optimal and self tuning deconvolution in time domain this paper is concerned with both the optimal minimum mean square error variance and self tuning deconvolution problems for discrete time systems when the signal model measurement model and noise statistics are known a novel approach for the design of the optimal deconvolution filter predictor and smoother is proposed based on projection theory and innovation analysis in the time domain the estimators are given in terms of an autoregressive moving average arma innovation model and one unilateral linear polynomial equation where the arma innovation model is obtained by performing one spectral factorization a self tuning scheme can be incorporated when the noise statistics the input model and or colored noise model are unknown the self tuning estimator is designed by identifying two arma innovation models

a unified approach to optimal estimation using diophantine equations a simple and unified solution to the problem of estimating a signal corrupted by coloured as well as white measurement noise is presented the approach requires the solution of a single diophantine equation the unified formulation applies to the filtering smoothing and prediction problems a practical application of enhancing speech corrupted by noise is investigated

on the ni x integral function and its application to the airy s non homogeneous equation in this article we discuss a recently introduced function ni x to which we will refer as the nield kuznetsov function this function is attractive in the solution of inhomogeneous airy s equation we derive and document some elementary properties of this function and outline its application to airy s equation subject to initial conditions we introduce another function ki x that arises in connection with ni x when solving airy s equation with a variable forcing function in appendix a we derive a number of properties of both ni x and ki x their integral representation ascending and asymptotic series representations we develop iterative formulae for computing all derivatives of these functions and formulae for computing the values of the derivatives at x 0 an interesting finding is the type of differential equations ni x satisfies in particular it poses itself as a solution to langer s comparison equation

optimal recursive filtering prediction and smoothing for singular stochastic discrete time systems a new and simple approach to optimal recursive filtering prediction and smoothing for singular stochastic discrete time systems is presented by using a time domain innovation analysis method the estimators are calculated based on an arma innovation model which can be obtained using spectral factorization or a recursive identifier the prediction problem for the singular systems is solved with the aid of an output predictor further a simple solution is presented for the complex smoothing problem

new approach to information fusion steady state kalman filtering by the modern time series analysis method based on the autoregressive moving average arma innovation model a unified and general information fusion steady state kalman filtering approach is presented for the general multisensor systems with different local dynamic models and correlated noises it can handle the filtering smoothing and prediction fusion problems for state or signal the optimal fusion rule weighted by matrices is re derived as a weighted least squares wls fuser and is reviewed an optimal fusion rule weighted by diagonal matrices is presented which is equivalent to the optimal fusion rule weighted by scalars for components and it realizes a decoupled fusion the new algorithms of the steady state kalman estimator gains are presented in order to compute the optimal weights the formulas of computing the cross covariances among local estimation errors by lyapunov equations are presented the exponential convergence of the iterative solution of lyapunov equation is proved it is proved that the optimal fusion estimators under three weighted fusion rules are locally optimal but are globally suboptimal the proposed steady state kalman fusers can reduce the on line computational burden and are suitable for real time applications a simulation example for the 3 sensor steady state kalman tracking fusion estimators shows their effectiveness and correctness and gives the accuracy comparison of the fusion rules

self tuning decoupled information fusion wiener state component filters and their convergence for the multisensor systems with unknown noise variances using the modern time series analysis method based on on line identification of the moving average ma innovation models and based on the solution of the matrix equations for correlation function the on line estimators of the noise variances are obtained and under linear minimum variance optimal information fusion criterion weighted by scalars for state components a class of self tuning decoupled fusion wiener filters is presented it realizes the self tuning decoupled local wiener filters and self tuning decoupled fused wiener filters for the state components a new concept of convergence in a realization is presented which is weaker than the convergence with probability one the dynamic error system analysis desa method is presented by which the problem of convergence in a realization for self tuning fusers is transformed into the stability problems of non homogeneous difference equations and the decision criterions of the stability are also presented it is strictly proved that if the parameter estimation of the ma innovation models is consistent and if the measurement process is bounded in a realization or with probability one then the self tuning fusers will converge to the optimal fusers in a realization or with probability one so that they have the asymptotic optimality they can deal with the systems with the non stationary or gaussian measurement processes they can reduce the computational burden and are suitable for real time applications a simulation example for a target tracking system with 3 sensor shows their effectiveness

h spl infin deconvolution filtering prediction and smoothing a krein space polynomial approach this correspondence is concerned with the infinite horizon h spl infin deconvolution for discrete time invariant systems described by polynomial equations a simple frequency domain approach in krein space is developed for the deconvolution problem with the help of an arma innovation model solutions to the problems of deconvolution filtering prediction and fixed lag smoothing are obtained the estimators are calculated by performing one j spectral factorization

brief papers new results in state estimation and regulation an alternative technique to design linear state estimators and regulators is presented this technique is based on transfer matrix considerations the optimal regulator or estimator gain is obtained via spectral factorization and the solution of a simple equation in polynomial matrices this approach provides further insight displays the duality of estimation and control nicely and bridges the state space and frequency domain techniques the resulting design procedure is computationally attractive and particularly simple for system matrices in the observer or controller canonical form

technical communique robust state prediction for descriptor systems this paper deals with the problem of state prediction for descriptor systems subject to bounded uncertainties the problem is stated in terms of the optimization of an appropriate quadratic functional this functional is well suited to derive not only the robust predictor for descriptor systems but also that for usual state space systems numerical examples are included in order to demonstrate the performance of this new filter

polynomial equations for the linear mmse state estimation the linear minimum mean square error mmse state estimation problem is solved via spectral factorization and a pair of bilateral diophantine equations detectability and or stability requirements in the riccati based solution context are expressed in terms of the stability of the greatest common right and left divisors of polynomial matrices

error bounds for linear recurrence relations etude des relations de recurrence lineaires pour les systemes oscillatoires et monotones estimations des bornes d erreurs

optimal and self tuning white noise estimators with applications to deconvolution and filtering problems using the innovation analysis method in the time domain based on the autoregressive moving average arma innovation model this paper presents a unified white noise estimation theory that includes both input and measurement white noise estimators and presents a new steady state optimal state estimation theory non recursive optimal state estimators are given whose recursive version gives a steady state kalman filter where a new algorithm of the kalman filter gain is proposed two new algorithms of the kalman predictor gain are also derived local asymptotic stability of the kalman filter is proved the classical kalman filtering theory is extended and modified the method used covers unstable systems with correlation noises and singular transition matrix and also covers the self tuning white noise signal and state estimators when the noise statistics is unknown to illustrate three simulation examples are given

a new method for optimal deconvolution using an innovation analysis method in the time domain the problem of optimal input estimation is considered two algorithms for calculating optimal deconvolution estimators are presented a new tool for obtaining the estimators is described it is based on the projection method and innovation theory the approach covers input prediction filtering and smoothing problems the solution is also applied to unstable linear systems disturbances or input models

on nonoscillating integrals for computing inhomogeneous airy functions integral representations are considered of solutions of the inhomogeneous airy differential equation w z w pm1 pi the solutions of these equations are also known as scorer functions certain functional relations for these functions are used to confine the discussion to one function and to a certain sector in the complex plane by using steepest descent methods from asymptotics the standard integral representations of the scorer functions are modified in order to obtain non oscillating integrals for complex values of z in this way stable representations for numerical evaluations of the functions are obtained the methods are illustrated with numerical results

paper efficient algorithm for matrix spectral factorization an algorithm is presented for the spectral factorization of polynomial or rational matrices arising in optimal control and filtering theory as well as in network theory there are two versions of the algorithm one applicable to continuous time problems the other to discrete time ones both versions are based on newton s method feature quadratic convergence and provide a significant improvement in efficiency over the existing methods

discrete j spectral factorization abstract this paper deals with the j spectral factorization for general discrete rational matrices a simple approach based on the kalman filtering in krein space is proposed the main idea is to construct a stochastic state space filtering model in krein space such that the spectral matrix of the output is equal to the rational matrix to be factorized the spectral factor is then easily derived by using the generalized kalman filtering in krein space which is similar to the h 2 spectral factorization our approach unifies the treatment of the h 2 spectral factorization and the j spectral factorization the applications of the derived results in h and risk sensitive estimation for both nonsingular and singular systems are demonstrated

on the polynomial equations for the mimo lq stochastic regulator the role played by three polynomial equations in the lq stochastic regulation problem is discussed the emphasis is on establishing conditions under which the lq regulator can be obtained via the solution of a single uncoupled diophantine equation nevertheless the authors do not claim that there is any advantage in solving a single uncoupled equation in place of two coupled diophantine equations

optimal deconvolution based on polynomial methods the problem of estimating the input to a known linear system is treated in a shift operator polynomial formulation the mean square estimation error is minimized the input and a colored measurement noise are described by independent arma autoregressive moving average processes the filter is calculated by performing a spectral factorization and solving a polynomial equation the approach can be applied to input prediction filtering and smoothing problems as well as to the use of prefilters in the quadratic criterion it applies to nonminimum phase as well as unstable systems as illustrated by two examples

symbolic and numerical computation on bessel functions of complex argument and large magnitude the lanczos t method with perturbations proportional to faber polynomials is employed to approximate the bessel functions of the first kind j v z and the second kind y v z the hankel functions of the first kind h v 1 z and the second kind h v 2 z of integer order v for specific outer regions of the complex plane i e z r for some r the scaled symbolic representation of the faber polynomials and the appropriate automated t method approximation are introduced both symbolic and numerical computation are discussed in addition numerical experiments are employed to test the proposed t method computed accuracy for j 0 z and y 0 z for z 8 are presented the results are compared with those obtained from the truncated chebyshev series approximations and with those of the t method approximations on the inner disk z 8 some concluding remarks and suggestions on future research are given

numerical evaluation of airy functions with complex arguments abstract we present two methods for the evaluation of airy functions of complex argument the first method is accurate to any desired precision but is slow and unsuitable for fixed precision languages the second method is accurate to double precision 12 digits and is suitable for programming in a fixed precision language such as fortran the first method uses the symbolic manipulation language maple to evaluate either the taylor series expansion or an asymptotic expansion of each function the second method extends an idea of j c p miller to the complex plane it uses the first method to obtain a grid of points in the complex plane where the functions are known to high precision and then uses taylor series from these base points the resulting algorithm is accurate and efficient

optimal self tuning filtering prediction and smoothing for discrete multivariable processes an algorithm is proposed for self tuning optimal fixed lag smoothing or filtering for linear discrete time multivariable processes a z transfer function solution to the discrete multivariable estimation problem is first presented this solution involves spectral factorization of polynomial matrices and assumes knowledge of the process parameters and the noise statistics the assumption is then made that the signal generating process and noise statistics are unknown the problem is reformulated so that the model is in an innovations signal form and implicit self tuning estimation algorithms are proposed the parameters of the innovation model of the process can be estimated using an extended kalman filter or alternatively extended recursive least squares these estimated parameters are used directly in the calculation of the predicted smoothed or filtered estimates the approach is an attempt to generalize the work of hagander and wittenmark

information filtering and array algorithms for descriptor systems subject to parameter uncertainties this paper presents information filters in riccati recursions and in array algorithms for descriptor systems subject to parameters uncertainties the filters are developed in filtered and predicted forms the inversion of the state matrix is avoided in the new information recursive formulas therefore it turns out clear that the invertibility of the state matrix usually considered in the state space information recursions is not necessary a numerical example is provided to illustrate the performance of the proposed robust array algorithms

etale realization on the a1 homotopy theory of schemes abstract we compare friedlander s definition of the etale topological type for simplicial schemes to another definition involving realizations of pro simplicial sets this can be expressed as a notion of hypercover descent for etale homotopy we use this result to construct a homotopy invariant functor from the category of simplicial presheaves on the etale site of schemes over s to the category of pro spaces after completing away from the characteristics of the residue fields of s we get a functor from the morel voevodsky a 1 homotopy category of schemes to the homotopy category of pro spaces

single versus double diophantine equation debate comments on a polynomial approach to wiener filtering comments made on a paper by grimble concerning the number of diophantine equations which are needed to solve the optimal filtering problem are shown not to be valid for the system description employed a comment regarding the proof of optimality is also discussed

completions of pro spaces for every ring r we present a pair of model structures on the category of pro spaces in the first the weak equivalences are detected by cohomology with coefficients in r in the second the weak equivalences are detected by cohomology with coefficients in all r modules or equivalently by pro homology with coefficients in r in the second model structure fibrant replacement is essentially just the bousfield kan r tower when open image in new window the first homotopy category is equivalent to a homotopy theory defined by morel but has some convenient categorical advantages

stable etale realization and etale cobordism abstract we show that there is a stable homotopy theory of profinite spaces and use it for two main applications on the one hand we construct an etale topological realization of the stable a 1 homotopy theory of smooth schemes over a base field of arbitrary characteristic in analogy to the complex realization functor for fields of characteristic zero on the other hand we get a natural setting for etale cohomology theories in particular we define and discuss an etale topological cobordism theory for schemes it is equipped with an atiyah hirzebruch spectral sequence starting from etale cohomology finally we construct maps from algebraic to etale cobordism and discuss algebraic cobordism with finite coefficients over an algebraically closed field after inverting a bott element

a unified approach to optimal state estimation for stochastic singular systems the steady state optimal state estimation problem for discrete time stochastic singular linear systems is considered via the innovation analysis method in the time domain the filter predictor and smoother are derived by using the projection formula and are calculated based on the arma innovation model the three cases of filter predictor and smoother are shown to have a unified form also the optimal white noise estimation method including both input and measurement noises is presented asymptotic stability of the estimators is proved the results of this paper can be applied to normal systems as a special case

obstruction theory in model categories abstract many examples of obstruction theory can be formulated as the study of when a lift exists in a commutative square typically one of the maps is a cofibration of some sort and the opposite map is a fibration and there is a functorial obstruction class that determines whether a lift exists working in an arbitrary pointed proper model category we classify the cofibrations that have such an obstruction theory with respect to all fibrations up to weak equivalence retract and cobase change they are the cofibrations with weakly contractible target equivalently they are the retracts of principal cofibrations without properness the same classification holds for cofibrations with cofibrant source our results dualize to give a classification of fibrations that have an obstruction theory

brief risk sensitive filtering prediction and smoothing for discrete time singular systems this paper is concerned with steady state risk sensitive filtering prediction and smoothing problems for discrete time singular systems it is shown that a risk sensitive estimator can be obtained by ensuring the minimum of an indefinite quadratic form to be maximum minimum when the risk sensitivity parameter q is negative positive an auxiliary state space signal model and an innovation sequence in krein space are introduced to simplify the derivation of the estimator the estimator is calculated based on one j spectral factorization for risk seeking q 0 a numerical example is given to demonstrate the applicability of the result

wiener filter design using polynomial equations a simplified way of deriving realizable and explicit wiener filters is presented discrete time problems are discussed in a polynomial equation framework optimal filters predictors and smoothers are calculated by means of spectral factorizations and linear polynomial equations a tool for obtaining these equations for a given problem structure is described it is based on the evaluation of orthogonality in the frequency domain by means of canceling stable poles with zeros comparisons are made to previously known derivation methodologies such as completing the squares for the polynomial systems approach and the classical wiener solution the simplicity of the proposed derivation method is particularly evident in multistage filtering problems to illustrate two examples are discussed a filtering and a generalized deconvolution problem a new solvability condition for linear polynomial equation appearing in scalar problems is also presented

technical communique descriptor wiener state estimators based on the modern time series analysis method a new time domain wiener filtering approach is presented asymptotically stable wiener state estimators are presented for discrete linear stochastic descriptor systems they can be implemented via the autoregressive moving average arma recursive filters they can handle the optimal state filtering smoothing and prediction problems in a unified framework and can simply be obtained based on the arma innovation model the solution of the diophantine equations and riccati equations is avoided so that the computational burden is reduced a simulation example shows the effectiveness of the new approach

a general polynomial solution to the mmse deconvolution problem it is shown that in order to solve the minimum mean square error mmse deconvolution problem under general conditions two coupled polynomial equations must be used this is constructively proved by satisfying both the orthogonality principle and mean square boundedness of the estimation error