identification of linear stochastic systems via second and fourth order cumulant matching the identification problem for time invariant single input single output linear stochastic systems driven by non gaussian white noise is considered the system is not restricted to be minimum phase and it is allowed to contain all pass components a least squares criterion that involves matching the second and the fourth order cumulant functions of the noisy observations is proposed knowledge of the probability distribution of the driving noise is not required an order determination criterion that is a modification of the akaike information criterion is also proposed strong consistency of the proposed estimator is proved under certain sufficient conditions simulation results are presented to illustrate the method

the limiting behavior of lms a realization oriented analysis is given of the gradient noise misadjustment and lag misadjustment performance of the lms least mean square algorithm new formulas are given for both of these components of excess mean square error it is shown that the traditional formula for lag misadjustment needs to be modified by adding further terms due to gradient noise and noise variance to perform the analysis it is necessary to study the convergence with probability one of the noise free fixed parameter lms algorithm convergence is found under simple conditions that improve on those previously obtained

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

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

strongly consistent identification algorithms and noise insensitive mse criteria windowed cumulant projections of nongaussian linear processes yield autocorrelation estimators which are immune to additive gaussian noise of unknown covariance by establishing strong consistency of these estimators strongly consistent and noise insensitive recursive algorithms are developed for parameter estimation these computationally attractive schemes are shown to be optimal with respect to a modified mean square error mse criterion which implicitly exploits the high signal to noise ratio domain of cumulant statistics the novel mse objective function is expressed in terms of the noisy process but it is shown to be a scalar multiple of the standard mse criterion as if the latter was computed in the absence of noise simulations illustrate the performance of the proposed algorithms and compare them with the conventional algorithms

a unifying maximum likelihood view of cumulant and polyspectral measures for non gaussian signal classification and estimation classification and estimation of non gaussian signals observed in additive gaussian noise of unknown covariance are addressed using cumulants or polyspectra by integrating ideas from pattern recognition and model identification asymptotically optimum maximum likelihood classifiers and arma autoregressive moving average parameter estimators are derived without knowledge of the data distribution identifiability of noncausal and nonminimum phase arma models is established using a finite number of cumulant or polyspectral lags of any order greater than two a unifying view of cumulant and polyspectral discriminant measures utilizes these lags and provides a common framework for development and performance analysis of novel and existing estimation and classification algorithms tentative order determination and model validation tests for non gaussian arma processes are described briefly illustrative simulations are also presented

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

a new algorithm for the design of linear prediction error filters using cumulant based mse criteria proposes a new algorithm for the design of minimum phase linear prediction error lpe filters using two new cumulant higher order statistics based mse criteria when the given stationary random signal x n is nongaussian and contaminated by gaussian noise it is shown that the designed lpe filters based on the proposed criteria are identical to the conventional correlation second order statistics based lpe filter as if x n were noise free measurements as correlation based lpe filters coefficients of the designed cumulant based lpe filters can be obtained by solving a set of symmetric toeplitz linear equations using the well known computationally efficient levinson durbin recursion moreover the proposed two criteria are applicable for any cumulant order m spl ges 3 and one of the proposed criteria for m 3 reduces to delopoulos and giannakis 1992 third order cumulant based mse criterion some simulation results are then provided to support the analytical results

asymptotically optimal estimation of ma and arma parameters of non gaussian processes from high order moments a description is given of an asymptotically minimum variance algorithm for estimating the ma moving average and arma autoregressive moving average parameters of non gaussian processes from sample high order moments the algorithm uses the statistical properties covariances and cross covariances of the sample moments explicitly a simpler alternative algorithm that requires only linear operations is also presented the latter algorithm is asymptotically minimum variance in the class of weighted least squares algorithms

adaptive deconvolution and identification of nonminimum phase fir systems based on cumulants a novel adaptive deconvolution and system identification scheme is introduced for a linear non minimum phase finite impulse response fir system driven by non gaussian white noise the adaptive scheme is based on approximating the fir system by noncausal autoregressive ar models and using higher order cumulants of the system output as such it is a blind equalization deconvolution scheme the set of updated ar parameters is obtained by using a gradient type algorithm and by using higher order cumulants instead of time samples of the output signal it is demonstrated by means of extensive simulations that the adaptive scheme works well for both stationary and nonstationary cases as expected it outperforms the autocorrelation based gradient method for nonminimum phase system identification and deconvolution performance comparisons to existing methods are given using as figures of merit the probability of errors in the restored input sequence computational complexity and convergence rate

consistent identification of stochastic linear systems with noisy input output data abstract a novel criterion is introduced for parametric errors in variables identification of stochastic linear systems excited by non gaussian inputs the new criterion is at least theoretically insensitive to a class of input output disturbances because it implicitly involves higher than second order cumulant statistics in addition it is shown to be equivalent to the conventional mean squared error mse as if the latter was computed in the ideal case of noise free input output data the sampled version of the criterion converges to the novel mse and guarantees strongly consistent parameter estimators the asymptotic behavior of the resulting parameter estimators is analyzed and guidelines for minimum variance experiments are discussed briefly informative enough input signals and persistent of excitation conditions are specified computatonally attractive recursive least squares variants are also developed for on line implementation of arma modeling and their potential is illustrated by applying them to time delay estimation in low snr environment the performance of the proposed algorithms and comparisons with conventional methods are corroborated using simulated data

detection in correlated impulsive noise using fourth order cumulants we consider detection and estimation in correlated impulsive noise the non gaussian impulsive noise is modeled as the sum of two linear processes a nominal part and an impulsive part this model admits correlated impulsive bursts lasting many data samples identifiability of the noise model is established using fourth and second order cumulants under this model the correlated time series can be whitened and an appropriate memoryless nonlinearity applied to attenuate the impulsive events a detection statistic is then formed from the output of the nonlinearity in the threshold detection case the use of cumulants allows identification of the noise in the presence of the signal to be detected obviating the need for noise only training records simulation results with a sample size of 512 show small loss in detector performance versus an ideal detector with no impulsive part present

estimation and detection in non gaussian noise using higher order statistics one of the primary applications of higher order statistics has been for detection and estimation of nongaussian signals in gaussian noise of unknown covariance this is motivated by the fact that higher order cumulants of gaussian processes vanish we study the opposite problem namely detection and estimation in nongaussian noise we estimate cumulants of nongaussian processes in the presence of unknown deterministic and or gaussian signals which allows either parametric or nonparametric estimation of the covariance of the nongaussian noise our approach is to augment existing second order detection methods using cumulants we propose solutions for detection of deterministic signals based on matched filters and the generalized likelihood ratio test which incorporate cumulants where the resulting solutions are valid under either detection hypotheses this allows for single record detection and obviates the need for noise only training records the problem of estimating signal strength in the presence of nongaussian noise of unknown covariance is also considered and a cumulant based solution is proposed which uses a single data record examples are used throughout to illustrate our proposed methods

design of optimal scan tree based on compact test patterns for test time reduction scan tree architecture has been proposed to reduce the test application time of full scan chain by placing multiple scan cells in parallel most existing techniques rely on non compact test pattern sets to construct the scan tree however they produce inefficient scan tree when highly compact test sets with few don t cares are used in this paper the depth of the scan tree based on approximate compatibility relation for completely specified test data set is analyzed probabilistically by modeling its construction as a vertex coloring problem the upper bound of edges per vertex is computed and demonstrated to be a prime factor that limits the efficiency of scan tree construction based on both compatible and approximately compatible test data between two flip flops inverse compatibility and aggressive approximate compatibility are then proposed to increase the edges per vertex for vertex coloring the q sd connection between two adjacent scan cells is exploited to implement the inverse compatibility with no cost or timing impact to maintain the fault coverage the missing faults under the tree scan mode can be detected by switching the same base architecture into the linear scan mode with negligible hardware overhead as shown by the experimental results on iscas89 iscas99 and lgsynth93 benchmark circuits on average the scan tree generated by our method reduces the test time of the full scan chain by 56 65 percent and that of the scan tree designed by the approximate compatibility method by 39 18 percent under the same compact test sets

static test compaction for full scan circuits based on combinational test sets and nonscan input sequences and a lower bound on the number of tests a new class of static compaction procedures is described that generate test sets with reduced test application times for scan circuits the proposed class of procedures combines the advantages of two earlier static compaction procedures one that tends to generate large numbers of tests with a short primary input sequence included in every test and one that tends to generate small numbers of tests with a long primary input sequence included in one of the tests a procedure of the proposed class starts from an initial test set that has a large number of tests and long primary input sequences and it selects a subset of the tests and subsequences of their primary input sequences it thus has the flexibility of finding an appropriate balance between the number of tests and the lengths of the primary input sequences in order to minimize the test application time several ways of computing the primary input sequences for the initial test set are considered the most compact test sets are obtained when a test sequence for the nonscan circuit is available and this sequence is used as part of every test in the initial test set however it is shown that high levels of compaction can also be achieved without the overhead of test generation for the nonscan circuit specifically we show that the industry practice of holding a primary input vector constant between scan operations can be accommodated we estimate the ability of the procedure to achieve optimum test sets by computing a lower bound on the number of tests and demonstrating that the procedure achieves or approaches this lower bound

adaptive iir algorithms based on high order statistics recursive estimation algorithms are derived for moving average and autoregressive moving average processes these algorithms can be used for adaptive infinite impulse response iir filtering of non gaussian processes the behavior of these algorithms is illustrated by extensive numerical examples

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

time and lag recursive computation of cumulants from a state space model time and lag recursive algorithms for the computation of the cumulants of the state vector and the output process of a multiple input multiple output time varying state space model are derived using a kronecker product representation for the cumulants of vector processes the noise processes are not assumed to be stationary symmetry relations for the cumulants of vector processes are discussed computational aspects are examined in detail it is conjectured that the recursive equations derived will be useful in developing state estimators and even optimal controllers based on higher order statistics

fast adaptive algorithms for ar parameters estimation using higher order statistics time varying statistics in linear filtering and linear estimation problems necessitate the use of adaptive or time varying filters in the solution with the rapid availability of vast and inexpensive computation power models which are non gaussian even nonstationary are being investigated at increasing intensity statistical tools used in such investigations usually involve higher order statistics hos the classical instrumental variable iv principle has been widely used to develop adaptive algorithms for the estimation of arma processes despite the great number of iv methods developed in the literature the cumulant based procedures for pure autoregressive ar processes are almost nonexistent except lattice versions of iv algorithms this paper deals with the derivation and the properties of fast transversal algorithms hence by establishing a relationship between classical iv methods and cumulant based ar estimation problems new fast adaptive algorithms fast transversal recursive instrumental variable ftriv and generalized least mean squares glms are proposed for the estimation of ar processes the algorithms are seen to have better performance in terms of convergence speed and misadjustment even in low snr the extra computational complexity is negligible the performance of the algorithms as well as some illustrative tracking comparisons with the existing adaptive ones in the literature are verified via simulations the conditions of convergence are investigated for the glms