unbiased identification of systems with nonparametric uncertainty the set membership identification of systems with parametric and nonparametric uncertainty is studied the bias induced by the additive noise is eliminated by using the bias eliminated least squares method proposed previously by us 1991 a prefilter is connected to the input terminal of the system so that some zeros are inserted to the system by using the information obtained from these known zeros the bias induced by the additive noise is eliminated

statistical analysis of the least squares autoregressive estimator in the presence of noise this paper analyzes the asymptotic statistical properties of the least squares autoregressive ar estimator in the presence of noise the asymptotic covariance of this estimator is derived for an ar signal with additive white or colored noise the result is shown to hold for a general gaussian or linear stationary measurement the analysis is applied in detail to first order systems a procedure for using the result to solve problems in speech recognition biomedical diagnosis and fault detection is presented results of simulations confirm the theoretical analysis

conditions for local reversibility abstract the paper follows from work by quispel and capel on local reversibility of a dynamical system the approach adopted is to write down conditions for a mapping to behave like an involution in the neighbourhood of a fixed point and then to combine mappings which satisfy these conditions thus producing a composite mapping which is locally reversible in the main this confirms the results obtained by quispel and capel although additional conditions were found in some cases

passification based synchronization of nonlinear systems under communication constraints and bounded disturbances in brief the synchronization problem for nonlinear systems under communication constraints and bounded exogenous disturbances is analyzed the main contribution is in the evaluation of the synchronization error as a function of transmission rate and the upper bounds of the disturbances relevance of passifiability condition for controlled synchronization of master slave nonlinear systems for first order coder decoder pair is demonstrated experimental results obtained at three computer setup illustrating the theory are presented

recursive solutions of estimating equations and adaptive spectral factorization a recursive spectral factorization algorithm was developed by v solo ibid vol 34 no 10 pp 1047 1051 oct 1989 to be used with recursive instrumental variables for consistent estimation of the parameters of an armax system but the convergence of the spectral factorization algorithm is questionable herein a modified adaptive spectral factorization algorithm is shown to converge and a general method for constructing convergent recursive solutions of nonlinear equations that are used to define parameter estimates is also presented

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

adaptive multipath delay estimation two algorithms are proposed for the continuous tracking of multipath delay the first is an efficient method for adaptively tracking the secondary peak in the autocorrelation function caused by multipath in principle it is equivalent to the correlation method commonly used in practice the second is an adaptive inverse filter which can exactly remove the multipath transfer function the methods use an adaptive delay line interpolated by a first order filter the interpolation coefficient is explicitly estimated using the recursive gauss newton rgn algorithm often used for recursive system identification

modeling and identification of symmetric noncausal impulse responces spectrally equivalent causal sec models for single input single output noncausal systems are derived with the objective of estimating the noncausal impulse response attention is restricted to symmetric noncausal impulse responses and the measurements of the system output are assumed to be noisy it is shown that by using structured sec models either state space or arma plus noise consistent estimates of the noncausal impulse response can be obtained by exploiting only the second order statistics of the measurements a new version of the correlation technique particularly suited to structured models is presented and analyzed computer simulation results are also presented to illustrate the performance of the proposed approach

efficient construction of canonical ladder forms for vector autoregressive processes the paper treats the problem of constructing canonical ladder realizations for vector autoregressive ar processes specified by their characteristic matrix polynomials the difficulty of this problem is rooted in the fact that the backward matrix polynomial corresponding to a given vector ar process is a nontrivial function of the forward matrix polynomial the construction calls for solving a discrete lyapunov equation in block controller form two efficient procedures for solving this equation are presented both requiring a number of operations that is proportional to at most the square of the model order applications of the new procedures to stability tests simulation of ar processes and model reduction are described

robust methods for recursive autoregressive moving average estimation in this paper we consider the problem of fitting recursively in time an autoregressive moving average arma model to time series data where outliers may be present although many recursive estimation procedures are available for fitting arma models they are based on the recursive least squares algorithm which is known to be badly affected by additive outliers to minimize the impact of these sort of outliers we investigate some robustified versions of the recursive maximum likelihood procedure the problem of incorporating robust scale recursion is discussed and asymptotic properties of the procedures are examined

theory and methods abstract a self organizing filter and smoother for the general nonlinear non gaussian state space model is proposed an expanded state space model is defined by augmenting the state vector with the unknown parameters of the original state space model the state of the augmented state space model and hence the state and the parameters of the original state space model are estimated simultaneously by either a non gaussian filter smoother or a monte carlo filter smoother in contrast to maximum likelihood estimation of model parameters in ordinary state space modeling for which the recursive filter computation has to be done many times model parameter estimation in the proposed self organizing filter smoother is achieved with only two passes of the recursive filter and smoother operations examples such as automatic tuning of dispersion and the shape parameters adaptation to changes of the amplitude of a signal in seismic data state estimation for a nonlinear state space model with unknown parameters

coordination of passive systems under quantized measurements in this paper we investigate a passivity approach to collective coordination and synchronization problems in the presence of quantized measurements and show that coordination tasks can be achieved in a practical sense for a large class of passive systems

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

large sample identification and spectral estimation of noisy multivariate autoregressive processes when large samples are available identification and spectral estimation problems of a noisy multivariate autoregressive process are solved independently of the probability law governing the observed data the procedure of solving the problems is divided into 1 estimate parameters by solving pertinent block toeplitz and hankel matrices as well as compute the modified akaike information criterion for an assumed order 2 select the order and the parameter estimators corresponding to the ones which minimize the criterion function 3 compute the asymptotic distribution functions of the parameter estimators 4 estimate power spectral density functions and coherency spectra 5 compute the estimate confidence bounds these five steps are numerically very efficient because the matrix equations related to block hankel and toeplitz matrices are well studied in the literature the procedure is also robust because it is independent of the probability law governing the observed data

a multi time scale generalization of recursive identification algorithm for armax systems recently chen 2010 presented a new approach to recursive identification for armax systems which is a three stage recursive scheme and assumes independent and identically distributed input signals here we observe that unless the time scale of the algorithm at one stage is reasonably faster than those at the previous stages convergence to the true value may not take place to remedy this issue this note proposes a multi time scale modification of the algorithm in 5 such that convergence is achieved in addition the new scheme handles a wider class of input signals so that the input can be designed for some purpose the advantage of the multi time scale algorithm is verified with numerical examples

conditions for local reversing symmetries in dynamical systems abstract dynamical systems may possess symmetries and reversing symmetries local reversing symmetries around fixed points of dynamical systems are characterized as a property of their normal form expansions in this paper an inductive method is introduced to derive conditions for a fixed point to possess a local reversing symmetry of finite order the method is introduced for dynamical systems with continuous time flows the analogous problem for dynamical systems with discrete time mappings is discussed afterwards conditions for local reversing symmetries are given explicitly for fixed points of planar flows these conditions may be used as a negative criterion to show that a given dynamical system does not have a reversing symmetry

adaptive algorithms for constrained arma signals in the presence of noise a family of algorithms is developed for adaptive parameter estimation of constrained autoregressive moving average arma signals in the presence of noise these algorithms utilize a priori information about the signal s properties such as its spectral type for example low pass bandpass etc or a spatial domain characteristic special applications include modeling of autoregressions ar and signals of known spectral type in the presence of noise signal deconvolution image deblurring and multipath parameter estimation selected results of simulations are included to demonstrate the performance of the algorithms

arma spectral estimation of time series with missing observations the problem of estimating the power spectral density of stationary time series when the measurements are not contiguous is considered a new autoregressive moving average arma method is proposed for this problem based on nonlinear optimization of a weighted squared error criterion the method can handle either regularly or randomly missing observations as a special case the method can handle the problem of missing sample covariances the computational complexity is modest compared to exact maximum likelihood estimation of the same parameters the performance of the algorithm is illustrated by some numerical examples and is shown to be statistically efficient in these cases

adaptive parameter estimation for a constrained low pass system a novel algorithm is presented for adaptive parameter estimation for a constrained low pass butterworth system model the algorithm will estimate the system cutoff frequency and gain online when it is known that the true system has a low pass butterworth structure or some transfer function similar to it and its true order is used the algorithm will lead to a substantial savings in computation and more accurate results than unconstrained algorithms potential applications include filter design and adaptive decision on nyquist rate for systems

adaptive pole estimation an adaptive algorithm is developed for online estimation of the poles of autoregressive ar processes the method estimates the poles directly from the data without intermediate estimation of the ar coefficients or polynomial factorization it converges rapidly is computationally efficient and attains the cramer rao bound crb asymptotically a closed form expression for the asymptotic crb is provided convergence to the true solution is proved and methods are discussed for extending the algorithm for use with more general e g autoregressive moving average models numerical examples are presented to demonstrate the performance of the algorithm

adaptive spectral factorization an on line spectral factorization algorithm is used to devise a globally convergent self tuning identifier that does not suffer from restrictions that amount to knowledge of the true system e g the positive real condition the method developed uses two ideas one idea an old one which might be called the method of split recursions is used to estimate the parameters in blocks thus one block might get the transfer function parameters while the other gets the noise parameters the other idea is to use spectral factorization to estimate moving average parameters the algorithm does have its own weaknesses e g transient behavior may not be good and it relies on a condition that is only generically true but it does not need a positive real condition to be satisfied for global convergence

the parsimony principle for a class of model structures a new form of the parsimony principle is presented for a class of model structures containing a common subset of parameters the principle is applied to the problem of estimating the autoregressive ar parameters of an ar process corrupted by white measurement noise

robust recursive identification of multidimensional linear regression models stochastic adaptive estimation and control algorithms involving recursive prediction estimates have guaranteed convergence rates when the noise is not too coloured as when a positive real condition on the noise mode is satisfied moreover the whiter the noise environment the more robust are the algorithms this paper shows that for linear regression signal models the suitable introduction of while noise into the estimation algorithm can make it more robust without compromising on convergence rates indeed there are guaranteed attractive convergence rates independent of the process noise colour no positive real condition is imposed on the noise model

convergent dynamics a tribute to boris pavlovich demidovich we review and pay tribute to a result on convergent systems by the russian mathematician boris pavlovich demidovich in a sense demidovich s approach forms a prelude to a field which is now called incremental stability of dynamical systems developments on incremental stability are reviewed from a historical perspective

robust real time identification of linear systems with correlated noise the problem of recursive robust identification of linear discrete time single input single output dynamic systems with correlated disturbances is considered problems related to the construction of optimal robust stochastic approximation algorithms in the min max sense are demonstrated since the optimal solution cannot be achieved in practice several robustified stochastic approximation algorithms are derived on the basis of a suitable non linear transformation of normalized residuals as well as step by step optimization with respect to the weighting matrix of the algorithm the convergence of the developed algorithms is established theoretically using the ordinary differential equation approach monte carlo simulation results are presented for the quantitative performance evaluation of the proposed algorithms the results indicate the most suitable algorithms for applications in engineering practice

reversing symmetries in dynamical systems dynamical systems may possess in addition to symmetries that leave the equations of motion invariant reversing symmetries that invert the equations of motion such dynamical systems are called weakly reversible some consequences of the existence of reversing symmetries for dynamical systems with discrete time mappings are discussed a reversing symmetry group is introduced and it is shown that every weakly reversible mapping l can be decomposed into two mappings k0 and k1 of the same order 2l limit l to infinity included such that k02 k12 i some applications are discussed briefly

strong approximation of the recursive prediction error estimator of the parameters of an arma process abstract let n denote the recursive prediction error estimator of the parameters of an arma process and let n denote the off line prediction error estimator we show under reasonable assumptions that for any q 1 n n lq o m log n n this theorem enables us to show that most of the properties known for the off line estimator n are inherited by the on line estimator n

bifurcations in two dimensional reversible maps we give a treatment of the non resonant bifurcations involving asymmetric fixed points with jacobian j 1 in reversible mappings of the plane these bifurcations include the saddle node bifurcation not in the neighbourhood of a fixed point with j 1 as well as the so called transcritical bifurcations and generalized rimmer bifurcations taking place at a fixed point with jacobian j 1 the bifurcations are illustrated by some simple examples of model maps the rimmer type of bifurcation with e g a center point with j 1 changing into a saddle with jacobian j 1 an attractor and a repeller occurs under more general conditions i e also in non reversible mappings if only a certain order of local reversibility is satisfied these rimmer bifurcations are important in connection with the emergence of dissipative features in non measure preserving reversible dynamical systems

unbiased parameter estimation of linear systems with colored noises we report a study of the problem of consistent parameter estimation in the general case where the measurement noise is unknown and correlated not only with the system output but also with the system input a new method is presented for eliminating the noise induced biases in the least squares ls estimates in the proposed method two filters are introduced to filter the system input and output signals respectively so that an augmented system with some known zeros and poles is obtained by shifting the space of the parameters to be estimated and using the known zeros and poles of the parameters to be estimated and using the known zeros and poles a sufficient number of linear constraints are constructed to determine the noise induced biases after eliminating the biases in the ordinary ls estimates consistent estimates of the parameters are obtained analysis shows that the results of the proposed method are independent of the noise model used

time reversal symmetry in dynamical systems a survey abstract in this paper we survey the topic of time reversal symmetry in dynamical systems we begin with a brief discussion of the position of time reversal symmetry in physics after defining time reversal symmetry as it applies to dynamical systems we then introduce a major theme of our survey namely the relation of time reversible dynamical sytems to equivariant and hamiltonian dynamical systems we follow with a survey of the state of the art on the theory of reversible dynamical systems including results on symmetric periodic orbits local bifurcation theory homoclinic orbits and renormalization and scaling some areas of physics and mathematics in which reversible dynamical systems arise are discussed in an appendix we provide an extensive bibliography on the topic of time reversal symmetry in dynamical systems

on the parsimony principle the parsimony principle is frequently used in system identification on more or less heuristical grounds recently a formal proof of this principle has been given here the assumptions used in that proof are examined to some extent it will be shown by means of some counterexamples that these assumptions cannot be relaxed unless additional restrictions are introduced a result showing how the parsimony principle should be used when estimating the parameters of regression models by the least squares method is also presented

a self organizing state space model a self organizing filter and smoother for the general nonlinear non gaussian state space model is proposed an expanded state space model is defined by augmenting the state vector with the unknown parameters of the original state space model the state of the augmented state space model and hence the state and the parameters of the original state space model are estimated simultaneously by either a non gaussian filter smoother or a monte carlo filter smoother in contrast to maximum likelihood estimation of model parameters in ordinary state space modeling for which the recursive filter computation has to be done many times model parameter estimation in the proposed self organizing filter smoother is achieved with only two passes of the recursive filter and smoother operations examples such as automatic tuning of dispersion and the shape parameters adaptation to changes of the amplitude of a signal in seismic data state estimation for a nonlinear state space model with unknown parameters and seasonal adjustment with a nonlinear model with changing variance parameters are shown to exemplify the usefulness of the proposed method

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