performance analysis of an adaptive notch filter with constrained poles and zeros a statistical analysis of the sine wave frequency estimate obtained by the adaptive notch filter anf recently proposed by a nehorai ibid vol assp 33 p 983 96 aug 1985 is presented asymptotically valid expressions for the bias and mean square error of the frequency estimate are provided the analysis verifies the performance exhibited by the anf and clarifies the role of some user variables such as the notch bandwidth and the number of data samples processed

tracking properties of a gradient based second order adaptive iir notch filter with constrained poles and zeros gradient type adaptive iir notch filters have many attractive merits for various real life applications since they require a small number of computations and yet demonstrate practical performance however it is generally quite difficult to assess their performance analytically their tracking properties in particular have not yet been investigated in this paper the tracking performance of a plain gradient pg algorithm is analyzed in detail for a second order adaptive iir notch filter with constrained poles and zeros which takes a linear chirp signal as its input first two sets of difference equations for the frequency tracking error and mean square error mse are established in the sense of convergence in the mean and convergence in the mean square respectively closed form expressions for the asymptotic tracking error and mse are then derived from these difference equations an optimum step size parameter for the algorithm is also evaluated based on the minimization of the asymptotic tracking error or the tracking mse it is discovered that the asymptotic tracking error may be driven to zero for a positive chirp rate by selecting a proper step size which is an interesting property for a real valued adaptive filtering algorithm extensive simulations are performed to support the analytical findings

spectrum estimation notch filters and music a novel extension of the multiple signal classification music algorithm for the frequency estimation problem is proposed in this work it is shown that the music algorithm is a data dependent optimum notch filter design technique when the input data are passed through this optimum notch filter the signal to noise ratio snr of the output is minimized the zeros of the optimum notch filter are then used to estimate the frequencies in the classical music algorithm this optimization is carried out over the set of all finite impulse response fir filters having a fixed order the framework of this paper allows the use of rational notch filters the fact that the rational filters have sharper spectral characteristics is used to obtain improved estimates particularly at low snr some interesting properties of the proposed algorithm are derived and further perspectives on the implementation aspects are provided the analytical predictions are substantiated using numerical simulation results

statistical analysis of music and subspace rotation estimates of sinusoidal frequencies consideration is given to the analysis of the large sample second order properties of multiple signal classification music and subspace rotation sur methods such as esprit for sinusoidal frequency estimation explicit expressions for the covariance elements of the estimation errors associated with either method are derived these expressions of covariances are then used to analyze and compare the statistical performances of the music and sur estimation sure methods both music and sure are based on the eigendecomposition of a sample data covariance matrix the expressions for the estimation error variances derived are used to study the dependence of music and sure performances on the dimension of the data covariance matrix used

a minimal parameter adaptive notch filter with constrained poles and zeros a new algorithm is presented for adaptive notch filtering and parametric spectral estimation of multiple narrow band or sine wave signals in an additive broad band process the algorithm is of recursive prediction error rpe form and uses a special constrained model of infinite impulse response iir with a minimal number of parameters the convergent filter is characterized by highly narrow bandwidth and uniform notches of desired shape for sufficiently large data sets the variances of the sine wave frequency estimates are of the same order of magnitude as the cramer rao bound results from simulations illustrate the performance of the algorithm under a wide range of conditions

performance analysis of the sign algorithm for a constrained adaptive iir notch filter adaptive infinite impulse response iir notch filters are very attractive in terms of their reasonable performances and low computational requirements generally it is very difficult to assess their performances analytically due to their iir nature this paper analyzes in detail the steady state performance of the sign algorithm sa for a well known adaptive iir notch filter with constrained poles and zeros slow adaptation and gaussianity of the notch filter output are assumed for the sake of analysis two difference equations are first established for the convergences in the mean and mean square in the vicinity of the steady state of the algorithm steady state estimation error or bias and mean square error mse of the sa are then derived in closed forms a coarse stability bound is also derived for the algorithm theory based comparison between the algorithm and the plain gradient pg algorithm is done in some detail extensive simulations are conducted to demonstrate the validity of the analytical results for both slow and relatively fast adaptations

convergence analysis of recursive identification algorithms based on the nonlinear wiener model recursive identification algorithms based on the nonlinear wiener model are presented a recursive identification algorithm is first derived from a general parameterization of the wiener model using a stochastic approximation framework local and global convergence of this algorithm can be tied to the stability properties of an associated differential equation since inversion is not utilized noninvertible static nonlinearities can be handled which allows a treatment of for example saturating sensors and blind adaptation problems gauss newton and stochastic gradient algorithms for the situation where the static nonlinearity is known are then suggested in the single input single output case the proposed methods can outperform conventional linearizing inversion of the nonlinearity when measurement disturbances affect the output signal for fir finite impulse response models it is also proved that global convergence of the schemes is tied to sector conditions on the static nonlinearity in particular global convergence of the stochastic gradient method is obtained provided that the nonlinearity is strictly monotone the local analysis performed for iir infinite impulse response models illustrates the importance of the amplitude contents of the exciting signals

fast rls type algorithm for unbiased equation error adaptive iir filtering based on approximate inverse power iteration in this paper a fast approximate inverse power aip iteration is applied to compute recursively the total least squares tls solution for unbiased equation error adaptive infinite impulse response iir filtering which is established by approximating the well known inverse power iteration with galerkin method the aip algorithm is based on an interesting modification of the inverse power iteration in which the first entry of the parameter vector is constrained to the negative one the distinctive feature of the proposed algorithm lies in its high computational efficiency which is characterized by efficient computation of the fast gain vector fgv adaptation of the interesting modification of the inverse power iteration and rank one update of the augmented correlation matrix the shift structure of the input data vector is exploited to develop a fast algorithm for computing the gain vector this fgv algorithm can be implemented at a numerical cost lower than the well known fast kalman algorithm since the first entry of the parameter vector has been fixed as the negative one and the weight vector is updated along the input data vector a very efficient aip algorithm is obtained by using the fgv algorithm the proposed aip algorithm is of computational complexity o l per iteration moreover with no need to use the well known matrix inversion lemma the aip algorithm has another attractive feature of numerical stability the proposed algorithm is shown to have global convergence simulation examples are included to demonstrate the effectiveness of the proposed aip algorithm

a generalized least squares method for frequency estimation the application of the generalized least squares gls method to the estimation of the frequencies of sinusoids in additive colored noise is discussed an iterative algorithm is proposed starting from the assumption that the parameter vector in the model of the sinusoids is symmetric the algorithm utilizes an adaptive strategy for contracting the poles of the estimated signal model expressions for the probability limit and the asymptotic variance of the estimates are derived for the single sinusoid case possible convergence points and the asymptotic behavior of the algorithm in the case of low snrs signal to noise ratios are analyzed extensive simulation results show that the algorithm represents a simple and reliable tool for practical applications

optimal instrumental variable estimation and approximate implementations the accuracy properties of instrumental variables iv methods are investigated extensions such as prefiltering of data and use of additional instruments are included in the analysis the parameter estimates are shown to be asymptotically gaussian distributed an explicit expression is given for the covariance matrix of their distribution the covariance matrix is then taken as a multivariable measure of accuracy it is shown how it can be optimized by an appropriate selection of instruments and prefilter the so obtained optimal instrumental variable estimates cannot be used directly since the true system and the statistical properties of the disturbance must be known in order to compute the optimal instruments and prefilters a multistep procedure consisting of three or four simple steps is then proposed as a way to overcome this difficulty this procedure includes modeling of the disturbance as an arma process using a statistically efficient method such as a prediction error method the statistical properties of the estimates obtained with the multistep procedure are also analyzed those estimates are shown to be asymptotically gaussian distributed as well the covariance matrix of the estimation errors is compared to that corresponding to a prediction error method for some model structures these two approaches give the same asymptotic accuracy the conclusion is that the multistep procedure which is quite easy to implement and also has nice uniqueness properties can be viewed as an interesting alternative to prediction error methods

analysis of a general recursive prediction error identification algorithm a general class of algorithms for recursive identification of stochastic dynamical systems is studied in this class the discrepancy between the measured output and the output predicted from previous data according to a candidate model the prediction error is minimized over the model set using a stochastic approximation approach it is proved that this class of methods has the same convergence properties as its off line counterparts under mild and general assumptions these assumptions do not for example include stationary conditions or conditions that the true system can be exactly represented within the model set the considered class of methods contains as special cases several well known algorithms other common recursive identification methods like the extended least squares method and the extended kalman filter can be interpreted as approximate prediction error methods with simplified gradient calculations therefore the approach taken here may also serve as a basis for unified description of many recursive identification methods

technical communique convergence analysis of recursive identification algorithms with forgetting factor a convergence analysis of a modified version of the least squares recursive identification algorithm with forgetting factor is given it is shown that the parametric distance converges to a zero mean random variable it is also shown that under persistent excitation condition on both system input and output the condition number of the adaptation gain matrix is bounded the variance of the parametric distance is bounded by the product of the noise variance times the upper bound of the condition number of the gain matrix this is done by normalizing the measurement vector entering in the identification algorithm and by using a forgetting factor verifying l t 0

arma spectral estimation for noisy signals observed through a linear system spectral estimation for autoregressive moving average arma processes observed through a known linear system is considered an algorithm based on a system identification parameter estimation technique known as the recursive prediction error method is used for spectral estimation the algorithm is formulated in the state space to incorporate the constraints imposed by the linear system the linear system may represent the distortion introduced by the sensor or the channel several simulation examples are presented to illustrate the performance of the estimator

a recursive maximum likelihood algorithm for arma line enhancement optimal filtering of narrow band signals corrupted by noise requires an infinite impulse response iir filter a recursive maximum likelihood algorithm is proposed for adaptively adjusting the coefficients of an iir line enhancer the performance of this adaptive iir filter is analyzed and compared to that of a finite impulse response filter preliminary simulation results are presented to illustrate the behavior of the proposed algorithm under various signal to noise conditions

a fast recursive total least squares algorithm for adaptive fir filtering this paper proposes a new fast recursive total least squares n rtls algorithm to recursively compute the tls solution for adaptive finite impulse response fir filtering the n rtls algorithm is based on the minimization of the constrained rayleigh quotient c rq in which the last entry of the parameter vector is constrained to the negative one as analysis results on the convergence of the proposed algorithm we study the properties of the stationary points of the c rq the high computational efficiency of the new algorithm depends on the efficient computation of the fast gain vector fgv and the adaptation of the c rq since the last entry of the parameter vector in the c rq has been fixed as the negative one a minimum point of the c rq is searched only along the input data vector and a more efficient n rtls algorithm is obtained by using the fgv as compared with davila s rtls algorithms the n rtls algorithm saves the 6m number of multiplies divides and square roots mads the global convergence of the new algorithm is studied by lasalle s invariance principle the performances of the relevant algorithms are compared via simulations and the long term numerical stability of the n rtls algorithm is verified

stochastic approximation method with gradient averaging for unconstrained problems a stochastic approximation algorithm is studied in which random gradient estimates are averaged by an auxiliary filter convergence of the algorithm is proved under a rather general noise condition a practical version of the method is described and numerical results are given

factorized all pass based iir adaptive notch filters this paper introduces a new family of infinite impulse response adaptive notch filters that forms multiple notches using a second order factorization of an all pass transfer function the new orthogonal realization is amenable for adaptive filtering to obtain the unknown frequencies of interest two new adaptive filtering algorithms are presented that can achieve fast convergence at low computational cost local convergence analysis for the new algorithms is performed and a detailed discussion of their properties is provided the new all pass based notch realization introduces a different compromise between bias and signal to noise ratio snr when compared with realizations previously reported in the literature specifically it achieves lower bias than other approaches at low snr this property is particularly attractive for the estimation and tracking of multiple sinusoids furthermore the bias can be made arbitrarily small or can be accurately estimated and compensated for extensive computer simulations are provided to illustrate the performance of the proposed adaptive notch filters in terms of bias speed of convergence and tracking capability

tracking characteristics of the constrained iir adaptive notch filter the tracking behavior of a constrained iir notch filter the coefficients of which are estimated using a constant step size gauss newton algorithm is studied using weak convergence theory and the concept of prescaling it is shown that the mean behavior of the adaptive filter coefficients can be studied by using an ordinary differential equation ode approximate and simple closed form results are derived for the tracking behavior of a second order notch filter computer simulations are presented to substantiate the analysis

a parametric classification rule based on the exponentially embedded family in this paper we extend the exponentially embedded family eef a new approach to model order estimation and probability density function construction originally proposed by kay in 2005 to multivariate pattern recognition specifically a parametric classifier rule based on the eef is developed in which we construct a distribution for each class based on a reference distribution the proposed method can address different types of classification problems in either a data driven manner or a model driven manner in this paper we demonstrate its effectiveness with examples of synthetic data classification and real life data classification in a data driven manner and the example of power quality disturbance classification in a model driven manner to evaluate the classification performance of our approach the monte carlo method is used in our experiments the promising experimental results indicate many potential applications of the proposed method

analysis and performance evaluation of an adaptive notch filter an adaptive notch filter is derived by using a general prediction error framework the proposed infinite impulse response filler has a special structure that guarantees the desired transfer characteristics the filter coefficients are updated by a version of the recursive maximum likelihood algorithm the convergence properties of the algorithm and its asymptotic behavior are discussed and its performance is evaluated by simulation results

gradient based adaptive iir notch filtering for frequency estimation the use of gradient based algorithms with infinite impulse response iir notch filtering for estimating sinusoids imbedded in noise is investigated two notch filter model structures are presented the first is for applications where two signal sources with correlated noise components can be assessed the second can be used in situations where only one composite signal source is available error surface analysis indicates that second order modules are unimodal and result in guaranteed convergence higher order modules are multimodal and require judicious choice of initial parameter estimates simulation results are included to demonstrate the performance characteristics of both filter structures

a globally convergent frequency estimator online estimation of the frequency of a sinusoidal signal is a classical problem in systems theory that has many practical applications in this paper the authors provide a solution to the problem of ensuring a globally convergent estimation more specifically they propose a new adaptive notch filter whose dynamic equations exhibit the following remarkable features 1 all signals are globally bounded and the estimated frequency is asymptotically correct for all initial conditions and all frequency values 2 the authors obtain a simple tuning procedure for the estimator design parameters which trades off the adaptation tracking capabilities with noise sensitivity ensuring exponential stability of the desired orbit and 3 transient performance is considerably enhanced even for small or large frequencies as witnessed by extensive simulations to reveal some of the stability instability mechanisms of the existing algorithms and motivate our modifications the authors make appeal to a novel nonlinear state dependent time scaling the main advantage of working in the new time scale is that they remove the coupling between the parameter update law and the filter itself decomposing the system into a feedback form where the required modifications to ensure stability become apparent even though they limit their attention here to the simplest case of a single constant frequency without noise the algorithm is able to track time varying frequencies preserve local stability in the presence of multiple sinusoids and is robust with respect to noise

asymptotic geometry of multiple hypothesis testing we present a simple geometrical interpretation for the solution to the multiple hypothesis testing problem in the asymptotic limit under this interpretation the optimal decision rule is a nearest neighbor classifier on the probability simplex

constrained epsilon minimax test for simultaneous detection and classification a constrained epsilon minimax test is proposed to detect and classify nonorthogonal vectors in gaussian noise with a general covariance matrix and in presence of linear interferences this test is epsilon minimax in the sense that it has a small loss of optimality with respect to the purely theoretical and incalculable constrained minimax test which minimizes the maximum classification error probability subject to a constraint on the false alarm probability this loss is even more negligible as the signal to noise ratio is large furthermore it is also an epsilon equalizer test since its classification error probabilities are equalized up to a negligible difference when the signal to noise ratio is sufficiently large an asymptotically equivalent test with a very simple form is proposed this equivalent test coincides with the generalized likelihood ratio test when the vectors to classify are strongly separated in term of euclidean distance numerical experiments on active user identification in a multiuser system confirm the theoretical findings

the isolation of undistorted sinusoids in real time a single input multiple output adaptive filter that takes a multisinusoidal input signal and produces the individual sinusoids at each of the outputs is described the individual outputs have identical amplitudes and phases to the components of the original input signal the filter can be adapted in real time using approximate gauss newton updates without requiring any matrix operations or divisions the filter is an extension of a cascade adaptive iir infinite impulse response notch filter reported previously the filter is very amenable to being realized using custom ics or dsp digital signal processing ics as no divisions are required and most of the filter is composed of identical biquads which are very insensitive to the errors caused by finite accuracy in fixed point implementations the structure is especially good at isolating small amplitude sinusoids when in the proximity of much larger sinusoids of unknown frequencies

adaptive stochastic filters with no strict positive real condition a new adaptive stochastic filter structure is introduced which avoids the strict passivity test used as a sufficient condition for convergence required by existing adaptive schemes the proposed algorithm consists of three stages in the first stage an autoregressive model is fitted and the residue obtained is used as an estimate of the noise in the second stage an autoregressive recursive moving average model is fitted using the residual of the first stage a modified residual is then filtered using a parameter and the model obtained from the second stage to generate an improved estimate of the noise in the third stage this improved estimate of the noise is used to obtain a better autoregressive moving average model it is shown that the proposed algorithm will also reduce the bias in the estimated parameters the simulation results given show that the proposed filter compares favorably to the algorithm introduced by mayne and clark and also landau this filter is then applied to the adaptive line enhancement sinusoidal detection and adaptive spectral estimation problems to illustrate its usefulness

an adaptive notch filter with improved tracking properties an analysis of the properties of an adaptive notch filter anf applied to time varying frequency tracking is presented starting from the derivation of an expression for anf output power asymptotically optimal values for the pole contraction and forgetting factors are derived for recursive prediction error rpe type anf algorithms based on the obtained results a new anf algorithm that includes adaptation of both pole contraction and forgetting factors is proposed the given experimental results confirm the theoretical conclusions and show that the proposed algorithm is highly efficient in practice

a recursive maximum likelihood algorithm for arma spectral estimation a spectral estimation technique is presented for autoregressive moving average arma processes the technique is based on a parameter estimation technique known as the rec ursive maximum likelihood rml method the recursive spectral estimation algorithm is presented and its asymptotic properties are discussed simulation results are presented to illustrate the performance of the estimator for various types of data

single section least squares adaptive notch filter a true least squares single section adaptive notch filter is presented internal variables of the algorithm are analyzed theoretically an approximate iterative algorithm is derived from the exact method

a constrained optimization algorithm for total energy minimization in electronic structure calculations a new direct constrained optimization algorithm for minimizing the kohn sham ks total energy functional is presented in this paper the key ingredients of this algorithm involve projecting the total energy functional into a sequence of subspaces of small dimensions and seeking the minimizer of total energy functional within each subspace the minimizer of a subspace energy functional not only provides a search direction along which the ks total energy functional decreases but also gives an optimal step length to move along this search direction numerical examples are provided to demonstrate that this new direct constrained optimization algorithm can be more efficient than the self consistent field scf iteration

on nonparametric identification of wiener systems in this paper a new method for the identification of the wiener nonlinear system is proposed the system being a cascade connection of a linear dynamic subsystem and a nonlinear memoryless element is identified by a two step semiparametric approach the impulse response function of the linear part is identified via the nonlinear least squares approach with the system nonlinearity estimated by a pilot nonparametric kernel regression estimate the obtained estimate of the linear part is then used to form a nonparametric kernel estimate of the nonlinear element of the wiener system the proposed method permits recovery of a wide class of nonlinearities which need not be invertible as a result the proposed algorithm is computationally very efficient since it does not require a numerical procedure to calculate the inverse of the estimate furthermore our approach allows non gaussian input signals and the presence of additive measurement noise however only linear systems with a finite memory are admissible the conditions for the convergence of the proposed estimates are given computer simulations are included to verify the basic theory

direction finding in the presence of colored noise by candidate identification a method is developed for identifying correct angles of arrivals from a set of candidate angles that contains spurious angles and the true ones under the assumption that the colored noise is an autoregressive process and that a uniform linear array of sensors is used the procedure is based on a relation derived for the higher order reflection coefficients corresponding to the autocorrelation sequence of the signal plus noise it is shown that the higher order reflection coefficients of a set of plane waves impinging on a uniform linear array of sensors in the presence of an unknown spatially autoregressive colored noise process are equal to an order independent linear combination of the values of the fourier transform of the corresponding optimal linear least squares normalized prediction error filter at the electric phase angles of the plane waves the magnitudes of the coefficients are then used to decide whether a given candidate direction of arrival corresponds to an actual plane wave or not the estimation of candidate angles is also briefly discussed

iterative filtering for multiple frequency estimation it is well known that prony s least squares estimator gives inconsistent estimates for multiple frequency estimation in a recent attempt to diminish this problem dragosevic and stankovic 1989 couple the least squares method of autoregressive ar estimation with an iterative filtering scheme discussed by kay 1988 using an all pole filter but the inconsistency still persists this paper attacks the chronic inconsistency with a general approach of parametric filtering that unifies and extends the previous work it is shown that the inconsistency can be eliminated with an appropriately parametrized filter the clue for the correct parametrization comes from a formula for the bias of the least squares ar estimator the fact of the matter is that as long as a filter satisfies the parametrization requirement consistent estimates can be obtained from the least squares ar estimator on the basis of the filtered data in particular the all pole filter considered by dragosevic and stankovic can be easily reparametrized so that it too satisfies the parametrization requirement and thus leads to a consistent estimator experimental results show that the modified method has a higher resolution than the discrete fourier transform and that its overall performance is quite remarkable

a stable and efficient adaptive notch filter for direct frequency estimation we investigate the problem of direct frequency estimation a new adaptive algorithm is developed for constrained pole zero notch filters the basic characteristic of this algorithm is that the notch filter is cascaded and hence purely parametrized by the notching frequencies this makes the algorithm much simpler and hence more efficient and more robust such that the poles and zeros are automatically located on the respective constrained circle no matter if the algorithm is implemented with infinite or finite precision the algorithm is analyzed and compared with some existing algorithms several numerical examples are given as well as the corresponding simulations

a structural view of stability in adaptive iir filters this correspondence deals with the stability issue in adaptive iir filters from a structural view a new condition under which the bounded input bounded output bibo stability of the filters can be ensured is derived based on this result a normal state space realization for second order iir filters is proposed it is shown that the adaptive iir filter realized with such a structure is bibo stable no matter it is implemented with infinite or finite precision this property is very important for real time applications though both the proposed and the normalized lattice based structures are bibo stable the former is simpler and has minimal pole sensitivities two adaptive iir filter structures are developed based on a cascade form of second order filters the first structure is fit for the filters whose poles are all complex and the second one is for the constrained notch filters simulations are given to demonstrate the performance of the proposed structures

on the asymptotics of m hypothesis bayesian detection in two hypothesis detection problems with i i d observations the minimum error probability decays exponentially with the amount of data with the constant in the exponent equal to the chernoff distance between the probability distributions characterizing the hypotheses we extend this result to the general m hypothesis bayesian detection problem where zero cost is assigned to correct decisions and find that the bayesian cost function s exponential decay constant equals the minimum chernoff distance among all distinct pairs of hypothesized probability distributions

maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements the problem of estimating the frequencies phases and amplitudes of sinusoidal signals is considered a simplified maximum likelihood gauss newton algorithm which provides asymptotically efficient estimates of these parameters is proposed initial estimates for this algorithm are obtained by a variation of the overdetermined yule walker method and periodogram based procedure use of the maximum likelihood gauss newton algorithm is not however limited to this particular initialization method some other possibilities to get suitable initial estimates are briefly discussed an analytical and numerical study of the shape of the likelihood function associated with the sinusoids in noise process reveals its multimodal structure and clearly sets the importance of the initialization procedure some numerical examples are presented to illustrate the performance of the proposed estimation procedure comparison to the performance corresponding to the cramer rao lower bound is also presented using a simple expression for the asymptotic cramer rao bound covariance matrix derived in the paper

stationary points of the recursive generalized least squares algorithm for adaptive notch filtering possible convergence points of the generalized least squares adaptive notch filtering algorithm are analytically derived for the multiple sinusoid case showing explicitly the dependence of the asymptotic bias on the pole contraction factor signal to noise ratio and the true model parameters the results for symmetric and nonsymmetric parameterization are compared

unbiased estimation of a sinusoid in colored noise via adapted notch filters standard notch models for the estimation of a sinusoid in noise are characterized by two poles on the unit circle and two zeros aligned with the poles these models provide biased estimates of the unknown frequency the bias increasing with the zero pole distance on the other hand keeping the zeros far from the poles has the beneficial effect of making the identification algorithm less sensitive to the adopted initialization in this paper we remove the pole zero alignment constraint the extra degree of freedom thus obtained is used to alleviate the traditional trade off between unbiasedness of the estimates and robustness against poor initializations the proposed technique applies to the case of both white and colored additive noise

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

funnel filters a new class of filters for frequency estimation of harmonic signals second order notch filters are commonly used for frequency estimation purposes they are characterized by a single design parameter the value of which is selected so as to achieve a suitable compromise between tracking performance and bias variance errors in this paper a new class of filters of fourth order is presented the funnel shaped filters or funnel filters for short these filters enables one to estimate harmonic signals with enhanced tracking capability without any deterioration of the steady state performance

adaptive notch filtering for the retrieval of sinusoids in noise in this paper an adaptive notch filter is developed employing a frequency domain and time domain analysis for the enhancement and tracking of sinusoids in additive noise colored or white the notch filter is implemented as a constrained infinite impulse response filter with the constraint enforced by a single parameter termed the debiasing parameter the resulting notch filter requires few parameters facilitates the formation of the desired band rejection filter response and also leads to various useful implementations cascade parallel for the adaptation of the filter coefficients the stochastic gauss newton algorithm is used the convergence of this updating procedure is established by studying the associated differential equation also it is shown that the structure present in the problem enables truncation of the gradient thereby reducing the complexity of adapting the filter coefficients simulation results are presented to substantiate the analysis and to demonstrate the potential of the notch filtering technique

minimizing the kohn sham total energy for periodic systems abstract we describe how a previously developed constrained minimization algorithm can be adapted to minimize the total energy of a periodic atomistic system under the kohn sham density functional theory framework the algorithm uses the bloch theorem to reduce the complexity of the calculation by working with a number of unit cells separately we present the bloch theorem in terms of linear algebra and point out its implication on the spectral property of the kohn sham hamiltonian

least squares yule walker and overdetermined yule walker estimation of ar parameters a monte carlo analysis of finite sample properties a monte carlo analysis of the accuracy properties of least squares ls yule walker yw and overdetermined yule walker oyw methods for estimating the parameters of autoregressive ar processes is presented comparisons of the estimated finite sample accuracy to the theoretical asymptotic accuracy are included it is shown that considerable differences may occur in some cases choice of the number of equations in the yw system of equations is discussed some remarks concerning the feasiblity and usefulness of an analytical study of the finite sample accuracy properties are also included

the extended kalman filter as a pulmonary blood flow estimator pulmonary blood flow is represented as a time varying parameter in a simple model of the bodily uptake of gases that are soluble in blood the pulmonary blood flow is estimated on line using ljung s modification of the extended kalman filter the experimental technique for estimation of pulmonary blood flow is based on zwart s soluble gas method modified to permit time varying ventilation and pulmonary perfusion and also to permit binary dynamic forcing of the inhaled soluble gas computer simulations were performed to determine the convergence time and to choose values of algorithmic parameters experiments done in humans gave agreement to within the accuracy of that measured invasively by a thermal dilution technique the method shows promise for use in many biomedical applications including patient monitoring physiological experimentation and clinical heart function tests

recursive identification algorithms for right matrix fraction description models multivariable identification algorithms are usually designed only for left matrix fraction description lmfd models in this paper we consider recursive identification algorithms for right matrix fraction description rmfd models with diagonal denominator matrices the algorithms are of prediction error pe and model reference mr type results from simulations illustrate the performance of the algorithms

chernoff information between gaussian trees abstract in this paper we deal with gaussian graphical classifiaction problem we aim to provide a systematic study of the relationship between chernoff information and topological as well as algebraic properties of the corresponding gaussian graphs for the underlying graphical testing problems we first show the relationship between chernoff information and generalized eigenvalues of the associated covariance matrices it is then proved that chernoff information between two gaussian trees sharing certain local subtree structures can be transformed into that of two smaller trees in this way we provide a sequence of equivalent gaussian tree pairs in terms of chernoff information under our proposed grafting operations bottleneck gaussian trees namely gaussian trees connected by one such operation can thus be simplified into two 3 node gaussian trees thereafter we provide a thorough study about how chernoff information changes when small differences are accumulated into bigger ones via concatenated grafting operations as well as partial ordering in the end we propose an optimal linear dimension reduction method based on generalized eigenvalues for the purpose of classification which is proved to achieve maximum chernoff information among all linear transformations

adaptive algorithms for joint time delay estimation and iir filtering a new class of gradient based algorithms for joint adaptive time delay estimation and iir filtering for the recursive identification of systems with long pure delays is introduced the algorithms update an adaptive delay estimate and the coefficients of an iir filter using familiar gradient descent methods in addition interpolation of the input sequence is used to obtain delays that are not constrained to integer numbers of samples three algorithms using a direct form filter parametrization and one using a normalized lattice filter are derived and computer simulations are used to demonstrate their convergence and tracking properties

paper adaptive control based on explicit criterion minimization a common approach to regulator design is to define an objective function which is minimized with respect to adjustable regulator parameters here we discuss how such objective functions can be minimized on line thus providing adaptive control such an approach to adaptive control has its roots in early contributions to learning systems and it is here further developed and discussed in the light of the recent development of the field a general algorithm is given and special attention is paid to minimization of quadratic criteria a key problem is to obtain information about the system dynamics in order to compute the derivatives of the criterion with respect to the regulator parameters it is shown that the self tuning regulator is obtained as a special case corresponding to a particular quadratic criterion and a particular way of estimating the system dynamics explicit ways using instrumental variables techniques based on extra injected noise are also discussed a specific feature of the algorithm is that it does not utilize specific knowledge about how to calculate the optimal regulator the algorithm is the same for minimum phase as well as for non minimum phase systems

stability bounds and steady state coefficient variance for a second order adaptive iir notch filter in this correspondence we present a stochastic convergence analysis of a second order adaptive iir notch filter the approach is based on a linearization of the gradient in the vicinity of the optimal solution expressions for stability bounds on the algorithm step size and the steady state coefficient variance are derived these closed form analytical results are verified by computer simulations for different signal and noise conditions

multiple fully adaptive notch filter design based on allpass sections we develop a canonical adaptive cascade structure iir notch filter to detect and track multiple time varying frequencies in additive white gaussian noise the algorithm uses allpass frequency transformation filters and a truncated gradient simulations indicate that our algorithm is computationally simple converges rapidly and has good frequency resolution

an improved lattice based adaptive iir notch filter a novel lattice based adaptive infinite impulse response iir notch filter is developed which features independent tuning of the notch frequency and attenuation bandwidth the internal structure is based on planar rotators ensuring reliable numerical behaviour and high processing rates in cordic environments a simple update law allows a simpler implementation than previously proposed designs rather than minimizing an output error cost function the algorithm is designed to achieve a stable associated differential equation resulting in a globally convergent unbiased frequency estimator in the single sinusoid case independent of the notch filter bandwidth using a second order structure in the multiple sinusoid case unbiased estimation of one of the input frequencies is achieved by thinning the notch bandwidth the tracking behavior is superior to conventional output error designs and the estimation of extremal frequencies is less prone to overflow instability than previously reported structures

recursive parameter estimation for noisy autoregressive signals corresp the problem of recursively estimating the unknown parameters of a scalar autoregressive ar signal observed in additive white noise including signal power and noise variance is considered a state space model in a canonical but noninnovations form is used to represent the noisy ar signal an algorithm based on a system identification parameter estimation technique known as the recursive prediction error method is presented for recursive parameter estimation two simulation examples illustrate the effectiveness of the proposed algorithm

adaptive comb filtering for harmonic signal enhancement a new algorithm is presented for adaptive comb filtering and parametric spectral estimation of harmonic signals with additive white noise the algorithm is composed of two cascaded parts the first estimates the fundamental frequency and enhances the harmonic component in the input and the second estimates the harmonic amplitudes and phases performance analysis provides new results for the asymptotic cramer rao bound crb on the parameters of harmonic signals with additive white noise results of simulations indicate that the variances of the estimates are of the same order of magnitude as the crb for sufficiently large data sets and illustrate the performance in enhancing noisy artificial periodic signals

two discrete oscillator based adaptive notch filters osc anfs for noisy sinusoids we propose two adaptive notch filters anfs for sinusoids embedded in a noisy environment both of the anfs as usual are structurally composed of a time variant infinite impulse response iir filter that serves as a line enhancer and an adaptive mechanism that serves as a frequency estimator the novelty of anfs is that the derivations of the coefficient updating algorithms for the adaptive mechanisms are both inspired by a discrete oscillator model and moreover are both independent of the structures of the line enhancement filters chosen a second order iir bandpass filter is selected to serve the line enhancement portions for both of the two anfs analyses and computer simulations show that the performances of the proposed anfs are very promising

a trust region direct constrained minimization algorithm for the kohn sham equation the self consistent field scf iteration widely used for computing the ground state energy and the corresponding single particle wave functions associated with a many electron atomistic system is viewed in this paper as an optimization procedure that minimizes the kohn sham ks total energy indirectly by minimizing a sequence of quadratic surrogate functions we point out the similarity and difference between the total energy and the surrogate and show how the scf iteration can fail when the minimizer of the surrogate produces an increase in the ks total energy a trust region technique is introduced as a way to restrict the update of the wave functions within a small neighborhood of an approximate solution at which the gradient of the total energy agrees with that of the surrogate the use of trust regions in scf is not new however it has been observed that directly applying a trust region based scf trscf to the ks total energy often leads to slow convergence we propose to use trscf within a direct constrained minimization dcm algorithm we developed in j comput phys 217 2006 pp 709 721 the key ingredients of the dcm algorithm involve projecting the total energy function into a sequence of subspaces of small dimensions and seeking the minimizer of the total energy function within each subspace the minimizer of a subspace energy function which is computed by the trscf not only provides a search direction along which the ks total energy function decreases but also gives an optimal step length that yields a sufficient decrease in total energy a numerical example is provided to demonstrate that the combination of trscf and dcm is more efficient than scf

tracking analysis of an adaptive notch filter with constrained poles and zeros this paper analyzes the asymptotic tracking properties of an adaptive notch filter anf with pole zero constraints for the cancellation or retrieval of multiple time varying sine waves in additive noise the asymptotic mean square error mse is analyzed using the methods of ljung and gunnarsson 1990 when the variations in the underlying frequencies are assumed to be sufficiently small closed form expressions for the mse are derived as functions of the tuning variables of the algorithm the results give insight into the operational properties of the algorithm and are used in order to minimize the mse with respect to the tuning variables computer simulations confirm the validity of the derived results