on error saturation nonlinearities in nlms adaptation the effect of a saturation type error nonlinearity in the weight update equation in normalized least mean square nlms adaptation is investigated for system identification for a white gaussian data model nonlinear recursions are derived for the weight mean error and mean square deviation msd that include the effect of an error function erf saturation type nonlinearity on the error sequence driving the algorithm the nonlinear recursion for the msd is solved numerically and shown in excellent agreement with monte carlo simulations supporting the theoretical model assumptions the theory is extended to tracking a markov channel and accurately predicts the tracking behavior as well the saturation behavior of the algorithm is easily studied by varying a single parameter in the error function varying from a linear device to a hard limiter for the white data case the excess mean square error emse is simply related to the msd the tradeoff between the extent of error saturation steady state emse and algorithm convergence rate is studied using these results

optimal prediction with memory abstract optimal prediction methods estimate the solution of nonlinear time dependent problems when that solution is too complex to be fully resolved or when data are missing the initial conditions for the unresolved components of the solution are drawn from a probability distribution and their effect on a small set of variables that are actually computed is evaluated via statistical projection the formalism resembles the projection methods of irreversible statistical mechanics supplemented by the systematic use of conditional expectations and new methods of solution for an auxiliary equation the orthogonal dynamics equation needed to evaluate a non markovian memory term the result of the computations is close to the best possible estimate that can be obtained given the partial data we present the constructions in detail together with several useful variants provide simple examples and point out the relation to the fluctuation dissipation formulas of statistical physics

adaptive filter performance with nonlinearities in the correlation multiplier it is well known that the correlation multiplier used to form the update signal in adaptive transversal filters need not be a true multiplier by using an approximate multiplier such as a sign bit only multiplier implementation can be made less costly in this paper we derive expressions for the convergence rate and misalignment noise of adaptive transversal filters with arbitrary correlation multiplier non linearities the analysis shows any such nonlinearities to always harm performance and quantifies the penalty suffered sign bit only multiplication suffers a significant penalty and power of two multiplication is suggested as a better alternative its performance is almost equal to that of a true multiplier and in a digital implementation at least it is only slightly more difficult to realize than a sign bit only multiplier the theory is developed in a way emphasizing physical understanding and has been verified to be in good agreement with simulation

non linear flexural flexural torsional extensional dynamics of beams i formulation abstract the non linear differential equations of motion and boundary conditions for euler bernoulli beams able to experience flexure along two principal directions and thus flexure in any direction in space torsion and extension are formulated the beam s material is assumed to be hookean but its properties may vary along its span the nonlinearities present in the differential equations include contributions from the curvature expression and from inertia terms a set of differential equations with polynomial nonlinearities to cubic order suitable for a perturbation analysis of the motion is also developed and the validity of the inextensional approximation is assessed the equations developed here reduce to those for an inextensional beam in part ii of this paper a specific example of application is analyzed and the results obtained are compared with those available in the literature where several non linear terms have been neglected a priori

an o n complexity recursive algorithm for multi flexible body dynamics based on absolute nodal coordinate formulation summary a new algorithm called recursive absolute nodal coordinate formulation algorithm rec ancf is presented for dynamic analysis of multi flexible body system including nonlinear large deformation this method utilizes the absolute nodal coordinate formulation ancf to describe flexible bodies and establishes a kinematic and dynamic recursive relationship for the whole system based on the articulated body algorithm aba in the ordinary differential equations odes obtained by the rec ancf a simple form of the system generalized jacobian matrix and generalized mass matrix is obtained thus a recursive forward dynamic solution is proposed to solve the odes one element by one element through an appropriate matrix manipulation utilizing the parent array to describe the topological structure the rec ancf is suitable for generalized tree multibody systems besides the cutting joint method is used in simple closed loop systems to make sure the o n algorithm complexity of the rec ancf compared with common ancf algorithms the rec ancf has several advantages the optimal algorithm complexity o n under limited processors simple derivational process no location or speed constraint violation problem higher algorithm accuracy the validity and efficiency of this method are verified by several numerical tests this article is protected by copyright all rights reserved

locally optimum adaptive signal processing algorithms we propose a new analytic method for comparing constant gain adaptive signal processing algorithms specifically estimates of the convergence speed of the algorithms allow for the definition of a local measure of performance called the efficacy that can be theoretically evaluated by definition the efficacy is consistent with the fair comparison techniques used in signal processing applications using the efficacy as a performance measure we prove that the lms newton algorithm is optimum and is thus the fastest algorithm within a very rich algorithmic class furthermore we prove that regular lms is better than any of its variants that apply the same nonlinear transformation on the elements of the regression vector such as signed regressor quantized regressor etc for an important class of input signals simulations support all our theoretical conclusions

on error saturation nonlinearities in lms adaptation the effect of a saturation type error nonlinearity in the weight update equation in least mean squares lms adaptation is investigated for a white gaussian data model nonlinear difference equations are derived for the eight first and second moments which include the effect of an error function erf saturation type nonlinearity on the error sequence driving the algorithm a nonlinear difference equation for the mean norm is explicitly solved using a differential equation approximation and integration by quadratures the steady state second moment weight behavior is evaluated exactly for the erf nonlinearity using the above results the tradeoff between the extent of error saturation steady state excess mean square error and rate of algorithm convergence is studied the tradeoff shows that 1 starting with a sign detector the convergence rate is increased by nearly a factor of two for each additional bit and 2 as the number of bits is increased further the additional bit by very little in convergence speed asymptotically approaching the behavior of the linear algorithm

tracking analysis of the sign algorithm in nonstationary environments a tracking analysis of the adaptive filters equipped with the sign algorithm and operating in nonstationary environments is presented under the assumption that the nonstationary can be modeled using a random disturbance it is shown that the long term time average of the mean absolute error is bounded and that there exists an optimal choice of the convergence constant mu which minimizes this quality applying the commonly used independence assumption and under the assumption that the nonstationarity is solely due to the time varying behavior of the optimal coefficients it is shown that the distributions of the successive coefficient misalignment vectors converge to a limiting distribution when the adaptive filter is used in the system identification mode finally under the additional assumption that the signals involved are zero mean and gaussian a set of nonlinear difference equations is derived that characterizes the mean and mean squared behavior of the filter coefficients and the mean squared estimation error during adaptation and tracking results of several experiments that show very good correlation with the theoretical analyses are presented

convergence and performance analysis of the normalized lms algorithm with uncorrelated gaussian data it is demonstrated that the normalized least mean square nlms algorithm can be viewed as a modification of the widely used lms algorithm the nlms is shown to have an important advantage over the lms which is that its convergence is independent of environmental changes in addition the authors present a comprehensive study of the first and second order behavior in the nlms algorithm they show that the nlms algorithm exhibits significant improvement over the lms algorithm in convergence rate while its steady state performance is considerably worse

particle filters for state estimation of jump markov linear systems jump markov linear systems jmls are linear systems whose parameters evolve with time according to a finite state markov chain in this paper our aim is to recursively compute optimal state estimates for this class of systems we present efficient simulation based algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixed lag smoothing problem our algorithms combine sequential importance sampling a selection scheme and markov chain monte carlo methods they use several variance reduction methods to make the most of the statistical structure of jmls computer simulations are carried out to evaluate the performance of the proposed algorithms the problems of on line deconvolution of impulsive processes and of tracking a maneuvering target are considered it is shown that our algorithms outperform the current methods

quantized kernel least mean square algorithm in this paper we propose a quantization approach as an alternative of sparsification to curb the growth of the radial basis function structure in kernel adaptive filtering the basic idea behind this method is to quantize and hence compress the input or feature space different from sparsification the new approach uses the redundant data to update the coefficient of the closest center in particular a quantized kernel least mean square qklms algorithm is developed which is based on a simple online vector quantization method the analytical study of the mean square convergence has been carried out the energy conservation relation for qklms is established and on this basis we arrive at a sufficient condition for mean square convergence and a lower and upper bound on the theoretical value of the steady state excess mean square error static function estimation and short term chaotic time series prediction examples are presented to demonstrate the excellent performance

random weight particle filtering of continuous time processes it is possible to implement importance sampling and particle filter algorithms where the importance sampling weight is random such random weight algorithms have been shown to be efficient for inference for a class of diffusion models as they enable inference without any time discretization approximation of the underlying diffusion model one difficulty of implementing such random weight algorithms is the requirement to have weights that are positive with probability 1 we show how wald s identity for martingales can be used to ensure positive weights we apply this idea to analysis of diffusion models from high frequency data for a class of diffusion models we show how to implement a particle filter which uses all the information in the data but whose computational cost is independent of the frequency of the data we use the wald identity to implement a random weight particle filter for these models which avoids time discretization error

coarse projective kmc integration forward reverse initial and boundary value problems in equation free multiscale computation a dynamic model is given at a fine microscopic level yet we believe that its coarse grained macroscopic dynamics can be described by closed equations involving only coarse variables these variables are typically various low order moments of the distributions evolved through the microscopic model we consider the problem of integrating these unavailable equations by acting directly on kinetic monte carlo microscopic simulators thus circumventing their derivation in closed form in particular we use projective multi step integration to solve the coarse initial value problem forward in time as well as backward in time under certain conditions macroscopic trajectories are thus traced back to unstable source type and even sometimes saddle like stationary points even though the microscopic simulator only evolves forward in time we also demonstrate the use of such projective integrators in a shooting boundary value problem formulation for the computation of coarse limit cycles of the macroscopic behavior and the approximation of their stability through estimates of the leading coarse floquet multipliers

analysis of multiscale methods for stochastic differential equations we analyze a class of numerical schemes proposed in 26 for stochastic differential equations with multiple time scales both advective and diffusive time scales are considered weak as well as strong convergence theorems are proven most of our results are optimal they in turn allow us to provide a thorough discussion on the efficiency as well as optimal strategy for the method c 2005 wiley periodicals inc

a recursive least m estimate algorithm for robust adaptive filtering in impulsive noise fast algorithm and convergence performance analysis this paper studies the problem of robust adaptive filtering in impulsive noise environment using a recursive least m estimate algorithm rlm the rlm algorithm minimizes a robust m estimator based cost function instead of the conventional mean square error function mse previous work has showed that the rlm algorithm offers improved robustness to impulses over conventional recursive least squares rls algorithm in this paper the mean and mean square convergence behaviors of the rlm algorithm under the contaminated gaussian impulsive noise model is analyzed a lattice structure based fast rlm algorithm called the huber prior error feedback least squares lattice h pef lsl algorithm is derived part of the h pef lsl algorithm was presented in icassp 2001 it has an order o n arithmetic complexity where n is the length of the adaptive filter and can be viewed as a fast implementation of the rlm algorithm based on the modified huber m estimate function and the conventional pef lsl adaptive filtering algorithm simulation results show that the transversal rlm and the h pef lsl algorithms have better performance than the conventional rls and other rls like robust adaptive algorithms tested when the desired and input signals are corrupted by impulsive noise furthermore the theoretical and simulation results on the convergence behaviors agree very well with each other

non linear dynamics of three dimensional rods exact energy and momentum conserving algorithms the long term dynamic response of non linear geometrically exact rods under going finite extension shear and bending accompanied by large overall motions is addressed in detail the central objective is the design of unconditionally stable time stepping algorithms which exactly preserve fundamental constants of the motion such as the total linear momentum the total angular momentum and for the hamiltonian case the total energy this objective is accomplished in two steps first a class of algorithms is introduced which conserves linear and angular momentum this result holds independently of the definition of the algorithmic stress resultants second an algorithmic counterpart of the elastic constitutive equations is developed such that the law of conservation of total energy is exactly preserved conventional schemes exhibiting no numerical dissipation symplectic algorithms in particular are shown to lead to unstable solutions when the high frequencies are not resolved compared to conventional schemes there is little if any additional computational cost involved in the proposed class of energy momentum methods the excellent performance of the new algorithm in comparison to other standard schemes is demonstrated in several numerical simulations

a mathematical framework for stochastic climate models there has been a recent burst of activity in the atmosphere ocean sciences community in utilizing stable linear langevin stochastic models for the unresolved degrees of freedom in stochastic climate prediction here a systematic mathematical strategy for stochastic climate modeling is developed and some of the new phenomena in the resulting equations for the climate variables alone are explored the new phenomena include the emergence of both unstable linear langevin stochastic models for the climate mean variables and the need to incorporate both suitable nonlinear effects and multiplicative noise in stochastic models under appropriate circumstances all of these phenomena are derived from a systematic self consistent mathematical framework for eliminating the unresolved stochastic modes that is mathematically rigorous in a suitable asymptotic limit the theory is illustrated for general quadratically nonlinear equations where the explicit nature of the stochastic climate modeling procedure can be elucidated the feasibility of the approach is demonstrated for the truncated equations for barotropic flow with topography explicit concrete examples with the new phenomena are presented for the stochastically forced three mode interaction equations the conjecture of smith and waleffe phys fluids 11 1999 1608 1622 for stochastically forced three wave resonant equations in a suitable regime of damping and forcing is solved as a byproduct of the approach examples of idealized climate models arising from the highly inhomogeneous equilibrium statistical mechanics for geophysical flows are also utilized to demonstrate self consistency of the mathematical approach with the predictions of equilibrium statistical mechanics in particular for these examples the reduced stochastic modeling procedure for the climate variables alone is designed to reproduce both the climate mean and the energy spectrum of the climate variables c 2001 john wiley sons inc

adaptive equalizer using finite bit power of two quantizer the stochastic gradient algorithm using a simplified arithmetic is analyzed in this paper a power of two quantizer is used for the input of the multiplier to reduce the multiplication to at most a simple shift in spite of its simple implementation the performance is shown to be comparable to the classical lms algorithm a linearized approximation to the quantizer is first derived followed by the analysis of an exact nonlinear model the derivation is based on the gaussian assumption and the effects of removing the gaussian assumption are later considered the roundoff error due to the finite bit computation is calculated computer simulation results are provided to support the analysis

stochastic gradient adaptation under general error criteria examines a family of adaptive filter algorithms of the form w sub k 1 w sub k spl mu f d sub k w sub k sup t x sub k x sub k in which f spl middot is a memoryless odd symmetric nonlinearity acting upon the error such algorithms are a generalization of the least mean square lms adaptive filtering algorithm for even symmetric error criteria for this algorithm family the authors derive general expressions for the mean and mean square convergence of the filter coefficients for both arbitrary stochastic input data and gaussian input data they then provide methods for optimizing the nonlinearity to minimize the algorithm misadjustment for a given convergence rate using the calculus of variations it is shown that the optimum nonlinearity to minimize misadjustment near convergence under slow adaptation conditions is independent of the statistics of the input data and can be expressed as p x p x where p x is the probability density function of the uncorrelated plant noise for faster adaptation under the white gaussian input and noise assumptions the nonlinearity is shown to be x 1 spl mu spl lambda x sup 2 spl sigma sub k sup 2 where spl lambda is the input signal power and spl sigma sub k sup 2 is the conditional error power thus the optimum stochastic gradient error criterion for gaussian noise is not mean square it is shown that the equations governing the convergence of the nonlinear algorithm are exactly those which describe the behavior of the optimum scalar data nonlinear adaptive algorithm for white gaussian input simulations verify the results for a host of noise interferences and indicate the improvement using non mean square error criteria

sequential imputations and bayesian missing data problems abstract for missing data problems tanner and wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors their method of constructing the complete data sets is closely related to the gibbs sampler both required iterations and similar to the em algorithm convergence can be slow we introduce in this article an alternative procedure that involves imputing the missing data sequentially and computing appropriate importance sampling weights in many applications this new procedure works very well without the need for iterations sensitivity analysis influence analysis and updating with new data can be performed cheaply bayesian prediction and model selection can also be incorporated examples taken from a wide range of applications are used for illustration

nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales we present an efficient numerical algorithm for simulating chemical kinetic systems with multiple time scales this algorithm is an improvement of the traditional stochastic simulation algorithm ssa also known as gillespie s algorithm it is in the form of a nested ssa and uses an outer ssa to simulate the slow reactions with rates computed from realizations of inner ssas that simulate the fast reactions the algorithm itself is quite general and seamless and it amounts to a small modification of the original ssa our analysis of such multi scale chemical kinetic systems allows us to identify the slow variables in the system derive effective dynamics on the slow time scale and provide error estimates for the nested ssa efficiency of the nested ssa is discussed using these error estimates and illustrated through several numerical examples

adaptive threshold nonlinear algorithm for adaptive filters with robustness against impulse noise a new adaptation algorithm for adaptive filters is proposed introducing adaptive threshold in the nonlinear correlation function the adaptive threshold controlled by the long term average of the error signal power makes the filtering system highly robust against impulse noise which is demonstrated by the results of simulation and theoretical calculation

convergence analysis of an algorithm for blind equalization the authors consider a key algorithm for blind equalization and derive expressions for the evolution of the equalizer output error trajectory the authors develop a model to examine the convergence behavior of this algorithm suitable approximations are incorporated into the model to facilitate analysis the validity of these approximations is demonstrated for a typical communication channel it is shown that even for a channel for which the assumption of gaussianity of the equalizer input data may not be very good the analysis presented predicts the convergence behavior reasonably well

convergence of the signed output error adaptive identifier this paper considers an adaptive output error identifier with a signum function in its update kernel it is shown that the classical strict positive real spr condition required for the convergence of traditional adaptive identifiers does not suffice for the convergence of this signed identifier instead what is needed is a stronger operator condition called the strict dominant passive sdp condition we give an analog of the kalman yakubovic popov lemma for the sdp conditions and using it give a convergence proof under the assumptions of persistent excitation and sdp

on weight update saturation nonlinearities in lms adaptation the effect of a saturation type nonlinearity in the weight update equation in least mean square lms adaptation is investigated for a white gaussian data model nonlinear difference equations that include the effect of a 1 e sup ax saturation type nonlinearity on the update term driving the algorithm are derived for the weight first and second moments a nonlinear difference equation for the mean norm is explicitly solved using a differential equation approximation and integration by quadratures the steady state second moment weight behavior is evaluated approximately for the nonlinearity using these results the tradeoff between the extent of weight update saturation steady state excess mean square error and rate of algorithm convergence is studied for the same steady state misadjustment error the tradeoff results are discussed

analysis of the normalized lms algorithm with gaussian inputs the lms adaptive filter algorithm requires a priori knowledge of the input power level to select the algorithm gain parameter for stability and convergence since the input power level is usually one of the statistical unknowns it is normally estimated from the data prior to beginning the adaptation process it is then assumed that the estimate is perfect in any subsequent analysis of the lms algorithm behavior in this paper the effects of the power level estimate are incorporated in a data dependent that appears explicitly within the algorithm the transient mean and second moment behavior of the modified lms nlms algorithm are evaluated taking into account the explicit statistical dependence of upon the input data the mean behavior of the algorithm is shown to converge to the wiener weight a constant coefficient matrix difference equation is derived for the weight fluctuations about the wiener weight the equation is solved for a white data covariance matrix and for the adaptive line enhancer with a single frequency input in steady state for small expressions for the misadjustment error are also presented it is shown for the white data covariance matrix case that the averaging of about ten data samples causes negligible degradation as compared to the lms algorithm in the ale application the steady state weight fluctuations are shown to be mode dependent being largest at the frequency of the input

application of the absolute nodal co ordinate formulation to multibody system dynamics abstract the floating frame of reference formulation is currently the most widely used approach in flexible multibody simulations the use of this approach however has been limited to small deformation problems in this investigation the computer implementation of the newabsolute nodal co ordinate formulationand its use in the small and large deformation analysis of flexible multibody systems that consist of interconnected bodies are discussed while in the floating frame of reference formulation a mixed set of absolute reference and local elastic co ordinates are used in the absolute nodal co ordinate formulation only absolute co ordinates are used in the absolute nodal co ordinate formulation new interpretation of the nodal co ordinates of the finite elements is used no infinitesimal or finite rotations are used as nodal co ordinates from beams and plates instead global slopes are used to define the element nodal co ordinates using this interpretation of the element co ordinates beams and plates can be considered as isoparametric elements and as a result exact modelling of the rigid body dynamics can be obtained using the element shape function and the absolute nodal co ordinates unlike the floating frame of reference approach no co ordinate transformation is required in order to determine the element inertia the mass matrix of the finite elements is a constant matrix and therefore the centrifugal and coriolis forces are equal to zero when the absolute nodal co ordinate formulation is used another advantage of using the absolute nodal co ordinate formulation in the dynamic simulation of multibody systems is its simplicity in imposing some of the joint constraints and also its simplicity in formulating the generalized forces due to spring damper elements the results obtained in this investigation show an excellent agreement with the results obtained using the floating frame of reference formulation when large rotation small deformation problems are considered

particle filtering with path sampling and an application to a bimodal ocean current model this paper introduces a recursive particle filtering algorithm designed to filter high dimensional systems with complicated non linear and non gaussian effects the method incorporates a parallel marginalization pmmc step in conjunction with the hybrid monte carlo hmc scheme to improve samples generated by standard particle filters parallel marginalization is an efficient markov chain monte carlo mcmc strategy that uses lower dimensional approximate marginal distributions of the target distribution to accelerate equilibration as a validation the algorithm is tested on a 2516 dimensional bimodal stochastic model motivated by the kuroshio current that runs along the japanese coast the results of this test indicate that the method is an attractive alternative for problems that require the generality of a particle filter but have been inaccessible due to the limitations of standard particle filtering strategies

projective methods for stiff differential equations problems with gaps in their eigenvalue spectrum we show that there exist classes of explicit numerical integration methods that can handle very stiff problems if the eigenvalues are separated into two clusters one containing the stiff or fast components and one containing the slow components these methods have large average step sizes relative to the fast components conventional implicit methods involve the solution of nonlinear equations at each step which for large problems requires significant communication between processors on a multiprocessor machine for such problems the methods proposed here have significant potential for speed improvement

development of simple models for the elastic forces in the absolute nodal co ordinate formulation abstract the objective of this study is to develop simple and accurate elastic force models that can be used in the absolute nodal co ordinate formulation for the analysis of two dimensional beams these force models which account for the coupling between bending and axial deformations are derived using a continuum mechanics approach without the need for introducing a local element co ordinate system four new different force models that include different degrees of complexity are presented it is shown that the vector of the elastic forces can be significantly simplified as compared to the elastic force model developed for the absolute nodal co ordinate formulation using a local element frame 1 despite the simplicity of the new models they account for elastic non linearity in the strain displacement relationship therefore they lead to more accurate results as compared to the more complex models developed using the local frame method which does not account for the non linearities in the strain displacement relationships numerical results are presented in order to demonstrate the use of the new models and test their performances in the analysis of large deformations of flexible multibody systems

energy preserving decaying schemes for non linear beam dynamics using the helicoidal approximation abstract we develop two unconditionally stable displacement based time stepping schemes for the non linear dynamic response of beams the first algorithm guarantees the exact discrete conservation of energy and momentum the second is associated with an energy decay inequality that achieves control of the unresolved frequencies by means of a numerical dissipation mechanism both schemes emanate from a weak form of the equations of dynamic equilibrium referred to a fixed pole space and time discretizations are based on the exponential parameterization of motion this implies that the beam reference line and the trajectories of the beam nodes are helicoids in space the exponential mapping approach allows a unified treatment of translations and rotations greatly simplifying the derivation of the algorithms and their analysis the capabilities and performance of the new schemes are demonstrated and discussed with the aid of numerical simulations

finite elements using absolute nodal coordinates for large deformation flexible multibody dynamics a family of structural finite elements using a modern absolute nodal coordinate formulation ancf is discussed in the paper with many applications this approach has been initiated in 1996 by a shabana it introduces large displacements of 2d 3d finite elements relative to the global reference frame without using any local frame the elements employ finite slopes as nodal variables and can be considered as generalizations of ordinary finite elements that use infinitesimal slopes in contrast to other large deformation formulations the equations of motion contain constant mass matrices and generalized gravity forces as well as zero centrifugal and coriolis inertia forces the only nonlinear term is a vector of elastic forces this approach allows applying known abstractions of real elastic bodies euler bernoulli beams timoshenko beams and more general models as well as kirchhoff and mindlin plate theories shabana et al proposed a sub family of thick beam and plate finite elements with large deformations and employ the 3d theory of continuum mechanics despite the universality of such approach it has to use extra degrees of freedom when simulating thin beams and plates which case is most important in our research we propose another sub family of thin beams as well as rectangular and triangle plates we use kirchhoff plate theory with nonlinear strain displacement relationships to obtain elastic forces a number of static and dynamic simulation examples of problems with 2d 3d very elastic beams and plate underwent large displacements and or deformations will be shown in the presentation

improved convergence analysis of stochastic gradient adaptive filters using the sign algorithm convergence analysis of stochastic gradient adaptive filters using the sign algorithm is presented in this paper the methods of analysis currently available in literature assume that the input signals to the filter are white this restriction is removed for gaussian signals in our analysis expressions for the second moment of the coefficient vector and the steady state error power are also derived simulation results are presented and the theoretical and empirical curves show a very good match

characterizing persistent excitation for the sign sign equation error identifier abstract the sign sign ss algorithm is a computationally efficient adaptive identifier often used in signal processing tasks it is obtained by introducing signum functions on both the regressor and the prediction error multiplicands in the update kernel of the well known lms algorithm this paper gives a deterministic persistent excitation condition on the regressor sequence which guarantees ss convergence it also gives conditions under which ss may diverge and discusses how these persistent excitation conditions may be verified through a finite amount of computations

analysis and implementation of variable step size adaptive algorithms stochastic gradient adaptive filtering algorithms using variable step sizes are investigated the variable step size algorithm improves the convergence rate while sacrificing little in steady state error expressions describing the convergence of the mean and mean squared values of the coefficients are developed and used to calculate the mean square error evolution the initial convergence rate and the steady state error are also investigated the performance of the algorithm is studied when a power of two quantizer algorithm is used and finite word length effects are considered the analytical results are verified with simulations encompassing variable applications two cmos implementations of the variable step size power of two quantizer algorithm are presented to demonstrate that the performance gains are attainable with only a modest increase in circuit complexity

a dynamic convergence analysis of blind equalization algorithms blind equalizers do not require a training sequence to start up or to restart after a communications breakdown making them particularly useful in applications such as broadcast and point to multipoint networks we study in parallel the dynamic convergence behavior of three blind equalization algorithms the multimodulus algorithm mma the constant modulus algorithm cma and the reduced constellation algorithm rca using a conditional gaussian approximation we first derive the theoretical mean squared error mse trajectory for mma this analysis leads to accurate but somewhat cumbersome expressions alternatively we apply a taylor series approximation to derive mse trajectories for mma cma and rca this approach yields simpler but somewhat less accurate expressions for the steady state operation however we derive even simpler formulas that accurately predict the asymptotic mse values we finally study the convergence rates of the three blind algorithms using their theoretical mse trajectories computer simulations and a laboratory experiment

on the optimum data nonlinearity in lms adaptation the effect of an arbitrary nonlinear operation on the data input to the weight update equation in the lms adaptive algorithm is investigated for a gaussian data model exact difference equations are derived for the weight first and second moments that include the effects of an arbitrary nonlinear operation on the data sequence the difference equations are used to obtain expressions for the transient behavior of the mean square error the mean square error is minimized over the choice of nonlinearity for a fixed transient behavior the best choice of nonlinearity is shown exactly to be of the form x 1 bx2 when the input data are white for an arbitrary data covariance matrix the optimum nonlinearity is shown to be linear when the product of the algorithm step size and input power is much less than unity

performance analysis of adaptive filters equipped with the dual sign algorithm a convergence analysis for stochastic gradient adaptive filters equipped with the dual sign algorithm dsa is presented expressions for the mean and mean squared values of the coefficient misalignment vector are derived under the assumption that the input signal is gaussian the main differences between the current analysis and previous analyses are 1 the present analysis is valid for arbitrary autocorrelation matrices and 2 the analysis does not approximate the behavior for the dsa as switching between two sign algorithms a certain amount of time after the dsa is initialized a simulation example comparing the analytical results with empirical ones is presented and the two curves show excellent agreement with each other

on the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach abstract in finite element methods that are based on position and slope coordinates a representation of axial and bending deformation by means of an elastic line approach has become popular such beam and plate formulations based on the so called absolute nodal coordinate formulation have not yet been verified sufficiently enough with respect to analytical results or classical nonlinear rod theories examining the existing planar absolute nodal coordinate element which uses a curvature proportional bending strain expression it turns out that the deformation does not fully agree with the solution of the geometrically exact theory and even more serious the normal force is incorrect a correction based on the classical ideas of the extensible elastica and geometrically exact theories is applied and a consistent strain energy and bending moment relations are derived the strain energy of the solid finite element formulation of the absolute nodal coordinate beam is based on the st venant kirchhoff material therefore the strain energy is derived for the latter case and compared to classical nonlinear rod theories the error in the original absolute nodal coordinate formulation is documented by numerical examples the numerical example of a large deformation cantilever beam shows that the normal force is incorrect when using the previous approach while a perfect agreement between the absolute nodal coordinate formulation and the extensible elastica can be gained when applying the proposed modifications the numerical examples show a very good agreement of reference analytical and numerical solutions with the solutions of the proposed beam formulation for the case of large deformation pre curved static and dynamic problems including buckling and eigenvalue analysis the resulting beam formulation does not employ rotational degrees of freedom and therefore has advantages compared to classical beam elements regarding energy momentum conservation

weak convergence and local stability properties of fixed step size recursive algorithms a recursive equation that subsumes several common adaptive filtering algorithms is analyzed for general stochastic inputs and disturbances by relating the motion of the parameter estimate errors to the behavior of an unforced deterministic ordinary differential equation ode the odes describing the motion of several common adaptive filters are examined in some simple settings including the least mean square lms algorithm and all three of its signed variants the signed regressor the signed error and the sign sign algorithms stability and instability results are presented in terms of the eigenvalues of a correlation like matrix this generalizes known results for lms signed regressor lms and signed error lms and gives new stability criteria for the sign sign algorithm the ability of the algorithms to track moving parameterizations can be analyzed in a similar manner by relating the time varying system to a forced ode the asymptotic distribution about the forced ode is an ornstein uhlenbeck process the properties of which can be described in a straightforward manner

blind deconvolution via sequential imputations abstract the sequential imputation procedure is applied to adaptively and sequentially reconstruct discrete input signals that are blurred by an unknown linear moving average channel and contaminated by additive gaussian noises a problem known as blind deconvolution in digital communication a rejuvenation procedure for improving the efficiency of sequential imputation is introduced and theoretically justified the proposed method does not require the channel to be nonminimum phase and can be used in real time signal restoration two simulated systems are studied to illustrate the proposed method our result shows that the ideas of multiple imputations and flexible simulation techniques are as powerful in engineering as in survey sampling

variance reduction for particle filters of systems with time scale separation we present a particle filter construction for a system that exhibits time scale separation the separation of time scales allows two simplifications that we exploit 1 the use of the averaging principle for the dimensional reduction of the dynamics for each particle during the prediction step and 2 the factorization of the transition probability for the rao blackwellization of the update step the resulting particle filter is faster and has smaller variance than the particle filter based on the original system the method is tested on a multiscale stochastic differential equation and on a multiscale pure jump diffusion motivated by chemical reactions

on the convergence behavior of the lms and the normalized lms algorithms it is shown that the normalized least mean square nlms algorithm is a potentially faster converging algorithm compared to the lms algorithm where the design of the adaptive filter is based on the usually quite limited knowledge of its input signal statistics a very simple model for the input signal vectors that greatly simplifies analysis of the convergence behavior of the lms and nlms algorithms is proposed using this model answers can be obtained to questions for which no answers are currently available using other perhaps more realistic models examples are given to illustrate that even quantitatively the answers obtained can be good approximations it is emphasized that the convergence of the nlms algorithm can be speeded up significantly by employing a time varying step size the optimal step size sequence can be specified a priori for the case of a white input signal with arbitrary distribution

normalized data nonlinearities for lms adaptation properly designed nonlinearly modified lms algorithms in which various quantities in the stochastic gradient estimate are operated upon by memoryless nonlinearities have been shown to perform better than the lms algorithm in system identification type problems the authors investigate one such algorithm given by w sub k l w sub k spl mu d sub k w sub k sup t x sub k x sub k f x sub k in which the function f x sub k is a scalar function of the sum of the squares of the n elements of the input data vector x sub k this form of algorithm generalizes the so called normalized lms nlms algorithm they evaluate the expected behavior of this nonlinear algorithm for both independent input vectors and correlated gaussian input vectors assuming the system identification model by comparing the nonlinear algorithm s behavior with that of the lms algorithm they then provide a method of optimizing the form of the nonlinearity for the given input statistics in the independent input case they show that the optimum nonlinearity is a single parameter version of the nlms algorithm with an additional constant in the denominator and show that this algorithm achieves a lower excess mean square error mse than the lms algorithm with an equivalent convergence rate additionally they examine the optimum step size sequence for the optimum nonlinear algorithm and show that the resulting algorithm performs better and is less complex to implement than the optimum step size algorithm derived for another form of the nlms algorithm simulations verify the theory and the predicted performance improvements of the optimum normalized data nonlinearity algorithm

a two dimensional shear deformable beam element based on the absolute nodal coordinate formulation in this study a new two dimensional shear deformable beam element is proposed for large deformation problems the kinematics of the beam are defined using an exact displacement field where the rotation angles of the cross section caused by bending and shear deformations are described separately cubic interpolation is used for determining the curvature of the beam due to bending while linear interpolation polynomials are used for the shear strain the absolute nodal coordinate formulation in which global displacements and slopes are used as the nodal coordinates is employed for the finite element discretization of the beam the capability of the element to predict static deformation is studied using numerical examples the results imply that the element is free of a phenomenon called shear locking the capability of the element to model highly nonlinear behaviour is established using a bending test where the cantilever is bent into a full circle using only four elements a flexible pendulum and a spin up manoeuvre are modelled in order to study the behaviour of the element in dynamical problems the proposed element is also compared with an existing shear deformable beam element based on the absolute nodal coordinate formulation finally the simple linearization of the beam curvature based on the assumption of small strain will be discussed

analysis of adaptive filters using normalized signed regressor lms algorithm in this paper adaptive filters using the normalized signed regressor lms algorithm nsra with gaussian reference inputs are proposed and analyzed to yield difference equations for theoretically calculating expected convergence of the filters a simple difference equation for mean squared error mse is derived when the filter input is a white and gaussian process whereas approximate difference equations for colored gaussian inputs are proposed and tested stability conditions and residual mse after convergence are also obtained agreement of theoretical results with those of simulation in the experiment with some examples of filter convergence shows sufficient accuracy of the theory and assures the usefulness of the difference equations in estimating filter performances thus facilitating the design of adaptive filters using the nsra