calculation of cfie impedance matrix elements with rwg and n spl times rwg functions the method of moments mom solution of combined field integral equation cfie for electromagnetic scattering problems requires calculation of singular double surface integrals when galerkin s method with triangular vector basis functions rao wilton glisson functions and the cfie are applied to solve electromagnetic scattering by a dielectric object both rwg and n spl times rwg functions n is normal unit vector should be considered as testing functions robust and accurate methods based on the singularity extraction technique are presented to evaluate the impedance matrix elements of the cfie with these basis and test functions in computing the impedance matrix elements including the gradient of the green s function we can avoid the logarithmic singularity on the outer testing integral by modifying the integrand in the developed method all singularities are extracted and calculated in closed form and numerical integration is applied only for regular functions in addition we present compact iterative formulas for computing the extracted terms in closed form by these formulas we can extract any number of terms from the singular kernels of cfie formulations with rwg and n spl times rwg functions

fuzzy model validation using the local statistical approach the local statistical approach for fault detection and isolation is applied to fuzzy models validation the method detects the inconsistencies between a fuzzy rule base and the modelled system it can also identify which are the faulty parameters of the fuzzy model the fisher information matrix explains the detectability of changes in the parameters of the fuzzy model simulation tests illustrate the method s credibility

exact algorithms for l 1 tv regularization of real valued or circle valued signals we consider l 1 tv regularization of univariate signals with values on the real line or on the unit circle while the real data space leads to a convex optimization problem the problem is nonconvex for circle valued data in this paper we derive exact algorithms for both data spaces a key ingredient is the reduction of the infinite search spaces to a finite set of configurations which can be scanned by the viterbi algorithm to reduce the computational complexity of the involved tabulations we extend the technique of distance transforms to nonuniform grids and to the circular data space in total the proposed algorithms have complexity mathcal o kn where n is the length of the signal and k is the number of different values in the data set in particular the complexity is mathcal o n for quantized data it is the first exact algorithm for total variation regularization with circle valued data and it is competitive with the state of the art methods for scalar data assuming that the

analysis of subspace fitting and ml techniques for parameter estimation from sensor array data it is shown that the multidimensional signal subspace method termed weighted subspace fitting wsf is asymptotically efficient this results in a novel compact matrix expression for the cramer rao bound crb on the estimation error variance the asymptotic analysis of the maximum likelihood ml and wsf methods is extended to deterministic emitter signals the asymptotic properties of the estimates for this case are shown to be identical to the gaussian emitter signal case i e independent of the actual signal waveforms conclusions concerning the modeling aspect of the sensor array problem are drawn

efficient recursive algorithms for detection of abrupt changes in signals and control systems this paper addresses a number of open problems concerning the generalized likelihood ratio glr rules for online detection of faults and parameter changes in control systems it is shown that with an appropriate choice of the threshold and window size these glr rules are asymptotically optimal the rules are also extended to non likelihood statistics that are widely used in monitoring adaptive algorithms for system identification and control by establishing gaussian approximations to these statistics when the window size is chosen suitably recursive algorithms are developed for practical implementation of the procedure and importance sampling techniques are introduced for determining the threshold of the rule to satisfy prescribed bounds on the false alarm rate

on global identifiability for arbitrary model parametrizations it is a fundamental problem of identification to be able even before the data have been analyzed to decide if all the free parameters of a model structure can be uniquely recovered from data this is the issue of global identifiability in this contribution we show how global identifiability for an arbitrary model structure basically with analytic non linearities can be analyzed using concepts and algorithms from differential algebra it is shown how the question of global structural identifiability is reduced to the question of whether the given model structure can be rearranged as a linear regression an explicit algorithm to test this is also given furthermore the question of persistent excitation for the input can also be tested explicitly is a similar fashion the algorithms involved are very well suited for implementation in computer algebra one such implementation is also described

subspace based fault detection robust to changes in the noise covariances the detection of changes in the eigenstructure of a linear time invariant system by means of a subspace based residual function has been proposed previously while enjoying some success in its applicability in particular in the context of vibration monitoring the robustness of this framework against changes in the noise properties has not been properly addressed yet in this paper a new robust residual is proposed and the robustness of its statistics against changes in the noise covariances is shown the complete theory for hypothesis testing for fault detection is derived and a numerical illustration is provided

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

a new methodology for observer design and implementation observers are usually formulated as explicit systems of differential equations and implemented using standard ode solvers in this paper we show that there can be advantages in formulating the observer as a differential algebraic equation dae we propose a canonical dae observer and show that it can be implemented using standard dae solvers the dae implementation of the observer can be considered regardless of the design philosophy used we present a simple design strategy for this canonical dae observer based on the extended linearization method

diagnosis of unknown parametric faults in non linear stochastic dynamical systems a new detection and isolation scheme for unknown parametric faults in non linear stochastic systems is presented that is particularly suited for small parametric changes the proposed residual is the moving angle between two stochastic processes the error derived from the reference model and the expected error in case a certain fault has occurred since the fault is unknown fault classes are defined most of the faults that belong to such a fault class can be detected and isolated by just testing one representative of this fault class as the moving angle itself is a stochastic process an estimator is designed and characterised conditions for the detectability and isolability of fault classes are given for this estimator based on hypotheses tests finally the theoretical results are confirmed by simulations and monte carlo tests

bayesian selection for the ell _2 potts model regularization parameter 1 d piecewise constant signal denoising piecewise constant denoising can be solved either by deterministic optimization approaches based on the potts model or by stochastic bayesian procedures the former lead to low computational time but require the selection of a regularization parameter whose value significantly impacts the achieved solution and whose automated selection remains an involved and challenging problem conversely fully bayesian formalisms encapsulate the regularization parameter selection into hierarchical models at the price of high computational costs this contribution proposes an operational strategy that combines hierarchical bayesian and potts model formulations with the double aim of automatically tuning the regularization parameter and maintaining computational efficiency the proposed procedure relies on formally connecting a bayesian framework to a ell 2 potts functional behaviors and performance for the proposed piecewise constant denoising and regularization parameter tuning techniques are studied qualitatively and assessed quantitatively and shown to compare favorably against those of a fully bayesian hierarchical procedure both in accuracy and computational load

nonlinear black box models in system identification mathematical foundations we discuss several aspects of the mathematical foundations of the nonlinear black box identification problem we shall see that the quality of the identification procedure is always a result of a certain trade off between the expressive power of the model we try to identify the larger the number of parameters used to describe the model the more flexible is the approximation and the stochastic error which is proportional to the number of parameters a consequence of this trade off is the simple fact that a good approximation technique can be the basis of a good identification algorithm from this point of view we consider different approximation methods and pay special attention to spatially adaptive approximants we introduce wavelet and neuron approximations and show that they are spatially adaptive then we apply the acquired approximation experience to estimation problems finally we consider some implications of these theoretical developments for the practically implemented versions of the spatially adaptive algorithms

asymptotic optimality of mixture rules for detecting changes in general stochastic models the paper addresses a sequential changepoint detection problem for a general stochastic model assuming that the observed data may be non i i d i e dependent and non identically distributed and prior distribution of the change point is arbitrary tartakovsky and veeravalli 2005 baron and tartakovsky 2006 and more recently tartakovsky 2017 developed a general asymptotic theory of changepoint detection for non i i d stochastic models assuming certain stability of the log likelihood ratio process in the case of simple hypotheses when both pre change and post change models are completely specified however in most applications the post change distribution is not completely known in the present paper we generalize previous results to the case of parametric uncertainty assuming that the parameter of the post change distribution is unknown we introduce two detection rules based on mixtures the mixture shiryaev rule and the mixture shiryaev roberts rule and study their asymptotic properties in the bayesian context in particular we provide sufficient conditions under which these rules are first order asymptotically optimal minimizing moments of the delay to detection as the probability of false alarm approaches zero

statistical model based damage detection and localization subspace based residuals and damage to noise sensitivity ratios the vibration based structural health monitoring problem is addressed as the double task of detecting damages modeled as changes in the eigenstructure of a linear dynamic system and localizing the detected damages within a fem of the monitored structure the proposed damage detection algorithm is based on a residual generated from a stochastic subspace based covariance driven identification method and on the statistical local approach to the design of detection algorithms this algorithm basically computes a global test which performs a sensitivity analysis of the residuals to the damages relative to uncertainties and noises how this residual relates to some residuals for damage localization and model updating is discussed damage localization is stated as a detection problem this problem is addressed by plugging aggregated sensitivities of the modes and mode shapes w r t fem structural parameters in the above setting this results in directional tests which perform the same type of damage to noise sensitivity analysis of the residual as for damage detection how the sensitivity aggregation mechanism relates to sub structuring is outlined numerical results obtained on one example are reported

a robustness property of doa estimators based on covariance a simple general formula is derived under a gaussian model for the asymptotic covariance of direction of arrival doa estimators based on the covariance of the sensor array data it is then established that the same formula remains valid for a wide class of statistical models for source signals hence under mild assumptions the asymptotic performance of most high resolution covariance based doa estimators is independent of the distribution of the source signals

scattering from multiple objects buried beneath two dimensional random rough surface using the steepest descent fast multipole method generalized formulations are presented to analyze the electric field scattered from multiple penetrable shallow objects buried beneath two dimensional random rough surfaces these objects could have different materials shapes or orientations in addition their separation distance may range from a fraction of a wavelength to several wavelengths the fast algorithm steepest descent fast multipole method sdfmm is used to compute the unknown electric and magnetic surface currents on the rough ground surface and on the buried objects parametric investigations are presented to study the effect of the objects proximity orientations materials shapes the incident waves polarization and the ground roughness on the scattered fields a significant interference is observed between the objects when they are separated by less than one free space wavelength even when the clutter due to the rough ground is removed the return from the second object can be dominating causing a possible false alarm in detecting the target the results show that the distortion in target signature significantly increases with the increase of both the proximity to a clutter item and the ground roughness

bistatic scattering and emissivities of random rough dielectric lossy surfaces with the physics based two grid method in conjunction with the sparse matrix canonical grid method bistatic em wave scattering from 2 d lossy dielectric random rough surfaces 3 d scattering problem with large permittivity is studied for media with large permittivities the fields can vary rapidly on the surface thus a dense discretization of the surface is required to implement the method of moments mom for the surface integral equations such a dense discretization is also required to ensure that the emissivity can be calculated to the required accuracy of 0 01 for passive remote sensing applications we have developed a physics based two grid method pbtg that can give the accurate results of the surface fields on the dense grid and also the emissivities the pbtg consists of using two grids on the surface the coarse grid and the required dense grid the pbtg only requires moderate increase in central processing unit cpu and memory in this paper the numerical results are calculated by using the pbtg in conjunction with the sparse matrix canonical grid smcg method the computational complexity and memory requirement for the present algorithm are o n sub scg log n sub scg and o n sub scg respectively where n sub scg is the number of grid points on the coarse grid numerical simulations are illustrated for root mean square rms height of 0 3 wavelengths and correlation length of 1 0 wavelength the relative permittivity used is as high as 17 2i the numerical results are compared with that of the second order small perturbation method spm the comparisons show that a large difference in brightness temperature exists between the spm and numerical simulation results for cases with moderate rms slope

high level primitives for recursive maximum likelihood estimation this paper proposes a high level language constituted of a small number of primitives and macros for describing recursive maximum likelihood ml estimation algorithms this language is applicable to estimation problems involving linear gaussian models or processes taking values in a finite set the use of high level primitives allows the development of highly modular ml estimation algorithms based on simple numerical building blocks the primitives which correspond to the combination of different measurements the extraction of sufficient statistics and the conversion of the status of a variable from unknown to observed or vice versa are first defined for linear gaussian relations specifying mixed deterministic stochastic information about the system variables these primitives are used to define other macros and are illustrated by deriving new filtering and smoothing algorithms for linear descriptor systems the primitives are then extended to finite state processes and used to implement the viterbi ml state sequence estimator for a hidden markov model

3 d scattering from a pec target buried beneath a dielectric rough surface an efficient pile aca algorithm for solving a hybrid ka efie formulation an efficient hybrid ka efie formulation is deployed to analyze the electromagnetic em scattering from a 3 d perfectly electric conducting pec object buried beneath a 2 d dielectric rough surface in this approach the electric and magnetic current densities on the rough surface are analytically obtained through the current based kirchhoff approximation ka whereas the electric current density on the buried object is rigorously determined by solving the electric field integral equation efie using the galerkin s method of moments mom with rao wilton glisson rwg basis functions the ka efie matrix system is then efficiently solved by the iterative propagation inside layer expansion pile method combined with the algebraic adaptive cross approximation aca the current densities on the dielectric rough surface are thereafter used to handle the bistatic normalized radar cross section nrcs patterns the proposed hybrid approach allows a significant reduction in computation time and memory requirements compared to the rigorous poggio miller chang harrington wu pmchw efie formulation which requires solving a large mom matrix equation moreover the hybridization of the aca algorithm with the pile method improves further the computational cost thanks to the rank deficient propriety of the coupling matrices to validate the hybrid approach we compare its results with those of the rigorous pmchw efie approach

statistical performance analysis of the algebraic constant modulus algorithm this paper presents a large sample analysis of the covariance of the beamformers computed by the analytical constant modulus algorithm acma method for blindly separating constant modulus sources this can be used to predict the signal to interference plus noise ratio sinr performance of these beamformers as well as their deviation from the nonblind wiener receivers to which they asymptotically converge the analysis is based on viewing acma as a subspace fitting optimization where the subspace is spanned by the eigenvectors of a fourth order covariance matrix the theoretical performance is illustrated by numerical simulations and shows a good match

change detection in teletraffic models we propose a likelihood based ratio test to detect distributional changes in common teletraffic models these include traditional models like the markov modulated poisson process and processes exhibiting long range dependency in particular gaussian fractional arima processes a practical approach is also developed for the case where the parameter after the change is unknown it is noticed that the algorithm is robust enough to detect slight perturbations of the parameter value after the change a comprehensive set of numerical results including results for the mean detection delay is provided

sequential changepoint detection in quality control and dynamical systems after a brief survey of a large variety of sequential detection procedures that are widely scattered in statistical references on quality control and engineering references on fault detection and signal processing we study some open problems concerning these procedures and introduce a unified theory of sequential changepoint detection this theory leads to a class of sequential detection rules which are not too demanding in computational and memory requirements for on line implementation and yet are nearly optimal under several performance criteria

subspace algorithms for the stochastic identification problem abstract in this paper we derive a new subspace algorithm to consistently identify stochastic state space models from given output data without forming the covariance matrix and using only semi infinite block hankel matrices the algorithm is based on the concept of principal angles and directions we describe how they can be calculated with qr and quotient singular value decomposition we also provide an interpretation of the principal directions as states of a non steady state kalman filter bank

a subspace algorithm for certain blind identification problems the problem of blind identification of p inputs q outputs fir transfer functions is addressed existing subspace identification methods derived for p 1 are first reformulated in particular the links between the noise subspace of a certain covariance matrix of the output signals on which subspace methods build on and certain rational subspaces associated with the transfer function to be identified are elucidated based on these relations we study the behavior of the subspace method in the case where the order of the transfer function is overestimated next an asymptotic performance analysis of this estimation method is carried out consistency and asymptotical normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are presented to demonstrate the potential of the subspace method finally we take advantage of our new reformulation to discuss the extension of the subspace method to the case p 1 we show where the difficulties lie and we briefly indicate how to solve the corresponding problems the possible connections with classical approaches for ma model estimations are also outlined

a generalized change detection problem the purpose of this paper is to give a new statistical approach to the change diagnosis detection isolation problem the change detection problem has received extensive research attention however the change isolation problem has for the most part been ignored we consider a stochastic dynamical system with abrupt changes and investigate the multiple hypotheses extension of lorden s 1971 results we introduce a joint criterion of optimality for the detection isolation problem and then design a change detection isolation algorithm we also investigate the statistical properties of this algorithm we prove a lower bound for the criterion in a class of sequential change detection isolation algorithms it is shown that the proposed algorithm is asymptotically optimal in this class the theoretical results are applied to the case of additive changes in linear stochastic models

joint segmentation and shape regularization with a generalized forward backward algorithm this paper presents a method for the simultaneous segmentation and regularization of a series of shapes from a corresponding sequence of images such series arise as time series of 2d images when considering video data or as stacks of 2d images obtained by slicewise tomographic reconstruction we first derive a model where the regularization of the shape signal is achieved by a total variation prior on the shape manifold the method employs a modified kendall shape space to facilitate explicit computations together with the concept of sobolev gradients for the proposed model we derive an efficient and computationally accessible splitting scheme using a generalized forward backward approach our algorithm treats the total variation atoms of the splitting via proximal mappings whereas the data terms are dealt with by gradient descent the potential of the proposed method is demonstrated on various application examples dealing with 3d data we explain how to extend the proposed combined approach to shape fields which for instance arise in the context of 3d t imaging modalities and show an application in this setup as well

enhancement of robustness in observer based fault detection a prerequisite for the feasibility of the technique of observer based fault detection and isolation fdi in dynamic systems is a satisfactory robustness with respect to modelling uncertainties this paper surveys the most relevant methods to increase the robustness in both the stage of residual generation and residual evaluation among these methods are the generalized observer scheme the robust parity space check the unknown input and h observer scheme the decorrelation filter and the concept of adaptive threshold selection it is pointed out that the unknown input observer concept which provides perfect decoupling from the modelling errors or its optimal approximation with the aid of h techniques constitutes a general framework of robust residual generation that generalizes and unifies numerous other approaches among them the parity space and detection filter approach it is further shown that this fdi method can even be applied to a certain class of nonlinear systems

optimally robust redundancy relations for failure detection in uncertain systems all failure detection methods are based either explicitly or implicitly on the use of redundancy i e on possibly dynamic relations among the measured variables the robustness of the failure detection process consequently depends to a great degree on the reliability of the redundancy relations which in turn is affected by the inevitable presence of model uncertainties in this paper the problem of determining redundancy relations that are optimally robust is addressed in a sense that includes several major issues of importance in practical failure detection and that provides a significant amount of intuition concerning the geometry of robust failure detection a procedure is given involving the construction of a single matrix and its singular value decomposition for the determination of a complete sequence of redundancy relations ordered in terms of their level of robustness this procedure also provides the basis for comparing levels of robustness in redundancy provided by different sets of sensors

optimal sensor location for detecting changes in dynamical behavior we address the problem of optimal sensor location for monitoring the eigenstructure of a multivariable dynamical system the criterions which are optimized are the power of new tests designed for detecting and diagnosing changes in the eigencharacteristics of a system 3 12 the key points are the choice of the parameterization for computing the criterion and the comparison of designs with a different number of sensors the discussion of the numerical results for sensor location includes the analysis of the effect of the geometry of the unknown excitation

music like estimation of direction of arrival for noncircular sources this paper examines the asymptotic performance of music like algorithms for estimating directions of arrival doa of narrowband complex noncircular sources using closed form expressions of the covariance of the asymptotic distribution of different projection matrices it provides a unifying framework for investigating the asymptotic performance of arbitrary subspace based algorithms valid for gaussian or non gaussian and complex circular or noncircular sources we also derive different robustness properties from the asymptotic covariance of the estimated doa given by such algorithms these results are successively applied to four algorithms to two attractive music like algorithms previously introduced in the literature to an extension of these algorithms and to an optimally weighted music algorithm proposed in this paper numerical examples illustrate the performance of the studied algorithms compared to the asymptotically minimum variance amv algorithms introduced as benchmarks

in variance of subspace based estimators subspace based estimates i e estimates obtained by exploiting the orthogonality between a sample subspace and a parameter dependent subspace have proved useful in many applications including array processing and system identification the purpose of this paper is to complement the already available theoretical results generally obtained in specific contexts we discuss the generalization of the optimal weighted subspace fitting approach introduced by viberg 1989 in the doa estimation context we exhibit some invariance properties of optimally weighted estimate and we show the equivalence between subspace fitting and subspace matching

a generalization of weighted subspace fitting to full rank models the idea of subspace fitting provides a popular framework for different applications of parameter estimation and system identification previously some algorithms have been suggested based on similar ideas for a sensor array processing problem where the underlying data model is not low rank we show that two of these algorithms dspe and dispare fail to give consistent estimates and introduce a general class of subspace fitting like algorithms for consistent estimation of parameters from a possibly full rank data model the asymptotic performance is analyzed and an optimally weighted algorithm is derived the result gives a lower bound on the estimation performance for any estimator based on a low rank approximation of the linear space spanned by the sample data we show that in general for full rank data models no subspace based method can reach the cramer rao lower bound crb

two strategies in the problem of change detection and isolation the comparison between optimal sequential and nonsequential fixed size sample strategies in the problem of abrupt change detection and isolation is discussed in particular we show that sometimes a simple fixed size sample algorithm is almost as efficient as an optimal sequential algorithm which leads to a burdensome number of arithmetical operations

tapered wave with dominant polarization state for all angles of incidence typical applications of the method of moments mom to rough surface three dimensional 3 d electromagnetic scattering require a truncation of the surface considered and call for a tapered incident wave it is shown how such a wave can be constructed as a superposition of plane waves avoiding problems near both normal and grazing incidence and providing clean footprints and clear polarization at all angles of incidence the proposed special choice of polarization vectors removes an irregularity at the origin of the wavenumber space and leads to a least squared error property of the wave issues in the application to 3 d scattering from an object over a rough surface are discussed approximate 3 d scalar and vector tapered waves which can be evaluated without resorting to any numerical integrations are derived and important limitations to the accuracy and applicability of these approximations are pointed out

sensor array processing based on subspace fitting algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem the methods considered are the deterministic maximum likelihood method ml esprit and a recently proposed multidimensional signal subspace method these methods are formulated in a subspace fitting based framework which provides insight into their algebraic and asymptotic relations it is shown that by introducing a specific weighting matrix the multidimensional signal subspace method can achieve the same asymptotic properties as the ml method the asymptotic distribution of the estimation error is derived for a general subspace weighting and the weighting that provides minimum variance estimates is identified the resulting optimal technique is termed the weighted subspace fitting wsf method numerical examples indicate that the asymptotic variance of the wsf estimates coincides with the cramer rao bound the performance improvement compared to the other techniques is found to be most prominent for highly correlated signals

a fault detection scheme for linear discrete time systems with an integrated online performance evaluation this paper is concerned with the design of the fault detection systems into which a residual generation evaluation and threshold are integrated for linear discrete time varying processes over a finite horizon in the proposed design scheme the residual generation is realised in the context of h fault estimation with a prescribed attenuation level this attenuation level is minimised by using the krein space linear estimation theory and subsequently an h fault estimator with the minimum attenuation level is designed in terms of the solution to a set of riccati like recursions for the residual evaluation and decision making purpose the false alarm rate and fault detection rate indicators are introduced in the norm based framework which is integrated into the decision making procedure for the online computations of the false alarm rate and fault detection rate indicators further estimates delivered by the h fault estimator are applied without additional online computations by means of checki

fault detection and isolation in nonlinear dynamic systems a combined input output and local approach the problem of fault detection and isolation fdi is addressed for nonlinear dynamic systems modeled by polynomial differential algebraic equations ritt s algorithm is used to obtain an input output representation of the monitored system by eliminating unknown variables a local approach to change detection is then applied to the input output representation for fdi residual generation and evaluation simulation results on a microbial growth process are provided which illustrate the relevance of the proposed fdi method

a new structural framework for parity equation based failure detection and isolation abstract the paper describes a new framework for developing parity equations that prevent incorrect isolation decisions under marginal size failures in a decision process that tests each residual independently test thresholds that take the noise conditions into account are set high to reduce the occurrence of false alarms while maintaining the algorithm s ability to detect and isolate larger failures the method is applicable to additive failures on the measured input and output variables and to additive plant disturbances a transformation algorithm provides a multitude of models that satisfy the isolability requirements a search procedure utilizing this model redundancy integrates model robustness considerations into the design

on board component fault detection and isolation using the statistical local approach we describe both the key principles and real application examples of a unified theory which allows us to perform the on board incipient fault detection and isolation tasks involved in monitoring for condition based maintenance this theory is known under the name of local approach and it is especially suited to component faults it aims at transforming complex detection problems concerning a parameterized stochastic process into the universal problem of monitoring the mean of a gaussian vector based on a small deviation assumption the key tools are the first order taylor expansion and the asymptotic gaussianity of a convenient parameter estimating function ml ls iv and subspace identification methods are addressed in this perspective in the case of dynamic processes given in state space form the approach may also call for observer based state estimation or state elimination experiments concerning both simulated and real data for linear and nonlinear dynamical processes are reported how the key principles and features of the local approach compare with those of other approaches is discussed

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

subspace based methods for the identification of linear time invariant systems subspace based methods for system identification have attracted much attention during the past few years this interest is due to the ability of providing accurate state space models for multivariable linear systems directly from input output data the methods have their origin in classical state space realization theory as developed in the 1960s the main computational tools are the qr and the singular value decompositions here an overview of existing subspace based techniques for system identification is given the methods are grouped into the classes of realization based and direct techniques similarities between different algorithms are pointed out and their applicability is commented upon we also discuss some recent ideas for improving and extending the methods a simulation example is included for comparing different algorithms the subspace based approach is found to perform competitive with respect to prediction error methods provided the system is properly excited

modular and numerically stable fast transversal filters for multichannel and multiexperiment rls the authors present scalar implementations of multichannel and multiexperiment fast recursive least squares algorithms in transversal filter form known as fast transversal filter ftf algorithms by processing the different channels and or experiments one at a time the multichannel and or multiexperiment algorithm decomposes into a set of intertwined single channel single experiment algorithms for multichannel algorithms the general case of possibly different filter orders in different channels is handled geometrically this modular decomposition approach corresponds to a gram schmidt orthogonalization of multiple error vectors algebraically this technique corresponds to matrix triangularization of error covariance matrices and converts matrix operations into a regular set of scalar operations modular algorithm structures that are amenable to vlsi implementation on arrays of parallel processors naturally follow from the present approach numerically the resulting algorithm benefits from the advantages of triangularization techniques in block processing

evam an eigenvector based algorithm for multichannel blind deconvolution of input colored signals a new algorithm is proposed for the deconvolution of an unknown possibly colored gaussian or nonstationary signal that is observed through two or more unknown channels described by rational system transfer functions more specifically not only the root pole and zero locations but also the orders of the channel transfer functions are unknown it is assumed that the channel orders may be overestimated the proposed algorithm estimates the orders and root locations of the channel transfer functions therefore it can also be used in multichannel system identification problems the input signal is allowed to be nonstationary and the channel transfer functions may be a nonminimum phase as well as noncausal hence the proposed algorithm is particularly suitable for applications such as dereverberation of speech signals recorded through multiple microphones several experimental results indicate improvement compared to the existing methods in the literature

single sample modal identification of a nonstationary stochastic process gauss markov processes excited by nonstationary noises are encountered in the modeling of vibrating systems we prove that the classical instrumental variable method as well as the ho kalman realization algorithm for identifying the pole part modal characteristics of the model are consistent when used on a single sample of the nonstationary signal

a sequential procedure for multihypothesis testing the sequential testing of more than two hypotheses has important applications in direct sequence spread spectrum signal acquisition multiple resolution element radar and other areas a useful sequential test which we term the msprt is studied in this paper the test is shown to be a generalization of the sequential probability ratio test under bayesian assumptions it is argued that the msprt approximates the much more complicated optimal test when error probabilities are small and expected stopping times are large bounds on error probabilities are derived and asymptotic expressions for the stopping time and error probabilities are given a design procedure is presented for determining the parameters of the msprt two examples involving gaussian densities are included and comparisons are made between simulation results and asymptotic expressions comparisons with bayesian fixed sample size tests are also made and it is found that the msprt requires two to three times fewer samples on average

an invariance property of some subspace based detection algorithms subspace fitting estimates involve multidimensional parameter estimating functions having a particular product form based on estimating functions the statistical local approach builds detection algorithms that enjoy a simple invariance property this article investigates that invariance property for the detectors built on those two concepts

information criteria for residual generation and fault detection and isolation using an information point of view we discuss deterministic versus stochastic tools for residual generation and evaluation for fault detection and isolation fdi in linear time invariant lti state space systems in both types of approaches to off line fdi residual generation can be viewed as the design of a linear transformation of a gaussian vector the finite window input adjusted observations several statistical isolation methods are revisited using both a linear transform formulation and the information content of the corresponding residuals we formally state several multiple fault cases with or without causality assumptions and discuss an optimality criterion for the most general one new information criteria are proposed for investigating the residual optimization problem

state space formulation a solution to modal parameter estimation abstract as an alternative to fourier techniques based on transfer function fitting modal parameters identification methods derived from a state space formulation of the dynamic equation have been recently studied and developed this formulation leads to the solution of the modal problem via multi dimensional arma model parameters identification in this paper the transition from the dynamic equation to the arma model is described and the algorithms of identification are explained for the very common case of uncontrolled and unmeasured excitation these techniques the qualities of which have been established during extensive processing of offshore structures measurements have been generalized to more complex excitation models such as those of turbo alternators several examples illustrate these different application domains

nonlinear black box modeling in system identification a unified overview a nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics there has been considerable recent interest in this area with structures based on neural networks radial basis networks wavelet networks and hinging hyperplanes as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules this paper describes all these approaches in a common framework from a user s perspective it focuses on what are the common features in the different approaches the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques it is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space these mappings are discussed separately the latter mapping is usually formed as a basis function expansion the basis functions are typically formed from one simple scalar function which is modified in terms of scale and location the expansion from the scalar argument to the regressor space is achieved by a radial or a ridge type approach basic techniques for estimating the parameters in the structures are criterion minimization as well as two step procedures where first the relevant basis functions are determined using data and then a linear least squares step to determine the coordinates of the function approximation a particular problem is to deal with the large number of potentially necessary parameters this is handled by making the number of used parameters considerably less than the number of offered parameters by regularization shrinking pruning or regressor selection