the steiglitz mcbride identification algorithm revisited convergence analysis and accuracy aspects the convergence and accuracy properties of the steiglitz and mcbride identification method are examined the analysis is valid for a sufficiently large number of data it is shown that the method can converge to the true parameter vector only when the additive output noise is white in that case the method is proved to be locally convergent to the true parameters the global convergence properties are also investigated it is pointed out that the method is not always globally convergent some sufficient conditions guaranteeing global convergence are given assuming convergence takes place the estimates are shown to be asymptotically gaussian distributed an explicit expression is given for their asymptotic covariance matrix

a complex adaptive algorithm for iir filtering this correspondence generalizes the gauss newton algorithm 1 for adaptive iir filters to include complex coefficients the resulting algorithm simultaneously updates the real and imaginary parts of the filter coefficients to minimize the average squared estimation error it has application in frequency domain adaptive iir filtering 2 where the signals and filter coefficients are complex

cost function shaping of the output error criterion identification of an output error model using the prediction error method leads to an optimization problem built on input output data collected from the system to be identified it is often hard to

discrete time adaptive control utilizing prior information we present schemes for discrete time adaptive control of a linear time invariant system which is partially known along with an analysis of their convergence properties

identification with nonparametric uncertainty an identification technique that is robust to nonparametric uncertainty i e model mismatch is presented the identifier produces either a parameter set estimate or a frequency response set estimate the estimates result from the inclusion of a model of the nonparametric uncertainty in the plant model the frequency response set estimate is shown to always contain the frequency response of the plant as long as certain modeling conditions are met this type of identifier would be useful in applications such as control where a property such as stability or performance level must be achieved in the face of low order modeling and its associated nonparametric uncertainty

schlomilch series that arise in diffraction theory and their efficient computation we are concerned with a certain class of schlomilch series that arise naturally in the study of diffraction problems when the scatterer is a semi infinite periodic structure by combining new results derived from integral representations and the poisson summation formula with known identities we obtain expressions which enable the series to be computed accurately and efficiently many of the technical details of the derivations are omitted they can however be obtained from linton 2005 schlomilch series that arise in diffraction theory and their efficient computation technical report loughborough university available online at http www staff lboro ac uk macml1 schlomilch techreport pdf

a unified approach to time and frequency domain realization of fir adaptive digital filters specific implementations of the finite impulse response fir block adaptive filter in the frequency domain are presented and some of their important properties are discussed the time domain block adaptive filter implemented in the frequency domain is shown to be equivalent to the frequency domain adaptive filter derived in the frequency domain provided data sectioning is done properly all of the known time and frequency domain adaptive filters 1 12 16 18 are contained in the set of possible block adaptive filter structures thus the block adaptive filter is generic and its formulation unifies the current theory of time and frequency domain fir adaptive filter structures a detailed analysis of overlap save and overlap add implementations shows that the former is to be preferred for adaptive applications because it requires less computation a fact that is not true for fixed coefficient filters

adaptive iir filtering using parallel form realizations several parallel form adaptive iir infinite impulse response filters are presented including a frequency domain implementation based on the discrete fourier transform and a recursive frequency sampling structure the performance of the frequency domain adaptive iir filter is investigated in a system identification application which includes an analysis of its modeling capabilities and a discussion of the mean square error performance surface computer simulation results are presented to illustrate the robust convergence properties of the adaptive algorithm and to demonstrate the stability of the filter

identification of partially known systems abstract the concepts of partially known system identification are introduced and the advantages of a method whereby process information can be utilized in a linear transfer function representation of the system are highlighted and discussed in particular an algorithm for identifying a single unknown physical system parameter associated with a linear system is given it is assumed that the system is polynomial as opposed to linear in the physical parameter the bond graph representation is used as the basis for deriving a system dependent algorithm for each partially known system the method is illustrated by simulated examples

locally robust identification of linear systems containing unknown gain elements with application to adapted iir lattice models abstract we consider the identification of stable linear systems whose unknown parameters may be interpreted as feedback gains by using the output error between the true system and a model of it containing adjustable parameters we develop a recursive algorithm for estimating the unknown parameters we describe a persistency of excitation condition on the system input which guarantees a robust local convergence property for the algorithm we then apply our results to the identification of the parameters of a tapped lattice model of a linear infinite impulse response iir plant considering the identification of a lattice rather than a direct form model of a linear system is attractive due to i the simplicity of its crucial stability check and maintenance procedure for the adapted iir parametrization and ii the numerical insensitivity properties of the lattice structure reproducible simulation evidence is presented that supports our results

quasialgebra structure of the octonions abstract we show that the octonions are a twisting of the group algebra of z 2 z 2 z 2 in the quasitensor category of representations of a quasi hopf algebra associated to a group 3 cocycle in particular we show that they are quasialgebras associative up to a 3 cocycle isomorphism we show that one may make general constructions for quasialgebras exactly along the lines of the associative theory including quasilinear algebra representation theory and an automorphism quasi hopf algebra we study the algebraic properties of quasialgebras of the type which includes the octonions further examples include the higher 2n onion cayley algebras and examples associated to hadamard matrices

brief paper some properties of the output error method the output error identification method is studied in various respects the stationary points of the associated loss function are investigated sufficient conditions for a unique local minimum are given the loss functions can be minimized using a quasilinearization algorithm such an algorithm will give good local convergence it is however shown that global convergence does not always occur the output error method is also compared with some other estimation methods from the accuracy point of view it is proved that a prediction error method will give better accuracy an instrumental variable technique may give better or worse accuracy depending on the actual noise correlation

lattice sums for the helmholtz equation a survey of different representations for lattice sums for the helmholtz equation is made these sums arise naturally when dealing with wave scattering by periodic structures one of the main objectives is to show how the various forms depend on the dimension d of the underlying space and the lattice dimension d lambda lattice sums are related to and can be calculated from the quasi periodic green s function and this object serves as the starting point of the analysis

on error surfaces of sufficient order adaptive iir filters proofs and counterexamples to a unimodality conjecture it is shown that although a conjecture proposed by s stearns ibid vol assp 29 p 763 6 june 1981 concerning sufficient conditions to guarantee unimodality of error surfaces for adaptive pole zero infinite impulse response iir filters is valid for first and second order filters it is not true in general without an additional constraint introduced by t soderstrom autom vol 11 p 93 9 jan 1982 proofs of the conjecture for a first and second order adaptive filters are given counterexamples are presented to illustrate the failure of this conjecture for higher order filters when the condition of soderstrom is not satisfied for both matching order and overparameterizing cases

on parameter convergence in adaptive control it is well known that the parameter error as well as the model plant mismatch error in a model reference adaptive scheme tends exponentially to zero iff a certain sufficient richness condition holds for signals inside the time varying plant control loop in this paper we give conditions on the reference signal the exogenous input to the adaptive loop namely that it have as many spectral lines as there are unknown parameters in order to guarantee parameter convergence

weak hopf algebras i integral theory and c structure we give an introduction to the theory of weak hopf algebras proposed as a coassociative alternative of weak quasi hopf algebras we follow an axiomatic approach keeping as close as possible to the classical theory of hopf algebras the emphasis is put on the new structure related to the presence of canonical subalgebras al and ar in any weak hopf algebra a that play the role of non commutative numbers in many respects a theory of integrals is developed in which we show how the algebraic properties of a such as the frobenius property or semisimplicity or innerness of the square of the antipode are related to the existence of non degenerate normalized or haar integrals in case of c weak hopf algebras we prove the existence of a unique haar measure h a and of a canonical grouplike element g a implementing the square of the antipode and factorizing into left and right elements g glg 1r gl al gr ar further discussion of the c case will be presented in part ii

frequency domain green s function for a planar periodic semi infinite phased array i truncated floquet wave formulation this two part sequence deals with the derivation and physical interpretation of a uniform high frequency solution for the field radiated at finite distance by a planar semi infinite phased array of parallel elementary electric dipoles the field obtained by direct summation over the contributions from the individual radiators is restructured into a double series of wavenumber spectral integrals whose asymptotic reduction yields a series encompassing propagating and evanescent floquet waves fws together with corresponding diffracted rays which arise from scattering of the fw at the edge of the array the formal aspects of the solution are treated in the present paper they involve a sequence of manipulations in the complex spectral wavenumber planes that prepare the integrands for subsequent efficient and physically incisive asymptotics based on the method of steepest descent different species of spectral poles define the various species of propagating and evanescent fw their interception by the steepest descent path sdp determines the variety of shadow boundaries for the edge truncated fw the uniform asymptotic reduction of the sdp integrals performed by the van der waerden 1951 procedure and yielding a variety of edge diffracted fields completes the formal treatment

a clifford algebra is a weak hopf algebra in a suitable symmetric monoidal category abstract it is well known that clifford algebras are group algebras deformed by a 2 cocycle furthermore these algebras which are not commutative in the usual sense can be viewed as commutative algebras in certain symmetric monoidal categories of graded vector spaces in this note we invent a clifford process for coalgebras that will allow us to show that clifford algebras have also cocommutative coalgebra structures and consequently commutative and cocommutative weak braided hopf algebras structures within the same symmetric monoidal categories where they lie as commutative algebras also we will show that they are selfdual weak braided hopf algebras monoidal frobenius algebras and monoidal cofrobenius coalgebras

the effect on bending waves by defects in pinned elastic plates abstract this paper presents solutions to a number of problems posed for the out of plane displacement of infinite thin elastic plates that are rigidly pinned in periodic configurations but that possess a finite number of defects we begin by considering a single one dimensional periodic array of pins we derive an analytic solution for the displacement produced by the forced oscillation of the central pin in the array and this solution is shown to be closely connected to the problem of scattering of plane waves by an array when a finite number of pins are removed attention then focuses on doubly periodic rectangular arrays of pinned points possessing defects central to approaching such problems is an understanding of bloch floquet waves in periodic arrays in the absence of defects and a simple method is described for computing the associated dispersion surfaces the solutions to three problems are then sought the trapping of localised waves by a finite number of missing pins trapping of waves by entire rows of missing pins and the wave radiation pattern due to the forcing of a single pin all problems are treated analytically using bounded green s functions for thin elastic plates a discrete fourier transform solution method and simple explicit and rapidly convergent evaluations of the one and two dimensional lattice sums that arise

persistence of excitation conditions for partially known systems abstract this note derives persistence of excitation conditions on the input for systems with partially known transfer functions the assumed transfer function model is p 0 s k t p s q 0 s k t q s where k is the unknown parameter vector p 0 s q 0 s are known scalar polynomials and p s and q s are known vector polynomials

comparison of some instrumental variable methods consistency and accuracy aspects a general analysis of various instrumental variable methods is given the investigation includes methods for open loop operation as well as methods designed for closed loop operation the instrumental variables are formed as different combinations of inputs delayed inputs delayed outputs filtered inputs and external setpoint variations necessary conditions as well as sufficient conditions for consistency are explicitly derived and discussed the paper also includes some simple counter examples to general consistency for some common instrumental variable methods also asymptotic accuracy properties are reviewed it is e g studied how the use of filters will influence the covariance matrix of the parameter estimates

on the computation of the cramer rao bound for arma parameter estimation the cramer rao lower bound crlb provides a useful tool for evaluating the performance of parameter estimation techniques several techniques for the computation of the asymptotic form of the crlb for arma models are presented it is shown that the asymptotic crlb can be expressed as an explicit function of the model parameters

a structural view of asymptotic convergence speed of adaptive iir filtering algorithms i infinite precision implementation for pt i see ibid vol 41 no 4 p 1493 1517 1993 finite precision fp implementation is the ultimately inevitable reality of all adaptive filters including adaptive infinite impulse response iir filters this paper continues to examine the asymptotic convergence speed of adaptive iir filters of various structures and algorithms including the simple constant gain type and the newton type but under fp implementation a stochastic differential equation sde approach is used in the analysis such an approach not only greatly simplifies the fp analysis which is traditionally very involved algebraically but it also provides valuable information about the first order as well as the second order moments that the latter are not available using the ordinary differential equation ode approach the asymptotic convergence speed as well as the convergent values of the pertinent moments of fp errors are examined in terms of unknown system pole zero locations the adverse effects of lightly damped low frequency ldlf poles resulting from fast sampling on the local transient and convergent behavior of various structures and algorithms are analyzed and compared the new results agree with the existing ones when reduced to the finite impulse response fir case in particular the explosive behavior of pertinent error variances of newton type iir algorithms when the forgetting factor spl lambda 1 is also concluded computer simulation verifies the predicted theoretical results

edge effects in axial arrays of circular rings a boundary value problem is solved for the current induced by any source in particular for an incident plane wave on any number of identical rings that are arranged to form an axisymmetric linear array the net aperture distribution along the finite array is approximated by a combination of three physically identifiable components a term from the related infinite array plus contributions from two independent edge effect waves that originate from each of the two ends however if individually resonant loops are closer than a critical spacing the entire structure exhibits a wild resonance and the simple approximation becomes invalid

paper an approach to stable indirect adaptive control stable indirect adaptive control of minimum and nonminimum phase plants is established for cases where a priori bounds on the unknown plant parameters are known and where for each set of parameter values within these bounds the plant has no unstable pole zero cancellation by incorporating this partial parameter knowledge in the adaptive law and using a nonminimal representation of the plant it is shown that the adaptive closed loop control system can be written as an exponentially stable system driven by the identification error the stability of the adaptive control system is then shown using techniques similar to those known from the model reference adaptive control approach

uniqueness of estimated k step prediction models of arma processes the direct estimation of the k step prediction models of arma processes is discussed the emphasis is on the uniqueness properties of the parameter estimates of such models obtained by using either a prediction error method pem or a pseudo linear regression plr algorithm the main result is that both pem and plr when applied to such models have a certain uniqueness property more specifically it is shown that all the limit models corresponding to either method behave precisely as the true optimal predictor furthermore if a minimal parameterization is used then the true predictor is the unique limit model both for pem and for plr

analysis of finite arrays a new approach a novel method for the analysis of finite arrays is presented the method is based on a global array concept where the array problem for single mode elements is reduced to a solution of a single fredholm integral equation of the second kind this formulation offers several types of solutions not all explored yet with illuminating results the approximate solution of this integral equation for example yields finite array characteristics in terms of equivalent infinite array scattering parameters and mutual admittances the method is general i e applicable to any element type and periodic array geometry presently the method applies to single mode elements one unknown per element however it can be extended to a multimode analysis

a truncated floquet wave diffraction method for the full wave analysis of large phased arrays i basic principles and 2 d cases this two part sequence deals with the formulation of an efficient method for the full wave analysis of large phased array antennas this is based on the method of moments mom solution of a fringe integral equation ie in which the unknown function is the difference between the exact solution of the finite array and that of the associated infinite array the unknown currents can be interpreted as produced by the field diffracted at the array edge which is excited by the floquet waves fws pertinent to the infinite configuration following this physical interpretation the unknown in the ie is efficiently represented by a very small number of basis functions with domain on the entire array aperture in order to illustrate the basic concepts the first part of this sequence deals with the two dimensional example of a linearly phased slit array it is shown that the dominant phenomenon fur describing the current perturbation with respect to the infinite array is accurately represented in most cases by only three diffracted ray shaped unknown functions this also permits a simple interpretation of the element by element current oscillation which was described by other authors

a construction relating clifford algebras and cayley dickson algebras a review of the applications of the octonions in physics is given a construction is presented both the cayley dickson algebras and the clifford algebras arise naturally under this construction from the quaternion algebras the mathematical properties of the algebras constructed are discussed

on the local stability properties of adaptive parameter estimators with composite errors and split algorithms the stability characteristics of a generalized error system structure are examined for adaptive parameter estimation systems this error system form encompasses the structure of a number of particular applications of adaptive parameter estimation theory which fall outside the framework of more familiar error system models the consequences for error system stability which derive from the added generality are analyzed it is demonstrated that when using averaging theory techniques to analyze the error system stability conditions must be augmented for the basic error system in order to ensure stability for the generalized error system the inadequacy of regressor spectral restrictions and persistent spanning conditions to guarantee local error system stability of the generalized structure is rigorously established alternative conditions which will yield such local stability are demonstrated to illustrate the concepts involved the recursive identification of parameters is examined in a parallel form realization of a linear system

analysis of a frequency domain adaptive iir filter convergence of frequency domain adaptive pole zero iir infinite impulse response filter is studied the algorithm is shown to converge in probability to an associated ordinary differential equation ode which in turn converges to a local minimum of its performance surface an analysis of the performance surface shows that the algorithm converges to one of n factorial members in an equivalence class of global minimum points where n is the number of adaptive poles saddle points exist on manifolds that separate members in the equivalence class this explains shoulders in the mse convergence curves and also suggests one way of avoiding these shoulders which cause slow convergence a second order simulation example confirms the above results

physically based parameterizations for designing adaptive algorithms abstract structural properties are examined of systems with physical component values as parameters both state variable realizations and transfer function descriptions are investigated the transfer functions in particular are shown to be the ratios of polynomials with coefficients multilinear in the parameters these structures prove useful in formulating adaptive algorithms

the weak braided hopf algebra structure of some cayley dickson algebras abstract it has been shown by albuquerque and majid that a class of unital k algebras not necessarily associative obtained through the cayley dickson process can be viewed as commutative associative algebras in some suitable symmetric monoidal categories in this note we will prove that they are moreover commutative and cocommutative weak braided hopf algebras within these categories to this end we first define a cayley dickson process for coalgebras we then see that the k vector space of complex numbers of quaternions of octonions of sedenions etc fit to our theory hence they are all monoidal coalgebras as well and therefore weak braided hopf algebras

large signal to noise ratio quantification in mle for ararmax models it has been shown that closed loop linear system identification by indirect method can be generally transferred to open loop ararmax autoregressive autoregressive moving average with exogenous input estimation for such models the gradient related optimisation with large enough signal to noise ratio snr can avoid the potential local convergence in maximum likelihood estimation to ease the application of this condition the threshold snr needs to be quantified in this paper we build the amplitude coefficient which is an equivalence to the snr and prove the finiteness of the threshold amplitude coefficient within the stability region the quantification of threshold is achieved by the minimisation of an elaborately designed multi variable cost function which unifies all the restrictions on the amplitude coefficient the corresponding algorithm based on two sets of physically realisable system input output data details the minimisation and also points out how to use the gradient related method to est

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

on acoustic and electric faraday cages two dimensional problems involving many identical small circles are considered the circles are the cross sections of parallel wires modelling a cage or a grating both electrostatic and acoustic fields are considered the main emphasis is on periodic configurations of n circles distributed evenly around a large circle a ring foldy s theory is used for acoustic problems and then adapted for electrostatic problems in both cases circulant matrices are encountered the fields can be calculated explicitly then the limit n is studied a connection between the n circle problem and the limiting problem fields exterior to the ring is established using known results on the convergence of a defective form of the trapezoidal rule defective in that endpoint contributions are ignored because the integrand has logarithmic singularities at those points this shows that the solution of the limiting problem is approached very slowly as n 1 log n as n

unconstrained frequency domain adaptive filter an unconstrained frequency domain least mean squares uflms algorithm is presented the algorithm is based on the overlap save technique used in frequency domain filtering the proposed algorithm converges to the wiener solution without the time domain constraint on the impulse response as proposed by ferrara for a large number of taps geq32 the uflms algorithm offers a significant reduction in computation another advantage is its fast convergence for highly correlated input signals the performance of the algorithm is illustrated by a simulation

stable and efficient lattice algorithms for adaptive iir filtering previous attempts at applying lattice structures to adaptive infinite impulse response iir filtering have met with gradient computations of o n sup 2 complexity to overcome this computational burden two new lattice based algorithms are proposed for adaptive iir filtering and system identification with both algorithms of o n complexity the first algorithm is a reinterpretation of the steiglitz mcbride method 1965 while the second is a variation on the output error method state space models are employed to make the derivations transparent and the methods can be extended to other parameterizations if desired the set of possible stationary points of the algorithms is shown to be consistent with the convergent points obtained from the direct form versions of the steiglitz mcbride and output error methods whose properties are well studied the derived algorithms are as computationally efficient as existing direct form based algorithms while overcoming the stability problems associated with time varying direct form filters

wave diffraction by semi infinite venetian blind type grating the h polarized electromagnetic wave diffraction by semi infinite periodic venetian blind type grating is considered the grating consists of strips placed in the parallel planes the problem is reduced to a nonlinear operator equation with respect to the unknown reflection operator of a structure for its solution a complex approach which consists in using the successive over relaxation method and the gauss seidel method is suggested the near and far fields scattered by the grating are calculated the dependences of the reflection coefficient and diffraction patterns are analyzed for different incidence angles width of strips and distance between them

a mildly weaker sufficient condition in iir adaptive filtering the cross covariance matrix of two stable autoregressive ar sequences is considered a mildly weaker condition is identified that ensures the nonsingularity of this matrix as one consequence of this result a weaker sufficient condition is obtained that would guarantee the unimodality of the mean square output error surface of an iir adaptive filter with white noise excitation

semi infinite arrays of isotropic point scatterers a unified approach we solve the two dimensional problem of acoustic scattering by a semi infinite pe riodic array of identical isotropic point scatterers i e objects whose size is negligible compared to the incident wavelength and which are assumed to scatter incident waves uniformly in all directions this model is appropriate for scatterers on which dirichlet boundary conditions are applied in the limit as the ratio of wavelength to body size tends to infinity the problem is also relevant to the scattering of an e polarized electromagnetic wave by an array of highly conducting wires the actual geometry of each scatterer is characterized by a single parameter in the equations related to the single body scattering problem and determined from a harmonic boundary value problem using a mixture of analytical and numerical techniques we confirm that a number of phenomena reported for specific geometries are in fact present in the general case such as the presence of shadow boundaries in the far field and the vanishing of the circular wave scattered by the end of the array in certain specific directions we show that the semi infinite array problem is equivalent to that of inverting an infinite toeplitz matrix which in turn can be formulated as a discrete wiener hopf problem numerical results are presented which compare the amplitude of the wave diffracted by the end of the array for scatterers having different shapes