estimating the covariance matrix by signal subspace averaging an efficient algorithm is presented for estimating a covariance matrix consisting of a low rank signal term and a full rank noise term known apart from a scalar factor for each sample of the vector of sensor outputs the algorithm approximates in the least squares sense a rank one update of the covariance matrix under the side condition that the rank of the signal term remains bounded if the model noise is spatially colored the least squares approximation is preceded by spatial prewhitening it is shown that if the rank of the signal term is small compared to the number of sensors then the proposed algorithm requires substantially less computational work than conventional averaging some simulation results are included indicating that the proposed algorithm reduces the variance of some commonly used spectral estimators in off target directions without impairing their detection and resolution properties

koszul duality and extensions of exponential functors we study koszul duality in the category of strict polynomial functors we compute koszul duals of various functors and apply these results to the problem of calculating ext groups between exponential functors the main application is a full description of the ext groups between twisted exterior and divided powers and between twisted symmetric and divided powers which completes the program started in v franjou e friedlander a scorichenko a suslin general linear and functor cohomology over finite fields ann of math 150 2 1999 663 728

ringel duality as an instance of koszul duality abstract in 30 s koenig s ovsienko and the second author showed that every quasi hereditary algebra is morita equivalent to the right algebra i e the opposite algebra of the left dual of a coring let a be an associative algebra and v an a coring whose right algebra r is quasi hereditary in this paper we give a combinatorial description of an associative algebra b and a b coring w whose right algebra is the ringel dual of r we apply our results in small examples to obtain restrictions on the a structure of the ext algebra of standard modules over a class of quasi hereditary algebras related to birational morphisms of smooth surfaces

closed loop behavior of a class of nonlinear systems under ekf based control we study the closed loop behavior of the extended kalman filter ekf for a class of deterministic nonlinear systems that are transformable to the special normal form with linear internal dynamics we argue that the closed loop system is asymptotically stable and the estimation error exponentially converges to zero we compare the performance of the ekf to a high gain observer through simulation

an extended robust h _infty filter for nonlinear constrained uncertain systems in this correspondence a robust filter is proposed to effectively estimate the system states in the case where system model uncertainties as well as disturbances are present the proposed robust filter is constructed based on the linear approximation methods for a general nonlinear uncertain system with an integral quadratic constraint we also derive the important characteristic of the proposed filter a modified hinfin performance index analysis results show that the proposed filter has robustness against disturbances such as process and measurement noises and against parameter uncertainties simulation results show that the proposed filter provides a performance improvement

orthogonal eigensubspace estimation using neural networks we present a neural network nn approach for simultaneously estimating all or some of the orthogonal eigenvectors of a symmetric nonindefinite matrix corresponding to its repeated minimum in magnitude eigenvalue this problem has its origin in the constrained minimization framework and has extensive applications in signal processing we recast this problem into the nn framework by constructing an appropriate energy function which the nn minimizes the nn is of feedback type with the neurons having sigmoidal activation function the proposed approach is analyzed to characterize the nature of the minimizers of the energy function the main result is that the matrix w is a minimizer of the energy function if and only if the columns of w are the orthogonal eigenvectors with a given norm corresponding to the smallest eigenvalue of the given matrix further all minimizers are global minimizers bounds on the integration time step that is required to numerically solve the system of differential equations which define the dynamics of the nn have also been derived results of computer simulations are presented to support our analysis

linear prediction methods for blind fractionally spaced equalization we describe adaptive methods for estimating fir zero forcing blind equalizers with arbitrary delay directly from the linear predictions of the observations while most current methods require inversion or singular value decomposition svd of the correlation matrix our methods need only to solve two linear prediction problems they can be implemented as rls or lms algorithms to recursively update the equalizer estimation they are computationally efficient the computational complexity in each recursion can be less than 15 ln sup 2 in the rls case where ln equals the equalizer length and 3l ln in the lms case where l is the number of subchannels the performance of the proposed methods and comparisons with existing approaches are shown by simulation to demonstrate their effectiveness

extensions of symmetric tensors by alternating tensors on demontre que les groupes d extension des tenseurs symetriques par des tenseurs alternes sont determines par les composantes homogenes des modules d homologie de l hyperalgebre du groupe additif g a

schur de rham complex and its cohomology abstract we associate to a young diagram the schur de rham complex s we show that this complex is exact when the p core of is nontrivial and compute its cohomology when the p core is trivial and the p quotient of consists of a single diagram

observer design for nonlinear systems with discrete time measurements this paper focuses on the development of asymptotic observers for nonlinear discrete time systems it is argued that instead of trying to imitate the linear observer theory the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations in particular it is shown that the discrete newton method properly interpreted yields an asymptotic observer for a large class of discrete time systems while the continuous newton method may be employed to obtain a global observer furthermore it is analyzed how the use of broyden s method in the observer structure affects the observer s performance and its computational complexity an example illustrates some aspects of the proposed methods moreover it serves to show that these methods apply equally well to discrete time systems and to continuous time systems with sampled outputs

qr factorization based blind channel identification with second order statistics most eigenstructure based blind channel identification and equalization algorithms with second order statistics need svd or evd of the correlation matrix of the received signal in this paper we address new algorithms based on qr factorization of the received signal directly without calculating the correlation matrix this renders the qr factorization based algorithms more robust against ill conditioned channels i e those channels with almost common zeros among the subchannels first we present a block algorithm that performs the qr factorization of the received data matrix as a whole then a recursive algorithm is developed based on the qr factorization by updating a rank revealing ulv decomposition compared with existing algorithms in the same category our algorithms are computationally more efficient the computation in each recursion of the recursive algorithm is on the order of o m sup 2 if only equalization is required where m is the dimension of the received signal vector our recursive algorithm preserves the fast convergence property of the subspace algorithms thus converging faster than other adaptive algorithms such as the super exponential algorithm with comparable computational complexities moreover our proposed algorithms do not require noise variance estimation numerical simulations demonstrate the good performance of the proposed algorithms

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

subspace based channel estimation for code division multiple access communication systems we consider the estimation of channel parameters for code division multiple access cdma communication systems operating over channels with either single or multiple propagation paths the multiuser channel estimation problem is decomposed into a series of single user problems through a subspace based approach by exploiting the eigenstructure of the received signal s sample correlation matrix the observation space can be partitioned into a signal subspace and a noise subspace without prior knowledge of the unknown parameters the channel estimate is formed by projecting a given user s spreading waveform into the estimated noise subspace and then either minimizing the likelihood or minimizing the euclidean norm of this projection both of these approaches yield algorithms which are near far resistant and do not require a preamble

a robust past algorithm for subspace tracking in impulsive noise the past algorithm is an effective and low complexity method for adaptive subspace tracking however due to the use of the recursive least squares rls algorithm in estimating the conventional correlation matrix like other rls algorithms it is very sensitive to impulsive noise and the performance can be degraded substantially to overcome this problem a new robust correlation matrix estimate based on robust statistics concept is proposed in this paper it is derived from the maximum likelihood ml estimate of a multivariate gaussian process in contaminated gaussian noise cg similar to the m estimates in robust statistics this new estimator is incorporated into the past algorithm for robust subspace tracking in impulsive noise furthermore a new restoring mechanism is proposed to combat the hostile effect of long burst of impulses which sporadically occur in communications systems the convergence of this new algorithm is analyzed by extending a previous ordinary differential equation ode based method for past both theoretical and simulation results show that the proposed algorithm offers improved robustness against impulsive noise over the past algorithm the performance of the new algorithm in nominal gaussian noise is very close to that of the past algorithm

sonar based robot navigation using non linear robust discrete time observers in this paper we address the sonar based nagivation of mobile robots the extended kalman filtering ekf technique is considered but from a deterministic not a stochastic point of view for this problem we present results on the robustness of the non linear discrete time observation scheme this work is strongly based on our previous paper on continuous time ekf here we provide the discrete time counterpart of these results the original feature of our approach is that the region of convergence question is posed in its complete non linear framework that is considering the dynamics not only of the estimation error but also of the covariance matrix p in this way the approach followed makes the treatment less conservative and improves the convergence analysis in discrete time new problems and difficulties appeared for proving convergence the jacobians of f and h a k and c k respectively are evaluated at different trajectories and the exponential weighting factor has a multiplicative effec

projection approximation subspace tracking subspace estimation plays an important role in a variety of modern signal processing applications we present a new approach for tracking the signal subspace recursively it is based on a novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem we show that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation the resulting algorithms have a computational complexity of o nr where n is the input vector dimension and r is the number of desired eigencomponents simulation results demonstrate that the tracking capability of these algorithms is similar to and in some cases more robust than the computationally expensive batch eigenvalue decomposition relations of the new algorithms to other subspace tracking methods and numerical issues are also discussed

plane rotation based evd updating schemes for efficient subspace tracking we present new algorithms based on plane rotations for tracking the eigenvalue decomposition evd of a time varying data covariance matrix these algorithms directly produce eigenvectors in orthonormal form and are well suited for the application of subspace methods to nonstationary data after recasting evd tracking as a simplified rank one evd update problem computationally efficient solutions are obtained in two steps first a new kind of parametric perturbation approach is used to express the eigenvector update as an unimodular orthogonal transform which is represented in exponential matrix form in terms of a reduced set of small unconstrained parameters second two approximate decompositions of this exponential matrix into products of plane or givens rotations are derived one of which being previously unknown these decompositions lead to new plane rotation based evd updating schemes proteus whose main feature is the use of plane rotations for updating the eigenvectors thereby preserving orthonormality finally the proteus schemes are used to derive new evd trackers whose convergence and numerical stability are investigated via simulations one algorithm can track all the signal subspace evd components in only o lm operations where l and m respectively denote the data vector and signal subspace dimensions while achieving a performance comparable to an exact evd approach and maintaining perfect orthonormality of the eigenvectors the new algorithms show no signs of error buildup

an updating algorithm for subspace tracking in certain signal processing applications it is required to compute the null space of a matrix whose rows are samples of a signal with p components the usual tool for doing this is the singular value decomposition however the singular value decomposition has the drawback that it requires o p sup 3 operations to recompute when a new sample arrives it is shown that a different decomposition called the urv decomposition is equally effective in exhibiting the null space and can be updated in o p sup 2 time the updating technique can be run on a linear array of p processors in o p time

blind adaptive multiuser detection in multipath cdma channels based on subspace tracking a blind adaptive technique for signal demodulation in multipath code division multiple access cdma communication channels is proposed this technique is based on signal subspace estimation the receiver employs a bank of linear filters decorrelating filters or linear mmse filters at the front end to mitigate the multiple access interference and the multipath interference a channel estimator is used to estimate the channel state for diversity combining it is shown that through the use of signal subspace estimation both the decorrelating filterbank and the linear mmse filterbank can be obtained blindly i e they can be estimated from the received signal with the prior knowledge of only the signature waveform of the desired user two forms of the subspace based linear filterbanks are developed and their equivalence in terms of the interference suppression capability is established these subspace based blind adaptive interference suppression techniques require at each symbol epoch the eigenvalues and the eigenvectors of an appropriate signal subspace which ran be obtained using computationally efficient sequential adaptive eigendecomposition subspace tracking algorithms moreover a blind adaptive method for estimating the channel state is developed which also produces the postcombining decision statistic as a byproduct

ulv and generalized ulv subspace tracking adaptive algorithms traditional adaptive filters assume that the effective rank of the input signal is the same as the input covariance matrix or the filter length n therefore if the input signal lives in a subspace of dimension less than n these filters fail to perform satisfactorily in this paper we present two new algorithms for adapting only in the dominant signal subspace the first of these is a low rank recursive least squares rls algorithm that uses a ulv decomposition stewart 1992 to track and adapt in the signal subspace the second adaptive algorithm is a subspace tracking least mean squares lms algorithm that uses a generalized ulv gulv decomposition developed in this paper to track and adapt in subspaces corresponding to several well conditioned singular value clusters the algorithm also has an improved convergence speed compared with that of the lms algorithm bounds on the quality of subspaces isolated using the gulv decomposition are derived and the performance of the adaptive algorithms are analyzed

general linear and functor cohomology over finite fields in recent years there has been considerable success in computing extgroups of modular representations associated to the general linear group by relating this problem to one of computing ext groups in functor categories f l s f s in this paper we extend our ability to make such ext group calculations by establishing several fundamental results throughout this paper we work over fields of positive characteristic p the reader familiar with the representation theory of algebraic objects will recognize the importance of an understanding of ext groups for example the existence of nonzero ext groups of positive degree is equivalent to the existence of objects which are not direct sums of simple objects indeed a knowledge of ext groups provides considerable knowledge of compound objects in the study of modular representation theory of finite chevalley groups such as gln fq ext groups play an even more central role it has been shown in cps that a knowledge of certain ext groups is sufficient to prove lusztig s conjecture concerning the dimension and characters of irreducible representations we consider two different categories of functors the category f fq of all functors from finite dimensional fq vector spaces to fq vector spaces where fq is the finite field of cardinality q and the category p fq of strict polynomial functors of finite degree as defined in f s the category p fq presents several advantages over the category f fq from the point of view of computing extgroups these are the accessibility of injectives and projectives the existence of a base change and an even easier access to ext groups of tensor products this explains the usefulness of our comparison in theorem 3 10 of ext groups in the category p fq with ext groups in the category f fq weaker forms of this theorem have been known to us since 1995 and to s betley independently

direct estimation of blind zero forcing equalizers based on second order statistics most existing zero forcing equalization algorithms rely either on higher than second order statistics or on partial or complete channel identification we describe methods for computing fractionally spaced zero forcing blind equalizers with arbitrary delay directly from second order statistics of the observations without channel identification we first develop a batch type algorithm then adaptive algorithms are obtained by linear prediction and gradient descent optimization our adaptive algorithms do not require channel order estimation nor rank estimation compared with other second order statistics based approaches ours do not require channel identification at all on the other hand compared with the cma type algorithms ours use only second order statistics thus no local convergence problem exists and faster convergence can be achieved simulations show that our algorithms outperform most typical existing algorithms

efficient numerically stabilized rank one eigenstructure updating signal processing rank one eigenvalue decomposition evd updating is well suited to the problem of tracking time varying subspaces previously published rank one evd updating algorithms suffer from a linear buildup of roundoff error which makes them impractical for a large number of recursive updates in the present work the authors develop a numerical stabilization technique which eliminates the error buildup problem in a computationally efficient manner and makes the rank one evd update a practical numerical tool for online computation a simplified eigenvalue iteration is also given it reduces the complexity of the algorithm somewhat as well as the computation time simulations are presented to illustrate numerical performance

blind equalization and multiuser detection in dispersive cdma channels the problem of blind demodulation of multiuser information symbols in a high rate code division multiple access cdma network in the presence of both multiple access interference mai and intersymbol interference isi is considered the dispersive cdma channel is first cast into a multiple input multiple output mimo signal model framework by applying the theory of blind mimo channel identification and equalization it is then shown that under certain conditions the multiuser information symbols can be recovered without any prior knowledge of the channel or the users signature waveforms including the desired user s signature waveform although the algorithmic complexity of such an approach is prohibitively high however in practice the signature waveform of the user of interest is always available at the receiver it is shown that by incorporating this knowledge the impulse response of each user s dispersive channel can be identified using a subspace method it is further shown that based on the identified signal subspace parameters and the channel response two linear detectors that are capable of suppressing both mai and isi i e a zero forcing detector and a minimum mean square error mmse detector can be constructed in closed form at almost no extra computational cost data detection can then be furnished by applying these linear detectors obtained blindly to the received signal the major contribution of this paper is the development of these subspace based blind techniques for joint suppression of mai and isi in the dispersive cdma channels

implementation of adaptive array algorithms some new efficient and numerically stable algorithms for the recursive solution of matrix problems arising in optimal beam forming and direction finding are described and analyzed the matrix problems considered are systems of linear equations and spectral decomposition while recursive solution procedures based on the matrix inversion lemma may be unstable ours are stable furthermore these algorithms are extremely fast

brief paper an ekf based nonlinear observer with a prescribed degree of stability the topic of this article is a nonlinear observer based on a slight modification of the extended kalman filter the purpose of this modification is twofold first the degree of stability can be assigned in advance and secondly this modification allows an effective treatment of the nonlinearities using the second method of lyapunov it is proved that the proposed observer is an exponential observer to examine the practical usefulness the proposed observer is applied to the highly nonlinear flux and angular velocity estimation problem for induction machines

widely linear versus linear blind multiuser detection with subspace based channel estimation finite sample size effects in a recent paper a s cacciapuoti et al ldquofinite sample performance analysis of widely linear multiuser receivers in ds cdma systems ieee transactions on signal processing vol 56 no 4 pp 1572 1588 apr 2008 we presented the finite sample theoretical performance comparison between linear l and widely linear wl minimum output energy moe receivers for direct sequence code division multiple access ds cdma systems worked out under the assumption that the channel impulse response of the desired user is exactly known the main scope of this paper is to extend such an analysis taking into account not only autocorrelation matrix acm estimation effects but also the accuracy of subspace based blind channel estimation ce we aim to answer the two following questions which of the two estimation processes acm or ce is the main source of degradation when implementing the receivers on the basis of a finite sample size compared with the l moe one is the finite sample wl moe receiver with blind ce capable of achieving the performance gains predicted by the theory to this goal simple and easily interpretable formulas are developed for the signal to interference plus noise ratio sinr at the output of the l and wl moe receivers with blind ce when they are implemented using either the sample acm or its eigendecomposition in addition the derived formulas which are validated by simulations allow one to recognize and discuss interesting tradeoffs between the main parameters of the ds cdma system

the extended kalman filter as an exponential observer for nonlinear systems we analyze the behavior of the extended kalman filter as a state estimator for nonlinear deterministic systems using the direct method of lyapunov we prove that under certain conditions the extended kalman filter is an exponential observer i e the dynamics of the estimation error is exponentially stable furthermore we discuss a generalization of the kalman filter with exponential data weighting to nonlinear systems

foncteurs polynomiaux stricts et modules instables sur l algebre de steenrod resume soient u f et p respectivement les categories des modules instables sur l algebre de steenrod modulo p sans bockstein des representations generiques des groupes lineaires generaux h w henn j lannes and l schwartz 1993 1 n j kuhn 1994 2 et des foncteurs polynomiaux stricts a la friedlander and suslin 1997 3 un foncteur f u f est construit dans h w henn j lannes and l schwartz 1993 1 utilisant le foncteur de lannes en degre 0 on construit dans cet article un foncteur m p u exact et commutant au produit tensoriel et a la torsion de frobenius qui constitute un relevement du foncteur oubli o p f m f o

prediction error method for second order blind identification blind channel identification methods based on the oversampled channel output are a problem of current theoretical and practical interest in this paper we introduce a second order blind identification technique based on a linear prediction approach in contrast to eigenstructure based methods it will be shown that the linear prediction error method is robust to order overdetermination an asymptotic performance analysis of the proposed estimation method is carried out consistency and asymptotic normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are finally presented to demonstrate the potential and the robustness of the proposed method

a subspace algorithm for certain blind identification problems the problem of blind identification of p inputs q outputs fir transfer functions is addressed existing subspace identification methods derived for p 1 are first reformulated in particular the links between the noise subspace of a certain covariance matrix of the output signals on which subspace methods build on and certain rational subspaces associated with the transfer function to be identified are elucidated based on these relations we study the behavior of the subspace method in the case where the order of the transfer function is overestimated next an asymptotic performance analysis of this estimation method is carried out consistency and asymptotical normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are presented to demonstrate the potential of the subspace method finally we take advantage of our new reformulation to discuss the extension of the subspace method to the case p 1 we show where the difficulties lie and we briefly indicate how to solve the corresponding problems the possible connections with classical approaches for ma model estimations are also outlined

an ordinary differential equation technique for continuous time parameter estimation an ordinary differential equation technique is developed via averaging theory and weak convergence theory to analyze the asymptotic behavior of continuous time recursive stochastic parameter estimators this technique is an extension of l ljung s 1977 work in discrete time using this technique the following results are obtained for various continuous time parameter estimators the recursive prediction error method with probability one converges to a minimum of the likelihood function the same is true of the gradient method the extended kalman filter fails with probability one to converge to the true values of the parameters in a system whose state noise covariance is unknown an example of the extended least squares algorithm is analyzed in detail analytic bounds are obtained for the asymptotic rate of convergence of all three estimators applied to this example

high gain estimation for nonlinear systems abstract this work is a continuation of 4 where the third author exhibits a high gain exponential observer for miso nonlinear systems affine in the input and observable for any input with continuous dynamics and measurements in this paper we establish stability results for continuous continuous and continuous discrete extended kalman filters derived from the observer of 4

a contraction theory based analysis of the stability of the deterministic extended kalman filter the contraction properties of the extended kalman filter viewed as a deterministic observer for nonlinear systems are analyzed the approach relies on the study of an auxiliary virtual dynamical system some conditions under which exponential convergence of the state error can be guaranteed are derived moreover contraction provides a simple formalism to study some robustness properties of the filter especially with respect to measurement errors as illustrated by a simplified inertial navigation example this technical note sheds another light on the theoretical properties of this popular observer

blind fractionally spaced equalization of noisy fir channels direct and adaptive solutions blind fractionally spaced equalizers reduce intersymbol interference using second order statistics without the need for training sequences methods for finding fir zero forcing blind equalizers directly from the observations are described and adaptive versions are developed in contrast most current methods require channel estimation as a first step to estimating the equalizer the direct methods can be zero forcing minimum mean square error or even minimum mean square error mmse within the class of zero forcing equalizers performance of the proposed methods and comparisons with existing approaches are shown for a variety of channels including an empirically measured digital microwave channel

autour de la cohomologie de maclane des corps finis nous decrivons une nouvelle methode de calcul de la cohomologie de maclane des corps finis cette theorie est intimement reliee aux extensions du groupe additif deja etudiees par l breen et a l homologie de hochschild topologique de m bokstedt et donc a la k theorie stable notre approche utilise de maniere cruciale l annulation de la cohomologie de maclane du corpsf p avec pour coefficients l algebre symetrique ou l on a inverse le frobenius nous recourons alors a l analyse des complexes de koszul et de de rham en caracteristique non nulle

noniterative subspace tracking a rank one spherical subspace update that is appropriate for subspace based methods like music and minimum norm is introduced this noniterative highly parallel numerically stabilized subspace update is closely related to rank one eigenstructure updating however a rank one subspace update involves less computation than simple rank one correlation accumulation moreover the frequency tracking capabilities of the noniterative subspace update are virtually identical to and in some case more robust than the more computationally expensive eigen based methods

investigations in the numerical behavior of the adaptive rank revealing qr factorization we present a tracking procedure based on the rank revealing qr rrqr factorization and investigate its numerical properties by applying it to the direction of arrival problem we address numerical issues raised by the related work proposed earlier by prasad et al 1991 and we compare the performance of the proposed algorithm to that obtained using an evd based technique

two algorithms for fast approximate subspace tracking new fast algorithms are presented for tracking singular values singular vectors and the dimension of a signal subspace through an overlapping sequence of data matrices the basic algorithm is called fast approximate subspace tracking fast the algorithm is derived for the special case in which the matrix is changed by deleting the oldest column shifting the remaining columns to the left and adding a new column on the right a second algorithm fast2 is specified by modifying fast to trade reduced accuracy for higher speed the speed and accuracy are compared with the pl algorithm the past and pastd algorithms and the fst algorithm an extension to multicolumn updates for the fast algorithm is also discussed

motion recovery by using stereo perspective observation the motion recovery for a class of movements in the space is considered in this note by using the stereo perspective observation of at least three points the motion equation that is considered can cover a wide class of practical movements in the space the asymptotic estimation of the motion parameters which are all time dependent variables is developed based on the second method of lyapunov furthermore the proposed algorithm can be modified to deal with occlusion phenomenon to illustrate the performance of the proposed algorithm it is compared with the extended kalman filter ekf by computer simulations

blind multiuser detection a subspace approach a new multiuser detection scheme based on signal subspace estimation is proposed it is shown that under this scheme both the decorrelating detector and the linear minimum mean square error mmse detector can be obtained blindly i e they can be estimated from the received signal with the prior knowledge of only the signature waveform and timing of the user of interest the consistency and asymptotic variance of the estimates of the two linear detectors are examined a blind adaptive implementation based on a signal subspace tracking algorithm is also developed it is seen that compared with the previous minimum output energy blind adaptive multiuser detector the proposed subspace based blind adaptive detector offers lower computational complexity better performance and robustness against signature waveform mismatch two extensions are made within the framework of signal subspace estimation first a blind adaptive method is developed for estimating the effective user signature waveform in the multipath channel secondly a multiuser detection scheme using spatial diversity in the form of an antenna array is considered a blind adaptive technique for estimating the array response for diversity combining is proposed it is seen that under the proposed subspace approach blind adaptive channel estimation and blind adaptive array response estimation can be integrated with blind adaptive multiuser detection with little attendant increase in complexity

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

performance analysis of an adaptive algorithm for tracking dominant subspaces this paper provides a performance analysis of a least mean square lms dominant invariant subspace algorithm based on an unconstrained minimization problem this algorithm is a stochastic gradient algorithm driving the columns of a matrix w to an orthonormal basis of a dominant invariant subspace of a correlation matrix we consider the stochastic algorithm governing the evolution of ww sup h to the projection matrix onto this dominant invariant subspace and study its asymptotic distribution a closed form expression of its asymptotic covariance is given in the case of independent observations and is further analyzed to provide some insights into the behavior of this lms type algorithm in particular it is shown that even though the algorithm does not constrain w to have orthonormal columns there is deviation from orthonormality of the first order we also give a closed form expression of the asymptotic covariance of the doas estimated by the music algorithm applied to the adaptive estimate of the projector it is found that the asymptotic distributions have a structure that is very similar to those describing batch estimation techniques because both algorithms are obtained from the minimization of the same criterion finally the accuracy of the asymptotic analysis is checked by numerical simulations and is found to be valid not only for a small step size but in a very large domain

moving horizon observer with regularisation for detectable systems without persistence of excitation a constrained moving horizon observer is developed for nonlinear discrete time systems the algorithm is proved to converge exponentially under a detectability assumption with the data being exciting at all times however in many practical estimation problems such as combined state and parameter estimation the data may not be exciting for every period of time the algorithm therefore has regularisation mechanisms to ensure robustness and graceful degradation of performance in cases when the data are not exciting this includes the use of a priori estimates in the moving horizon cost function and the use of thresholded singular value decomposition to avoid ill conditioned or ill posed inversion of the associated nonlinear algebraic equations that define the moving horizon cost function the latter regularisation relies on monitoring of the rank of an estimate of a hessian like matrix and conditions for uniform exponential convergence are given the method is in particular useful with augmented state sp

the monoidal structure on strict polynomial functors abstract the category of strict polynomial functors inherits an internal tensor product from the category of divided powers to investigate this monoidal structure we consider the category of representations of the symmetric group s d which admits a tensor product coming from its hopf algebra structure it is classical that there exists a functor f from the category of strict polynomial functors to the category of representations of the symmetric group our main result is that this functor f is monoidal in addition we study the relations under f between projective strict polynomial functors and permutation modules and the link to symmetric functions

on updating signal subspaces the authors develop an algorithm for adaptively estimating the noise subspace of a data matrix as is required in signal processing applications employing the signal subspace approach the noise subspace is estimated using a rank revealing qr factorization instead of the more expensive singular value or eigenvalue decompositions using incremental condition estimation to monitor the smallest singular values of triangular matrices the authors can update the rank revealing triangular factorization inexpensively when new rows are added and old rows are deleted experiments demonstrate that the new approach usually requires o n sup 2 work to update an n n matrix and that it accurately tracks the noise subspace

on estimating the condition of eigenvalues and eigenvectors abstract a method is developed for estimating the accuracy of computed eigenvalues and eigenvectors that are obtained via certain eispack subroutines it does this at a cost of o n 2 flops per eigenpair assuming that the eigenpair is known and assuming that the original matrix has been reduced to hessenberg form the heart of the technique involves estimating the smallest singular value of a certain nearly triangular submatrix this is accomplished by some standard zero chasing with givens transformations and with a 2 norm version of the linpack condition estimator an eispack compatible code has been developed and its performance is discussed

comparative study of non linear state observation techniques abstract this paper contains a comparative study of four techniques for observing the slates of non linear systems the first technique examined is inspired by bestle and zeitz and icrener and respondek in this method a non linear transformation is found that brings the system into a canonical form from where observer design is facilitated the second technique is attributable to thau in this method the error between the system s true state and the output of the observer is shown to be asymptotically convergent to zero provided that an additional assumption is valid the third technique is due to baumann and rugh in this method extended or pseudolinearization of the error differential equation about a family of equilibrium points results in an observer design such that the eigenvalues of the linearized error equation are locally invariant finally techniques from variable structure systems are utilized to design an observer that yields an exponentially decaying error like thau s observer but unl

blind channel identification subspace tracking method without rank estimation subspace ss methods are an effective approach for blind channel identification however these methods also have two major disadvantages 1 they require accurate channel length estimation and or rank estimation of the correlation matrix which is difficult with noisy channels and 2 they require a large amount of computation for the singular value decomposition svd which makes it inconvenient for adaptive implementation although many adaptive subspace tracking algorithms can be applied the computational complexity is still o m sup 3 where m is the data vector length in this paper we introduce new recursive subspace algorithms using ulv updating and successive cancellation techniques the new algorithms do not need to estimate the rank of the correlation matrix furthermore the channel length can be overestimated initially and be recovered at the end by a successive cancellation procedure which leads to more convenient implementations the adaptive algorithm has computations of o m sup 2 in each recursion the new methods can be applied to either the single user or the multiuser cases simulations demonstrate their good performance

schur functors and schur complexes the study of schur functors has a relatively long history its main impetus derived from representation theory originally in characteristic zero over the years however with the development of modular representations and algebraic geometry over fields of positive characteristic the need for a theory of universal polynomial functors increased and since the mid 1960s approaches to a characteristic free treatment of schur functors have been developing see for instance the recent book of green 1 l in which the treatments by carter and lusztig 6 higman 12 and towber 20 among others are discussed our own interest in such a treatment was awakened by the work of lascoux 141 on resolutions of determinantal ideals although his thesis treated only the characteristic zero case it suggested that a general and elementary theory of schur functors could be developed using only the rudiments of multilinear algebra involving the hopf algebra structures of the symmetric exterior and divided power algebras moreover this elementary development admitted of a natural generalization to the idea of schur complexes whose usefulness was demonstrated for instance in our construction of a universal minimal

a new state observer for perspective systems in this note we consider the problem of estimating the state of a class of perspective systems the problem can be converted into the observation of a dynamical system with nonlinearities a new discontinuous state observer which is motivated by the sliding mode control method and adaptive techniques is proposed for the obtained dynamical system the assumptions are reasonable and the convergence conditions are intuitive and have apparently physical interpretations the attraction of the new method is that the algorithm is very simple and easy to be implemented and it is robust to measurement noises further minor a priori knowledge of the system is required in the new formulation simulation results show the superiority of the new method to the traditional ones

the invariant extended kalman filter as a stable observer we analyze the convergence aspects of the invariant extended kalman filter iekf when the latter is used as a deterministic nonlinear observer on lie groups for continuous time systems with discrete observations one of the main features of invariant observers for left invariant systems on lie groups is that the estimation error is autonomous in this paper we first generalize this result by characterizing the much broader class of systems for which this property holds for those systems the lie logarithm of the error turns out to obey a linear differential equation then we leverage this log linear property of the error evolution to prove for those systems the local stability of the iekf around any trajectory under the standard conditions of the linear case one mobile robotics example and one inertial navigation example illustrate the interest of the approach simulations evidence the fact that the ekf is capable of diverging in some challenging situations where the iekf with identical tuning keeps converging

the exogenous kalman filter xkf abstractit is well known that the time varying kalman filter kf is globally exponentially stable and optimal in the sense of minimum variance under some conditions however nonlinear approximations such as the extended kf linearises the system about the estimated state trajectories leading in general to loss of both global stability and optimality nonlinear observers tend to have strong often global stability properties they are however often designed without optimality objectives considering the presence of unknown measurement errors and process disturbances we study the cascade of a global nonlinear observer with the linearised kf where the estimate from the nonlinear observer is an exogenous signal only used for generating a linearised model to the kf it is shown that the two stage nonlinear estimator inherits the global stability property of the nonlinear observer and simulations indicate that local optimality properties similar to a perfectly linearised kf can be achieved this two stag