on the maximum entropy negation of a probability distribution we suggest a transformation to obtain the negation of a probability distribution we investigate the properties of this negation using the dempster shafer theory of evidence we show of all the possible negations our proposed negation is one having a maximal type entropy

on almost sure bounds for the lms algorithm almost sure a s bounds for linear constant gain adaptive filtering algorithms are investigated for instance under general pseudo stationarity and dependence conditions on the driving data spl psi k k 1 2 3 y sub k k 0 1 2 a s convergence and rates of a s convergence as the algorithm gain spl epsiv spl rarr 0 are established for the lms algorithm h sub k 1 sup spl epsiv h sub k sup spl epsiv spl epsiv y sub k spl psi sub k 1 y sub k sup t h sub k sup spl epsiv subject to some nonrandom initial condition h sub 0 sup spl epsiv h sub 0 in particular defining g sub k sup spl epsiv sub k 0 sup spl infin by g sub 0 sup spl epsiv h sub 0 and g sub k 1 sup spl epsiv g sub k sup spl epsiv spl epsiv e y sub k spl psi sub k 1 e y sub k y sub k sup t g sub k sup spl epsiv for k 0 1 2 the author shows that for any spl gamma 0 max sub 0 spl les k spl les spl gamma spl epsiv 1 h sub k sup spl epsiv g sub k sup spl epsiv spl rarr 0 as spl epsiv spl rarr 0 a s and under a stronger dependency condition the author shows that for any 0 0 max sub 0 spl les k spl les spl gamma spl epsiv spl zeta h sub k sup spl epsiv g sub k sup spl epsiv converges as spl epsiv spl rarr 0 a s at a rate marginally slower than o spl epsiv sup 2 spl zeta log log spl epsiv sup spl zeta sup 1 2 then under a stronger pseudostationarity assumption it is shown that similar results hold if the sequences g sub k sup spl epsiv sub k 0 sup spl infin spl epsiv 0 in the above results are replaced with the solution g sup 0 spl middot of a nonrandom linear ordinary differential equation i e one has max sub 0 spl les k spl les spl gamma spl epsiv spl zeta h sub k sup spl epsiv g sup 0 spl epsiv k spl rarr 0 as spl epsiv spl rarr 0 a s where one can attach a rate to this convergence under the stronger dependency condition the almost sure bounds contained in the paper complement previously developed weak convergence results in kushner and shwartz ieee trans information theory it 30 2 177 182 1984 and as are near optimal moreover the proofs used to establish these bounds are quite elementary

convergence of the sign algorithm for adaptive filtering with correlated data convergence of a decreasing gain sign algorithm sa for adaptive filtering is analyzed the presence of the hard limiter in the algorithm makes a rigorous analysis difficult therefore there are few results available such results normally include restrictive assumptions such as the assumptions that successive observation vectors are independent and the new error signal of the adaptive filter has a time invariant probability density function the former assumption is not valid in the context of adaptive filtering since two successive observation vectors share most of their components while the latter assumption is a restriction on the adaptive weights whose evolution is a priori unknown in lieu of using these assumptions an almost sure convergence of the sa is proved under the assumption that the sequence of observation vectors is m dependent this assumption allows strong correlation between successive observations

analysis of boundedness and convergence of online gradient method for two layer feedforward neural networks this paper presents a theoretical boundedness and convergence analysis of online gradient method for the training of two layer feedforward neural networks the well known linear difference equation is extended to apply to the general case of linear or nonlinear activation functions based on this extended difference equation we investigate the boundedness and convergence of the parameter sequence of concern which is trained by finite training samples with a constant learning rate we show that the uniform upper bound of the parameter sequence which is very important in the training procedure is the solution of an inequality regarding the bound it is further verified that for the case of linear activation function a solution always exists and moreover the parameter sequence can be uniformly upper bounded while for the case of nonlinear activation function some simple adjustment methods on the training set or the activation function can be derived to improve the boundedness property then for the convergence analysis it is shown that the parameter sequence can converge into a zone around an optimal solution at which the error function attains its global minimum where the size of the zone is associated with the learning rate particularly for the case of perfect modeling a strong global convergence result where the parameter sequence can always converge to an optimal solution is proved

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 analysis of self adaptive equalizers a theoretical analysis of self adaptive equalization for data transmission is carried out starting from known convergence results for the corresponding trained adaptive filter the development relies on a suitable ergodicity model for the sequence of observations at the output of the transmission channel thanks to the boundedness of the decision function used for data recovery it can be proved that the algorithm is bounded strong convergence results can be reached when a perfect noiseless equalizer exists the algorithm will converge to it if the eye pattern is initially open otherwise convergence may take place towards certain other stationary points of the algorithm for which domains of attraction have been defined some of them will result in a poor error rate the case of a noisy channel exhibits limit points for the algorithm that differ from those of the classical trained algorithm the stronger the noise the greater the difference is one of the principal results of this study is the proof of the stability of the usual decision feedback algorithms once the learning period is over

application of dcim to mpie mom analysis of 3d pec objects in multilayered media the formulation c green s functions for multilayered media are reformulated in this paper to extract z dependent part when the source and observation points are in different layers the discrete complex image method dcim is applied to obtain complex images independent on z but dependent on z spl acute for simulation of three dimensional 3 d perfectly electrical conduction pec objects penetrating two or more layers tables of complex images are built in a z spl acute grid during the matrix filling stage of the mixed potential integral equation together with method of moments mpie mom the spatial domain green s functions are interpolated from values in the z spl acute grid while these values are calculated from complex images in the z spl acute grid this interpolation scheme is more efficient than those directly storing the spatial domain green s functions numerical examples are given for analyzing a dipole in a two layered media

convergence of the robbins monro method for linear problems in a banach space on etudie la convergence de la methode de robbins monro pour les problemes lineaires dans un espace de banach

analysis of mean square error and transient speed of the lms adaptive algorithm for the least mean square lms algorithm we analyze the correlation matrix of the filter coefficient estimation error and the signal estimation error in the transient phase as well as in steady state we establish the convergence of the second order statistics as the number of iterations increases and we derive the exact asymptotic expressions for the mean square errors in particular the result for the excess signal estimation error gives conditions under which the lms algorithm outperforms the wiener filter with the same number of taps we also analyze a new measure of transient speed we do not assume a linear regression model the desired signal and the data process are allowed to be nonlinearly related the data is assumed to be an instantaneous transformation of a stationary markov process satisfying certain ergodic conditions

quiver diagrams and signed adaptive filters a graphical technique for exploring the behavior of deterministic discrete time adaptive algorithms excited by periodic inputs is examined the constraint to periodic inputs is convenient the underlying concepts used also apply to stationary inputs drawn from finite alphabets the resulting graph is based on plotting single period parameter trajectories in the parameter error space and is essentially a discrete version of flow diagrams associated with continuous time systems for the least mean square lms adaptive fir filter with the algorithm step size sufficiently small the change of adapted parameters from a particular initial value is given by the total update over the input period with the parameterization frozen at its initial value this results in the familiar elliptical hyperparaboloid surface steepest descent interpretation this method can be extended to the lms adaptive infinite input response iir filter with suitable approximations based on a small step size

on the almost sure rate of convergence of linear stochastic approximation algorithms the almost sure rate of convergence of linear stochastic approximation algorithms is analyzed as the main result it is demonstrated that their almost sure rate of convergence is equivalent to the almost sure rate of convergence of the averages of their input data sequences as opposed to most of the existing results on the rate of convergence of stochastic approximation which cover only algorithms with the noise decomposable as the sum of a martingale difference vanishing and telescoping sequence the main results of this paper hold under assumptions not requiring the input data sequences to admit any particular decomposition although no decomposition of the input data sequences is required the results on the almost sure rate of convergence of linear stochastic approximation algorithms obtained in this correspondence are as tight as the rate of convergence in the law of iterated logarithm moreover the main result of this correspondence yields the law of iterated logarithm for linear stochastic approximation if the law of iterated logarithm holds for the input data sequences the obtained general results are illustrated with two nontrivial examples where the input data sequences are strongly mixing strictly stationary random processes or functions of a uniformly ergodic markov chain these results are also applied to the analysis of least mean square lms algorithms

on convergence analysis of fractionally spaced adaptive blind equalizers in this paper we study the convergence analysis of fractionally spaced adaptive blind equalizers we show that based on the trivial and nontrivial nullspaces of a channel convolution matrix all equilibria can be classified as channel dependent equilibria cde or algorithm dependent equilibria ade because oversampling provides channel diversity the nullspace of the channel convolution matrix is affected we show that fractionally spaced equalizers fses do not possess any cde if a length zero condition is satisfied the convergence behavior of these fse are clearly determined by the specific choice of cost function alone we characterize the global convergence ability of several popular algorithms simply based on their ade we also present an fse implementation of the super exponential algorithm we show that the fse implementation does not introduce any nonideal approximation simulation results are also presented to illustrate the robustness and the improved performance of fse under the super exponential algorithm

convergence analysis of adaptive linear estimation for dependent stationary processes the convergence properties of an adaptive linear mean square estimator that uses a modified lms algorithm are established for generally dependent processes bounds on the mean square error of the estimates of the filter coefficients and on the excess error of the estimate of the signal are derived for input processes which are either strong mixing or asymptotically uncorrelated it is shown that the mean square deviation is bounded by a constant multiple of the adaptation step size and that the same holds for the excess error of the signal estimation the present findings extend earlier results in the literature obtained for independent and m dependent input data

stochastic approximation with correlated data new almost sure convergence results for a special form of the multidimensional robbins monro stochastic approximation procedure are developed the results are applicable to cases where the training data is heavily correlated no conditional expectation properties or boundedness assumptions are required to apply the new results for example when the data sequence is normal and i m dependent ii autoregressive moving average or iii band limited the results can be used to establish the almost sure convergence of each algorithm treated the special form of the robbins monro procedure considered is motivated by a consideration of several algorithms that have been proposed for discrete time adaptive signal processing applications most of these algorithms can also be viewed as stochastic gradient following algorithm the ease with which the new results can be applied is illustrated

adaptive filtering with binary reinforcement recently there has been increased interest in high speed adaptive filtering where the usual stochastic gradient or least mean square lms algorithm is replaced with the simpler algorithm where adaptation is guided only by the polarity of the error signal in this paper the convergence of this binary reinforcement br algorithm is proved under the usual independence assumption and the surprising observation is made that unlike the lms algorithm convergence occurs for any positive value of the step size parameter while the stochastic gradient algorithm attempts to minimize a mean square error cost function the binary reinforcement algorithm in fact attempts to minimize a mean absolute error cost function it is proved for the binary reinforcement algorithm that the tap weight vector converges in distribution to a random vector that is suitably concentrated about the optimal value based on a least mean absolute error cost function for a sufficiently small step size the expected cost of the asymptotic weight vector can be made as close as desired to thc minimum cost attain ed by the optimum weight vector

comparison of the convergence of two algorithms for adaptive fir digital filters the convergence properties of two different algorithms for the updating of the coefficients of an adaptive fir digital filter are investigated and compared with one another these algorithms are the stochastic iteration algorithm and the sign algorithm in this latter algorithm a one bit gradient estimation is used which makes its implementation very simple the convergence is characterized by the residual echo variance after convergence and a parameter that indicates the speed of the convergence it is shown that the convergence of the sign algorithm can always be assured but is much slower than that of the stochastic iteration algorithm if the same variance of the residual echo is to be obtained

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

on the completion of qualitative possibility measures a relational description of a possibility introduced by d dubois and h prade in their 1988 book called a qualitative possibility measure is discussed among the requirements of these kinds of relationships is that they be complete the focus is on the issue of completing these relationships a measure associated with weak orderings called buoyancy is introduced the principle of maximal buoyancy is suggested as a means for completion the connection between the principle of maximal buoyancy and the principle of minimal specificity is shown a special family of buoyancy measures called badd buoyancies is also introduced that have the properties of entropy measures when the aggregates are restricted to be a probability distribution

complex time representation of the sommerfeld type integrals and its application to 1 d periodic structures the concept of complex time is employed to derive the time domain representation of the green s function of a periodic structure for the first time the spatial domain green s function of the periodic structure in the frequency domain is separated into singular and nonsingular terms the nonsingular terms are approximated by using exponential functions resulting in the well known complex time representation of the time domain green s function in order to find a closed form expression for the singular terms a novel time domain representation of the sommerfeld type integrals is derived the proposed procedure is applied to the computation of the time domain green s function of a one dimensional periodic structure numerical experiments demonstrate the high accuracy of this method

gradient algorithms for designing predictive vector quantizers a predictive vector quantizer pvq is a vector extension of a predictive quantizer it consists of two parts a conventional memoryless vector quantizer vq and a vector predictor two gradient algorithms for designing a pvq are developed in this paper the steepest descent sd algorithm and the stochastic gradient sg algorithm both have the property of improving the quantizer and the predictor in the sense of minimizing the distortion as measured by the average mean squared error the differences between the two design approaches are the period and the step size used in each iteration to update the codebook and predictor the sg algorithm updates once for each input training vector and uses a small step size while the sd updates only once for a long period possibly one pass over the entire training sequence and uses a relatively large step size code designs and tests are simulated for both gauss markov sources and for sampled speech waveforms and the results are compared to codes designed using techniques that attempt to optimize only the quantizer for the predictor and not vice versa

tracking analysis of the sign sign algorithm for nonstationary adaptive filtering with gaussian data this correspondence is concerned with the analysis of the sign sign algorithm ssa when used to track a plant with randomly time varying parameters the input of the plant and the plant noise are assumed stationary and gaussian the paper derives expressions of the steady state excess mean square error spl xi the steady state mean square weight misalignment spl eta and the step sizes that minimize each one of them the paper also presents a comparison among the tracking properties of the ssa the sign algorithm sa and the signed regressor algorithm sra it is found that the three algorithms share the features that 1 spl xi does not depend on the eigenvalue spread of the input covariance matrix 2 spl eta depends on the eigenvalue spread and 3 the step size that minimizes spl xi is different from the one that minimizes spl eta the minimum values of spl xi attained by the sa and the sra are equal to each other and they are 1 db less than the one attained by the ssa the ratio of the minimum value of spl eta of the ssa to the one of the sa is found to be dependent on the input eigenvalue spread for equal eigenvalues this ratio is equal to 1 db the minimum value of spl eta of the ssa is found to be 1 db higher than the one of the sra independently of the input eigenvalue spread it is found that an advantage of the ssa with respect to both the sa and the sra is that the two optimum step sizes of the ssa are independent of the mean square plant input and the mean square plant noise

the 2r th mean convergence of adaptive filters with stationary dependent random variables the 2r th mean convergence of an adaptive filtering algorithm c n 1 c n a n c n t x n alpha n x n is studied where alpha n s and x n s are useful random signals and observation vectors respectively and a n is a sequence of positive numbers decreasing to zero in this work we suppose that the sequence alpha n x n is a stationary mixing sequence rho mixing phi mixing or psi mixing under some additional conditions it is shown that c n converges to c ast in the 2r th mean where c ast is the unique solution of the wiener hopf equation

efficient analysis of input impedance and mutual coupling of microstrip antennas mounted on large coated cylinders an efficient and accurate hybrid method based on the combination of the method of moments mom with a special green s function in the space domain is presented to analyze antennas and array elements conformal to electrically large material coated circular cylinders the efficiency and accuracy of the method depend strongly on the computation of the green s function which is the kernel of the integral equation that is solved via mom for the unknown equivalent currents representing only the antenna elements three types of space domain green s function representations are used each accurate and computationally efficient in a given region of space consequently a computationally optimized analysis tool for conformal microstrip antennas is obtained input impedance of various microstrip antennas and mutual coupling between two identical antennas are calculated and compared with published results to assess the accuracy of this hybrid method

rates of convergence of adaptive step size of stochastic approximation algorithms we propose a new adaptive algorithm with decreasing step size for stochastic approximations the use of adaptive algorithms in various applications is widely spread across fields such as system identification and adaptive control we analyze the rate of convergence of the proposed algorithms an averaging algorithm on its optimality of the rate of convergence is used to control the step sizes our proofs are based on recent results in stochastic approximations and gaussian approximation theorem

logical representation and fusion of prioritized information based on guaranteed possibility measures in the possibility theory framework prioritized information can be logically expressed in different formats the most usual way used in standard possibilistic logic is to associate necessity degrees with propositional formulas this paper considers another representation and fusion of prioritized information using guaranteed possibility measures prioritized pieces of information are then represented by sets of weighted formulas called knowledge bases where weights are lower bounds of guaranteed possibility degrees of formulas we first show that the basic notions of standard possibilistic logic have natural counterparts when dealing with knowledge bases in particular we present the inference machinery and provide syntactic but semantically meaningful merging of knowledge bases in the second part of the paper we show that distance based merging propositional knowledge bases can be naturally encoded using knowledge bases moreover this encoding is more efficient than the necessity based encoding of distance based merging operator

on line blind multichannel equalization based on mutually referenced filters this paper presents a novel approach to the blind linear equalization of possibly nonminimum phase and time varying communication channels in the context of channel diversity we introduce the concept of mutually referenced equalizers mres in which several filters are considered the outputs of which act as training signals for each other a corresponding constrained multidimensional mean square error mse cost function is derived the minimization of which is shown to be a necessary and sufficient condition for equalization the links with a standard linear prediction problem are demonstrated the proposed technique exhibits properties of important practical concern 1 the proposed algorithm is globally convergent 2 simple closed form solutions exist for the mres but the mres also lend themselves readily to adaptive implementation in particular the recursive least squares rls algorithm can be used to offer optimal convergence rate 3 the mre method provides a solution for all equalization delays which results in robustness properties with respect to snr and ill defined channel lengths

blind equalization based on joint minimum mse criterion a joint minimum mean square error mse criterion is presented for blind adaptive channel equalization of qam signals by jointly estimating the transmitted sequence and the equalizer parameters through the minimization of mse the equalizer parameters can be optimized and the channel input sequence can be restored at the equalizer output to improve computational efficiency a reduced constellation recursive least squares rls algorithm is introduced for blind equalisation simulation results show the success of both the least square and the reduced constellation rls algorithms

robust blind learning algorithm for nonlinear equalization using input decision information in this paper we propose a new blind learning algorithm namely the benveniste goursat input output decision bg iod to enhance the convergence performance of neural network based equalizers for nonlinear channel equalization in contrast to conventional blind learning algorithms where only the output of the equalizer is employed for updating system parameters the bg iod exploits a new type of extra information the input decision information obtained from the input of the equalizer to mitigate the influence of the nonlinear equalizer structure on parameters learning thereby leading to improved convergence performance we prove that with the input decision information a desirable convergence capability that the output symbol error rate ser is always less than the input ser if the input ser is below a threshold can be achieved then the bg soft switching technique is employed to combine the merits of both input and output decision information where the former is used to guarantee ser convergence and the latter is to improve ser performance simulation results show that the proposed algorithm outperforms conventional blind learning algorithms such as stochastic quadratic distance and dual mode constant modulus algorithm in terms of both convergence performance and ser performance for nonlinear equalization

analytical technique to evaluate the asymptotic part of the impedance matrix of sommerfeld type integrals the propagation of electromagnetic waves in a grounded dielectric slab has numerous applications in printed antenna technology and in the analysis of microwave and millimeter wave integrated circuits for the accurate analysis of microstrip dipoles and circuits based on the moment of method mom a crucial step is the precise evaluation of the impedance matrix elements which contain the integration of sommerfeld type integrals the integral transform method with the asymptotic extraction technique is formulated for calculating a sommerfeld type integral problem this formulation allows the infinite double integral of the asymptotic part of the impedance matrix to be transformed into a finite one dimensional 1 d integral this finite 1 d integral contains a spherical legendre function and can be easily evaluated numerically after the singular part of the integral is performed analytically it is shown that the proposed method dramatically reduces the computation time and improves the accuracy over the conventional method to evaluate the asymptotic part of impedance matrix

linear stochastic approximation driven by slowly varying markov chains we study a linear stochastic approximation algorithm that arises in the context of reinforcement learning the algorithm employs a decreasing step size and is driven by markov noise with time varying statistics we show that under suitable conditions the algorithm can track the changes in the statistics of the markov noise as long as these changes are slower than the rate at which the step size of the algorithm goes to zero

efficient analysis of phased arrays of microstrip patches using a hybrid generalized forward backward method green s function technique with a dft based acceleration algorithm a hybrid method based on the combination of generalized forward backward method gfbm and green s function for the grounded dielectric slab together with the acceleration of the combination via a discrete fourier transform dft based algorithm is developed for the efficient and accurate analysis of electromagnetic radiation scattering from electrically large irregularly contoured two dimensional arrays consisting of finite number of probe fed microstrip patches in this method unknown current coefficients corresponding to a single patch are first solved by a conventional galerkin type hybrid method of moments mom green s function technique that uses the grounded dielectric slab s green s function because the current distribution on the microstrip patch can be expanded using an arbitrary number of subsectional basis functions the patch can have any shape the solution for the array currents is then found through gfbm where it sweeps the current computation element by element the computational complexity of this method which is originally being the total number of unknowns for each iteration is reduced to using a dft based acceleration algorithm making use of the fact that array elements are identical and the array is periodic numerical results in the form of array current distribution are given for various sized arrays of probe fed microstrip patches with elliptical and or circular boundaries and are compared with the conventional mom results to illustrate the efficiency and accuracy of the method

convergence analysis of an adaptive filter equipped with the sign sign algorithm convergence with probability 1 of the sign sign algorithm with a decreasing step size is proven when it is used in adaptive plant identification the plant input and plant noise are assumed stationary and m dependent the assumptions do not pose any upper bound on the memory m of the plant input and plant noise and hence they allow arbitrarily strong correlation in these signals a main interest of the paper is that it provides a condition of persistent excitation of the algorithm examples satisfying this condition are provided

analysis of stochastic gradient algorithms for linear regression problems parameter estimation problems that can be formulated as linear regressions are quite common in many applications recursive on line sequential estimation of such parameters can be performed using the recursive least squares rls algorithm or a stochastic gradient version of this algorithm in this paper the convergence properties of the gradient algorithm are analyzed under the assumption that the gain tends to zero the technique is the same as the so called ordinary differential equation approach but the treatment here is self contained and includes a proof of the boundedness of the estimates a main result is that the convergence conditions for the gradient algorithm are the same as those for the recursive least squares algorithm

convergence of an adaptive linear estimation algorithm in this work we prove the almost sure convergence of an adaptive linear estimator governed by a stochastic gradient algorithm with decreasing step size in the presence of correlated observations two complementary contributions are added to the famous 1977 ljung theorem first we drop the condition of nondivergence of the algorithm assumed by ljung while that condition can be ensured by adding a barrier the convergence of the suitably bounded algorithm itself is not established even on the basis of ljung theorem here the barrier problem is overcome by proving that it is not necessary for the convergence our second contribution is to generalize the model describing the correlated observations no state space model is used and no linear relationship between the observations and the signal to be estimated needs to be assumed instead we use a decreasing covariance model that agrees with a very wide class of practical applications

fast recursive least squares transversal filters for adaptive filtering fast transversal filter ftf implementations of recursive least squares rls adaptive filtering algorithms are presented in this paper substantial improvements in transient behavior in comparison to stochastic gradient or lms adaptive algorithms are efficiently achieved by the presented algorithms the true not approximate solution of the rls problem is always obtained by the ftf algorithms even during the critical initialization period first n iterations of the adaptive filter this true solution is recursively calculated at a relatively modest increase in computational requirements in comparison to stochastic gradient algorithms factor of 1 6 to 3 5 depending upon application additionally the fast transversal filter algorithms are shown to offer substantial reductions in computational requirements relative to existing fast rls algorithms such as the fast kalman algorithms of morf ljung and falconer 1976 and the fast ladder lattice algorithms of morf and lee 1977 1981 they are further shown to attain steady state unnormalized or improve upon first n initialization steps the very low computational requirements of the efficient rls solutions of carayannis manolakis and kalouptsidis 1983 finally several efficient procedures are presented by which to ensure the numerical stability of the transversal filter algorithms including the incorporation of soft constraints into the performance criteria internal bounding and rescuing procedures and dynamic range increasing square root normalized variations of the transversal filters

a unified approach to the steady state and tracking analyses of adaptive filters most adaptive filters are inherently nonlinear and time variant systems the nonlinearities in the update equations tend to lead to difficulties in the study of their steady state performance as a limiting case of their transient performance this paper develops a unified approach to the steady state and tracking analyses of adaptive algorithms that bypasses many of these difficulties the approach is based on the study of the energy flow through each iteration of an adaptive filter and it relies on a fundamental error variance relation

an asymptotic extraction technique for evaluating sommerfeld type integrals an asymptotic extraction process is developed which leads to an efficient method for the evaluation of the electric field from a hertzian dipole in a layered geometry this technique allows for a rapidly converging expression for the electric field which remains well behaved as the source and observation heights z z coincide a useful application of this method is in the calculation of mutual impedance between printed dipoles

on the statistical efficiency of the lms algorithm with nonstationary inputs a fundamental relationship exists between the quality of an adaptive solution and the amount of data used in obtaining it quality is defined here in terms of misadjustment the ratio of the excess mean square error mse in an adaptive solution to the minimum possible mse the higher the misadjustment the lower the quality is the quality of the exact least squares solution is compared with the quality of the solutions obtained by the orthogonalized and the conventional least mean square lms algorithms with stationary and nonstationary input data when adapting with noisy observations a filter trained with a finite data sample using an exact least squares algorithms will have a misadjustment given by m frac n n frac number of weights number of training samples if the same adaptive filter were trained with a steady flow of data using an ideal orthogonalized lms algorithm the misadjustment would be m frac n 4 tau mse frac number of weights number of training samples thus for a given time constant tau mse of the learning process the ideal orthogonalized lms algorithm will have about as low a misadjustment as can be achieved since this algorithm performs essentially as an exact least squares algorithm with exponential data weighting it is well known that when rapid convergence with stationary data is required exact least squares algorithms can in certain cases outperform the conventional widrow hoff lms algorithm it is shown here however that for an important class of nonstationary problems the misadjustment of conventional lms is the same as that of orthogonalized lms which in the stationary case is shown to perform essentially as an exact least squares algorithm

convergence rates and decoupling in linear stochastic approximation algorithms almost sure convergence rates for linear algorithms h k 1 h k frac 1 k chi b k a kh k are studied where chi in 0 1 a k k 1 infty are symmetric positive semidefinite random matrices and b k k 1 infty are random vectors it is shown that n gamma h n a 1 b rightarrow 0 a s for the gamma in 0 chi positive definite a and vector b such that frac 1 n chi gamma sum k 1 n a k a to 0 and frac 1 n chi gamma sum k 1 n b k b to 0 a s when chi gamma in left frac12 1 right these assumptions are implied by the marcinkiewicz strong law of large numbers which allows the a k and b k to have heavy tails long range dependence or both finally corroborating experimental outcomes and decreasing gain design considerations are provided

a tight upper bound of the average absolute error in a constant step size sign algorithm a direct performance index of the adaptive filtering sign algorithm sa is the average absolute error aae at the output of the filter adopting this performance index an easy analysis of sa is achieved under a weak assumption it is proved for both deterministic and random inputs to the filter that the aae has a tight upper bound that exceeds the minimum aae by half the product of the step size and power of the filter input the assumption used is existence of average squared and average absolute values of filter input signals a practical interest of the result is that it provides a formula for the biggest step size as a function of tolerable adaptation noise to desired signal ratio

asymptotic properties of sign algorithms for adaptive filtering this paper develops asymptotic properties of a class of sign error algorithms with expanding truncation bounds for adaptive filtering under merely stationary ergodicity and finite second moments of the reference and output signals and using trajectory subsequence ts method it is proved that the algorithm convergers almost surely then a mean squares estimate is derived for the estimation error and a suitably scaled sequence of the estimation error is shown to converge to a diffusion process the scaling factor together with the stationary covariance gives the rate of convergence result moreover an algorithm under mean squares criterion with expanding truncation bounds is also examined compared with the existing results in the literature sufficient conditions for almost sure convergence are much relaxed a simple example is provided for demonstration purpose

an asymptotic closed form representation for the grounded double layer surface green s function an efficient closed form asymptotic representation for the grounded double layer substrate superstrate green s function is presented the formulation is valid for both source a horizontal electric dipole and observation points anywhere inside the superstate or at the interfaces the asymptotic expressions are developed via a steepest descent evaluation of the original sommerfeld type integral representation of the green s function and the large parameter in this asymptotic development is proportional to the lateral separation between source and observation points the asymptotic solution is shown to agree with the exact green s function for lateral distances even as small as a few tenths of the free space wavelengths thus constituting a very efficient tool for analyzing printed circuits antennas since the asymptotic approximation gives separate contributions pertaining to the different wave phenomena it provides physical insight into the field behavior as shown by examples

paraxial space domain formulation for surface fields on a large dielectric coated circular cylinder a new method to evaluate the surface fields excited within the paraxial nearly axial region of an electrically large dielectric coated circular cylinder is presented this representation is obtained by performing the watson s transformation in the standard eigenfunction solution and using the fact that the circumferentially propagating series representation of the appropriate green s function is periodic in one of its two variables therefore it can be approximated by a fourier series where the two leading terms of the expansion yield engineering accuracy in most cases this work can be used in conjunction with a method of moments solution for the design analysis of conformal microstrip antennas and arrays numerical results are presented and compared with a standard eigenfunction expansion

asymptotic green s function of a surface magnetic current element on a perfect electric conductor plane covered by a lossy dielectric substrate published analyses of radiation modeling for slot structures on dielectric substrate are empirical or numerical this paper proposes exact analytical asymptotic expressions of the far field green s functions of a surface magnetic current element on a perfect electric conductor plane covered by a lossy dielectric substrate of finite thickness from these expressions the radiation pattern of both the space wave and surface wave far away from an arbitrary shaped slot antenna structure can be calculated provided the source distribution across the slot is known the potentials used in the analysis are defined and their boundary conditions are expressed the helmholtz equation is solved in the laplace domain and the solutions are transformed into the space domain using the inverse hankel transform and steepest descent method the influences of the substrate thickness and dielectric constant are analyzed using the calculated expressions the model is validated by comparison with surface wave and space wave measurements and with numerical results obtained from a commercial electromagnetic simulator

convergence analysis of the sign algorithm without the independence and gaussian assumptions the paper is concerned with rigorous convergence analysis of the sign algorithm sa in the context of adaptive plant identification asymptotic time averaged convergence for the mean absolute weight misalignment is proved for all values of the algorithm step size and initial weight vector the paper has three main contributions with respect to available convergence results of the sa the first is the deletion of the gaussian assumption which is important when covering the case of discrete valued data no assumption about the distribution of the regressor sequence is used except for the usual assumption of positive definite covariance matrix the assumptions used about the noise allow nonexistence unboundedness and vanishing of the noise probability density function for arguments strictly different from zero the second contribution is the deletion of the assumption of independent successive regressors this deletion is important since in applications two successive regressors usually share all their components except two hence they are strongly dependent even for white plant input the case of colored noise is also analyzed finally the third contribution is the extension of the above results to the nonstationary case the used assumptions allow nonstationarity of the plant input plant noise and plant parameters

iterate averaging sign algorithms for adaptive filtering with applications to blind multiuser detection motivated by the developments on iterate averaging of recursive stochastic approximation algorithms and asymptotic analysis of sign error algorithms for adaptive filtering this work develops two stage sign algorithms for adaptive filtering the proposed algorithms are based on constructions of a sequence of estimates using large step sizes followed by iterate averaging our main effort is devoted to improving the performance of the algorithms by establishing asymptotic normality of a suitably scaled sequence of the estimation errors the asymptotic covariance is calculated and shown to be the smallest possible hence the asymptotic efficiency or asymptotic optimality is obtained then variants of the algorithm including sign regressor procedures and constant step algorithms are studied the minimal window width of averaging is also dealt with finally iterate averaging algorithms for blind multiuser detection in direct sequence code division multiple access ds cdma systems are proposed and developed and numerical examples are examined

computation of the sommerfeld integral tails using the matrix pencil method the oscillating infinite domain sommerfeld integrals si are difficult to integrate using a numerical procedure when dealing with structures in a layered media even though several researchers have attempted to do that generally integration along the real axis is used to compute the si however significant computational effort is required to integrate the oscillating and slowly decaying function along the tail extrapolation methods are generally applied to accelerate the rate of convergence of these integrals however there are difficulties with the extrapolation methods such as locations for the breakpoints in this paper we illustrate a simplified approach for accurate and efficient calculation of the integrals dealing with the tails of the si in this paper we fit the tail by a sum of finite usually 10 to 20 complex exponentials using the matrix pencil method mpm the integral of the tail of the si is then simply calculated by summing some complex numbers no numerical integration is needed in this process as the integrals can be done analytically good accuracy is achieved with a small number of evaluations for the integral kernel 60 points for the mpm as compared with hundreds or thousands of functional evaluations using the traditional extrapolation methods along the tails of the si simulation results show that to obtain the similar accuracy in the evaluation of the si the mpm is approximately 10 times faster than the traditional extrapolation methods moreover since the mpm is robust to the effects of noise this method is more stable especially for large values of the horizontal distances the method proposed in this paper is thus a new and better technique to obtain accurate results for the computation of the green s function for a layered media in the spatial domain

on the qualitative necessity possibility measure i investigation in the framework of measurement theory abstract in this paper we try to investigate the qualitative possibility and or necessity measures introduced by d dubois computer and artificial intelligence 5 1986 403 416 and d dubois and h prade artificial intelligence 50 1991 223 239 as an extension of a qualitative or subjective probability studied by t fine theory of probability academic press new york 1973 we particularly review some relationship between these concepts and the basic qualitative possibility distribution as introduced by r r yager ieee trans fuzzy systems 1 3 1993 184 193 this will then be studied in the general framework of preference relations when the qualitative possibility necessity measures are real valued graded from 0 to 1 the justification of the proposal real valued relation will be carried out in the framework of measurement theory where a relationship between the difference measurement scale and our proposal will be established two kinds of relations will be proposed the first one is based on some appropriate exponential form and the second one is based on a more general form of r implication operators finally we briefly investigate some heuristic approach concerning the problem of how to obtain a real valued qualitative possibility from a quantitative possibility distribution

transient and tracking performance bounds of the sign sign algorithm the paper provides a rigorous tracking analysis of the sign sign algorithm when used in the identification of a time varying plant with a white gaussian input the plant parameters vary according to a random walk model the assumptions allow nonstationarity of the plant input plant noise and increments of the plant parameters upper bounds are derived for the long term averages of the mean of the weight misalignment norm mean absolute error mean square weight misalignment and mean square error these bounds hold for all values of the algorithm step size all initial filter weight settings and all degrees of nonstationarity of the plant input plant noise and plant parameter increments lower bounds of the mean square weight misalignment and mean square error are also derived the step sizes that minimize the above bounds are derived a transient analysis of the algorithm is done in the case of a time invariant plant a tight lower bound of the convergence time is derived the above analytical results are supported by computer simulations

adaptive linear procedures under general conditions under mild conditions on the observation processes the almost sure convergence properties of linear stochastic approximation are summarized for least squares and for some of its applications adaptive filtering echo cancellation detection of binary data in gaussian noise identification and linear classification

the expansion wave concept i efficient calculation of spatial green s functions in a stratified dielectric medium a procedure is given to perform the inverse fourier transformation relating a spatial green s function to its spectral equivalent the procedure is applied to the spectral green s functions of the double scalar mixed potential integral expression formulation of the electromagnetic field in a stratified dielectric medium the extraction technique is used to annihilate every type of problematic behavior of the spectral green s functions every annihilating function is inverse fourier transformed analytically it is shown that the annihilation of both the surface wave poles and the singularities at the branch point results in a set of analytical spatial functions which are a very good approximation of the exact spatial green s function down to relatively small lateral distances

comparison of rls lms and sign algorithms for tracking randomly time varying channels the performance of adaptive fir filters governed by the recursive least squares rls algorithm the least mean square lms algorithm and the sign algorithm sa are compared when the optimal filtering vector is randomly time varying the comparison is done in terms of the steady state excess mean square estimation error spl xi and the steady state mean square weight deviation spl eta it is shown that spl xi does not depend on the spread of eigenvalues of the input covariance matrix r in the cases of the lms algorithm and the sa while it does in the case of the rls algorithm in the three algorithms spl eta is found to be increasing with the eigenvalue spread the value of the adaptation parameter that minimizes spl xi is different from the one that minimizes spl eta it is shown that the minimum values of spl xi and spl eta attained by the rls algorithm are equal to the ones attained by the lms algorithm in any one of the three following cases 1 if r has equal eigenvalues 2 if the fluctuations of the individual elements of the optimal vector are mutually uncorrelated and have the same mean square value or 3 if r is diagonal and the fluctuations of the individual elements of the optimal vector have the same mean square value conditions that make the values of spl xi and spl eta of the lms algorithm smaller or greater than the ones of the rls algorithm are derived for gaussian input data the minimum values of spl xi and spl eta attained by the sa are found to exceed the ones attained by the lms algorithm by 1 db independently of r and the mutual correlation between the elements of the optimal vector

blind equalization by direct examination of the input sequences this paper presents a novel approach to blind equalization deconvolution which is based on direct examination of possible input sequences in contrast to many other approaches it does not rely on a model of the approximative inverse of the channel dynamics to start with the blind equalization identifiability problem for a noise free finite impulse response channel model is investigated a necessary condition for the input which is algorithm independent for blind deconvolution is derived this condition is expressed in an information measure of the input sequence a sufficient condition for identifiability is also inferred which imposes a constraint on the true channel dynamics the analysis motivates a recursive algorithm where all permissible input sequences are examined the exact solution is guaranteed to be found as soon as it is possible an upper bound on the computational complexity of the algorithm is given this algorithm is then generalized to cope with time varying infinite impulse response channel models with additive noise the estimated sequence is an arbitrary good approximation of the maximum a posteriori estimate the proposed method is evaluated on a rayleigh fading communication channel the simulation results indicate fast convergence properties and good tracking abilities

theoremes de convergence presque sure pour une classe d algorithmes stochastiques a pas decroissant the paper studies the pathwise asymptotic behaviour of stochastic algorithms of the following general form theta n 1 theta n gamma n 1 f theta n y n 1 the hypotheses allowing discontinuities on the adaptation termf the process y n n 0 is a markov chain controlled by n for each fixed the markov chain y n n 0 is essentially of positive recurrent type

almost sure convergence of a decreasing gain sign algorithm for adaptive filtering the convergence analysis of a sign algorithm with decreasing gain when governing the weights of an adaptive filter is presented the analysis is done in a noiseless case a rigorous proof of almost sure convergence to the optimal filter is attained under a weak ergodicity assumption that includes the case important in practice of correlated observations

optimization of adaptive identification for time varying filters adaptive identification in a time varying context is studied when controlled by the lms algorithm with constant gain under the assumption of correlated successive input vectors it is well known by experience that the tracking mean square error mse epsilon mu results from the tradeoff between the gradient part which is increasing and the lag contribution which is decreasing in this note we clarify the relative roles of the gradient and lag errors by proving their decoupled character this property relies upon independence between the additive noise at the output of the plant to be identified and the information vector at the plant input convergence of the mse is established rather than assumed quantitative evaluations of upper and lower bounds allow an approximate optimization of the gain in two important cases the optimum is exact one of these cases is slow variations it is defined in a quantitative manner thanks to the ratio of the variation noise to the output additive noise

second order convergence analysis of stochastic adaptive linear filtering the convergence of an adaptive filtering vector is studied when it is governed by the mean square error gradient algorithm with constant step size we consider the mean square deviation between the optimal filter and the actual one during the steady state this quantity is known to be essentially proportional to the step size of the algorithm however previous analyses were either heuristic or based upon the assumption that successive observations were independent which is far from being realistic actually in most applications two successive observation vectors share a large number of components and thus they are strongly correlated in this work we deal with the case of correlated observations and prove that the mean square deviation is actually of the same order or less than the step size of the algorithm this result is proved without any boundedness or barrier assumption for the algorithm as it has been done previously in the literature to ensure the nondivergence our assumptions are reduced to the finite strong memory assumption and the finite moments assumption for the observation they are satisfied in a very wide class of practical applications

asymptotic analysis of stochastic gradient based adaptive filtering algorithms with general cost functions this paper presents an analysis of stochastic gradient based adaptive algorithms with general cost functions the analysis holds under mild assumptions on the inputs and the cost function the method of analysis is based on an asymptotic analysis of fixed stepsize adaptive algorithms and gives almost sure results regarding the behavior of the parameter estimates whereas previous stochastic analyses typically considered mean and mean square behavior the parameter estimates are shown to enter a small neighborhood about the optimum value and remain there for a finite length of time furthermore almost sure exponential bounds are given for the rate of convergence of the parameter estimates the asymptotic distribution of the parameter estimates is shown to be gaussian with mean equal to the optimum value and covariance matrix that depends on the input statistics specific adaptive algorithms that fall under the framework of this paper are signed error least mean square lms dual sign lms quantized state lms least mean fourth dead zone algorithms momentum algorithms and leaky lms

recursive estimators with markovian jumps recursive stochastic algorithms have various applications in the literature it is assumed that the true value lies in a connected domain but in many cases it is known that the true value is contained in the union of a finite number of pairwise disjoint sets instead of a connected domain in these situations the existing algorithms may be not applicable to cope with this problem this paper proposes recursive stochastic algorithms with event triggered markovian jumps and presents sufficient conditions for almost sure convergence of the proposed algorithms as an example of applications this paper significantly improves an existing adaptive algorithm with the proposed method for consistent estimation of non minimum phase zeros

closed form uniform asymptotic expansions of green s functions in layered media far field closed form expressions are derived for spatial domain multilayered green s functions gf for the derivation of these far field expressions the spectral domain multilayered gf are approximated by means of the total least square algorithm tlsa in terms of the spectral variable u0 k 2 k02 1 2 and uniform asymptotic expansions are determined for the sommerfeld integrals of the resulting tlsa approximations numerical results show that the far field asymptotic expressions are accurate within 0 1 for distances between source and field points larger than one free space wavelength also it is shown that the hybrid use of the discrete complex image method and the tlsa in terms of the spectral variable k leads to near field closed form expressions of multilayered gf that are typically accurate within 0 1 for distances between source and field points smaller than one free space wavelength therefore the combination of the novel far field asymptotic expressions and the well known near field expressions makes it possible to compute multilayered gf with a great accuracy in the whole range of distances between source and field points and in a wide range of frequencies

an asymptotic closed form microstrip surface green s function for the efficient moment method analysis of mutual coupling in microstrip antennas a relatively simple closed form asymptotic representation for the single layer microstrip dyadic surface green s function is developed the large parameter in this asymptotic development is proportional to the lateral separation between the source and field points along the air dielectric interface this asymptotic solution remains surprisingly accurate even for very small a few tenths of a free space wavelength lateral separation of the source and field points thus using the present asymptotic approximation of the green s function can lead to a very efficient moment method mm solution for the currents on an array of microstrip antenna patches and feed lines numerical results based on the efficient mm analysis using the present closed form asymptotic approximation to the microstrip surface green s function are given for the mutual coupling between a pair of printed dipoles on a single layer grounded dielectric slab the accuracy of the latter calculation is confirmed by comparison with numerical results based on a mm analysis which employs an exact integral representation for the microstrip green s function

analysis of a sign algorithm with delayed data an adaptive filter whose weights are adapted using a sign algorithm with a delayed error signal is analyzed for stationary environments it is proved that the excess average absolute estimation error is bounded for all values of the error signal delay and the algorithm step size for the nonstationary case when the optimal filter weights are time varying the optimum step size which minimizes the excess average absolute error is derived it is shown that the optimum step size does not depend on the additive noise power the analytical results are supported by computer simulations

applications of a kushner and clark lemma to general classes of stochastic algorithms two general classes of stochastic algorithms are considered including algorithms considered by ljung as well as algorithms of the form theta n 1 theta n gamma n 1 v n 1 theta n z where z is a stationary ergodic process it is shown how one can apply a lemma of kushner and clark to obtain properties of these algorithms this is done by using in particular martingale arguments in the generalized ljung case in these various situations the convergence is obtained by the method of the associated ordinary differential equation under the classical boundedness assumptions in the case of linear algorithms the boundedness assumptions are dropped

joint signal detection and parameter estimation in multiuser communications the problem of simultaneously detecting the information bits and estimating signal amplitudes and phases in a k user asynchronous direct sequence spread spectrum multiple access communication system is addressed the joint maximum likelihood ml estimator has a computational complexity that is exponential in the total number of bits transmitted and thus does not represent a practical solution to the problem an estimator that combines a suboptimum tree search algorithm with a recursive least squares estimator of complex signal amplitude is considered the complexity of this estimator is o k sup 2 computations per decoded bit and its performance is very close to that of the joint ml receiver this receiver has the advantage that the transmitted signal powers and phases are extracted from the received signal in an adaptive fashion without using a test sequence

some convergence considerations in space domain moment method analysis of a class of wide band microstrip antennas the method of moments mom analysis of probe fed rectangular microstrip patches requires the inclusion of a probe to patch attachment mode expansion function when the substrate thickness d spl ges 0 02 spl lambda where spl lambda is the free space wavelength the results for the input impedance showed increased divergence with measurements when the attachment mode was omitted from the full wave analysis the attachment mode can be expressed as an infinite eigenfunction series that increases the fill time of the impedance matrix in an mom analysis in an earlier investigation the infinite eigenfunction series was reduced to a residue series that required one or two terms compared to about 55 terms for the eigenfunction series in this paper the convergence properties of the eigenfunction and residue series are investigated in view of rigorous mom analysis the relative errors resulting from replacing the eigenfunction by the residue series for the attachment mode are compared by numerically evaluating a class of two dimensional 2 d spatial integrals shown to be closely related to the elements of an mom impedance matrix additionally the computation times for the evaluation of these integrals for the two forms of the attachment mode expansion function are also included based on the superior convergence properties of the residue series for the attachment mode expansion function it is mathematically justified that this form can readily be used for analytic reduction of the spatial reaction integrals from four to 2 d forms this feature allows further reduction of the fill time of the mom impedance matrix suggesting the possibility of developing an efficient space domain mom technique for modeling of wide band microstrip antennas

on the convergence of linear stochastic approximation procedures many stochastic approximation procedures result in a stochastic algorithm of the form h sub k 1 h sub k 1 k b sub k a sub k h sub k for all k 1 2 3 here b sub k k 1 2 3 is a r sup d valued process a sub k k 1 2 3 is a symmetric positive semidefinite re sup d spl times d valued process and h sub k k 1 2 3 is a sequence of stochastic estimates which hopefully converges to h sup spl delta lim sub n spl rarr spl infin 1 n spl sigma sub k 1 sup n ea sub k sup 1 lim sub n spl rarr spl infin 1 n spl sigma sub k 1 sup n eb sub k assuming everything here is well defined we give an elementary proof which relates the almost sure convergence of h sub k k 1 2 3 to strong laws of large numbers for b sub k k 1 2 3 and a sub k k 1 2 3

convergence of the delayed normalized lms algorithm with decreasing step size in several practical applications of the lms algorithm including certain vlsi implementations the coefficient adaptation can be performed only after some fixed delay the resulting algorithm is known as the delayed lms dlms algorithm in the literature previous published analyses of this algorithm are based on mean and moment convergence under the independence assumption between successive input vectors these analyses are interesting and give valuable insights into the convergence properties but from a practical viewpoint they do not guarantee the correct performance of the particular realization with which the user must live we consider a normalized version of this algorithm with a decreasing step size spl mu n and prove the almost sure convergence of the nonhomogeneous algorithm assuming a mixing input condition and the satisfaction of a certain law of large numbers

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

averaging procedures in adaptive filtering an efficient approach an averaging procedure for adaptive filtering is developed in contrast to the traditional approach two sequences x sub n and x sub n are constructed where x sub n is the arithmetic average of x sub n the authors show that the algorithm so designed has optimal rate of convergence therefore the averaging approach is asymptotically efficient

persistence of excitation conditions and the convergence of adaptive schemes in the study of the behavior of adaptive filtering algorithms persistence of excitation of the input process arises as a sufficient condition for convergence and perhaps more importantly for convergence rate of the parameter estimates in this paper the underlying nature of the persistence requirement is presented and discussed relating its normal specification in terms of moment conditions with covariance decays etc to sample path properties deterministic and stochastic persistence conditions and persistence measures are treated as well as persistence conditions for output error equation error and adaptive control schemes

real axis integration of sommerfeld integrals with applications to printed circuit antennas printed circuit antennas are becoming an integral part of imaging arrays in microwave millimeter and submillimeter wave frequencies the electrical characteristics of such antennas can be analyzed by solving integral equations of the fredholm first kind the kernel involves sommerfeld integrals which are particularly difficult to solve when source and field points lie on an electrical discontinuity as it occurs in the determination of the characteristics of printed circuit antennas an analytic numeric real axis integration technique has been developed for such integrals and it is combined with piece wise sinusoidal expansions to solve the fredholm integral equation for the unknown current density

convergence analysis of adaptive filtering algorithms with singular data covariance matrix the paper provides a rigorous analysis of the behavior of adaptive filtering algorithms when the covariance matrix of the filter input is singular the analysis is done in the context of adaptive plant identification the considered algorithms are lms rls sign sa and signed regressor sra algorithms both the signal and weight behavior of the algorithms are considered the signal behavior is evaluated in terms of the moments of the excess output error of the filter the weight behavior is evaluated in terms of the moments of the filter weight misalignment vector it is found that the rls and sra diverge when the input covariance matrix is singular the steady state signal behavior of the lms and sa can be made arbitrarily fine by using sufficiently small step sizes of the algorithms indeed the long term average of the mean square excess error of the lms is proportional to the algorithm step size the long term average of the mean absolute excess error of the sa is proportional to the square root of the algorithm step size on the other hand the steady state weight behavior of both the lms and sa have biases that depend on the weight initialization the analytical results of the paper are supported by simulations

techniques for evaluating the uniform current vector potential at the isolated singularity of the cylindrical wire kernel the cylindrical wire kernel possesses a singularity which must be properly treated in order to evaluate the uniform current vector potential traditionally the singular part of the kernel is extracted resulting in a slowly varying function which is convenient for numerical integration this paper provides some new accurate and computationally efficient methods for evaluating the remaining singular integral it is shown that this double integral may be converted to a single integral which no longer possesses a singular integrand and consequently may be efficiently evaluated numerically this form of the integral is independent of the restrictions involving wire length and radius which are inherent in various approximations also presented is a highly convergent exact series representation of the integral which is valid except in the immediate vicinity of the singularity finally a new approximation is derived which is found to be an improvement over the classical thin wire approximation it is demonstrated that each of these methods provides extremely accurate as well as efficient results for a wide range of wire radii and field point locations

analytic properties of maximum entropy owa operators we discuss the maximum entropy approach to obtaining the weights associated with the ordered weighted averaging owa aggregation operator the resulting weights are called the meowa weights using the method of lagrange multipliers we obtain an analytic form for these weights and describe some of their properties the concept of immediate probabilities is introduced as being a transformation of a probability distribution based on a decision maker s degree of optimism this transformation which is affected by an owa operator is shown to result in a relationship between the transformed expected value and the degree of optimism that is monotone when the weights used are the meowa weights

continuous time tracking algorithms involving two time scale markov chains this work is concerned with least mean squares lms algorithms in continuous time for tracking a time varying parameter process a distinctive feature is that the true parameter process is changing at a fast pace driven by a finite state markov chain the states of the markov chain are divisible into a number of groups within each group the transitions take place rapidly among different groups the transitions are infrequent introducing a small parameter into the generator of the markov chain leads to a two time scale formulation the tracking objective is difficult to achieve nevertheless a limit result is derived yielding algorithms for limit systems moreover the rates of variation of the tracking error sequence are analyzed under simple conditions it is shown that a scaled sequence of the tracking errors converges weakly to a switching diffusion in addition a numerical example is provided and an adaptive step size algorithm developed

optimum step size of sign algorithm for nonstationary adaptive filtering the adaptive filtering sign algorithm is analyzed in the case of nonstationary and correlated data the excess time average absolute estimation error eaae is used as a performance index of the algorithm it is proved that the eaae is the sum of two terms one proportional to the algorithm step size mu and the other proportional to 1 mu the optimum step size that minimizes the eaae is found equal to square root q p with q being the power of fluctuations of the optimal filter weights and p being the power of filter input this formula is derived under the assumption that increments of optimal filter weights are white computer simulations are used to examine the validity of the formula for other models of variation of the optimal filter simulation results show a good fit with the obtained optimum step size formula

on the location of proper and improper surface wave poles for the grounded dielectric slab microstrip antennas a recently obtained closed form asymptotic representation due to s barkeshli 1988 of the microstrip surface green s function is known to provide an efficient moment method analysis of microstrip problems however in order to make this closed form expression accurate even for very small separation of source and field points to within a few tenths of a wavelength both the proper and improper surface wave transition effects must be included in the solution this requires finding the location of the corresponding proper and improper poles a good initial estimate that allows the poles to be located rapidly by using an iterative procedure is presented the number of proper and improper surface wave poles that have to be considered and their values are tabulated