system given its impulse response for each method we introduce a rational function whose complex poles contain the desired doa the magnitude of its residues are the channel gains and the phase of its residues are in terms of the channel delays we also derive and numerically evaluate the pertinent crame spl acute r rao lower bound crlb for the estimation process our error analysis based on a perturbation series formulation of the parameter estimation reveals that doa and the channel parameters are extracted from a gaussian signal dependent noise for both methods the amount of computations are also determined some simulations are provided to assess the capabilities of the new methods

a note on the range of the derivatives of analytic approximations of uniformly continuous functions on c0 this paper is a contribution to the body of results concerning the size of the set of derivatives of differentiable functions on a banach space the results so far have consisted of examples of highly differentiable bump functions or functions approximating a given continuous function whose set of derivatives either is surprisingly small or has a given shape the paper under review treats the case of analytic smoothness the main result states that every uniformly continuous function on c0 more generally on a space with property k can be approximated by a real analytic function whose set of derivatives is contained in t p 0 lp this is a significant step forward as analytic functions are substantially harder to deal with than c1 smooth ones indeed a local perturbation of an analytic function necessarily changes the values of the function everywhere also of particular value is the quite precise and elegant description of the set of derivatives of the approximating function

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

analytic approximations of uniformly continuous functions in real banach spaces abstract it is shown that if a separable real banach space x admits a separating analytic function with an additional condition property k concerning uniform behaviour of radii of convergence then every uniformly continuous mapping on x into any real banach space y can be approximated by analytic operators in particular the result applies to c0

identification of linear systems with noisy input using input output cumulants abstract an identification method is presented for estimating the parameters of a discrete time linear dynamic system excited by non gaussian input signals using the fourth order cumulants of the input and output signals both of which are contaminated by additive gaussian noise two types of estimators of the fourth order cumulants of the input and output signals are proposed for this method the first is conventional the second which is new allows us only to have a recursive algorithm for computing the parameter estimators the parameter estimators obtained by this algorithm are shown to be strongly consistent under certain weak conditions simulation examples are included to demonstrate the effectiveness of the proposed method

polynomial algebras and smooth functions in banach spaces abstract let a n x be the algebra of polynomials on a real banach space x which is generated by all continuous polynomials of degree not exceeding n let m be the minimal integer such that there is a non compact m homogeneous polynomial p p x m l 1 then n m implies that the uniform closure of a n x does not contain all polynomials of degree n 1 and hence the chain of closures a n x n m is strictly increasing in the rest of the note we give solutions to three problems concerning the behaviour of smooth functions on banach spaces posed in the literature in particular we construct an example of a uniformly differentiable real valued function f on the unit ball of a certain banach space x such that there exists no uniformly differentiable function g on b x for any 1 which coincides with f in some neighbourhood of the origin

paper identification of scalar errors in variables models with dynamics the paper considers the task of identifying a causal linear dynamic system excited by stationary gaussian zero mean noise of unknown spectrum and given measurements of the system input and output contaminated by independent additive stationary noise signals of unknown spectra while the solution is normally not unique finite dimensional parameterizations of the solution set are given in some cases involving just one parameter even though the various spectra may not be rational

on time delay estimation with unknown spatially correlated gaussian noise using fourth order cumulants and cross cumulants the problem of estimating the difference in arrival times of a linear non gaussian signal at two spatially separated sensors is considered the signal is assumed to be corrupted by spatially correlated gaussian noises of unknown cross correlation a parameter estimation approach is adopted and the fourth order cumulant statistics of the noisy measurements are exploited to obtain the time delay estimate specific and mild sufficient conditions are given for time delay identifiability via a persistence of excitation condition illustrative monte carlo simulation examples are also presented

an embedding of c in c 2 with hyperbolic complement this paper was motivated by the question of whether there exists a proper holomorphic embedding i c c 2 such that c 2 c is kobayashi hyperbolic for the case of a polynomial embedding p c c 2 abhyankar and mob a m and suzuki s proved that there exists a polynomial automorphism f of c 2 such that f op c c x 0 in contrast forstneric globevnik and rosay if g r have shown that there exists a proper holomorphic embedding b c c 2 such that for no automorphism h of c 2 is it true that h o c c x 0 this leaves open the question of whether the complement of an embedded copy of c can be kobayashi hyperbolic we answer this question in the following theorem

low rank estimation of higher order statistics low rank estimators for higher order statistics are considered in this paper the bias variance tradeoff is analyzed for low rank estimators of higher order statistics using a tensor product formulation for the moments and cumulants in general the low rank estimators have a larger bias and smaller variance than the corresponding full rank estimator and the mean squared error can be significantly smaller this makes the low rank estimators extremely useful for signal processing algorithms based on sample estimates of the higher order statistics the low rank estimators also offer considerable reductions in the computational complexity of such algorithms the design of subspaces to optimize the tradeoffs between bias variance and computation is discussed and a noisy input noisy output system identification problem is used to illustrate the results

stochastic system identification with noisy input using cumulant statistics addresses the problem of estimating the parameters of stochastic linear systems when the measurements of the system input as well as the system output are noise contaminated it is assumed that the input is non gaussian and the noises are gaussian the square root of the magnitude of the fourth cumulant of a generalized error signal is proposed as a performance criterion for parameter estimation an optimization algorithm is presented strong consistency of the proposed parameter estimators is proved under certain sufficient conditions both single input single output and multiple input multiple output cases are investigated finally simulation results are presented to illustrate the proposed approach

oka s principle for holomorphic submersions with sprays the oka principle is a fundamental principle of complex analysis which says that on stein manifolds closed complex submanifolds of affine spaces analytic problems of cohomological or even homotopical nature have only topological obstructions the story began in 1939 when k oka proved that on a domain of holomorphy a secondcousin problem is solvable by holomorphic functions if it is solvable by continuous functions oka oka s result has the following equivalent formulation ife x is a holomorphicc bundle over adomainof holomorphy then every continuous section of e is homotopic to a holomorphic section in 1957 h grauert gra extended oka s result to sections of holomorphic fiber bundles with complex homogeneous fibers over stein manifolds see also the papers car fr hl in 1989 m gromov gr1 announced a major generalization of grauert s theorem replacing complex lie groups and homogeneous spaces by a larger class of complex manifolds with a spray a spray on a complex manifold y is a holomorphic vector bundle p e y with a holomorphic map s e y the spray map which is the identity on the zero section and whose restriction to each fibre of e is a submersion at zero such sprays exist on complex homogeneous spaces on complements of affine algebraic subvarieties of codimension at least two and more generally on manifolds whose holomorphic tangent bundle is spanned by finitely many c complete holomorphic vector fields the notion of spray extends in a natural way to submersions the following is theorem 4 5 in gr1 if h z x is a holomorphic submersion onto a stein manifold x such that every point x x has an open neighborhood u x such that z u h 1 u u admits a fiber dominating spray then the inclusion of the