gevd based low rank approximation for distributed adaptive node specific signal estimation in wireless sensor networks in this paper we address the problem of distributed adaptive estimation of node specific signals for signal enhancement or noise reduction in wireless sensor networks with multi sensor nodes the estimation is performed by a multi channel wiener filter mwf in which a low rank approximation based on a generalized eigenvalue decomposition gevd is incorporated in non stationary or low snr conditions this gevd based mwf has been demonstrated to be more robust than the original mwf in a centralized realization where a fusion center has access to all the nodes sensor signal observations the network wide sensor signal correlation matrices and the low rank approximation can be directly estimated and used to compute the network wide gevd based mwf however in this paper we aim to avoid centralizing the sensor signal observations in which case the network wide sensor signal correlation matrices cannot be estimated to this end we start from the so called distributed adaptive node specific signal estimation danse algorithm and include gevd based low rank approximations in the per node local computations remarkably the new algorithm is able to significantly compress the signal observations transmitted between the nodes while still converging to the network wide gevd based mwf as if each node would have access to all sensor signal observations even though the low rank approximations are applied locally at each node we provide a theoretical convergence analysis which shows that the algorithm converges to the network wide gevd based mwf under conditions that are less strict than in the original danse algorithm the convergence and performance of the algorithm are further investigated via numerical simulations

stochastic gradient based implementation of spatially preprocessed speech distortion weighted multichannel wiener filtering for noise reduction in hearing aids recently a generalized noise reduction scheme has been proposed called the spatially preprocessed speech distortion weighted multichannel wiener filter sp sdw mwf it encompasses the generalized sidelobe canceller gsc and a multichannel wiener filtering technique as extreme cases compared with the widely studied gsc with quadratic inequality constraint qic gsc the sp sdw mwf achieves a better noise reduction performance for a given maximum speech distortion level we develop a low cost stochastic gradient implementation of the sp sdw mwf to speed up convergence and reduce computational complexity the algorithm is implemented in the frequency domain experimental results with a behind the ear hearing aid show that the proposed frequency domain stochastic gradient algorithm preserves the benefit of the exact sp sdw mwf over the qic gsc while its computational cost is comparable to the least mean square based scaled projection algorithm for qic gsc

optimized estimation of moments for nonstationary signals the behavior of nonstationary moment estimators that are based on linear time invariant filtering is analyzed the performance of such estimators is evaluated in terms of their time averaged variance and time averaged squared bias optimal estimators that minimize a convex combination of bias and variance are derived the superiority of such optimally weighted filtering over the conventional exponentially windowed moment estimation technique is demonstrated by means of a simple example the same example also serves to illustrate the difficulties encountered when the construction of optimal estimators relies on uncertain prior information as well as to demonstrate the feasibility of overcoming such difficulties by using appropriately designed robust optimal estimators we also include a brief discussion of the relevance of the proposed moment estimation technique to identification of linear time variant systems and to estimation of time variant spectra

error probability bounds for nuclear detection a collection of static and mobile radiation sensors is tasked with deciding within a fixed time interval whether a moving target carries radioactive material formally this is a problem of detecting weak time inhomogeneous poisson signals target radiation concealed in another poisson signal naturally occurring background radiation each sensor locally processes its observations to form a likelihood ratio which is transmitted once at the end of the decision interval to a fusion center the latter combines the transmitted information to optimally in the neyman pearson sense decide whether the measurements contain a radiation signal or just noise we provide a set of analytically derived upper bounds for the probabilities of false alarm and missed detection which are used to design threshold tests without the need for computationally intensive monte carlo simulations these analytical bounds couple the physical quantities of interest to facilitate planning the motion of the mobile sensors for minimizing the probability of missed detection the network reconfigures itself in response to the target motion to allow more accurate collective decisions within the given time interval the approach is illustrated in numerical simulations and its effectiveness demonstrated in experiments that emulate the statistics of nuclear emissions using a pulsed laser

dual h _ infty algorithms for signal processing application to speech enhancement this paper deals with the joint signal and parameter estimation for linear state space models an efficient solution to this problem can be obtained by using a recursive instrumental variable technique based on two dual kalman filters in that case the driving process and the observation noise in the state space representation for each filter must be white with known variances these conditions however are too strong to be always satisfied in real cases to relax them we propose a new approach based on two dual hinfin filters once a new observation of the disturbed signal is available the first hinfin algorithm uses the latest estimated parameters to estimate the signal while the second hinfin algorithm uses the estimated signal to update the parameters in addition as the hinfin filter behavior depends on the choice of various weights we present a way to recursively tune them this approach is then studied in the following cases 1 consistent estimation of the ar parameters from noisy observations and 2 speech enhancement where no a priori model of the additive noise is required for the proposed approach in each case a comparative study with existing methods is carried out to analyze the relevance of our solution

the frisch scheme in dynamic system identification abstract the use of the frisch scheme in the identification of linear dynamic systems is investigated in order to describe the whole family of models that can explain given input output noisy sequences unlike the algebraic case it is shown that in general only a single model is compatible with the data these results are first proposed for single input single output systems and then generalized to the multivariable case

brief paper on the identifiability of errors in variables models with white measurement errors we discuss identifiability of dynamic siso errors in variables eiv models with white measurement errors although this class of models turns out to be generically identifiable it has been pointed out that in certain circumstances there may be two eiv models which are indistinguishable from external input output experiments this lack of global identifiability may be prejudicial to identification and needs better understanding the identifiability conditions found in the literature guarantee uniqueness under certain coprimality assumptions on the rational transfer function of the ideal true system and the spectral density of the noiseless true input unfortunately these conditions are not testable since they concern precisely the unknowns of the problem which are not available to the experimenter we provide new identifiability conditions which are instead expressible in terms of the external description of the observable signals namely their joint power spectral densities

a simplified form of the bias eliminating least squares method for errors in variables identification this note considers the bias eliminating least squares bels method for identifying the errors in variables systems with white input noise and colored output noise a simplified form of the bels algorithm is proposed that is proved to be equivalent to the existing one some expositions of this simplified bels expression are also given the new relation is a form of linear iv equations which will not only reduce the computational load but also simplify the analysis of the properties of the bels estimates

on a class of frozen regularized gauss newton methods for nonlinear inverse problems in this paper we consider a class of regularized gauss newton methods for solving nonlinear inverse problems for which an a posteriori stopping rule is proposed to terminate the iteration such methods have the frozen feature that they require only the computation of the frechet derivative at the initial approximation thus the computational work is considerably reduced under certain mild conditions we give the convergence analysis and derive various estimates including the order optimality on these methods

accuracy analysis of the frisch scheme for identifying errors in variables systems several estimation methods have been proposed for identifying errors in variables systems where both input and output measurements are corrupted by noise one of the promising approaches is the so called frisch scheme this paper provides an accuracy analysis of the frisch scheme applied to system identification the estimates of the system parameters and the noise variances are shown to be asymptotically gaussian distributed an explicit expression for the covariance matrix of the asymptotic distribution is given as well numerical simulations support the theoretical results a comparison with the cramer rao lower bound is also given in the examples and it is shown that the frisch scheme gives a performance close to the cramer rao bound for large signal to noise ratios snrs

newton s method for a class of optimal shape design problems a class of optimal shape design problems is considered where a part of the boundary of the domain represents the free parameter the variable domain is parametrized by a class of functions in such a way that the optimal design problem results in an optimal control problem on a fixed domain the functions for the parametrization of the domain are used as controls and the corresponding states are then given by the solution of an elliptic boundary value problem on a fixed domain discretizing this control problem normally leads to a large scale optimization problem where the corresponding solution methods are characterized by the requirement of solving many boundary value problems in spite of this interesting numerical challenge until now little work has been done to derive more efficient algorithms by taking advantage of the specific structure of this kind of problem in this report newton s method in function space is derived resulting in an efficient algorithm for the discretized optimization problems by using the specific structure of these optimal shape design problems an efficient implementation of the numerical algorithm is introduced the properties of this algorithm are compared with those of the gradient method using illustrative numerical examples

brief identification of dynamic errors in variables models approaches based on two dimensional arma modeling of the data in this paper we propose a parametric and a non parametric identification algorithm for dynamic errors in variables model we show that the two dimensional process composed of the input output data admits a finite order arma representation the non parametric method uses the arma structure to compute a consistent estimate of the joint spectrum of the input and the output a frisch scheme is then employed to extract an estimate of the joint spectrum of the noise free input output data which in turn is used to estimate the transfer function of the system the parametric method exploits the arma structure to give estimates of the system parameters the performances of the algorithms are illustrated using the results obtained from a numerical simulation study

errors in variables system identification using structural equation modeling errors in variables eiv identification refers to the problem of consistently estimating linear dynamic systems whose output and input variables are affected by additive noise various solutions have been presented for identifying such systems in this study eiv identification using structural equation modeling sem is considered two schemes for how eiv single input single output siso systems can be formulated as sems are presented the proposed formulations allow for quick implementation using standard sem software by simulation examples it is shown that compared to existing procedures here represented by the covariance matching cm approach sem based estimation provide parameter estimates of similar quality

a simplified generalized gauss newton method for nonlinear ill posed problems iterative regularization methods for nonlinear ill posed equations of the form f x y where f d f x y is an operator between hilbert spaces x and y usually involve calculation of the frechet derivatives of f at each iterate and at the unknown solution x in this paper we suggest a modified form of the generalized gauss newton method which requires the frechet derivative of f only at an initial approximation x0 of the solution x the error analysis for this method is done under a general source condition which also involves the frechet derivative only at x0 the conditions under which the results of this paper hold are weaker than those considered by kaltenbacher 1998 for an analogous situation for a special case of the source condition

second order methods for optimal control of time dependent fluid flow second order methods for open loop optimal control problems governed by the two dimensional instationary navier stokes equations are investigated optimality systems based on a lagrangian formulation and adjoint equations are derived the newton and quasi newton methods as well as various variants of sqp methods are developed for applications to optimal flow control and their complexity in terms of system solves is discussed local convergence and rate of convergence are proved a numerical example illustrates the feasibility of solving optimal control problems for two dimensional instationary navier stokes equations by second order numerical methods in a standard workstation environment

optimal stopping times for detecting changes in distributions it is shown that page s stopping time is optimal for the detection of changes in distributions in a well defined sense this work is a generalization of an existing result where it was shown that page s stopping time is optimal asymptotically

a generalized instrumental variable estimation method for errors in variables identification problems the errors in variables identification problem concerns dynamic systems whose input and output variables are affected by additive noise several estimation methods have been proposed for identifying dynamic errors in variables models in this paper it is shown how a number of common methods for errors in variables methods can be put into a general framework resulting into a generalized instrumental variable estimator give various computational aspects of give are presented and the asymptotic distribution of the parameter estimates is derived

nar estimators of spatial covariance matrices for adaptive array detection the theory of noise alone reference nar power estimation is extended to the estimation of spatial covariance matrices a nar covariance estimator insensitive to signal presence is derived the snr signal to noise ratio loss incurred by using this estimator is independent of the input snr and is less than that encountered with the maximum likelihood covariance estimator given that the same number of uncorrelated snapshots is available to both estimators the analysis assumes first a deterministic signal the results are extended and generalized to signals with unknown parameters or random signals for the random signal case generalized and quasi nar covariance estimators are presented

speech enhancement combining optimal smoothing and errors in variables identification of noisy ar processes in the framework of speech enhancement several parametric approaches based on an a priori model for a speech signal have been proposed when using an autoregressive ar model three issues must be addressed 1 how to deal with ar parameter estimation indeed due to additive noise the standard least squares criterion leads to biased estimates of ar parameters 2 can an estimation of the variance of the additive noise for each speech frame be obtained a voice activity detector is often used for its estimation 3 which estimation rules and techniques filtering smoothing etc can be considered to retrieve the speech signal our contribution in this paper is threefold first we propose to view the identification of the noisy ar process as an errors in variables problem this blind method has the advantage of providing accurate estimations of both the ar parameters and the variance of the additive noise second we propose an alternative algorithm to standard kalman smoothing based on a constrained minimum variance estimation procedure with a lower computational cost third the combination of these two steps is investigated it provides better results than some existing speech enhancement approaches in terms of signal to noise ratio snr segmental snr and informal subjective tests

performance analysis of sequential tests between poisson processes the problem of performance computation for sequential tests between poisson processes is considered the average sample numbers and error probabilities of the sequential probability ratio test sprt between two homogeneous poisson processes are known to solve certain delay differential equations ddes exact numerically stable solutions to these ddes are developed here and their asymptotic properties are explored these solutions are seen to be superior to earlier solutions of dvoretsky kiefer and wolfowitz 1953 which suffer from severe numerical instability in some ranges of parameters of interest in applications the application of these results is illustrated in the problem of performance approximation for the cumulative sum cusum quickest detection procedure

speech enhancement using a minimum mean square error short time spectral amplitude estimator this paper focuses on the class of speech enhancement systems which capitalize on the major importance of the short time spectral amplitude stsa of the speech signal in its perception a system which utilizes a minimum mean square error mmse stsa estimator is proposed and then compared with other widely used systems which are based on wiener filtering and the spectral subtraction algorithm in this paper we derive the mmse stsa estimator based on modeling speech and noise spectral components as statistically independent gaussian random variables we analyze the performance of the proposed stsa estimator and compare it with a stsa estimator derived from the wiener estimator we also examine the mmse stsa estimator under uncertainty of signal presence in the noisy observations in constructing the enhanced signal the mmse stsa estimator is combined with the complex exponential of the noisy phase it is shown here that the latter is the mmse estimator of the complex exponential of the original phase which does not affect the stsa estimation the proposed approach results in a significant reduction of the noise and provides enhanced speech with colorless residual noise the complexity of the proposed algorithm is approximately that of other systems in the discussed class

identification of dynamic errors in variables models this paper deals with the identifiability of scalar dynamic errors in variables models characterized by rational spectra the hypothesis of causality for the underlying dynamic system is taken into account by making use of stochastic realization theory and of the structural properties of state space representations it is shown that under mild assumptions the model is uniquely identified

certain models from uncertain data the algebraic case abstract the problem of deriving possible linear relations from data affected by additive noise has received remarkable attention in recent years particularly regarding the assumptions prejudices behind the procedures leading to unique models unlike traditional approaches leading to unique solutions least squares maximum likelihood etc the frisch scheme belonging to the family of errors in variables ev schemes leads to a whole family of models compatible with a set of noisy data and is considered as mildly affected by prejudices this paper shows how also under the assumptions of the frisch scheme it is possible to obtain a unique model from uncertain data and also to derive the actual amount of noise when the noiseless data are linked by a single linear relation the more general ev case of non independent additive noises is then considered and it is shown how also under these assumptions it is possible to obtain the unique set of parameters linking the noiseless data and how the family of compatible noise covariance matrices is defined in this case by the infinite elements of a linear variety

subspace algorithms for the identification of multivarible dynamic errors in variables models abstract we consider the problem of identifying multivariable finite dimensional linear time invariant systems from noisy input output measurements apart from the fact that both the measured input and output are corrupted by additive white noise the output may also be contaminated by a term which is caused by a white input process noise furthermore all these noise processes are allowed to be correlated with each other we shall develop a solution to this problem in the framework of subspace identification and we shall show that our algorithms give consistent estimates when the system is operating in open or closed loop two realistic simulation studies are presented to demonstrate the practical applicability of the proposed algorithms 1997 elsevier science ltd

frisch scheme identification for dynamic diagonal bilinear models the article addresses the problem of dynamic system identification in the errors in variables framework for a class of discrete time time invariant input output bilinear models when subjected to a white input signal the proposed algorithm is based on an extension of the bias compensated least squares method and utilises the frisch scheme equations to determine the parameter vector together with the variances of the input and output noise sequences the appropriateness of the approach is analysed and its performance evaluated when compared to other errors in variables identification techniques by means of a monte carlo simulation the results obtained demonstrate the accuracy of the proposed method and the performance in terms of noise robustness is also observed

a generalised instrumental variable estimator for multivariable errors in variables identification problems a new and very general estimation method the generalised instrumental variable estimator give has been introduced to deal with the errors in variables identification the give contains several well known estimation methods as special cases that can be obtained by various user choices in give these methods include the bias eliminating least squares method a number of different versions of the frisch scheme and the extended compensated least squares method this article shows how previous analysis for single input single output systems can be extended in a non trivial way to also cope with multi input multi output systems various computational aspects of give are presented and it is shown how the parameter estimates can be computed in an efficient way the asymptotic distribution of the parameter estimates is also derived and analysed

identification of the maximal number of linear relations from noisy data the problem of evaluating the maximal number of linear relations compatible with data affected by additive noise is considered in the context of the frisch scheme some new algebraic and geometric properties of the family of solutions in the noise space are derived and applied to determine the maximal corank of the noisy data covariance matrix

an upper bound on the number of linear relations identified from noisy data by the frisch scheme abstract the frisch scheme is one of many approaches to the identification of linear relations from noisy data solution of the associated matrix optimization problem leads to the identification of a maximal number of such relations to date no general solution procedure is known here an upper bound on the maximal number of relations that can be identified is presented the upper bound is derived using the theory of schur complements in conjunction with a result for the case where only one relation can be identified the possibility of developing a completely general solution procedure using these ideas is also briefly discussed

extended accuracy analysis of a covariance matching approach for identifying errors in variables systems a system identification method for errors in variables problems based on covariance matching was recently proposed in the first step a small amount of covariances of noisy input output data are computed and then a parametric model is fitted to these covariances in this paper the method is further analyzed and the asymptotic accuracy of the parameter estimates is derived an explicit algorithm for computing the asymptotic covariance matrix of the parameter estimates is given and the identification method is shown to be asymptotically statistically efficient assuming that the given information is the computed covariances as an important byproduct an efficient algorithm is presented for computing the covariance matrix of the computed input output covariances

identification of piecewise affine models in noisy environment this paper addresses the identification of non linear systems a wide class of these systems can be described using non linear time invariant regression models that can be approximated by means of piecewise affine prototypes with an arbitrary degree of accuracy this work concerns the identification of piecewise affine model parameters through input output data affected by additive noise in order to show the effectiveness of the developed technique the results obtained in the identification of both a simple simulated system and a real dynamic process are reported

brief paper accuracy analysis of time domain maximum likelihood method and sample maximum likelihood method for errors in variables and output error identification for identifying errors in variables models the time domain maximum likelihood tml method and the sample maximum likelihood sml method are two approaches both methods give optimal estimation accuracy but under different assumptions in the tml method an important assumption is that the noise free input signal is modelled as a stationary process with rational spectrum for sml the noise free input needs to be periodic it is interesting to know which of these assumptions contain more information to boost the estimation performance in this paper the estimation accuracy of the two methods is analyzed statistically for both errors in variables eiv and output error models oem numerical comparisons between these two estimates are also done under different signal to noise ratios snrs the results suggest that tml and sml have similar estimation accuracy at moderate or high snr for eiv for oem identification these two methods have the same accuracy at any snr

a subspace approach to estimation of autoregressive parameters from noisy measurements this correspondence describes a method for estimating the parameters of an autoregressive ar process from a finite number of noisy measurements the method uses a modified set of yule walker yw equations that lead to a quadratic eigenvalue problem that when solved gives estimates of the ar parameters and the measurement noise variance

a covariance matching approach for identifying errors in variables systems the errors in variables identification problem concerns dynamic systems whose input and output variables are affected by additive noise several estimation methods have been proposed for identifying dynamic errors in variables models in this paper a covariance matching approach is proposed to solve the identification problem it applies for general types of input signals the method utilizes a small set of covariances of the measured input output data this property applies also for some other methods such as the frisch scheme and the bias eliminating least squares method algorithmic details for the proposed method are provided user choices for example specification of which input output covariances to utilize are discussed in some detail the method is evaluated by using numerical examples and is shown to have competitive properties as compared to alternative methods

invariants and canonical forms for systems structural and parametric identification the basic definitions regarding invariant functions and canonical forms for an equivalence relation on a generic set are first recalled with reference to observable state space models and to the equivalence relation induced by a change of basis it is then shown how the image of a complete set of independent invariants for the considered equivalence relation can be used to parametrize a subset of canonical forms in the given set then the set of polynomial input output models of the type p z y t q z u t and the equivalence relation induced by the premultiplication of p and q by a unimodular matrix are considered and canonical forms parametrized by a complete set of independent invariants introduced since the two sets of canonical forms share common sets of complete independent invariants very simple algebraical links between state space and input output canonical forms can be deduced the previous results are used to design efficient algorithms solving the problem of the canonical structural and parametric realization and identification of generic input output sequences generated by a linear discrete time invariant multivariable system the results obtained in the identification of a real process are then reported

brief paper relations between bias eliminating least squares the frisch scheme and extended compensated least squares methods for identifying errors in variables systems there are many methods for identifying errors in variables systems among them bias eliminating least squares bels the frisch scheme and extended compensated least squares ecls methods are attractive approaches because of their simplicity and good estimation accuracy these three methods are all based on a bias compensated least squares bcls principle in this paper the relationships between them are considered in particular the set of nonlinear equations utilized in these three methods are proved to be equivalent under different noise conditions also for finite samples it is shown that bels frisch and ecls methods have the same asymptotic estimation accuracy providing the same extended vector is used

on the local convergence study for an efficient k step iterative method research was supported in part by programa de apoyo a ia investigacion de ia fundacion seneca agencia de ciencia y tecnologia de la region de murcia 19374 pi 14 by the project of generalitat valenciana prometeo 2016 089 and the projects mtm2015 64382 p mineco feder mtm2014 52016 c2 1 p and mtm2014 52016 c2 2 p of the spanish ministry of science and innovation

prewhitening for rank deficient noise in subspace methods for noise reduction a fundamental issue in connection with subspace methods for noise reduction is that the covariance matrix for the noise is required to have full rank in order for the prewhitening step to be defined however there are important cases where this requirement is not fulfilled e g when the noise has narrowband characteristics or in the case of tonal noise we extend the concept of prewhitening to include the case when the noise covariance matrix is rank deficient using a weighted pseudoinverse and the quotient singular value decomposition and we show how to formulate a general rank reduction algorithm that works also for rank deficient noise we also demonstrate how to formulate this algorithm by means of a quotient ulv decomposition which allows for faster computation and updating finally we apply our algorithm to a problem involving a speech signal contaminated by narrowband noise

risk adjusted monitoring of time to event recently there has been interest in risk adjusted cumulative sum charts cusums to monitor the performance of e g hospitals taking into account the heterogeneity of patients even though many outcomes involve time only conventional regression models are commonly used in this article we investigate how time to event models may be used for monitoring purposes we consider monitoring using cusums based on the partial likelihood ratio between an out of control state and an in control state we consider both proportional and nonproportional alternatives as well as a head start against proportional alternatives we present an analytic method of computing the expected number of observed events before stopping or the probability of stopping before a given observed number of events in a stationary set up the former is roughly proportional to the average run length in calendar time adding a head start changes the threshold only slightly if the expected number of events until hitting is used as a criterion however it changes the threshold substantially if a false alarm probability is used in simulation studies charts based on survival analysis perform better than simpler monitoring schemes we present one example from retail finance and one medical application

the set of observationally equivalent errors in variables models abstract linear dynamic errors in variables or factor models with uncorrelated noise components are considered we give a description of the set of all noise spectra which are oberservationally equivalent with respect to the second moments of observations

an improved bias compensation approach for errors in variables model identification parametric estimation of the dynamic errors in variables models is considered in this paper in particular a bias compensation approach is examined in a generalized framework sufficient conditions for uniqueness of the identified model are presented subsequently a statistical accuracy analysis of the estimation algorithm is carried out the asymptotic covariance matrix of the system parameter estimates depends on a user chosen filter and a certain weighting matrix it is shown how these can be tuned to boost the estimation performance the numerical simulation results suggest that the covariance matrix of the estimated parameter vector is very close to the cramer rao lower bound for the estimation problem

transformations between input output multistructural models properties and applications some general properties of recently introduced inputs output multistructural overlapping models are analysed and compared with the properties of the well known input output canonical forms algorithms for the transformation of a generic input output model to a multi structural one and for transformation between adjacent multistructural models are then proposed the use of the models in on line multivariate identification is also discussed and a numerical example given

system identification by dynamic factor models this paper concerns the modeling of stochastic processes by means of dynamic factor models in such models the observed process is decomposed into a structured part called the latent process and a remainder that is called noise the observed variables are treated in a symmetric way so that no distinction between inputs and outputs is required this motivates the additional condition that the prior assumptions on the noise are symmetric in nature one of the central questions in this paper is how uncertainty about the noise structure translates into nonuniqueness of the possible underlying latent processes we investigate several possible noise specifications and analyze properties of the resulting class of observationally equivalent factor models this concerns in particular the characterization of optimal models and properties of continuity and consistency

detection of stochastic processes this paper reviews two streams of development from the 1940 s to the present in signal detection theory the structure of the likelihood ratio for detecting signals in noise and the role of dynamic optimization in detection problems involving either very large signal sets or the joint optimization of observation time and performance this treatment deals exclusively with basic results developed for the situation in which the observations are modeled as continuous time stochastic processes the mathematics and intuition behind such developments as the matched filter the rake receiver the estimator correlator maximum likelihood sequence detectors multiuser detectors sequential probability ratio tests and cumulative sum quickest detectors are described

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

comparing some classes of bias compensating least squares methods three different classes of bias compensating least squares identification methods are compared and shown to be identical it is also discussed how the user parameters in the classes can be chosen to achieve optimal accuracy of the parameter estimates

suppression of bursting abstract we investigate the possibility of using a single small amplitude control input and feedback to stabilize equilibrium sets in a class of highly nonlinear o 2 symmetric dynamical systems possessing structurally stable heteroclinic cycles the leading order behavior near the equilibria is bilinear and homogeneous in the state variables while nonlinearities representing the symmetry breaking effect of the controller are crucial after a series of simplifying transformations we use ideas from optimal control theory to construct a stabilizing controller this study is motivated by the desire to stabilize the burst sweep cycle in low dimensional models of a turbulent boundary layer in the last two sections we apply the techniques to the 10 dimensional system of aubry et al 1988 kw bilinear systems dynamical systems heteroclinic cycles normal forms optimal control symmetry

a bias corrected estimator for nonlinear systems with output error type model structures parametric identification of linear time invariant lti systems with output error oe type of noise model structures has a well established theoretical framework different algorithms like instrumental variables based approaches or prediction error methods pems have been proposed in the literature to compute a consistent parameter estimate for linear oe systems although the prediction error method provides a consistent parameter estimate also for nonlinear output error noe systems it requires to compute the solution of a nonconvex optimization problem therefore an accurate initialization of the numerical optimization algorithms is required otherwise they may get stuck in a local minimum and as a consequence the computed estimate of the system might not be accurate in this paper we propose an approach to obtain in a computationally efficient fashion a consistent parameter estimate for output error systems with polynomial nonlinearities the performance of the method is demonstrated through a simulation example

identification of linear relations from noisy data geometrical aspects abstract the problem of determining linear models from data corrupted by noise has been revisited by several authors in recent years with reference to the frisch scheme this work presents some geometrical aspects regarding the sets of solutions obtained in the identification procedure an analysis is made on how these sets vary as the amount of noise on the data varies the existence of particular solutions for data linked by a number of linear relations greater than one is also shown

gsvd based optimal filtering for single and multimicrophone speech enhancement a generalized singular value decomposition gsvd based algorithm is proposed for enhancing multimicrophone speech signals degraded by additive colored noise this gsvd based multimicrophone algorithm can be considered to be an extension of the single microphone signal subspace algorithms for enhancing noisy speech signals and amounts to a specific optimal filtering problem when the desired response signal cannot be observed the optimal filter can be written as a function of the generalized singular vectors and singular values of a speech and noise data matrix a number of symmetry properties are derived for the single microphone and multimicrophone optimal filter which are valid for the white noise case as well as for the colored noise case in addition the averaging step of some single microphone signal subspace algorithms is examined leading to the conclusion that this averaging operation is unnecessary and even suboptimal for simple situations where we consider localized sources and no multipath propagation the gsvd based optimal filtering technique exhibits the spatial directivity pattern of a beamformer when comparing the noise reduction performance for realistic situations simulations show that the gsvd based optimal filtering technique has a better performance than standard fixed and adaptive beamforming techniques for all reverberation times and that it is more robust to deviations from the nominal situation as e g encountered in uncalibrated microphone arrays

fir filter representations of reduced rank noise reduction we show that the reduced rank output signal computed via truncated q svd is identical to that from an array of parallelly connected analysis synthesis finite impulse response fir filter pairs the filter coefficients are determined by the q svd and the filters provide an explicit description of the reduced rank noise reduction algorithm in the frequency domain

brief optimal errors in variables filtering this paper deals with optimal minimal variance filtering in an errors in variables framework differently from many other contexts errors in variables models treat all variables in a symmetric way no partition of the variables into inputs and outputs is required and assume additive noise on all the variables the filtering technique described in this paper can be easily implemented in a recursive way and does not require the use of a riccati equation at every update the results of monte carlo simulations have shown the effectiveness and consistency of the approach

adaptive ar modeling in white gaussian noise autoregressive ar modeling is widely used in signal processing the coefficients of an ar model can be easily obtained with a least mean square lms prediction error filter however it is known that this filter gives a biased solution when the input signal is corrupted by white gaussian noise treichler 1979 suggested the spl gamma lms algorithm to remedy this problem and proved that the mean weight vector can converge to the wiener solution in this paper we develop a new algorithm that extends works of vijayan et al 1990 for adaptive ar modeling in the presence of white gaussian noise by theoretical analysis we show that the performance of the new algorithm is superior to the spl gamma lms filter simulations are also provided to support our theoretical results

on an efficient k step iterative method for nonlinear equations this paper is devoted to the construction and analysis of an efficient k step iterative method for nonlinear equations the main advantage of this method is that it does not need to evaluate any high order frechet derivative moreover all the k step have the same matrix in particular only one lu decomposition is required in each iteration we study the convergence order the efficiency and the dynamics in order to motivate the proposed family we prove using some recurrence relations a semilocal convergence result in banach spaces finally a numerical application related to nonlinear conservative systems is presented

maximum efficiency for a family of newton like methods with frozen derivatives and some applications a generalized k step iterative application of newton s method with frozen derivative is studied and used to solve a system of nonlinear equations the maximum computational efficiency is computed a sequence that approximates the order of convergence is generated for the examples and it numerically confirms the calculation of the order of the method and computational efficiency this type of method appears in many applications where the authors have heuristically chosen a given number of steps with frozen derivatives an example is shown in which the total variation tv minimization model is approximated using the schemes described in this paper

brief identification of static errors in variables models the rank reducibility problem the problem of identifying linear static relations from noisy data is investigated under the assumptions of the frisch scheme the work presents an attempt to simplify the search for solutions of the related rank reducibility problem the proposed approach is based on a relaxation of the original problem by means of algebraic manipulations of the non linear equations which characterize the solution set it is shown that this method can be advantageously used when particular conditions regarding the number of variables and the number of linear relations are satisfied

consistency of system identification by global total least squares global total least squares gtls is a method for the identification of linear systems where no distinction between input and output variables is required this method has been developed within the deterministic behavioural approach to systems in this paper we analyse statistical properties of this method when the observations are generated by a multivariable stationary stochastic process in particular sufficient conditions for the consistency of gtls are derived this means that when the number of observations tends to infinity the identified deterministic system converges to the system that provides an optimal appoximation of the data generating process the two main results are the following gtls is consistent if a guaranteed stability bound can be given a priori if this information is not available then consistency is obtained if gtls is applied to the observed data extended with zero values in past and future

errors in variables identification of dynamic systems excited by arbitrary non white input abstract this work deals with the identification of dynamic systems from noisy input output observations where the noise free input is not parameterized the basic assumptions made are 1 the dynamic system can be modeled by a discrete or continuous time rational transfer function model 2 the temporal input output disturbances are mutually independent identically distributed noises and 3 the input power spectrum is non white not necessarily rational and is modeled nonparametrically the system identifiability is guaranteed by exploiting the non white spectrum property of the noise free input a frequency domain identification strategy is developed to estimate consistently the plant model parameters and the input output noise variances the uncertainty bound of the estimates is calculated and compared to the cramer rao lower bound the efficiency of the proposed algorithm is illustrated on numerical examples

combined instrumental variable and subspace fitting approach to parameter estimation of noisy input output systems the paper considers the problem of estimating the parameters of linear discrete time systems from noise corrupted input output measurements under fairly general conditions the output and input noises may be auto correlated and they may be cross correlated as well by using the instrumental variable iv principle a covariance matrix is obtained the singular vectors of which bear complete information on the parameters of the system under study a weighted subspace fitting wsf procedure is then employed on the sample singular vectors to derive estimates of the parameters of the system the combined iv wsf method proposed in the present paper is noniterative and simple to use its large sample statistical performance is analyzed in detail and the theoretical results so obtained are used to predict the behavior of the method in samples with practical lengths several numerical examples are included to show the agreement between the theoretically predicted and the empirically observed performances

projection approximation subspace tracking subspace estimation plays an important role in a variety of modern signal processing applications we present a new approach for tracking the signal subspace recursively it is based on a novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem we show that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation the resulting algorithms have a computational complexity of o nr where n is the input vector dimension and r is the number of desired eigencomponents simulation results demonstrate that the tracking capability of these algorithms is similar to and in some cases more robust than the computationally expensive batch eigenvalue decomposition relations of the new algorithms to other subspace tracking methods and numerical issues are also discussed

frequency domain identification of fir models in the presence of additive input output noise this paper describes a new approach for identifying fir models from a finite number of measurements in the presence of additive and uncorrelated white noise in particular two different frequency