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

polynomial filtering for linear discrete time non gaussian systems in this work we propose a new filtering approach for linear discrete time non gaussian systems that generalizes a previous result concerning quadratic filtering a de santis a germani and m raimondi ieee trans automat control 40 1995 pp 1274 1278 a recursive nu th order polynomial estimate of finite memory delta is achieved by defining a suitable extended state which allows one to solve the filtering problem via the classical kalman linear scheme the resulting estimate will be the mean square optimal one among those estimators that take into account nu polynomials of the last delta observations numerical simulations show the effectiveness of the proposed method

spread spectrum multiple access performance of orthogonal codes linear receivers this paper analyzes a direct sequence spread spectrum multiple access ssma communication system which assigns a set of m orthogonal sequences to each user with all direct sequence ssma systems k users share a channel by phase modulating their transmissions with signature sequences however the users of our system transmit log 2 m bits of information sequence this contrasts classical ssma schemes which use a pair of antipodal sequences and transmit 1 bit sequence in this paper we assume that the channel noise is a combination of additive white gaussian noise awgn and multiple access interference we employ the optimum single user demodulator for orthogonal signals in gaussian noise the multiple user performance of this receiver is analyzed we obtain approximations for the multiuser probability of error by using a gaussian approximation for the multiple access interference we also obtain an upper bound on the exact probability by using characteristic functions our ssma system is well suited for application at the lower radio frequencies therefore a companion paper describes a realistic model for low frequency radio noise modifies the receiver to include a zero memory nonlinearity and studies the performance of the nonlinear receiver

identifiability of minimal stable rational causal systems using second order output cyclic spectra in this paper the blind identifiability of systems using the second order output cyclic spectra is considered it is shown that the class of minimal stable rational causal msrc systems is not identifiable and the identification is limited by a nontrivial ambiguity associated with the so called cyclic all pass factor the largest subclass of msrc systems that ensures the unique identification is shown to be the set of msrc systems that do not have special uniformly spaced maximum phase zeros

efficient closed form estimation of multivariate moving average processes using higher order statistics an improved algorithm is proposed for estimation of non gaussian nonminimum phase multivariate moving average ma processes using higher order cumulants this algorithm improves upon earlier results and contains development beyond existing algorithms it provides a closed form solution to estimating the ma parameter matrices up to a post multiplication by a permutation matrix and under certain assumptions eliminates the indeterminacy associated with scaling the algorithm is theoretically derived and tested via computer simulations in addition it is shown that this algorithm is computationally more efficient than the one proposed by tong inouye and liu see ibid vol 40 no 10 p 2547 2558 1992 finally the effect of imperfect input data on our algorithm is tested via simulations

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

cumulant based order determination of non gaussian arma models the objective is the order determination of non gaussian and nonminimum phase autoregressive moving average arma models using higher order cumulant statistics the two methods developed assume knowledge of upper bounds on the arma orders the first method performs a linear dependence search among the columns of a higher order statistics matrix by means of the gram schmidt orthogonalization procedure in the second method the order of the ar part is found as the rank of the matrix formed by the higher order statistics sequence for numerically robust rank determination the singular value decomposition approach is adopted the argument principle and samples of the polyspectral phase are used to obtain the relative degree of the arma model from which the order of the ma part can be determined statistical analysis is included for determining the correct ma order with high probability when estimates of third order cumulants are only available simulations are used to verify the performance of the methods and compare autocorrelation with cumulant based order determination approaches

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

olriv a new fast adaptive algorithm for rectangular block toeplitz systems in this paper we propose a new algorithm for solving overdetermined systems when they are rectangular block toeplitz the blocks can have more rows than columns it is based on the expression of the matrix of the system to solve as the intercorrelation between two vectorial processes namely the original and the instrumental processes the instrumental process has generally more components than the original one therefore it takes the overdetermined character of the system into consideration the proposed algorithm known as the overdetermined lattice recursive instrumental variable olriv belongs to the fast rls family and lies on a double lattice structure where one lattice performs the prediction of the original process and the other one the prediction of the instrumental process the geometric complete derivation of the proposed algorithm is given in the paper afterwards we show how olriv can be applied to perform blind adaptive identification of ar channels using high order statistics where the systems to solve are often overdetermined to ensure identifiability both the scalar and the vectorial cases are investigated simulation results are finally given to show the performances of olriv

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

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

the behavior of the stahel donoho robust multivariate estimator abstract the stahel donoho estimators t v of multivariate location and scatter are defined as a weighted mean and a weighted covariance matrix with weights of the form w r where w is a weight function and r is a measure of outlyingness obtained by considering all univariate projections of the data it has a high breakdown point for all dimensions and order n consistency the asymptotic bias of v for point mass contamination for suitable weight functions is compared with that of rousseeuw s minimum volume ellipsoid mve estimator a simulation shows that for a suitable w t and v exhibit high efficiency for both normal and cauchy distributions and are better than their competitors for normal data with point mass contamination the performances of the estimators for detecting outliers are compared for both a real and a synthetic data set

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

multichannel arma processes parametric modeling of multichannel time series is accomplished by using higher than second order statistics hos of the observed nongaussian data cumulants of vector processes are defined using a kronecker product formulation and consistency of their sample estimators is addressed identifiability results in connection with the hos based parameter estimation of causal and noncausal multivariate arma processes are established estimates of the parameters of causal arma models are obtained as the solution to a set of linear equations whereas those of noncausal arma models are obtained as the solution to a cumulant matching algorithm conventional approaches based on second order statistics can identify a multichannel system only to within post multiplication by a unimodular matrix hos based methods yield solutions that are unique to within post multiplication by an extended permutation matrix additionally the multiminimum phase assumption can be relaxed and the observations may be contaminated with colored gaussian noise frequency domain methods for nonparametric system identification are discussed briefly simulations results validating the multichannel parameter estimation algorithms are provided

cumulant based identification of multichannel moving average models given cumulants of a stationary perhaps noisy non gaussian r variate moving average ma q process identifiability conditions are studied under which the ma coefficient matrices the input statistics and the order q can be uniquely determined the selection of a unique representative from the equivalence class corresponding to a given cumulant structure involves fewer restrictions than that corresponding to a given covariance structure two algorithms are derived for estimating the possibly nonminimum phase ma coefficient matrices

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

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

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

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