combined sequence of markov parameters and moments in linear systems the combined sequence of markov parameters and moments in linear systems is discussed this sequence is shown to be generated by a linear feedback shift register application to the minimal degree partial realization from a mixture of any number of markov parameters and moments is considered central in this particular realization problem is the extension of a toeplitz partial behavior matrix this is accomplished on the basis of the algebraic theory of iohvidov indexes for toeplitz matrices

improving differential detection of mdpsk by nonlinear noise prediction and sequence estimation a new technique is proposed to improve the performance of differential detection dd of m ary differential phase shift keying mdpsk significantly applying sequence estimation in order to obtain an appropriate representation of the received signal a nonlinear time variant finite impulse response or infinite impulse response prediction error filter is used for both filter structures the optimum coefficients are derived assuming transmission over an additive white gaussian noise awgn channel delayed decision feedback sequence estimation ddfse is employed to estimate the transmitted symbol sequence it is shown by simulations that even for decision feedback equalization which is a simple special case of ddfse a significant performance improvement of conventional dd under awgn conditions results in contrast to other noncoherent low complexity receivers proposed in literature this receiver is very robust under flat fading rayleigh and ricean conditions

covariance controllers for linear continuous time systems abstract necessary and sufficient conditions are given for the existence of a controller of specified order n c which will assign a specified matrix value x to the covariance of the closed loop system if a solution exists the entire set of stabilizing controllers that assign x are parameterized by a certain skew symmetric matrix

bit error rate of binary and quaternary dpsk signals with multiple differential feedback detection a differentially coherent detection scheme with improved bit error rate ber performance is presented for differentially encoded binary and quaternary phase shift keying psk modulation the improvement is based on using l symbol detectors with delays of 1 2 l symbol periods and on feeding back detected psk symbols exact formulas for the bit error probability are derived for the case that correct symbols are fed back the effect of symbol errors in the feedback path on the ber is determined by computer simulations

paper approximation of multivariable linear systems with impulse response and autocorrelation sequences this paper considers the construction of approximants of multi input multi output discrete time linear systems from the finite data of the impulse response and autocorrelation sequences in the approximation of a multivariable linear system it is common practice to use a finite portion of its impulse response sequence this is formally equivalent to the pade approximation technique which may produce unstable approximants even though the original system is stable mullis and roberts proposed a new method which yields stable approximants in connection with approximation of digital filters this is however restricted to the single input single output case this paper extends their method to the multi input multi output case and shows a fast recursive algorithm to construct stable approximants of linear systems

delayed decision feedback sequence estimation the authors delayed decision feedback sequence estimation ddfse for uncoded pam signals is considered estimates on the performance of the algorithm are given and simulation results are provided for several examples a more general form of ddfse applicable to coded modulation systems is also presented as an example detection of trellis coded qpsk quadrature phase shift keyed signals over intersymbol interference channels is discussed

an optimal controller reduction by covariance equivalent realizations based upon the theory of covariance equivalent realizations 1 this note presents a technique to obtain reduced order controllers via an optimal projection of full order lqg controllers this projection is optimal in the sense that it is a weighted least square approximation to a covariance equivalent projection of the full order optimal closed loop system the technique which is capable of extracting optimal minimal lqg controllers whenever they exist is also shown to yield controllers that are equivalent to those obtained by component cost analysis 12

inexact solves in interpolatory model reduction we investigate the use of inexact solves for interpolatory model reduction and consider associated perturbation effects on the underlying model reduction problem we give bounds on system perturbations induced by inexact solves and relate this to termination criteria for iterative solution methods we show that when a petrov galerkin framework is employed for the inexact solves the associated reduced order model is an exact interpolatory model for a nearby full order system thus demonstrating backward stability we also give evidence that for h2 optimal interpolation points interpolatory model reduction is robust with respect to perturbations due to inexact solves finally we demonstrate the effectiveness of direct use of inexact solves in optimal h2 approximation the result is an effective model reduction strategy that is applicable in realistically large scale settings

on the partial realization problem abstract in this paper we take a unified approach to the partial realization problem in which we seek to incorporate ideas from numerical linear algebra most of which were originally developed in other contexts we approach the partial realization problem from several different angles and explore the connections to such topics as factoriza tion of hankel matrices block tridiagonalization generalizations of the lanczos process for biorthogonalization the euclidean algorithm and the principal part con tinued fractions of arne magnus the pade table and the berlekamp masseyalgo rithm in this way we are able to clarify some previous results by rissanen kalman and others and place them in a broader context this leads to several results and concepts which we think are new our analysis is restricted to the scalar case but some definitions and formulations have been rigged to facilitate an extension to the matrix case

a projection approach to covariance equivalent realizations of discrete systems covariance equivalent realization theory has been used recently in continuous systems for model reduction 1 4 and controller reduction 2 5 in model reduction this technique produces a reduced order model that matches q 1 output covariances and q markov parameters of the full order model in controller reduction it produces a reduced controller that is close to matching q 1 output covariances of the full order controller and q markov parameters of the closed loop system for discrete systems a method was devised to produce a reduced order model that matches the q 1 covariances 6 but not any markov parameters this method requires a factorization to obtain the input matrix and since the dimension of this matrix factor depends upon rank properties not known a priori this method may not maintain the original dimension of the input vector hence this method 6 is obviously not suitable for controller reduction a new projection method is described that matches q covariances and q markov parameters of the original system while maintaining the correct dimension of the input vector

q markov covariance equivalent realizations this paper describes a class of reduced order models which match both the first q markov parameters and the first q output covariances for linear systems subject to white noise inputs the class of reduced models contains the earlier models 2 as a special case

adaptive noncoherent dfe for mdpsk signals transmitted over isi channels a novel noncoherent decision feedback equalization ndfe scheme for m ary differential phase shift keying signals transmitted over intersymbol interference channels is presented a suboptimum version with lower computational complexity and a noncoherent linear equalizer nle are derived from the original ndfe scheme furthermore the relation of the novel nle to a previously proposed nle is investigated in contrast to known ndfe schemes the novel scheme can approach the performance of coherent minimum mean squared error decision feedback equalization for adaptation of the feedforward and feedback filters efficient novel modified least mean square and recursive least squares algorithms are presented finally it is shown that the proposed adaptive ndfe scheme is robust against frequency offset

a generalization of the levinson algorithm for hermitian toeplitz matrices with any rank profile the paper describes a recursive algorithm for solving hermitian toeplitz systems of linear equations without any restriction on the ranks of their nested toeplitz subsystems such a general algorithm is needed e g to obtain the eigenfilters for signal processing applications or to compute the inverse of a nondefinite toeplitz matrix the regular portion of the algorithm is made of the classical levinson recursion the singular portion requires solving some well defined systems of linear equations with gradient structure the dimension of each of these sytems equals the amplitude of the corresponding singularity

weighted q markov covariance equivalent realizations abstract reduced order models which preserve the first q markov parameters and the first q covariances are called q markov covariance equivalent realizations q markov covers this paper extends these notions to the case where the input is coloured instead of white noise we call this the weighted q markov cover

pade techniques for model reduction in linear system theory a survey abstract techniques of pade approximation and continued fractions have been used often in model reduction problems an extensive bibliography on this topic is given the ideas are explained for the simple situation of a scalar function where no singular blocks appear in the pade table extensions to the matrix case and the multivariable case are not explained in detail

a new formulation of q markov covariance equivalent realization the q markov covariance equivalent realization q markov cover is a state space realization which matches the first q markov parameters and covariance parameters of a system king desai and skelton 5 developed a generalized approach to generate q markov covers desai and skelton 3 presented a recursive computational algorithm for generating q markov covers when q is very large based on the works of the above two papers we developed a new formula for generating q markov covers and also an algorithm to compute them when q is very large the new formula has been applied for model identification of large flexible structures by liu and skelton 6 8 compared with previously developed formulas and algorithms the new formula and algorithm are relatively straightforward and easy to program this formula may simplify the further analytical study of q markov covers and its application to system identification

recursive partial realization from the combined sequence of markov parameters and moments abstract in this paper we develop the recursive structure of partial realization from a two sided sequence of markov parameters and moments the specific feature of this recursive structure is that it accommodates sequences growing in two directions like in the two point pade approximation we present a recursive algorithm for the minimal partial realization from a sequence of markov parameters and moments that amounts to recursive lu factorization of a toeplitz behavior matrix leaping over nongeneric sections it turns out that this algorithm reveals a new continued fraction expansion which extends the classical cauer third form as a corollary various results related to toeplitz matrices two point pade approximations continued fractions etc are unified within this partial realization setting

formally biorthogonal polynomials and a look ahead levinson algorithm for general teoplitz systems abstract systems of linear equations with toeplitz coefficient matrices arise in many important applications the classical levinson algorithm computes solutions of toeplitz systems with only o n 2 arithmetic operations as compared to o n 3 operations that are needed for solving general linear systems however the levinson algorithm in its original form requires that all leading principal submatrices be nonsingular in this paper an extension of the levinson algorithm to general toeplitz systems is presented the algorithm uses look ahead to skip over exactly singular as well as ill conditioned leading submatrices and at the same time it still fully exploits the toeplitz structure in our derivation of this algorithm we make use of the intimate connection of toeplitz matrices with formally biorthogonal polynomials in particular the occurence of singular or ill conditioned submatrices corresponds to a breakdown or near breakdown in the standard recurrence relations for biorthogonal polynomials we present new general recurrence relations that connect successive pairs in any given subsequence of all existing formally biorthogonal polynomials these recurrences then immediately lead to the proposed look ahead levinson algorithm for solving toeplitz systems implementation details for this algorithm and operation counts are given numerical experiments for toeplitz systems with ill conditioned submatrices are reported

data aided noncoherent demodulation of dpsk considers noncoherent demodulation of dpsk when the receiver has partial knowledge of the information being transmitted this partial knowledge represents preamble symbols pilot symbols or past decisions when operating in a decision feedback mode the maximum likelihood ml noncoherent receiver for this case is derived it is shown that known demodulation schemes such as multi symbol differentially coherent receivers and decision feedback differential receivers can be considered as special cases of this data aided noncoherent dpsk demodulator a simple recursive structure for this receiver is introduced and its performance analyzed

interpolatory weighted h2 model reduction this paper introduces an interpolation framework for the weighted h 2 model reduction problem we obtain a new representation of the weighted h 2 norm of siso systems that provides new interpolatory first order necessary conditions for an optimal reduced order model the h 2 norm representation also provides an error expression that motivates a new weighted h 2 model reduction algorithm several numerical examples illustrate the effectiveness of the proposed approach

proper complex random processes with applications to information theory the covariance of complex random variables and processes when defined consistently with the corresponding notion for real random variables is shown to be determined by the usual complex covariance together with a quantity called the pseudo covariance a characterization of uncorrelatedness and wide sense stationarity in terms of covariance and pseudo covariance is given complex random variables and processes with a vanishing pseudo covariance are called proper it is shown that properness is preserved under affine transformations and that the complex multivariate gaussian density assumes a natural form only for proper random variables the maximum entropy theorem is generalized to the complex multivariate case the differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum if and only if the random vector is proper gaussian and zero mean the notion of circular stationarity is introduced for the class of proper complex random processes a discrete fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain an application of the theory is presented

differential phase detection using recursively generated phase references we show that decision feedback differential phase detection dfdpd is equivalent to a technique which generates a phase reference by averaging several primitive phase references we then modify the dfdpd into a differential phase detection dpd technique which generates the phase reference using a simple recursive form the proposed technique can be easily implemented and has satisfactory error performance

component cost analysis of large scale systems abstract a brief summary of component cost analysis cca is given cca provides a means to determine the contribution of each dynamical element of the system in the overall performance metric using cca a theory of cost equivalent realizations is developed cost equivalent realizations are realizations that have the same value of the performance metric as the original system and they can be of lower order than kalman s minimal realization

q markov cover identification using pseudo random binary signals the original q markov covariance equivalent realization q markov cover method for identification required white noise test signals which cannot be generated exactly this paper replaces the unrealizable white noise signal with a realizable signal the pseudo random binary signal prbs and proves that when the period of the prbs approaches infinity the q markov cover algorithm operating with prbs matches the first q markov and covariance parameters as in the original theory with white noise test signals the existing q markov cover algorithm will fail to match covariance and markov parameters exactly due to non white test signals the new algorithm will fail to match covariance and markov parameters exactly due to the finite period of prbss we demonstrate however that the results with prbss are far superior to results with white noise signals apparently the non whiteness of the test signal degrades the identification performance worse than the non infinite period of the prbs

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

stability preservation and computational aspects of a newly proposed reduction method the stability of the reduced order models obtained using the method suggested by a lepschy et al syst contr lett vol 8 pp 405 10 may 1987 is analyzed the relation between this method and the routh approximation is pointed out some interesting properties related to the construction of the reduced order transfer functions and to the evaluation of certain quadratic integrals are derived an examples shows the practicality of the procedures

the phase of a vector perturbed by gaussian noise and differentially coherent receivers some results are presented regarding the asymptotic distribution of the phase of a vector perturbed by gaussian noise it is shown that for large signal to noise ratio the asymptotic distribution of the phase is of the tikhonov type this framework is then used for the synthesis of differentially coherent receiver structures one for m ary phase shift keying mpsk and the other for minimum shift keying msk the first structure bridges the performance gap between coherent and differentially coherent demodulation of mpsk the msk receiver uses matched filtering with differential demodulation

differential detection with iir filter for improving dpsk detection performance this paper presents a method for improving the performance of differential detection of differentially encoded phase shift keying dpsk the structure of the proposed detection scheme consists of a conventional differential detection circuit equipped with an infinite impulse response iir filter combined with decision feedback the results of theoretical analysis and computer simulation show that performance of the proposed detection method can approach that of coherent detection of dpsk under additive white gaussian noise awgn conditions without any increase in architectural complexity furthermore a parameter of the proposed detector can be varied to optimize performance for static or fading conditions an adaptive scheme suitable for time varying rician fading channel conditions is presented and performance results obtained by computer simulation are given

ensemble tracking we consider tracking as a binary classification problem where an ensemble of weak classifiers is trained online to distinguish between the object and the background the ensemble of weak classifiers is combined into a strong classifier using adaboost the strong classifier is then used to label pixels in the next frame as either belonging to the object or the background giving a confidence map the peak of the map and hence the new position of the object is found using mean shift temporal coherence is maintained by updating the ensemble with new weak classifiers that are trained online during tracking we show a realization of this method and demonstrate it on several video sequences

interpolatory projection methods for parameterized model reduction we provide a unifying projection based framework for structure preserving interpolatory model reduction of parameterized linear dynamical systems i e systems having a structured dependence on parameters that we wish to retain in the reduced order model the parameter dependence may be linear or nonlinear and is retained in the reduced order model moreover we are able to give conditions under which the gradient and hessian of the system response with respect to the system parameters is matched in the reduced order model we provide a systematic approach built on established interpolatory mathcal h 2 optimal model reduction methods that will produce parameterized reduced order models having high fidelity throughout a parameter range of interest for single input single output systems with parameters in the input output maps we provide reduced order models that are optimal with respect to an mathcal h 2 otimes mathcal l 2 joint error measure the capabilities of these approaches are illustrated by several numerical examples from technical applications

receivers with widely linear processing for frequency selective channels we propose several equalization schemes based on widely linear processing wlp the received signal and its complex conjugate are separately filtered and the results are linearly combined it is shown that wlp yields a gain in performance if the noiseless received signal can be interpreted as the convolution of a real valued data sequence and an equivalent complex valued intersymbol interference channel impulse response such a model applies to e g amplitude shift keying offset quadrature amplitude modulation and binary minimum shift keying type modulation we consider receivers without and with decision feedback finite impulse response filters are derived for these structures which are optimum with respect to the zero forcing and minimum mean squared error mmse criteria respectively in the mmse case adaptive algorithms for filter adjustment are given infinite filter orders are investigated in order to obtain analytical performance results furthermore suboptimum trellis based detection with widely linear preprocessing is briefly discussed it is demonstrated analytically and by numerical examples that widely linear schemes may outperform conventional schemes significantly depending on the considered application

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

controller reduction concepts and approaches the problem of passing from a linear time invariant high order controller designed for a linear time invariant plant of presumably high order to a low order approximation of the controller is discussed the approximation problem is often best posed as a frequency weighted l sub infinity approximation problem many different controller representations are possible giving different performances of the various reduction algorithms

model reduction using new optimal routh approximant technique an optimal routh approximant of a single input single output dynamic system is a reduced order transfer function of which the denominator is obtained by the routh approximation method while the numerator is determined by minimizing a time response integral squared error ise criterion in this paper a new elegant approach is presented for obtaining the optimal routh approximants for linear time invariant continuous time systems the approach is based on the routh canonical expansion which is a finite term orthogonal series of rational basis functions and minimization of the ise criterion a procedure for combining the above approach with the bilinear transformation is also presented in order to obtain the optimal bilinear routh approximants of linear time invariant discrete time systems the proposed technique is simple in formulation and is amenable to practical implementation

optimal chained aggregation for reduced order modeling in this paper a theory is proposed for a new optimal process to perform chained aggregation in reduced order modelling notions of almost invariant subspaces and approximate aggregation are introduced in the proposed theory and are shown to be useful concepts in model reduction to derive an exact aggregated model from the approximately aggregated model obtained by optimal chained aggregation an algorithm is presented which is a variant of the well known shifted qr algorithm examples are given to illustrate the theory and its superiority over a previous approach

structure preserving tangential interpolation for model reduction of port hamiltonian systems port hamiltonian systems result from port based network modeling of physical systems and are an important example of passive state space systems in this paper we develop a framework for model reduction of large scale multi input multi output port hamiltonian systems via tangential rational interpolation the resulting reduced model is a rational tangential interpolant that retains the port hamiltonian structure hence it remains passive we introduce an h 2 inspired algorithm for effective choice of interpolation points and tangent directions and present several numerical examples illustrating its effectiveness

linear system approximation via covariance equivalent realizations abstract a truncation technique for model reduction to simultaneously match a specified number of output covariance derivatives is described these covariance equivalent realizations which match q 1 covariance derivatives are called q covers in general q covers are not unique the additional freedom is used herein so that the q cover obtained also matches q markov parameters the truncation technique uses a form of the observability matrices of the full order system to determine a priori the order required of the reduced order model to match a specified number of output covariance derivatives and markov parameters the resulting realization is shown to be independent of the basis of the complete model to within a unitary transformation stability conditions for the reduced order model are also described and the relationships are established between stochastically equivalent realizations and the q covers

robust feature point matching with sparse model feature point matching that incorporates pairwise constraints can be cast as an integer quadratic programming iqp problem since it is np hard approximate methods are required the optimal solution for iqp matching problem is discrete binary and thus sparse in nature this motivates us to use sparse model for feature point matching problem the main advantage of the proposed sparse feature point matching spm method is that it generates sparse solution and thus naturally imposes the discrete mapping constraints approximately in the optimization process therefore it can optimize the iqp matching problem in an approximate discrete domain in addition an efficient algorithm can be derived to solve spm problem promising experimental results on both synthetic points sets matching and real world image feature sets matching tasks show the effectiveness of the proposed feature point matching method

a least squares approach to reduce stable discrete linear systems preserving their stability abstract a new stability preserving model reduction algorithm for discrete linear siso systems based on a least squares approach is proposed similar to the pade approximation an equation system for the markov parameters involving a high dimensional hankel matrix is considered it is proved that approximate solutions computed via the moore penrose pseudo inverse give rise to a stability preserving reduction scheme furthermore the proposed algorithm is compared to the balanced truncation method showing comparable performance of the reduced systems

integrating graph partitioning and matching for trajectory analysis in video surveillance in order to track moving objects in long range against occlusion interruption and background clutter this paper proposes a unified approach for global trajectory analysis instead of the traditional frame by frame tracking our method recovers target trajectories based on a short sequence of video frames e g 15 frames we initially calculate a foreground map at each frame obtained from a state of the art background model an attribute graph is then extracted from the foreground map where the graph vertices are image primitives represented by the composite features with this graph representation we pose trajectory analysis as a joint task of spatial graph partitioning and temporal graph matching the task can be formulated by maximizing a posteriori under the bayesian framework in which we integrate the spatio temporal contexts and the appearance models the probabilistic inference is achieved by a data driven markov chain monte carlo algorithm given a period of observed frames the algorithm simulates an ergodic and aperiodic markov chain and it visits a sequence of solution states in the joint space of spatial graph partitioning and temporal graph matching in the experiments our method is tested on several challenging videos from the public datasets of visual surveillance and it outperforms the state of the art methods

layered graph matching with composite cluster sampling this paper presents a framework of layered graph matching for integrating graph partition and matching the objective is to find an unknown number of corresponding graph structures in two images we extract discriminative local primitives from both images and construct a candidacy graph whose vertices are matching candidates i e a pair of primitives and whose edges are either negative for mutual exclusion or positive for mutual consistence then we pose layered graph matching as a multicoloring problem on the candidacy graph and solve it using a composite cluster sampling algorithm this algorithm assigns some vertices into a number of colors each being a matched layer and turns off all the remaining candidates the algorithm iterates two steps 1 sampling the positive and negative edges probabilistically to form a composite cluster which consists of a few mutually conflicting connected components ccps in different colors and 2 assigning new colors to these ccps with consistence and exclusion relations maintained and the assignments are accepted by the markov chain monte carlo mcmc mechanism to preserve detailed balance this framework demonstrates state of the art performance on several applications such as multi object matching with large motion shape matching and retrieval and object localization in cluttered background

a hankel matrix approach to stochastic model reduction a procedure for stochastic model reduction is presented utilizing the hankel matrix results of adamjan arov and krein in a way not previously exploited it is shown thai the error variance of the resulting n th order approximation is bounded from above by the n 1 singular value of the system s hankel matrix

decision feedback differential detection of mdpsk for flat rayleigh fading channels in this paper decision feedback differential detection df dd of m ary differential phase shift keying mdpsk signals which has been introduced previously for the additive white gaussian noise awgn channel by leib et al 1988 and edbauer 1992 is extended to flat rayleigh fading channels the corresponding df dd metric is derived from the multiple symbol detection msd metric and for genie aided df dd an exact expression for the bit error rate ber of qdpsk m 4 is calculated furthermore the dependence of ber on the power spectrum of the fading process is investigated for feedback filters of infinite order it is shown that in this case for ideally bandlimited fading processes the error floor of conventional differential detection dd can be removed entirely simulation results confirm that both msd and df dd with feedback filters of finite order can reduce the error floor of conventional dd significantly df dd thereby causes considerably less computational load

q markov covariance equivalent realizations in fixed and floating point computations this paper produces all linear state space models which match a prespecified set of input output cross correlation and output autocorrelation data when the model is installed in a computational environment with specified bits assigned to the fixed point or floating point simulation with the assumed round off noise model these results allow the design of digital simulations or controller realizations with no error within the specified set of cross correlation and autocorrelation data

representing and recognizing objects with massive local image patches natural image patches are fundamental elements for visual pattern modeling and recognition by studying the intrinsic manifold structures in the space of image patches this paper proposes an approach for representing and recognizing objects with a massive number of local image patches e g 17x17 pixels given a large collection 10 4 of proto image patches extracted from objects we map them into two types of manifolds with different metrics explicit manifolds of low dimensions for structural primitives and implicit manifolds of high dimensions for stochastic textures we define these manifolds grown from patches as the e balls where e corresponds to the perception residual or fluctuation using these e balls as features we present a novel generative learning algorithm by the information projection principle this algorithm greedily stepwise pursues the object models by selecting sparse and independent e balls say 10 3 for each category during the detection and classification phase only a small number say 20 of features are activated by a fast kd tree indexing technique the proposed method owns two characters 1 automatically generating features e balls from local image patches rather than designing marginal feature carefully and category specifically 2 unlike the weak classifiers in the boosting models these selected e ball features are used to explain object in a generative way and are mutually independent the advantage and performance of our approach is evaluated on several challenging datasets with the task of localizing objects against appearance variance occlusion and background clutter

model reduction of large scale systems by least squares abstract in this paper we introduce an approximation method for model reduction of large scale dynamical systems this is a projection which combines aspects of the svd and krylov based reduction methods this projection can be efficiently computed using tools from numerical analysis namely the rational krylov method for the krylov side of the projection and a low rank smith type iteration to solve a lyapunov equation for the svd side of the projection for discrete time systems the proposed approach is based on the least squares fit of the r 1 th column of a hankel matrix to the preceding r columns where r is the order of the reduced system the reduced system is asymptotically stable matches the first r markov parameters of the full order model and minimizes a weighted h 2 error the method is also generalized for moment matching at arbitrary interpolation points application to continuous time systems is achieved via the bilinear transformation numerical examples prove the effectiveness of the approach the proposed method is significant because it combines guaranteed stability and moment matching together with an optimization criterion

identification of multivariable stochastic linear systems via polyspectral analysis given noisy input output time domain data the paper considers the problem of identification of unknown parameters of multivariable linear errors invariables models attention is focused on frequency domain approaches where the integrated polyspectrum bispectrum or trispectrum of the input and the integrated cross polyspectrum respectively of the given time domain input output data are exploited two new classes of parametric frequency domain approaches are proposed and analyzed an integrated polyspectrum based persistence of excitation condition on system input is defined both classes of the parameter estimators are shown to be strongly consistent in any measurement noise sequences with vanishing bispectra when integrated bispectrum based approaches are used the proposed parameter estimators are shown to be strongly consistent in gaussian measurement noise when integrated trispectrum based approaches are used the input to the system need not be a linear process but must have nonvanishing bispectrum or trispectrum

a multiple hypothesis approach for multiobject visual tracking in multiple object tracking applications it is essential to address the problem of associating targets and observation data for visual tracking of multiple targets which involves objects that split and merge a target may be associated with multiple measurements and many targets may be associated with a single measurement the space of such data association is exponential in the number of targets and exhaustive enumeration is impractical we pose the association problem as a bipartite graph edge covering problem given the targets and the object detection information we propose an efficient method of maintaining multiple association hypotheses with the highest probabilities over all possible histories of associations our approach handles objects entering and exiting the field of view merging and splitting objects as well as objects that are detected as fragmented parts experimental results are given for tracking multiple players in a soccer game and for tracking people with complex interaction in a surveillance setting it is shown through quantitative evaluation that our method tracks through varying degrees of interactions among the targets with high success rate

robust controller design based on reduced order plants two dual controller design methods are proposed for linear time invariant multi input multi output systems where designs based on a reduced order plant robustly stabilizer higher order plants with additional poles or zeros in the stable region the additional poles or zeros are considered as multiplicative perturbations of the reduced plant the methods are tailored towards closed loop stability and performance and they yield estimates for the stability robustness and performance of the final design they can be considered as formalizations of two classical heuristic model reduction techniques one method neglects a plant pole sufficiently far to the left of dominant poles and the other cancels a sufficiently small stable plant zero with a pole at the origin

brief paper krylov projection framework for fourier model reduction this paper analyzes the fourier model reduction fmr method from a rational krylov projection framework and shows how the fmr reduced model which has guaranteed stability and a global error bound can be computed in a numerically efficient and robust manner by monitoring the rank of the krylov subspace that underlies the fmr model the projection framework also provides an improved criterion for determining the number of fourier coefficients that are needed and hence the size of the resulting reduced order model the advantages of applying fmr in the rational krylov projection framework are demonstrated on a simple example

reduction of linear continuous time multivariable systems by matching first and second order information this paper considers the approximation of stable continuous time multivariable linear systems from a finite number of markov parameters and second order information indexes it is shown that by properly choosing these indexes it is possible to uniquely identify an input output model of given order from an equal number of first and second order data

computation of minimal order state space realizations and observability indices using orthogonal transformations in this paper an algorithm is presented for obtaining a minimal order state space realization of a strictly proper rational function matrix the algorithm can also be used to compute the observability indices of any given state space system a controllable but unobservable state space realization of the given rational function matrix is first obtained by inspection the algorithm then performs a sequence of simple coordinate transformations on the state vector of the system the coordinate transformation matrices are orthogonal and are easily constructed from the system matrices each coordinate transformation operates on submatrices of the state space system matrices of lower dimension than the preceding one the sequence of coordinate transformations terminates after at most v 1 1 transformations where v 1 is the maximal observability index of the state space model the observability indices of the system are also determined at this time the transformed system matrices are obtained in a form wh

an algorithm for solving discrete time wiener hopf equations based upon euclid s algorithm an algorithm for solving a discrete time wiener hopf equation is presented based upon euclid s algorithm the discrete time wiener hopf equation is a system of linear inhomogeneous equations with a given toeplitz matrix m a given vector b and an unknown vector lambda such that m lambda b the algorithm is able to find a solution of the discrete time wiener hopf equation for any type of toeplitz matrices except for the all zero matrix while the levinson algorithm and the trench algorithm are not available when at least one of the principal submatrices of the toeplitz matrix m is singular the algorithm gives a solution if one exists even when the toeplitz matrix m is singular while the brent gustavson yun algorithm only states that the toeplitz matrix m is singular the algorithm requires o t 2 arithmetic operations for t unknowns in the sense that the number of multiplications or divisions is directly proportional to t 2 like the levinson and trench algorithms furthermore a faster algorithm is also presented based upon the half greatest common divisor algorithm and hence it requires o t log 2 t arithmetic operations like the brent gustavson yun algorithm

reduced order models and controllers for continuous time stochastic systems an information theory approach reduced order models and controllers for continuous time stochastic systems are described the reduced order models are chosen to minimize the kullback leibler information distance klid between the outputs of the actual and reduced systems an lqg controller based on a reduced order system model is described a second reduced order controller is found to minimize the klid between the closed loop system outputs with the full and reduced order controllers

model reduction via balanced state space representations a model reduction procedure based on balanced state space representations is studied in this paper the reduced order model is examined from the point of view of stability controllability and observability both continuous time and discrete time systems are considered

some asymptotic properties of multivariable models identified by equation error techniques some interesting properties are derived for simple equation error identification techniques least squares and basic instrumental variable methods applied to a class of linear time invariant time discrete multivariable models the system at hand is not supposed to be contained in the chosen model set assuming that the input is unit variance white noise it is shown that the markov parameters of the system are estimated asymptotically unbiased over a certain interval around t 0

interpolatory projection methods for structure preserving model reduction abstract we present a framework for interpolatory model reduction that treats systems having a generalized coprime factorization c s s 1 b s d this includes rational krylov based interpolation methods as a special case the broader framework allows retention of special structure in reduced models such as symmetry second and higher order structure state constraints internal delays and infinite dimensional subsystems two numerical examples are provided for systems associated with viscoelastic dynamics and with an internal state delay that demonstrate the effectiveness and flexibility of the approach

multiple symbol differential detection of mpsk a differential detection technique for mpsk multiple phase shift keying which uses a multiple symbol observation interval is presented and its performance is analyzed and simulated the technique makes use of maximum likelihood sequence estimation of the transmitted phases rather than symbol by symbol detection as in the conventional differential detection thus the performance of this multiple symbol detection scheme fills the gap between conventional two symbol observation differentially coherent detection of mpsk and ideal coherent of mpsk with differential encoding the amount of improvement gained over conventional differential detection depends on the number of phases m and the number of additional symbol intervals added to the observation what is particularly interesting is that substantial performance improvement can be obtained for only one or two additional symbol intervals of observation the analysis and simulation results presented are for uncoded mpsk

an iterative svd krylov based method for model reduction of large scale dynamical systems abstract in this paper we propose a model reduction algorithm for approximation of large scale linear time invariant dynamical systems the method is a two sided projection combining features of the singular value decomposition svd based and the krylov based model reduction techniques while the svd side of the projection depends on the observability gramian the krylov side is obtained via iterative rational krylov steps the reduced model is asymptotically stable matches certain moments and solves a restricted h 2 minimization problem we present modifications to the proposed approach for employing low rank gramians in the reduction step and also for reducing discrete time systems several numerical examples from various disciplines verify the effectiveness of the proposed approach it performs significantly better than the q cover a yousouff r e skelton covariance equivalent realizations with applications to model reduction of large scale systems in c t leondes ed control and dynamic systems vol 22 academic press 1985 pp 273 348 a yousouff d a wagie r e skelton linear system approximation via covariance equivalent realizations journal of math anal and appl 196 1985 91 115 and the least squares s gugercin a c antoulas model reduction of large scale systems by least squares linear algebra appl 415 2 3 2006 290 321 methods that have a similar projection structure to the proposed method also in terms of both the h 2 and h error measures its performance is comparable to or sometimes better than that of balanced truncation moreover the method proves to be robust with respect to the perturbations due to usage of approximate gramians

model sets and parametrizations for identification of multivariable equation error models abstract equation error or linear regression models are known to inherently require the a priori choice for specific signal variables to be considered as regressand and or regressor this implies that a model set should be a priori restricted in some way in order to define an acceptable identification problem in the case of approximate identification i e the system to be modelled is not contained in the model set this restriction acts as a design variable with the identified models being dependent on its specific choice in this paper the necessity of this restriction is quantified by the property of discriminability i e the ability of an identification criterion to distinguish between all the different models in a model set employing a deterministic signal oriented framework several sets of sufficient conditions are derived for model sets to be discriminable by a least squares identification criterion to this end use is made of polynomial model representations in two shift operators although it is of a different nature the problem discussed is shown to be closely related to the problem of constructing identifiable parametrizations for sets of rational transfer functions it is shown that the pseudo canonical or overlapping parametrization of all transfer functions with fixed mcmillan degree constitutes a nonoverlapping set of equation error models that is discriminable by a least squares identification criterion

h2 norm optimal model reduction for large scale discrete dynamical mimo systems modeling strategies often result in dynamical systems of very high dimension it is then desirable to find systems of the same form but of lower complexity whose input output behavior approximates the behavior of the original system here we consider linear time invariant discrete time dynamical systems the cornerstone of this paper is a relation between optimal model reduction in the h 2 norm and tangential rational hermite interpolation first order necessary conditions for h 2 optimal model reduction are presented for discrete multiple input multiple output mimo systems these conditions suggest a specific choice of interpolation data and a novel algorithm aiming for anh 2 optimal model reduction for mimo systems it is also shown that the conditions are equivalent to two known gramian based first order necessary conditions numerical experiments demonstrate the approximation quality of the method

a generalized approach to q markov covariance equivalent realizations for discrete systems abstract a new algorithm is developed which constructs q markov covariance equivalent realizations q markov covers of multivariable linear discrete time systems a q markov cover is a state realization which matches exactly a finite portion of the impulse response sequence markov parameters and output autocorrelation sequence covariance parameters of a linear system the algorithm generates the q markov covers starting with only the basic data namely the q markov parameters and the q covariance parameters the algorithm leads to a parameterization of all minimal stable q markov covers which can be constructed since the data are easily computed from a given state space model the algorithm presented will be useful for both realization and model reduction of multivariable linear discrete time systems an example is presented to demonstrate the algorithm

convergence of the iterative rational krylov algorithm abstract the iterative rational krylov algorithm irka of gugercin et al 2008 8 is an interpolatory model reduction approach to the optimal h 2 approximation problem even though the method has been illustrated to show rapid convergence in various examples a proof of convergence has not been provided yet in this note we show that in the case of state space symmetric systems irka is a locally convergent fixed point iteration to a local minimum of the underlying h 2 approximation problem

past input reconstruction in fast least squares algorithms this paper solves the following problem given the computed variables in a fast least squares prediction algorithm determine all past input sequences that would have given rise to the variables in question this problem is motivated by the backward consistency approach to numerical stability in this algorithm class the set of reachable variables in exact arithmetic is known to furnish a stability domain our problem is equivalent to a first and second order interpolation problem introduced by mullis and roberts 1976 and studied by others our solution differs in two respects first relations to classical interpolation theory are brought out which allows us to parametrize all solutions by products of our formulation are correct necessary and sufficient conditions for the problem to be solvable in contrast to previous works whose claimed sufficient conditions are shown to fall short second our solution obtains any valid past input as the impulse response of an appropriately constrained orthogonal filter whose rotation parameters derive in a direct manner from the computed variables in a fast least squares prediction algorithm formulas showing explicitly the form of all valid past inputs should facilitate the study of what past input perturbation is necessary to account for accumulated arithmetic errors in this algorithm class this in turn is expected to have an impact in studying accuracy aspects in fast least squares algorithms

generation of a time series having a specified power spectrum with minimum roundoff noise the problem of determining a shaping filter which minimized the output roundoff noise variance is discussed it is shown that in the family of shaping filters of an identical mcmillan degree having an identical power spectrum the shaping filter of minimum phase attains a minimum output roundoff noise variance in either the case of optimal word lengths or the case of equal word lengths it is shown out by examples that this is not valid in the family of shaping filters having an identical power spectrum and different mcmillan degrees

discovering discriminative graphlets for aerial image categories recognition recognizing aerial image categories is useful for scene annotation and surveillance local features have been demonstrated to be robust to image transformations including occlusions and clutters however the geometric property of an aerial image i e the topology and relative displacement of local features which is key to discriminating aerial image categories cannot be effectively represented by state of the art generic visual descriptors to solve this problem we propose a recognition model that mines graphlets from aerial images where graphlets are small connected subgraphs reflecting both the geometric property and color texture distribution of an aerial image more specifically each aerial image is decomposed into a set of basic components e g road and playground and a region adjacency graph rag is accordingly constructed to model their spatial interactions aerial image categories recognition can subsequently be casted as rag to rag matching based on graph theory rag to rag matching is conducted by comparing all their respective graphlets because the number of graphlets is huge we derive a manifold embedding algorithm to measure different sized graphlets after which we select graphlets that have highly discriminative and low redundancy topologies through quantizing the selected graphlets from each aerial image into a feature vector we use support vector machine to discriminate aerial image categories experimental results indicate that our method outperforms several state of the art object scene recognition models and the visualized graphlets indicate that the discriminative patterns are discovered by our proposed approach

comments on model reduction by minimizing the equation error minimization of the equation error is a well known and powerful tool which has been introduced to the reduction of time invariant linear systems independently by obinata and inooka 1 2 and by eitelberg 3 5 the purpose of this note is to examine critically the methods in 1 2 and to propose to the readers of ieee transactions on automatic control an altenative formalism which has been tested successfully on systems of high order 3 5

iterative decision feedback differential demodulation of bit interleaved coded mdpsk for flat rayleigh fading channels a simple receiver structure previously proposed by the authors for convolutional coded m ary differential phase shift keying transmission over flat rayleigh fading channels without channel state information is analyzed in detail we present a thorough discussion of the iterative decoding procedure which is referred to as iterative decision feedback differential demodulation iterative df dm the convergence behavior of iterative df dm is theoretically examined the analysis supports the observation that the iterative decoding scheme works well for target bit error rates which are usually of interest furthermore the associated cut off rate for error free decision feedback is studied judging from this performance parameter remarkable gains in power efficiency compared to conventional differential demodulation are indicated while the computational complexity of the decoding remains low the results from information theory are in good agreement with the given simulation results

structural state space sensitivity in linear systems abstract the concept of transformation independent noise is introduced to define a general class of structurally insensitive state space realizations of a given transfer function a performance measure is minimized subject first to only an t 2 scaling constraint on the norm of each state node this constraint normalizes the contribution of each state in the performance measure later additional constraints are imposed on the class of allowable state space structures one constraint requires a covariance decoupled structure while another imposes a constraint on the markov parameters of a partitioned substructure

multichannel stable systems that extend the partial impulse response matrices this paper addresses the problem of identifying the class of all multichannel stable system transfer functions that extend the given partial impulse response matrix sequence this is achieved by making use of the left and right schur recursion algorithms for bounded matrix functions and in this context the classical pade approximations that are also stable are shown to be a special case of this general formulation further the theory developed here is utilized to generate multichannel non minimum phase optimal rational approximations to multichannel nonrational systems from their partial impulse response matrix sequence

model reduction by matching markov parameters time moments and impulse response energies this paper presents a simple procedure for constructing reduced order models that match some markov parameters and time moments of an original system as well as the energies of its impulse response and of other combinations of the system modes in this way the stability of the reduced model of a stable system is ensured

controller reduction using canonical interactions a conceptual approach to controller reduction is proposed that is based on closed loop considerations the method assesses the interactions between the plant and a high order controller as described by canonical correlation coefficients a free parameter in the algorithm of the reduced controller makes it possible to trade stability robustness versus performance several examples demonstrate the efficacy of the method

video tracking based on sequential particle filtering on graphs in this paper we develop a novel solution for particle filtering on general graphs we provide an exact solution for particle filtering on directed cycle free graphs the proposed approach relies on a partial order relation in an antichain decomposition that forms a high order markov chain over the partitioned graph we subsequently derive a closed form sequential updating scheme for conditional density propagation using particle filtering on directed cycle free graphs we also provide an approximate solution for particle filtering on general graphs by splitting graphs with cycles into multiple directed cycle free subgraphs we then use the sequential updating scheme by alternating among the directed cycle free subgraphs to obtain an estimate of the density propagation we rely on the proposed method for particle filtering on general graphs for two video tracking applications 1 object tracking using high order markov chains and 2 distributed multiple object tracking based on multi object graphical interaction models experimental results demonstrate the improved performance of the proposed approach to particle filtering on graphs compared with existing methods for video tracking

a simple hankel interpretation of the berlekamp massey algorithm abstract a simple interpretation of the berlekamp massey algorithm in the light of the hankel matrix is presented the salient result is that the jump of the linear feedback shift register lfsr length is derived almost trivially from the so called iohvidov index of the hankel matrix prior to making any reference to the berlekamp massey algorithm itself next the hankel system of equations that yields the updated connection polynomial is solved via the natural lu factorization of the hankel matrix which itself leads to the berlekamp massey algorithm in a simple and transparent manner

interpolatory h h model reduction abstract we introduce an approach to h model reduction that is founded on ideas originating in realization theory interpolatory h 2 optimal model reduction and complex chebyshev approximation within this new framework we are able to formulate a method that remains effective in large scale settings with the main cost dominated by sparse linear solves by employing loewner data driven partial realizations within each optimization cycle computationally demanding h norm calculations can be completely avoided several numerical examples illustrate that our approach will produce high fidelity reduced models consistently exhibiting better h performance than those produced by balanced truncation these models often are as good as and occasionally better than those models produced by optimal hankel norm approximation in all cases reduced models are produced at far lower cost than is possible either with balanced truncation or with optimal hankel norm approximation