arma modeling of time series a method for efficiently generating a rational model of a wide sense stationary time series is presented in this method the autoregressive parameters associated with an arma model consisting of q zeros and p poles are optimally chosen with the selection being based on a finite set of time series observations this selection is made so that a set of yule walker equation approximations are best satisfied the resultant autoregressive parameter estimates have the desired statistical feature of being unbiased and consistent this estimation method has been found to provide a modeling performance which typically equals or exceeds that of contemporary alternatives moreover this method is amenable to a computationally efficient adaptive solution procedure the autoregressive parameters characterizing the resultant arma model estimate can serve the role of decision variables in pattern classification schemes for example these parameters can be utilized in determining whether or not a member s of a given signal class is contained within a noise corrupted measurement signal this approach has been found to be particularly effective in doppler radar and array processing applications in which one is looking for the presence of spectral lines i e sinusoids in the measurement signal

noisy fir identification as a quadratic eigenvalue problem this correspondence describes a method for identifying fir models in the presence of input and output noise the proposed algorithm takes advantage of both the bias compensation principle and the instrumental variable method it is based on a nonlinear system of equations whose unknowns are the fir coefficients and the input noise variance this system allows mapping the noisy fir identification problem into a quadratic eigenvalue problem the identification problem is thus solved without requiring the use of iterative least squares algorithms the performance of the proposed approach has been tested and compared with that of other identification methods by means of monte carlo simulations

bispectrum estimation a parametric approach higher order spectra contain information about random processes that is not contained in the ordinary power spectrum such as the degree of nonlinearity and deviations from normality estimation of the bispectrum which is a third order spectrum has been applied in various fields to obtain information regarding quadratic phase coupling among harmonic components and non gaussianness of processes existing methods of bispectrum estimation are patterned after the conventional methods of power spectrum estimation which are known to possess certain limitations the paper proposes a parametric approach to bispectrum estimation based on a non gaussian white noise driven autoregressive ar model the ar parameter estimates are obtained by solving the third order recursion equations which may be toeplitz in form but not symmetric it is shown that the method provides bispectral estimates that are far superior to the conventional estimates in terms of bispectral fidelity and that in the case of detecting phase coupling among sinusoids the method provides significantly better resolution

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

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

central limit theorem for sequential monte carlo methods and its application to bayesian inference the term sequential monte carlo methods or equivalently particle filters refers to a general class of iterative algorithms that performs monte carlo approximations of a given sequence of distributions of interest t we establish in this paper a central limit theorem for the monte carlo estimates produced by these computational methods this result holds under minimal assumptions on the distributions t and applies in a general framework which encompasses most of the sequential monte carlo methods that have been considered in the literature including the resample move algorithm of gilks and berzuini j r stat soc ser b stat methodol 63 2001 127 146 and the residual resampling scheme the corresponding asymptotic variances provide a convenient measurement of the precision of a given particle filter we study in particular in some typical examples of bayesian applications whether and at which rate these asymptotic variances diverge in time in order to assess the long term reliability of the considered algorithm

linear prediction methods for blind fractionally spaced equalization we describe adaptive methods for estimating fir zero forcing blind equalizers with arbitrary delay directly from the linear predictions of the observations while most current methods require inversion or singular value decomposition svd of the correlation matrix our methods need only to solve two linear prediction problems they can be implemented as rls or lms algorithms to recursively update the equalizer estimation they are computationally efficient the computational complexity in each recursion can be less than 15 ln sup 2 in the rls case where ln equals the equalizer length and 3l ln in the lms case where l is the number of subchannels the performance of the proposed methods and comparisons with existing approaches are shown by simulation to demonstrate their effectiveness

fast maximum likelihood for blind identification of multiple fir channels this paper develops a fast maximum likelihood method for estimating the impulse responses of multiple fir channels driven by an arbitrary unknown input the resulting method consists of two iterative steps where each step minimizes a quadratic function the two step maximum likelihood tsml method is shown to be high snr efficient i e attaining the cramer rao lower bound crb at high snr the tsml method exploits a novel orthogonal complement matrix of the generalized sylvester matrix simulations show that the tsml method significantly outperforms the cross relation cr method and the subspace ss method and attains the crb over a wide range of snr this paper also studies a fisher information fi matrix to reveal the identifiability of the m channel system a strong connection between the fi based identifiability and the cr based identifiability is established

erratum classification of lie point symmetries for quadratic lienard type equation x f x x2 g x 0 j math phys 54 053506 2013

nonlinear techniques for interference suppression in spread spectrum systems the binary nature of direct sequence signals is exploited to obtain nonlinear filters that outperform the linear filters hitherto used for this purpose the case of a gaussian interferer with known autoregressive parameters is considered using simulations it is shown that an approximate conditional mean acm filter of the masreliez type performs significantly better than the optimum linear kalman bucy filter for the case of interferers with unknown parameters the nature of the nonlinearity in the acm filter is used to obtain an adaptive filtering algorithm that is identical to the linear transversal filter except that the previous prediction errors are transformed nonlinearly before being incorporated into the linear prediction two versions of this filter are considered one in which the filter coefficients are updated using the widrow lms algorithm and another in which the coefficients are updated using an approximate gradient algorithm simulations indicate that the nonlinear filter with lms updates performs substantially better than the linear filter for both narrowband gaussian and single tone interferers whereas the gradient algorithm gives slightly better performance for gaussian interferers but is rather ineffective in suppressing a sinusoidal interferer

hosm observer for a class of non minimum phase causal nonlinear mimo systems a higher order sliding mode observer is proposed for asymptotic identification of the full state vector and the vector of unknown inputs for mimo nonlinear causal systems with unstable internal dynamics the problem is addressed via consistent application of exact higher order sliding mode differentiators in conjunction with the method of stable system center a numerical example illustrates the performance of the proposed algorithm

multilevel monte carlo path simulation we show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using monte carlo path simulations in the simplest case of a lipschitz payoff and a euler discretisation the computational cost to achieve an accuracy of o e is reduced from o e 3 to o e 2 log e 2 the analysis is supported by numerical results showing significant computational savings

blind identification of fir systems driven by markov like input signals we propose a new algorithm for the blind identification and equalization of finite impulse response fir systems using the second order statistics of the received signal the new algorithm is set in the same context as the algorithms of tong et al 1994 and moulines et al 1995 however unlike those earlier approaches it is designed to allow correlated input signals specifically the algorithm accommodates finite memory sources and sources whose autocorrelation function decays exponentially numerical simulations compare the equalization performance of the new algorithm to those of tong and moulines it is shown that our algorithm yields consistently lower bit error rates at a wide variety of signal to noise ratios and at various equalizer lengths moreover the algorithm maintains this advantage even if it has no a priori information of source correlation or if source symbols are uncorrelated

time domain approaches to quadratic phase coupling estimation bicoherence is a quantity used to estimate the contribution of second order nonlinearity to the power in bifrequencies the conventional approach to the problem uses second and third order periodograms for bicoherence estimation time domain approaches that use autocorrelation and third order cumulant samples or their estimates are developed these techniques are suitable for use in situations where high resolution approaches are required for power spectrum and bispectrum estimation

comment on classification of lie point symmetries for quadratic lienard type equation x f x x2 g x 0 j math phys 54 053506 2013 and its erratum j math phys 55 059901 2014 we demonstrate a simplification of some recent works on the classification of the lie symmetries for a quadratic equation of lienard type we observe that the problem could have been resolved more simply

a generalized least absolute deviation method for parameter estimation of autoregressive signals this paper proposes a generalized least absolute deviation glad method for parameter estimation of autoregressive ar signals under non gaussian noise environments the proposed glad method can improve the accuracy of the estimation of the conventional least absolute deviation lad method by minimizing a new cost function with parameter variables and noise error variables compared with second and high order statistical methods the proposed glad method can obtain robustly an optimal ar parameter estimation without requiring the measurement noise to be gaussian moreover the proposed glad method can be implemented by a cooperative neural network nn which is shown to converge globally to the optimal ar parameter estimation within a finite time simulation results show that the proposed glad method can obtain more accurate estimates than several well known estimation methods in the presence of different noise distributions

instrumental variable methods for arma spectral estimation the modified yule walker technique of arma spectral estimation is shown to be a special case of the instrumental variable method of system identification several recursive instrumental variable algorithms are proposed for adaptive spectral estimation including a new algorithm for the overdetermined case an efficient lattice algorithm is presented for solving the modified yule walker equations given the sample correlation coefficients the performance of some of the algorithms is illustrated by simulation results

deconvolution and estimation of transfer function phase and coefficients for nongaussian linear processes nongaussian linear processes are considered it is shown that the phase of the transfer function can be estimated under broad conditions this is not true of gaussian linear processes and in this sense gaussian linear processes are atypical the asymptotic behavior of a phase estimate is determined the phase estimates make use of bispectral estimates these ideas are applied to a problem of deconvolution which is effective even when the transfer function is not minimum phase a number of computational illustrations are given

a seamless multilevel ensemble transform particle filter this paper presents a seamless algorithm for the application of the multilevel monte carlo mlmc method to the ensemble transform particle filter the algorithm uses a combination of optimal coupling transformations between coarse and fine ensembles in difference estimators within a multilevel framework to minimize estimator variance it differs from that of gregory cotter and reich siam j sci comput 38 2016 pp a1317 a1338 in that strong coupling between the coarse and fine ensembles is seamlessly maintained during all stages of the assimilation algorithm instead of using independent transformations to equal weights followed by recoupling with an assignment problem this modification is found to lead to an increased rate in variance decay between coarse and fine ensembles with level in the hierarchy a key component of mlmc this offers the potential for greater computational cost reductions this is shown alongside evidence of asymptotic consistency in numerical examples

a karhunen loeve like expansion for 1 f processes via wavelets while so called 1 f or scaling processes emerge regularly in modeling a wide range of natural phenomena as yet no entirely satisfactory framework has been described for the analysis of such processes orthonormal wavelet bases are used to provide a new construction for nearly 1 f processes from a set of uncorrelated random variables

a finite step global convergence algorithm for the parameter estimation of multichannel ma processes an iterative algorithm for the identification of multichannel moving average ma processes using higher order statistics is proposed it is shown that the algorithm has a finite step global convergence property three multichannel ma models including one nonminimum phase ma model are estimated by this algorithm with satisfactory performances

identification of non minimum phase linear stochastic systems abstract the identification of time invariant non minimum phase stochastic systems driven by non gaussian white noise is considered given only the noisy observations of the system output a two step procedure is proposed in the first step a spectrally equivalent system is estimated using a standard technique that exploits only the second order statistics of the measurements in the second step a partial set of 4th order cumulants of the measurements is exploited to resolve the location of the system zeros knowledge of the probability distribution of the driving noise is not required strong consistency of the proposed estimator is proved under certain sufficient conditions simulation results are also presented in support of the theory

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

computationally lag invariant recursive spectrum estimators this paper is concerned with fourier based nonparametric spectral estimation methods for time varying environments it presents a class of interactive spectrum estimators in which the number of computations required to update the estimate at every data sample is independent of the number of the autocorrelation lags employed to produce this estimate these estimators are termed lag invariant and form an important class due to their computational simplicity because of the lag invariant property resolution enhancement is achieved without additional cost in computations per frequency sample the proposed class of recursive spectral estimators is based on specific selection of the lagged product windows used in the autocorrelation function estimation in this paper the conditions necessary to produce the lag invariance property are delineated

on tracking characteristics of weighted least squares estimators applied to nonstationary system identification the parameter tracking abilities of weighted least squares wls estimators are characterized in terms of a suitably defined variability matrix and associated frequency characteristics using these concepts the conflict arising between the estimation variance and estimation bandwidth is easily explained and quantified

improved methods for the blind system identification using higher order statistics it is demonstrated by a detailed analysis of blind system identification that under specific system configurations a recently published least squares algorithm shows a poor convergence behavior especially if the system order is overdetermined to overcome these problems a supplementary condition is introduced that guarantees proper convergence in most cases an alternative approach for the blind identification of mixed phase systems the so called cumulant zero matching method is presented in this approach the solution of a set of nonlinear equations which is necessary in the least squares method is replaced by the calculation of zeros of polynomials the main advantage over the least squares solution is that overdetermination of the system order is rather harmless since it only results in additional zeros in the origin of the z plane the different methods for system identification presented are illustrated by simulation results

order reduction of siso nonminimum phase stochastic systems we consider the order reduction problem for single input single output nonminimum phase linear stochastic systems the problem is formulated as that of approximating the original system output process by another stochastic process generated via a reduced order model it is shown that in order to obtain a correct phase approximation it is necessary to consider some higher order statistics of the original process in addition to the usual second order statistics a computationally feasible approximation criterion is proposed and analyzed an example is also presented to illustrate the proposed method

a nonparametric ensemble transform method for bayesian inference many applications such as intermittent data assimilation lead to a recursive application of bayesian inference within a monte carlo context popular data assimilation algorithms include sequential monte carlo methods and ensemble kalman filters enkfs these methods differ in the way bayesian inference is implemented sequential monte carlo methods rely on importance sampling combined with a resampling step while enkfs utilize a linear transformation of monte carlo samples based on the classic kalman filter while enkfs have proven to be quite robust even for small ensemble sizes they are not consistent since their derivation relies on a linear regression ansatz in this paper we propose another transform method which does not rely on any a priori assumptions on the underlying prior and posterior distributions the new method is based on solving an optimal transportation problem for discrete random variables

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

on the noise compensated yule walker equations recently a method of estimating the parameters of an ar p random process based on measurements corrupted by additive white noise was described the method involves solving a matrix pencil called the noise compensated yule walker ncyw equations for the ar parameters and the variance of the measurement noise we give a necessary and sufficient condition for there to exist a unique solution to the ncyw equations

novel parameter estimation of autoregressive signals in the presence of noise this paper proposes a new method for estimating the parameters of an autoregressive ar signal from observations corrupted by white noise the feature of the new method is that the observation noise variance estimate is converted into the only solution of a nonlinear equation to yield unbiased estimate of the ar parameters moreover a convergent newton iterative algorithm with a deterministic initial point is presented for efficient implementation of the proposed new estimation method as a result the proposed new method can minimize the error of estimating the variance of the observation noise since more accurate estimates of this observation noise variance can be attained at earlier stages the proposed method can achieve a good performance in estimating the ar signal parameters numerical results demonstrate that the proposed new algorithm is more effective in terms of accuracy and robustness against noise than conventional algorithms

estimation of all pole model parameters from noise corrupted sequences least squares estimates of the parameters of all pole signal models are biased when applied to noise corrupted all pole sequences this bias has been shown to be proportional to the inverse of the signal to noise ratio an autocorrelation like procedure is shown to increase under some circumstances the signal to noise ratio while retaining the pole locations when the noise is white the signal to noise ratio improvement varies for each mode in the all pole sequence with modes corresponding to pole locations close to the unit circle showing the most improvement a signal to noise ratio cutoff exists for each mode below which no improvement can be obtained this cutoff depends on the proximity of the pole location to the unit circle approaching zero as the pole nears the origin this cutoff corresponds to the point at which a mode s spectral value just equals the level of the noise floor this procedure can be applied recursively until an acceptable signal to noise ratio is obtained the all pole parameters can then be estimated from the processed sequence using least squares estimation

comment on classification of lie point symmetries for quadratic lienard type equation ẍ f x ẋ2 g x 0 j math phys 54 053506 2013

an iterative algorithm for signal reconstruction from bispectrum the author presents a procedure to reconstruct a minimum or nonminimum phase discrete time signal from its bispectrum the algorithm is iterative and based on using the method of projections onto convex sets pocs in an inner product space in which the vector space consists of real sequences and vector addition is defined in terms of the convolution operation prior information such as an energy bound on the signal can be incorporated into this algorithm an algorithm that employs energy information was found to produce better results in simulation than one that ignores energy constraints

parameter estimation of exponentially damped sinusoids using a higher order correlation based approach a very common problem in signal processing is parameter estimation of exponentially damped sinusoids from a finite subset of noisy observations when the signal is contaminated with colored noise of unknown power spectral density a cumulant based approach provides an appropriate solution to this problem we propose a new class of estimator namely a covariance type estimator which reduces the deterministic errors associated with imperfect estimation of higher order correlations from finite data length this estimator allows a higher order correlation sequence to be modeled as a damped exponential model in certain slices of the moments plane this result shows a useful link with well known linear prediction based methods such as the minimum norm principal eigenvector method of kumaresan and tufts 1982 which can be subsequently applied to extracting frequencies and damping coefficients from the 1 d correlation sequence this paper discusses the slices allowed in the moments plane the uses and limitations of this estimator using multiple realizations and a single record in a noisy environment monte carlo simulations applied to standard examples are also performed and the results are compared with the kt method and the standard biased estimator based approach the comparison shows the effectiveness of the proposed estimator in terms of bias and mean square error when the signals are contaminated with additive gaussian noise and a single data record with short data length is available

3 d ar model order selection via rank test procedure this paper deals with the problem of three dimensional autoregressive 3 d ar model order estimation we show that the information for the 3 d ar model order is implicitly contained in an appropriate matrix rank built from the autocorrelation function acf of the underlying 3 d gaussian process exploiting this property we develop an algorithm to estimate the order p1 p2 p3 corresponding to the quarter space qs region of support the proposed method is based upon a rank test procedure rtp using singular value decomposition svd and solving nonlinear system equations numerical simulations are presented to illustrate the performances of the proposed algorithm

arma systems excited by non gaussian processes are not always identifiable it is a popular myth that the zeros of an arma autoregressive moving average process excited by an unobservable non gaussian process can be resolved from noisy output measurements a counterexample is given

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

recursive autoregressive spectral estimation by minimization of the free energy a digital signal processing technique applicable to power spectrum estimation designated as the minimum free energy method is described with no a priori model assumption and no attempt to extract special features such as sinusoids one can obtain high resolution even with high noise contamination of the measured signal the technique is demonstrated by modification of the burg recursive method of spectral analysis a recursive minimum free energy method in which the reflection coefficient is chosen at each step is proposed for minimizing the free energy the burg energy measure minus the product of a temperature and an information entropy the method produces a spectral estimator more impervious to high noise contamination than the burg method and diminishes the burg tendency to produce spurious peaks

performance analysis of estimation algorithms of nonstationary arma processes the correlation analysis based methods are not suitable for identifying parameters of nonstationary autoregressive ar moving average ma and arma systems by using estimation residuals in place of unmeasurable noise terms in information vector or matrix we develop a least squares based and gradient based algorithms and establish the consistency of the proposed algorithms without assuming noise stationarity ergodicity or existence of higher order moments furthermore we derive the conditions for convergence of the parameter estimation the simulation results validate the convergence theorems proposed

blind identification of linear subsystems of lti zmnl lti models with cyclostationary inputs discrete time nonlinear models consisting of two linear time invariant lti filters separated by a finite order zero memory nonlinearity zmnl of the polynomial type the lti zmnl lti model are appropriate in a large number of practical applications we discuss some approaches to the problem of blind identification of such nonlinear models it is shown that for an nth order nonlinearity the possibly non minimum phase finite memory linear subsystems of lti zmnl and lti zmnl lti models can be identified using the n 1th order cyclic statistics of the output sequence alone provided the input is cyclostationary and satisfies certain conditions the coefficients of the zmnl are not needed for identification of the linear subsystems and are not estimated it is shown that the theory presented leads to analytically simple identification algorithms that possess several noise and interference suppression characteristics

covariance sequence approximation for parametric spectrum modeling parametric methods of spectrum analysis are founded on finite dimensional models for covariance sequences rational spectrum approximants for continuous spectra are based on autoregressive ar moving average ma or autoregressive moving average arma models for covariance sequences line spectrum approximants to discrete spectra are based on cosinusoidal models for covariance sequences in this paper we make the point that a wide variety of spectrum types admit to modal analysis wherein the modes are characterized by amplitudes frequencies and damping factors the associated modal decomposition is appropriate for both continuous and discrete components of the spectrum the domain of attraction for the decomposition includes arma sequences harmonically or nonharmonically related sinusoids damped sinusoids white noise and linear combinations of these the parametric spectrum analysis problem now becomes one of identifying mode parameters this we achieve by solving two modified least squares problems numerical results are presented to illustrate the identification of mode parameters and corresponding spectra from finite records of perfect and estimated covariance sequences the results for sinusoids and sinusoids in white noise are interpreted in terms of in phase and quadrature effects attributable to the finite record length

closed form recursive estimation of ma coefficients using autocorrelations and third order cumulants the authors derive a simple recursive closed form algorithm for estimating the parameters of a moving average ma model of known order using only the autocorrelation and the 1 d diagonal slice of the third order cumulant of its response to excitation by an unobservable non gaussian iid process the output may be corrupted by zero mean nonskewed white noise of unknown variance the autoregressive moving average arma case is briefly discussed

information tradeoffs in using the sample autocorrelation function in arma parameter estimation this paper considers bounds on the statistical efficiency of estimators of the poles and zeros of an arma process based on estimates of the process autocorrelation function acf special attention is paid to autoregressive ar and ar plus white noise processes it is seen that reducing the arma process data to a given set of consecutive lags of the popular lagged product acf estimates prior to parameter estimation increases cramer rao bounds on the generalized error covariance a parametric study of the bound deterioration for some illustrative signal and noise situations reveals some empirical strategies for choosing acf estimate lags to preserve statistical information analysis is based on the relative information index rii 2 and derivations of the large sample fisher s information matrix for the raw data and for the lagged product acf estimate of an arma process are included

statistical analysis of initialization methods for rls adaptive filters theoretical analysis is used to evaluate the mean and second moment properties of recursive least squares algorithms incorporating the fast exact initialization and soft constrained initialization methods during the initialization period it is shown that the weight vector mean and covariance produced by fast exact initialization are undefined for this period theoretical results are derived for soft constrained initialization that show that the weight vector mean and covariance are finite and expressions are given for these quantities simulations for various cases are presented to support the accuracy of these theoretical results

matrix based higher order spectral analysis for three wave coupling processes composite linear and quadratic systems produce three wave coupling when stimulated by random phase input sinusoids due to the nonlinearity of the system the output frequencies are arithmetically related to the input using third order cumulant statistics and their associated bispectrum techniques are devised based on phase insensitive matrix structures for detection and frequency estimation of coupling frequencies the separation of the third order cumulant series into symmetric and skew symmetric portions allows one to exploit their characteristic eigendecompositions for frequency estimation after symmetrization biphases can be easily extracted as coefficients of the cumulant sequence using a generalized eigenvector representation one can relate symmetric and skew symmetric bases by a subspace rotation algorithm biphases can be estimated directly from generalized eigenvalues of the matrix pencil formed by symmetric and skew symmetric matrices the dimensionality of the matrices can be reduced through the use of cumulant projections that yield a slice of the bispectrum the radon transform procedure is related to bispectral processing through an isotropic radial slice volterra filter the compact third order kronecker product matrix formulation and algorithms for coupling frequency estimation can also be converted for use in biphase estimation simulations showing the performance of the above procedures are also presented for both synthetic and biomedical time series

on the identifiability of non gaussian arma models using cumulants a fixed set of output cumulants of order greater than two guarantees unique identification of known order causal arma autoregressive moving average models which are driven by unobservable non gaussian i i d noise the models are allowed to be non minimum phase and their outputs may be corrupted by additive colored gaussian noise of unknown covariance the arma parameters can be estimated either by means of linear equations and closed form expressions or by minimizing quadratic cumulant matching criteria the latter approach requires computation of cumulants in terms of the arma parameters which is carried out in the state space using kronecker products

on estimating noncausal nonminimum phase arma models of non gaussian processes the authors address the problem of estimating the parameters of non gaussian arma autoregressive moving average processes using only the cumulants of the noisy observation the measurement noise is allowed to be colored gaussian or independent and identically non gaussian distributed the arma model is not restricted to be causal or minimum phase and may even contain all pass factors the unique parameter estimates of both the ma and ar parts are obtained by linear equations the structure of the proposed algorithm facilitates asymptotic performance evaluation of the parameter estimators and model order selection using cumulant statistics the method is computationally simple and can be viewed as the least squares solution to a quadratic model fitting of a sampled cumulant sequence identifiability issues are addressed simulations are presented to illustrate the proposed algorithm

consistent estimation of the cyclic autocorrelation the cyclic autocorrelation is often used to describe nonstationary random processes the authors investigate the conditions under which the cyclic autocorrelation can be estimated consistently in mean square for discrete time gaussian processes they extend and generalize results of hurd 1989 and refine results of boyles and gardner 1983 they derive necessary and sufficient conditions for consistency in mean square of an estimator which are in the form of a single sum of autocorrelation coefficients in the form of a double sum of autocorrelation coefficients in the bifrequency domain and in terms of the average spectrum they also discuss the rate of convergence for this estimator

singular value decomposition based ma order determination of non gaussian arma models singular value decomposition svd based moving average ma order determination of non gaussian processes using higher order statistics is addressed it is shown that the ma order determination of autoregressive moving average arma models is equivalent to the rank determination of a certain error matrix and a svd approach is proposed its simplified form is applied to pure ma models to improve the robustness of the order selection a combination of the svd and the product of diagonal entries pode test is proposed some interesting applications of the two svd approaches are presented and simulations verify their performance

a parameter estimation approach to estimation of frequencies of sinusoids it is shown that with uniform sampling a sample of the sum of m sinusoids at time nt can be uniquely expressed as a linear combination of the 2m samples at times n 1 t n 2m t the 2m coefficients of linear combination are also the coefficients of a 2m order polynomial whose roots are e pmj omega i omega i being the frequencies of the sinusoids given the samples of sinusoids plus noise a consistent estimate of the 2m coefficients are obtained by the instrumental variable method of parameter estimation it is also possible to track time varying frequencies by a recursive algorithm that exponentially weighs out the past data simulation examples of one and two sinusoids are given

performance analysis of a split path lms adaptive filter for ar modeling a split path adaptive filter is proposed for extracting the model parameters of an autoregressive process the structure is composed of two linear phase filters connected in parallel one antisymmetric and the other symmetric the two filters are adapted independently on a sample by sample basis using the least mean square lms algorithm the performance of the system in terms of convergence speed and excess mean square error is analyzed in detail and comparisons with the conventional transversal structure are made theoretical analysis and experimental results show that the model can provide a much faster rate of convergence at the expense of only a moderate increase in computation two methods for choosing control parameters for the split path adaptive filter are also suggested to improve further the convergence behavior

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

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