maximum likelihood estimation of the autoregressive model by relaxation on the reflection coefficients a method for autoregressive parameter estimation which successively maximizes the likelihood with respect to each reflection coefficient while keeping the others fixed is presented the algorithm generalizes the recursive maximum likelihood technique of s m kay 1983 which corresponds to performing only one iteration cycle an interesting application is the estimation of a toeplitz covariance matrix simulations show that the algorithm converges quite fast and provides much better estimates than current procedures for short record length

source separation using a criterion based on second order statistics it is often assumed that blind separation of dynamically mixed sources cannot be done with second order statistics it is shown that separation of dynamically mixed sources indeed can be performed using second order statistics only a criterion based on second order statistics for the purpose of separating crosswise mixtures is stated the criterion is used in order to derive a gradient based separation algorithm as well as a newton type separation algorithm the uniqueness of the solution representing the separation is also investigated this reveals that 1 the channel system is parameter identifiable under weak conditions and 2 if the sources have the same color there exists at most two solutions the local convergence behavior of the proposed algorithm is studied and reveals a sufficient condition for local convergence furthermore the estimates of the channel system are shown to be consistent or to locally minimize the criterion

separation of an instantaneous mixture of gaussian autoregressive sources by the exact maximum likelihood approach this paper deals with the problem of blind separation of an instantaneous mixture of gaussian autoregressive sources without additive noise by the exact maximum likelihood approach the maximization of the likelihood function is divided using relaxation into two suboptimization problems solved by relaxation methods as well the first one consists of the estimation of the separating matrix when the autoregressive structure of the sources is fixed the second one aims at estimating this structure when the separating matrix is fixed we show that the first problem is equivalent to the determinant maximization of the separating matrix under nonlinear constraints we prove the existence and the consistency of the maximum likelihood estimator we also give the expression of fisher s information matrix then we study by computer simulations the performance of our estimator and show the improvement of its achievements w r t both quasimaximum likelihood and second order blind identification sobi estimators

blind separation of instantaneous mixture of sources via an independent component analysis in this paper we introduce a procedure for separating a multivariate distribution into nearly independent components based on minimizing a criterion defined in terms of the kullback leibner distance by replacing the unknown density with a kernel estimate we derive useful forms of this criterion when only a sample from that distribution is available we also compute the gradient and hessian of our criteria for use in an iterative minimization setting this gradient to zero yields a set of separating functions similar to the ones considered in the source separation problem except that here these functions are adapted to the observed data finally some simulations are given illustrating the good performance of the method

quick solution of least square equations and inversion of block matrices of low displacement rank a general algorithm for the inversion of block matrices of low displacement rank is proposed it is particularly adapted to the solution of the least squares linear prediction problem some explicit formulas for the inverses of such matrices and a characterization of them are also provided the method is based on the representation of the shift difference of the considered matrix as the difference between two low rank positive matrices

recursive maximum likelihood estimation of autoregressive processes a new method of autoregressive parameter estimation is presented the technique is a closer approximation to the true maximum likelihood estimator than that obtained using linear prediction techniques the advantage of the new algorithm is mainly for short data records and or sharply peaked spectra simulation results indicate that the parameter bias as well as the variance is reduced over the yule walker and the forward backward approaches of linear prediction also spectral estimates exhibit more resolution and less spurious peaks a stable all pole filter estimate is guaranteed the algorithm operates in a recursive model order fashion which allows one to successively fit higher order models to the data

separation of independent sources from correlated inputs the characterization of independent stationary stochastic components sources is generally achieved by using the spectral matrix of partially correlated measurements which are linearly related to the components of interest in the general case where no assumptions are made concerning the way the sources are mixed on the measurements the spectral matrix is not able to extract the true sources while spectral analysis only uses second order properties of independent stochastic sources a procedure based on higher order analysis fourth order cross cumulants is developed this approach leads to a complete identification of the sources

signal separation by symmetric adaptive decorrelation stability convergence and uniqueness the performance of signal enhancement systems based on adaptive filtering is highly dependent on the quality of the noise reference in the lms algorithm signal leakage into the noise reference leads to signal distortion and poor noise cancellation the origin of the problem lies in the fact that lms decorrelates the signal estimate with the noise reference which in the case of signal leakage makes little sense an algorithm is proposed that decorrelates the signal estimate with a signal free noise estimate obtained by adding a symmetric filter to the classical structure the symmetric adaptive decorrelation sad algorithm no longer makes a distinction between signal and noise and is therefore a signal separator rather than a noise canceler stability and convergence are of the utmost importance in adaptive algorithms and hence are carefully studied apart from limitations on the adaptation constants stability around the desired solution can only be guaranteed for a subclass of signal mixtures furthermore the decorrelation criterion does not yield a unique solution and expressions for the phantom solutions are derived simulations with short fir filters confirm the predicted behavior

underdetermined blind source separation based on subspace representation this paper considers the problem of blindly separating sub and super gaussian sources from underdetermined mixtures the underlying sources are assumed to be composed of two orthogonal components one lying in the rowspace and the other in the nullspace of a mixing matrix the mapping from the rowspace component to the mixtures by the mixing matrix is invertible using the pseudo inverse of the mixing matrix the mapping from the nullspace component to zero by the mixing matrix is noninvertible and there are infinitely many solutions to the nullspace component the latent nullspace component which is of lower complexity than the underlying sources is estimated based on a mean square error mse criterion this leads to a source estimator that is optimal in the mse sense in order to characterize and model sub and super gaussian source distributions the parametric generalized gaussian distribution is used the distribution parameters are estimated based on the expectation maximization em algorithm when the mixing matrix is unavailable it must be estimated and a novel algorithm based on a single source detection algorithm which detects time frequency regions of single source occupancy is proposed in our simulations the proposed algorithm compared to other conventional algorithms estimated the mixing matrix with higher accuracy and separated various sources with higher signal to interference ratio

sample partial autocorrelation function a new estimation procedure for a partial autocorrelation coefficient of a stationary time series based on a natural geometrical analysis of the sample data is proposed a method for autoregressive parameter estimation which is midway between the constrained least squares procedure of burg and the unconstrained one given by the for ward backward least squares method is then obtained the method provides a stable filter and operates in a recursive model order fash ion simulation results indicate that the method eliminates some short comings of classical least squares procedures and stays close to the ex act maximum likelihood estimation method

verification of iss iiss and ioss properties applying weighted homogeneity several conditions are proposed to check different robustness properties iss iiss ioss and oss for generic nonlinear systems applying the weighted homogeneity concept global or local the advantages of this result are that under some mild conditions the system robustness can be established as a function of the degree of homogeneity

analysis and online realization of the cca approach for blind source separation a critical analysis of the canonical correlation analysis cca approach in blind source separation bss is provided it is proved that by maximizing the autocorrelation functions of the recovered signals we can separate the source signals successfully it is further shown that the cca approach represents the same class of generalized eigenvalue decomposition gevd problems as the matrix pencil method finally online realizations of the cca approach are discussed with a linear predictor based algorithm studied as an example

backward euler discretization of fully nonlinear parabolic problems this paper is concerned with the time discretization of nonlinear evolution equations we work in an abstract banach space setting of analytic semigroups that covers fully nonlinear parabolic initial boundary value problems with smooth coefficients we prove convergence of variable stepsize backward euler discretizations under various smoothness assumptions on the exact solution we further show that the geometric properties near a hyperbolic equilibrium are well captured by the discretization a numerical example is given

second order blind separation of sources based on canonical partial innovations this paper is devoted to the study of the second order properties using partial autocorrelations of an instantaneous mixture of colored sources without additive noise we introduce the notion of symmetric recursive canonical partial innovation then their components for the observation process meet exactly with those of the source process from the order for which the autoregressive models underlying the sources are distinct this property leads to a new separation method based on the sample counterpart of partial autocorrelation matrices associated with these innovations simulation results show a notable improvement of the achievements of such an approach with respect to those of similar methods two other separation methods related to partial autocorrelation are also discussed

realization and discretization of asymptotically stable homogeneous systems sufficient conditions for the existence and convergence to zero of numeric approximations to solutions of asymptotically stable homogeneous systems are obtained for the explicit and implicit euler integration schemes it is shown that the explicit euler method has certain drawbacks for the global approximation of homogeneous systems with nonzero degrees whereas the implicit euler scheme ensures convergence of the approximating solutions to zero properties of absolute and relative errors of the respective discretizations are investigated

blind separation of mixture of independent sources through a quasi maximum likelihood approach we propose two methods for separating mixture of independent sources without any precise knowledge of their probability distribution they are obtained by considering a maximum likelihood ml solution corresponding to some given distributions of the sources and relaxing this assumption afterward the first method is specially adapted to temporally independent non gaussian sources and is based on the use of nonlinear separating functions the second method is specially adapted to correlated sources with distinct spectra and is based on the use of linear separating filters a theoretical analysis of the performance of the methods has been made a simple procedure for optimally choosing the separating functions is proposed further in the second method a simple implementation based on the simultaneous diagonalization of two symmetric matrices is provided finally some numerical and simulation results are given illustrating the performance of the method and the good agreement between the experiments and the theory

a blind source separation technique using second order statistics separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed in many situations no a priori information on the mixing matrix is available the linear mixture should be blindly processed this typically occurs in narrowband array processing applications when the array manifold is unknown or distorted this paper introduces a new source separation technique exploiting the time coherence of the source signals in contrast with other previously reported techniques the proposed approach relies only on stationary second order statistics that are based on a joint diagonalization of a set of covariance matrices asymptotic performance analysis of this method is carried out some numerical simulations are provided to illustrate the effectiveness of the proposed method

equivariant adaptive source separation source separation consists of recovering a set of independent signals when only mixtures with unknown coefficients are observed this paper introduces a class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called equivariant adaptive separation via independence easi the easi algorithms are based on the idea of serial updating this specific form of matrix updates systematically yields algorithms with a simple structure for both real and complex mixtures most importantly the performance of an easi algorithm does not depend on the mixing matrix in particular convergence rates stability conditions and interference rejection levels depend only on the normalized distributions of the source signals closed form expressions of these quantities are given via an asymptotic performance analysis the theme of equivariance is stressed throughout the paper the source separation problem has an underlying multiplicative structure the parameter space forms a matrix multiplicative group we explore the favorable consequences of this fact on implementation performance and optimization of easi algorithms

a first order isomorphism theorem we show that for most complexity classes of interest all sets complete under first order projections fops are isomorphic under first order isomorphisms that is a very restricted version of the berman hartmanis conjecture holds since natural complete problems seem to stay complete via fops this indicates that up to first order isomorphism there is only one natural complete problem for each nice complexity class

markovian source separation a maximum likelihood ml approach is used to separate the instantaneous mixtures of temporally correlated independent sources with neither preliminary transformation nor a priori assumption about the probability distribution of the sources a markov model is used to represent the joint probability density of successive samples of each source the joint probability density functions are estimated from the observations using a kernel method for the special case of autoregressive models the theoretical performance of the algorithm is computed and compared with the performance of second order algorithms and i i d based separation algorithms

efficient computation of autoregressive estimates through a sufficient statistic it is shown that various time reversible methods in particular burg s algorithm for autoregressive model estimation may be performed through the use of a simple sufficient statistic this provides more efficient computation of the estimators

statistical inference for independent component analysis application to structural var models abstract the well known problem of non identifiability of structural var models disappears if the structural shocks are independent and if at most one of them is gaussian in that case the relevant estimation technique is the independent component analysis ica since the introduction of ica by comon 1994 various semi parametric estimation methods have been proposed for orthogonalizing the error terms these methods include pseudo maximum likelihood pml approaches and recursive pml the aim of our paper is to derive the asymptotic properties of the pml approaches in particular to study their consistency we conduct monte carlo studies exploring the relative performances of these methods finally an application based on real data shows that structural var models can be estimated without additional identification restrictions in the non gaussian case and that the usual restrictions can be tested