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Decision and Control including the Symposium on Adaptive Processes, 1981 20th IEEE Conference on

Date 16-18 Dec. 1981

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  • [Front cover and table of contents]

    Publication Year: 1981 , Page(s): c1
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  • Foreword

    Publication Year: 1981 , Page(s): i
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  • Singular value decomposition and spectral analysis

    Publication Year: 1981 , Page(s): 1 - 11
    Cited by:  Papers (26)
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    Linear-Prediction-based (LP) methods for fitting multiple-sinusoid signal models to observed data, such as the forward-backward (FBLP) method of Nuttall (5) and Ulrych and Clayton (6), are very ill-conditioned. The locations of estimated spectral peaks can be greatly affected by a small amount of additive noise. LP estimation of frequencies can be greatly improved by singular value decomposition of the LP data matrix. The improved performance of the resulting new technique, which we called the principal eigenvector method (13, 14) is demonstrated by using it on one and two dimensional data. View full abstract»

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  • Multi-domain adaptive parameter estimation

    Publication Year: 1981 , Page(s): 12 - 16
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    Expressions are developed for obtaining an estimate of a set of related signal parameters which is optimal in the sense that the estimates are unbiased in the absence of background interference and minimum variance for a background whose statistics are specified. When these are not known a-priori the estimator may be implemented adaptively using an iterative algorithm or by matrix estimation and inversion. For the latter approach probability density distributions are presented for the parameter estimates when signal and background have Gaussian statistics. The expressions are similar in form to those which have been developed for single parameter estimation. Finally, an approach to adaptive frequency and bearing estimation is presented as an example of multiple parameter estimation, and expressions for the probability density distributions and moments of the estimates are presented. View full abstract»

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  • Adaptive algorithms and their convergence characteristics

    Publication Year: 1981 , Page(s): 17 - 24
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    The convergence characteristics of the gradient transversal filter (LMS), the one coefficient gradient lattice (GL1), and the least squares lattice (LSL) are explored via two examples. The first investigates their ability to track the frequency dynamics of dual sinusoids whose power levels are widely separated and the second investigates the rate at which each algorithm is able to whiten a fourth order, complex, autoregressive process. View full abstract»

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  • SNR enhancement of narrowband signals in colored noise using adaptive predictors

    Publication Year: 1981 , Page(s): 25 - 30
    Cited by:  Papers (1)
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    Use of the Linear Prediction Filter in cascade with an FFT is demonstrated as a sub-optimum realization of the optimum filter for maximization of instantaneous signal-to-rms noise power. Computer generated colored noise and sinusoidal signals are used to compare the suboptimum filter with a conventional matched filter (designed for white noise only) in terms of output SNR for cases in which the signal and noise spectra overlap. Significant improvements are seen with the LPF-FFT cascade. Four algorithms for implementing the LPF are compared for the application. Time - frequency plots are presented that graphically illustrate the filter effectiveness to extract signals masked by colored noise. View full abstract»

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  • Residual signal analysis - A subsystem approach to adaptive signal processing

    Publication Year: 1981 , Page(s): 31 - 37
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    A signal bus contains a multiplicity of signals to be recovered. A cooperative arrangement between estimation processors is shown in which each processor acts as an adaptive interference nulling device for all the other processors while performing an efficient estimation of its own signal. Signals being estimated are removed from the common bus driving all of the estimators except that a unique feedback arrangement gives to each estimator full access to its own assigned signal. View full abstract»

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  • Global convergence of output error recursions in colored noise

    Publication Year: 1981 , Page(s): 38 - 43
    Cited by:  Papers (1)
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    This paper presents a variation on a known extended least squares algorithm of the "output error" or "parallel model" type. Under reasonable conditions, the algorithms achieve global convergence of the one-step-ahead prediction error to the additive independent (possible colored) measurement noise. The convergence of the algorithms proposed is not critically sensitive to the color in the noise as are related extended least squares schemes which require a simultaneous noise model identification, nor is the convergence critically sensitive to the input signals as are realizations of the method of instrumental variables. The algorithms are also simpler to implement than for the competing schemes. In the paper, there is also studied an add on scheme which consists of additional processing of the prediction errors to achieve simultaneous noise model identification, and improved prediction. Such a scheme is attractive from the computational cost point of view. Global convergence results are developed for the algorithms based on martingale convergence theorems as in earlier theories for extended least squares schemes. The key contribution of the paper as far as the theory is concerned is to show how to cope with the colored noise in the martingale framework. View full abstract»

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  • Near supermartingales for convergence analysis of recursive identification and adaptive control schemes

    Publication Year: 1981 , Page(s): 44 - 49
    Cited by:  Papers (2)
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    An equivalent stochastic feedback system can be associated to many recursive identification and adaptive control schemes. This equivalent feedback system has a certain structure which is used for constructing near supermartingales allowing to establish a.s. convergence. Explicit convergence conditions are then obtained for recursive identification and adaptive control schemes which admit an equivalent stochastic feedback representation of the form considered. The usefulness of the results is llustrated by their application to the straightforward convergence analysis of Several schemes. View full abstract»

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  • Recursive maximum likelihood and related algorithms for parameter identification of dynamical processes

    Publication Year: 1981 , Page(s): 50 - 55
    Cited by:  Papers (1)
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    An algorithm recursive in the data (time) is developed for efficient computation of the approximate maximum of the exact log likelihood function (LLF) for general dynamical processes of finite state order. A numerical quadratic hill-climbing approach is used to incrementally determine the maximum interval (in time) of data for which the LLF is acceptably quadratic and simultaneously the corresponding Newton step in parameter space. The extended Kalman filter (EKF) for parameter identification is shown to be a special case of the recursive maximum likelihood algorithm with particular terms left out. The absence of one such term has been shown to cause divergence of the EKF. A hierarchy of self-checking, adaptive algorithms is outlined that enables choosing an algorithm of appropriate complexity and efficiency for a given application. View full abstract»

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  • On the localized estimators and generalized Akaike's criterions

    Publication Year: 1981 , Page(s): 56 - 61
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    The problem of nonstationary system modelling is considered and the local modelling approach ts proposed for it's solution. At the begining the concept of localized maximum likelihood estimators is introduced and applied to approximation of time-varying stochastic systems. Two types of such estimators, first based on the concept of weighting and the second based on the concept of data windowing are proposed and discussed in some detail In the case of autoregressire systems. The problem of the proper choice of the model structure is next considered. It is shown that the criterion for model order selection proposed by Akaike for the case of maximum likelihood estimation (Information Criterion) can be extended to the case of localized estimators. View full abstract»

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  • Parameter identification in infinite dimensional linear systems

    Publication Year: 1981 , Page(s): 62 - 66
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    Parameter identification is studied for infinite dimensional linear systems. An almost sure characterization of sample path-wise limit sets of maximum likelihood estimates is given. View full abstract»

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  • Adaptive estimation and identification for discrete systems with Markov jump parameters

    Publication Year: 1981 , Page(s): 67 - 68
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    First Page of the Article
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  • An approach to identification of linear systems and the optimal solution of a class of synthesis problems

    Publication Year: 1981 , Page(s): 69 - 70
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    A new formulation of the problem of identification of the impulse response of a discrete time linear time invariant system from a finite set of finite length noisy I-O measurements is given. This transforms the problem to an input estimation problem of a new type. We present a solution to this input estimation problem in the framework of maximum a posteriori (MAP) estimation. This involves an optimization problem of a special type which we solve largely based on some recent results in linear system theory related to system structure and the geometric and polynomial theories of linear systems which are algebraic in nature. Furthermore, the solution to the identification problem we consider in this paper also provides a solution to the problems of 1) Deadbeat output control with internal stability by minimum norm input, 2) Disturbance decoupling with internal stability by minimum norm input, and 3) Exact model matching of linear systems by minimum norm compensators. View full abstract»

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  • Recursive simultaneous state and parameter estimation by a robust filtering method and orthogonal polynomials

    Publication Year: 1981 , Page(s): 71 - 73
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    A method and algorithms are described which are practically attractive when performing simultaneous state and parameter estimation. The method is based on the use of a non-linear filter and the idea that the state and parameter estimates are properly phased to get good convergence conditions. The algorithms are given in the case where the system non-linearities are approximated by a polynomial, preferably orthogonal expansion. The method itself, however, does not assume such specification and can be applied to the case of given non-linearities as well. View full abstract»

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  • Optimal control and pathwise nonlinear filtering of nondegenerate diffusions

    Publication Year: 1981 , Page(s): 74 - 75
    Cited by:  Papers (1)
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    A linear parabolic partial differential equation describing the pathwise filter for a nondegenerate diffusion is changed, by an exponential substitution, into the dynamic programming equation of an optimal stochastic control problem. This substitution is applied to obtain results about the rate of decay as |x| ?? ?? of solutions p(x, t) to the pathwise filter equation, and for solutions of the corresponding Zakai equation. View full abstract»

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  • Asymptotically optimal estimation

    Publication Year: 1981 , Page(s): 76 - 79
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    The purpose of this paper is to investigate the use of asymptotic methods in the design of optimal state estimators for nonlinear systems and to use these methods to estimate the complexity of such filters. More specifically, we develop expansions for the autocorrelation function of the solution of a stochastic differential equation which is close to linear in a suitable sense. We then construct a realization of the corresponding autocorrelation function using a linear system driven by white noise. Finally, we explore the significance of the structure of this linear filter in the original nonlinear context. View full abstract»

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  • Robust nonlinear filtering for a problem with unbounded signal

    Publication Year: 1981 , Page(s): 80 - 82
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    We study the robust nonlinear filtering problem for the bilinear system dx1 = dw1, dx2 = x1dw2, with observation dy = x2dt + dv. For every continuous path y(??), the conditional density turns out to be well defined and smooth, up to a small (path-dependent) time. View full abstract»

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  • Filtering and smoothing equations for the filtering problem of Benes

    Publication Year: 1981 , Page(s): 83 - 88
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    Filtering of a diffusion with nonlinear drifts of a type defined by Bene?? is studied. Explicit, finite dimensional, recurisve filters are shown to exist for moments and polynomial functionals of the diffusion, and a smoothing formula is given. These results are related to current, geometric approaches to filtering. View full abstract»

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  • Asymptotic behavior of nonlinear filters

    Publication Year: 1981 , Page(s): 89
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    Since H. Kunita's 1971 paper "Asymptotic Behavior of the Nonlinear Filtering Errors of Markov Processes" (J. Multivariate Analysis), the subject of optimal "steady state" estimators for nonlinear diffusions has received little attention. We report on some preliminary results on this class of problems, including an examination of the asymptotic properties of solutions of the Duncan-Mortonsen-Zakai Equation. View full abstract»

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  • Filtering of diffusions controlled through their conditional measures

    Publication Year: 1981 , Page(s): 90 - 96
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    For the closed-loop nonlinear filtering problem with control in separated form (a functional of the conditional distribution measure), the Kallianpur-Striebel formula becomes a stochastic equation for the unnormalized conditional distribution, given the past of the observations. Existence, uniqueness and measurability of solutions to this equation are discussed. The results give a partially positive answer to the question of admissibility of separated control laws. However, "pathological" nonanticipative but noncausal solutions appear here, after the manner of Tsirelson's example. View full abstract»

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  • On the relationships between unbounded asymptote behaviour of multivariable root loci, impulse response and infinite zeros

    Publication Year: 1981 , Page(s): 97 - 104
    Cited by:  Papers (1)
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    Using singular value decomposition techniques, and making systematic use of the Schur complement for a partitioned matrix, an investigation is carried out of how the input and output spaces associated with a square transfer matrix can be decomposed in terms of the way in which a system responds to vector impulses of various orders. The results so obtained are then used to characterise the forms of the behaviour of the unbounded asymptotes of the multivariable root locus. A discussion is given of the asymptotes and infinite zeros. View full abstract»

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  • Generic pole assignment: Preliminary results

    Publication Year: 1981 , Page(s): 105 - 109
    Cited by:  Papers (1)
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    First Page of the Article
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  • On the common (left,right) divisors of two polynomial matrices

    Publication Year: 1981 , Page(s): 110 - 111
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    The notions of common right and common left divisors of two polynomial matrices are well established. They can be used to characterize the unobservable and the uncontrollable modes of a system and to study polynomial matrix equations of the form a1V1 + a2V2 = V3. The new notion of common (right, left) divisors of two polynomial matrices is introduced here and it is used to characterize the modes of the system which are both uncontrollable and unobservable; it is also used to study polynomial matrix equations of the form Nx1 + x2D = V where N(qxp), D(rxm) and V(qxm) are given polynomial matrices; (1) has attracted recently considerable attention ([1] to [7]) mainly because of its importance in the output regulation problem with internal stability. View full abstract»

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  • Structure at infinity of linear multivariable systems a geometric approach

    Publication Year: 1981 , Page(s): 112 - 117
    Cited by:  Papers (8)
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    The infinite zero structure of linear multivariable systems is investigated via the geometric approach. The basic tools used are the new concepts of almost (A, B)-invariant and almost controllability subspaces. These concepts permit advantageous geometric interpretation of infinite zeros. This interpretation is a natural generalization of the finite case. Connection is made with the Smith McMillan structure at infinity of the transfer matrix. Structural properties of irreducible systems are investigated leading to a generalization of Morse theorem on prime systems. View full abstract»

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