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

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

a novel orthonormalization matrix based fast and stable dpm algorithm for principal and minor subspace tracking we note that the well known fast rayleigh s quotient based adaptive noise subspace frans frans with householder transformation hfrans and fast data projection method fdpm algorithms all inherit from the data projection method dpm algorithm but with different orthonormalization matrices starting from the dpm we analyze the orthonormalization matrices of all these algorithms and develop a novel orthonormalization matrix for our algorithm based on this novel orthonormalization matrix a fast and stable implementation of the dpm algorithm which has the merits of both the frans and fdpm approaches is investigated for principal and minor subspace tracking the proposed algorithm can switch between the principal and minor subspace tracking with a simple sign change of its step size parameter moreover it reaches the 3np lower bound of the dominant complexity and guarantees the orthonormality of the tracked subspace the numerical stability of our algorithm is established theoretically and tested numerically the strengths and weaknesses of the proposed algorithm to some existing subspace tracking algorithms are demonstrated using a de facto benchmark example simulation results are presented to demonstrate the effectiveness of the tracking algorithm advocated

rotation based rls algorithms unified derivations numerical properties and parallel implementations this work presents a unified derivation of four rotation based recursive least squares rls algorithms they solve the adaptive least squares problems of the linear combiner the linear combiner without a desired signal the single channel and the multichannel linear prediction and transversal filtering compared to other approaches the authors derivation is simpler and unified and may be useful to readers for better understanding the algorithms and their relationships moreover it enables improvements of some algorithms in the literature in both the computational and the numerical issues all algorithms derived in this work are based on givens rotations they offer superior numerical properties as shown by computer simulations they are computationally efficient and highly concurrent aspects of parallel implementation and parameter identification are discussed

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

tracking of signal subspace projectors a new subspace tracking approach that directly operates on the projection matrix onto the signal subspace instead of tracking its unitary eigenbasis is proposed therefore the difficulties arising from introducing a calculus on the manifold of projection matrices are overcome by a proper parameterization of the projectors simulation results are presented from the field of angular frequency retrieval in array signal processing

signed rank nonparametric multiuser detection in non gaussian channels we present a novel nonparametric multiuser detector for non gaussian channels that is based on the signed rank norm for linear regression analytical and simulation results show that the proposed detector offers similar or better performance as compared to the minimax robust detector but without requiring any a priori information on the noise the complexity of this detector is lower than that of the pseudo norm nonparametric detector stated previously by the authors this is due to the fact that in contrast to the latter it is not necessary to compute the intercept parameter for the signed rank detector proposed in this correspondence we analyze the behavior of the blind version of this detector and show that it outperforms the blind minimax detector we also show that this detector has a bounded influence function and hence it is robust

modified quadratic discriminant functions and the application to chinese character recognition issues in the quadratic discriminant functions qdf are discussed and two types of modified quadratic disriminant functions mqdf1 mqdf2 which are less sensitive to the estimation error of the covariance matrices are proposed the mqdf1 is a function which employs a kind of a pseudo bayesian estimate of the covariance matrix instead of the maximum likelihood estimate ordinarily used in the qdf the mqdf2 is a variation of the mqdf1 to save the required computation time and storage two discriminant functions were applied to chinese character recognition to evaluate their effectiveness and remarkable improvement was observed in their performance

an analytical constant modulus algorithm iterative constant modulus algorithms such as godard 1980 and cma have been used to blindly separate a superposition of cochannel constant modulus cm signals impinging on an antenna array these algorithms have certain deficiencies in the context of convergence to local minima and the retrieval of all individual cm signals that are present in the channel we show that the underlying constant modulus factorization problem is in fact a generalized eigenvalue problem and may be solved via a simultaneous diagonalization of a set of matrices with this new analytical approach it is possible to detect the number of cm signals present in the channel and to retrieve all of them exactly rejecting other non cm signals only a modest amount of samples is required the algorithm is robust in the presence of noise and is tested on measured data collected from an experimental set up

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

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

adaptive eigensubspace algorithms for direction or frequency estimation and tracking the authors present an adaptive estimator of the complete noise or signal subspace of a sample covariance matrix as well as the estimator s practical implementations the general formulation of the proposed estimator results from an asymptotic argument which shows the signal or noise subspace computation to be equivalent to a constrained gradient search procedure a highly parallel algorithm denoted the inflation method is introduced for the estimation of the noise subspace the simulation results of these adaptive estimators show that the adaptive subspace algorithms perform substantially better than p a thompson s 1980 adaptive version of v f pisarenko s technique 1973 in estimating frequencies or directions of arrival doa of plane waves for tracking nonstationary parameters the simulation results also show that the adaptive subspace algorithms are better than direct eigendecomposition methods for which computational complexity is much higher than the adaptive versions

adaptive normalized quasi newton algorithms for extraction of generalized eigen pairs and their convergence analysis the main contributions of this paper are to propose and analyze fast and numerically stable adaptive algorithms for the generalized hermitian eigenvalue problem ghep which arises in many signal processing applications first for given explicit knowledge of a matrix pencil we formulate two novel deterministic discrete time ddt systems for estimating the generalized eigen pair eigenvector and eigenvalue corresponding to the largest smallest generalized eigenvalue by characterizing a generalized eigen pair as a stationary point of a certain function the proposed ddt systems can be interpreted as natural combinations of the normalization and quasi newton steps for finding the solution second we present adaptive algorithms corresponding to the proposed ddt systems moreover we establish rigorous analysis showing that for a step size within a certain range the sequence generated by the ddt systems converges to the orthogonal projection of the initial estimate onto the generalized eigensubspace corresponding to the largest smallest generalized eigenvalue numerical examples demonstrate the practical applicability and efficacy of the proposed adaptive algorithms

simple effective computation of principal eigenvectors and their eigenvalues and application to high resolution estimation of frequencies we present the results of an investigation of the prony lanczos p l method 14 38 and the power method 39 for simple computation of approximations to a few eigenvectors and eigenvalues of a hermitian matrix we are motivated by realization of high resolution signal processing in an integrated circuit the computational speeds of the above methods are analyzed they are completely dependent on the speed of a matrix vector product operation if only a few eigenvalues or eigenvectors are needed the suggested methods can substitute for methods of the linpack or eispack subroutine libraries the accuracies of the suggested methods are evaluated using matrices formed from simulated data consisting of two sinusoids plus gaussian noise comparisons are made to the corresponding eigenvalues and eigenvectors obtained using linpack as a reference also the accuracies of frequency estimates obtained from the eigenvectors are compared

discrete representation of straight lines if a continuous straight line segment is digitized on a regular grid obviously a loss of information occurs as a result the discrete representation obtained e g a chaincode string can be coded more conveniently than the continuous line segment but measurements of properties such as line length performed on the representation have an intrinsic inaccuracy due to the digitization process in this paper two fundamental properties of the quantization of straight line segments are treated 1 it is proved that every straight chaincode string can be represented by a set of four unique integer parameters definitions of these parameters are given 2 a mathematical expression is derived for the set of all continuous line segments which could have generated a given chaincode string the relation with the chord property is briefly discussed

a distributed framework for dimensionality reduction and denoising with the recent upsurge in the amount of data transmission and use in networks a lot of emphasis is placed on designing efficient methods to extract useful information by reducing the size of large data sets a major approach in data dimensionality reduction relies on the estimation of the principal data covariance eigenspace in this paper a distributed algorithmic framework is put forth for finding the principal eigenspace of spatially scattered sensor data toward this end the standard principal component analysis framework is reformulated as a separable constrained minimization problem which is solved by utilizing coordinate descent techniques combined with the alternating direction method of multipliers computationally simple local updating recursions are obtained that involve only single hop intersensor communications the proposed distributed algorithm is shown to be robust even in the presence of inter sensor communication noise and converge to the principal eigenspace when inter sensor links are ideal the proposed distributed framework is used in a data denoising setting while extensive numerical tests using both synthetic and real data demonstrate a fast convergence rate better steady state performance of the novel algorithm over existing alternatives and communication noise resilience

least squares type algorithm for adaptive implementation of pisarenko s harmonic retrieval method pisarenko s harmonic retrieval method involves determining the minimum eigenvalue and the corresponding eigenvector of the covariance matrix of the observed random process recently thompson 9 suggested a constrained gradient search procedure for obtaining an adaptive version of pisarenko s method and his simulations have verified that the frequency estimates provided by his procedure were unbiased however the main cost of this technique was that the initial convergence rate could be very slow for certain poor initial conditions restating the constrained minimization as an unconstrained nonlinear problem we derived an alternative gauss newton type recursive algorithm which also used the second derivative matrix or hessian this algorithm may also be viewed as an approximate least squares algorithm simulations have been performed to compare this algorithm to a slight variant of thompson s original algorithm the most important conclusions are that the least squares type algorithm has faster convergence in the beginning while its convergence rate close to the true parameters depends on the signal to noise ratio of the input signal the approximate least squares algorithm resolves the sinusoids much faster than the gradient version

blind adaptation of zero forcing projections and oblique pseudo inverses for subspace detection and estimation when interference dominates noise in much of modern radar sonar and wireless communication it seems more reasonable to model measurement noise as subspace interference plus broadband noise than as colored noise this observation leads naturally to a variety of detection and estimation problems in the linear statistical model to solve these problems one requires oblique pseudo inverses oblique projections and zero forcing orthogonal projections the problem is that these operators depend on knowledge of signal and interference subspaces and this information is often not at hand more typically the signal subspace is known but the interference subspace is unknown we prove a theorem that allows these operators to be estimated directly from experimental data without knowledge of the interference subspace as a byproduct the theorem shows how signal subspace covariance may be estimated when the strict identities of the theorem are approximated then the detectors estimators and beamformers of this paper take on the form of adaptive subspace estimators detectors and capon beamformers all of which are reduced in rank the fundamental operator turns out to be a certain reduced rank wiener filter which we clarify in the course of our derivations the results of this paper form a foundation for the rapid adaptation of receivers that are then used for detection and estimation they may be applied to detection and estimation in radar sonar and hyperspectral imaging and to data decoding in multiuser communication receivers

estimating shortest paths and minimal distances on digitized three dimensional surfaces abstract the estimation of minimal distances and shortest paths between points on a continuous three dimensional 3d surface given in digitized form is considered the suggested approach combines recently developed length estimators for digitized 3d curves with well known algorithms for computing shortest paths in sparse graphs to estimate the minimal distances and the corresponding shortest paths in a systematic computationally efficient way in comparison to differential geometry techniques for solving the continuous geodesic problem and to computational geometry algorithms for solving the discrete geodesic probelm the suggested hybrid continuous discrete approach is well suited to applications in which continuous surfaces are given in digitized form computation time must be relatively short and an approximate solution is acceptable in particular the suggested method can be used to efficiently obtain a good initial approximation as an input to other algorithms thus improving their speed of convergence and reducing their tendency to converge to insignificant local minima some confusion has recently arisen with respect to the relation between the design of length estimators and the optimization of local distances for distance transformations since 3d length estimation is a central concept in the suggested approach an effort is made to resolve discrepancies and to highlight the similarities and differences between these problems it is shown that while in two dimensions the design of length estimators and the design of local weights for distance transformations are rather similar in three dimensions digital geometry dictates that these problems are different the contexts in which each of the two approaches should be preferred are identified

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

three dimensional digital line segments digital arcs in 3 d digital pictures are defined the digital image of an arc is also defined a digital arc is defined to be a digital line segment if it is the digital image of a line segment it is shown that a digital line segment may be characterized by the chord property holding for its projections onto the coordinate planes it is also shown that a digital line segment may not be characterized by its own chord property a linear time algorithm is presented that determines whether or not a digital arc is a digital line segment

character independent font recognition on a single chinese character a novel algorithm for font recognition on a single unknown chinese character independent of the identity of the character is proposed in this paper we employ a wavelet transform on the character image and extract wavelet features from the transformed image after a box cox transformation and lda linear discriminant analysis process the discriminating features for font recognition are extracted and classified through a mqdf modified quadric distance function classifier with only one prototype for each font class our experiments show that our algorithm can achieve a recognition rate of 90 28 percent on a single unknown character and 99 01 percent if five characters are used for font recognition compared with existing methods all of which are based on a text block our method can provide a higher recognition rate and is more flexible and robust since it is based on a single unknown character additionally our method demonstrates that it is possible to extract subtle yet discriminative signals embedded in a much larger noisy background

asymptotic performance analysis of subspace adaptive algorithms introduced in the neural network literature in the neural network literature many algorithms have been proposed for estimating the eigenstructure of covariance matrices we first show that many of these algorithms when presented in a common framework show great similitudes with the gradient like stochastic algorithms usually encountered in the signal processing literature we derive the asymptotic distribution of these different recursive subspace estimators a closed form expression of the covariances in distribution of eigenvectors and associated projection matrix estimators are given and analyzed in particular closed form expressions of the mean square error of these estimators are given it is found that these covariance matrices have a structure very similar to those describing batch estimation techniques the accuracy of our asymptotic analysis is checked by numerical simulations and it is found to be valid not only for a small step size but in a very large domain finally convergence speed and deviation from orthonormality of the different algorithms are compared and several tradeoffs are analyzed

chain code probabilities and optimal length estimators for digitized three dimensional curves abstract length estimation of three dimensional digitized curves is considered three dimensional 26 directional chain code representation is assumed recent results on three dimensional euclidean distance maps are inapplicable to optimal three dimensional length estimation to support optimal design of three dimensional length estimators chain code probabilities in three dimensional chain encoded digital straight lines are derived optimal three dimensional length estimators are determined and their performance is evaluated analytically and experimentally

a generalized minimum mean output energy strategy for cdma systems with improper mai it has been shown that in a direct sequence code division multiple access ds cdma system employing binary phase shift keying bpsk modulation the baseband equivalent of the cdma multiplex is under very mild assumptions an improper complex random process i e it has a nonzero pseudoautocorrelation function the problem of linear multiuser detection for asynchronous ds cdma systems with improper multiaccess interference mai is considered a new mean output energy moe cost function is introduced whose constrained minimization leads to two new linear multiuser detectors exploiting the information contained in the pseudoautocorrelation of the observables and which generalize the classical decorrelating and minimum mean square error mmse receivers the problem of blind adaptive receiver implementation based on subspace tracking is also tackled finally the superiority of the new detectors with respect to the classical linear detection structures present in the literature is demonstrated through both theoretical considerations and computer simulations

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

a survey of conjugate gradient algorithms for solution of extreme eigen problems of a symmetric matrix a survey of various conjugate gradient cg algorithms is presented for the minimum maximum eigen problems of a fixed symmetric matrix the cg algorithms are compared to a commonly used conventional method found in imsl it is concluded that the cg algorithms are more flexible and efficient than some of the conventional methods used in adaptive spectrum analysis and signal processing

estimation of the original length of a straight line segment from its digitization in three dimensions abstract estimation of different properties of a continuous predigitized curve from its digitized contour is an important problem with applications in various disciplines of computer science in this context the problem of estimating the original length of a line segment in three dimensions given its quantization in a suitable form is considered four types of characterization schemes for the digitized contour are presented along with a set of estimators the average errors of these estimators are found out experimentally the domains of characterization are formulated for the first three schemes and the theoretical average errors are calculated for the first two the theoretical and the experimental errors are found to tally within computational accuracy

a feasible method for optimization with orthogonality constraints minimization with orthogonality constraints e g x top x i and or spherical constraints e g vert x vert 2 1 has wide applications in polynomial optimization combinatorial optimization eigenvalue problems sparse pca p harmonic flows 1 bit compressive sensing matrix rank minimization etc these problems are difficult because the constraints are not only non convex but numerically expensive to preserve during iterations to deal with these difficulties we apply the cayley transform a crank nicolson like update scheme to preserve the constraints and based on it develop curvilinear search algorithms with lower flops compared to those based on projections and geodesics the efficiency of the proposed algorithms is demonstrated on a variety of test problems in particular for the maxcut problem it exactly solves a decomposition formulation for the sdp relaxation for polynomial optimization nearest correlation matrix estimation and extreme eigenvalue problems the proposed algorithms run very fast and return solutions no worse than those from their state of the art algorithms for the quadratic assignment problem a gap 0 842 to the best known solution on the largest problem tai256c in qaplib can be reached in 5 min on a typical laptop

closed form blind mimo channel estimation for orthogonal space time block codes in this paper a new computationally simple approach to blind decoding of orthogonal space time block codes ostbcs is proposed using specific properties of ostbcs the authors approach estimates the channel matrix in a closed form and in a fully blind fashion this channel estimate is then used in the maximum likelihood ml receiver to decode the information symbols the proposed estimation technique provides consistent channel estimates and as a result the performance of the authors blind ml receiver approaches that of the coherent ml receiver which exploits the exact channel state information csi simulation results demonstrate the performance improvements achieved by the proposed blind decoding algorithm relative to the popular differential space time modulation scheme

performance analysis of adaptive eigenanalysis algorithms we present a rigorous analysis of several popular forms of short memory adaptive eigenanalysis algorithms using a stochastic averaging method a first order analysis shows that the algorithms do not have any equilibrium points despite published claims to the contrary through averaging analysis we show that they hover around an appropriate eigenvector a second order analysis is also given without the gaussian noise assumption and our results greatly outperform an earlier approximation in the literature the second order analysis has been of much interest in the offline study but in the dynamic adaptive case is uncommon

exact and approximate maximum likelihood parameter estimation for quasi synchronous cdma signals in order to construct the optimal decorrelator for a quasi synchronous qs code division multiple access receiver it is necessary to estimate the user delays however in a qs system it is shown that delay estimation is equivalent to estimating a parameter vector which is related linearly to the received signal an exact maximum likelihood ml solution using alternating maximization is first developed for joint estimation of the user delay vectors and amplitudes suboptimal recursive least squares rls and least mean square algorithms are then presented which approximate the true ml solution it is shown that the optimal decorrelator and demodulated symbols are also generated by the rls algorithm simulation and analytical results are presented for the bit error rate performance of the adaptive receiver and the average squared error of the estimated delay vectors is compared with the cramer rao bound

eigenvalues and eigenvectors of covariance matrices for signals closely spaced in frequency the eigenstructures of common covariance matrices are identified for the general case of m closely spaced signals it is shown that the largest signal space eigenvalue is relatively insensitive to signal separation by contrast the ith largest eigenvalue is proportional to delta omega sup 2 i 1 or delta omega sup 4 i 1 where delta omega is a measure of signal separation therefore matrix conditioning degrades rapidly as signal separation is reduced it is also shown that the limiting eigenvectors have remarkably simple structures the results are very general and apply to planar far field direction finding problems involving almost arbitrary scenarios and also to time series analysis of sinusoids exponentials and other signals

stable subspace tracking algorithm based on a signed urv decomposition subspace estimation and tracking are of fundamental importance in many signal processing algorithms the class of schur subspace estimators provides a complete parametrization of all principal subspace estimates defined as the column spans of corresponding low rank matrix approximants that lie within a specified 2 norm distance of a given matrix the parametrization is found in terms of a two sided hyperbolic decomposition hyperbolic urv or hurv which can be computed using hyperbolic rotations unfortunately such rotations are commonly associated with numerical instabilities in this paper we present a numerically stable non iterative algorithm to compute the hurv called the signed urv surv algorithm we show that this algorithm implicitly imposes certain constraints on the hurv such that important norm bounds that guarantee stability are satisfied the constraints also restrict the parametrization of the subspace estimate such that it becomes close to the principal subspace provided by the svd which is a special case within this class the complexity of the algorithm is of the same order as that of a qr update updating and downdating are of the same complexity and are both numerically stable surv is proven to provide rank estimates consistent with the svd with the same rank threshold it can replace an svd where only subspace estimation is needed typical applications would e g be the detection of the number of signals in array signal processing and subspace estimation for source separation and interference mitigation such as the first step in music and esprit type algorithms simulation results demonstrate the numerical stability and confirm that this algorithm provides exact rank estimates and good principal subspace estimates as compared to the svd

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

detection and estimation in sensor arrays using weighted subspace fitting the problem of signal parameter estimation of narrowband emitter signals impinging on an array of sensors is addressed a multidimensional estimation procedure that applies to arbitrary array structures and signal correlation is proposed the method is based on the recently introduced weighted subspace fitting wsf criterion and includes schemes for both detecting the number of sources and estimating the signal parameters a gauss newton type method is presented for solving the multidimensional wsf and maximum likelihood optimization problems the global and local properties of the search procedure are investigated through computer simulations most methods require knowledge of the number of coherent noncoherent signals present a scheme for consistently estimating this is proposed based on an asymptotic analysis of the wsf cost function the performance of the detection scheme is also investigated through simulations

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

digital representation schemes for 3d curves digital representation of three dimensional 3 d curves is considered two dimensional representation schemes are first reviewed then methods applicable to curves in three and higher dimensional spaces are described desirable properties of curve representation schemes are identified and used as a basis for qualitative and quantitative comparison of the various methods that have been suggested conclusions concerning the selection of a digital 3 d curve representation scheme for shape analysis and coding are drawn it is shown that grid intersect quantization is a poor choice for curve representation in 3 d space and that cube quantization that leads to 6 connected chain codes meets all the identified requirements and should be preferred

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

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

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed