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Showing papers by "John B. Moore published in 1994"


Book
16 Dec 1994
TL;DR: This paper presents a meta-modelling procedure called Markov Model Processing that automates the very labor-intensive and therefore time-heavy and therefore expensive process of HMMEstimation.
Abstract: Hidden Markov Model Processing.- Discrete-Time HMM Estimation.- Discrete States and Discrete Observations.- Continuous-Range Observations.- Continuous-Range States and Observations.- A General Recursive Filter.- Practical Recursive Filters.- Continuous-Time HMM Estimation.- Discrete-Range States and Observations.- Markov Chains in Brownian Motion.- Two-Dimensional HMM Estimation.- Hidden Markov Random Fields.- HMM Optimal Control.- Discrete-Time HMM Control.- Risk-Sensitive Control of HMM.- Continuous-Time HMM Control.

1,415 citations


Book
01 Feb 1994
TL;DR: Details of Matrix Eigenvalue Methods, including Double Bracket Isospectral Flows, and Singular Value Decomposition are revealed.
Abstract: Contents: Matrix Eigenvalue Methods.- Double Bracket Isospectral Flows.- Singular Value Decomposition.- Linear Programming.- Approximation and Control.- Balanced Matrix Factorizations.- Invariant Theory and System Balancing.- Balancing via Gradient Flows.- Sensitivity Optimization.- Linear Algebra.- Dynamical Systems.- Global Analysis.

800 citations


Book ChapterDOI
01 Jan 1994
TL;DR: The singular value decomposition of matrices is widely used in least squares estimation, systems approximations, and numerical linear algebra.
Abstract: Many numerical methods used in application areas such as signal processing, estimation, and control are based on the singular value decomposition (SVD) of matrices. The SVD is widely used in least squares estimation, systems approximations, and numerical linear algebra.

152 citations


Journal ArticleDOI
TL;DR: The solution of Oja's equation is exponentially convergent to an equilibrium from any initial value and the necessary and sufficient conditions are given on the initial value for the solution to converge to a dominant eigenspace of the associated autocorrelation matrix.
Abstract: A detailed study of Oja's learning equation in neural networks is undertaken in this paper. Not only are such fundamental issues as existence, uniqueness, and representation of solutions completely resolved, but also the convergence issue is resolved. It is shown that the solution of Oja's equation is exponentially convergent to an equilibrium from any initial value. Moreover, the necessary and sufficient conditions are given on the initial value for the solution to converge to a dominant eigenspace of the associated autocorrelation matrix. As a by-product, this result confirms one of Oja's conjectures that the solution converges to the principal eigenspace from almost all initial values. Some other characteristics of the limiting solution are also revealed. These facilitate the determination of the limiting solution in advance using only the initial information. Two examples are analyzed demonstrating the explicit dependence of the limiting solution on the initial value. In another respect, it is found that Oja's equation is the gradient flow of generalized Rayleigh quotients on a Stiefel manifold. >

113 citations


Journal ArticleDOI
TL;DR: An on-line state and parameter identification scheme for hidden Markov models (HMMs) with states in a finite-discrete set is developed using recursive prediction error (RPE) techniques and an improved version of an earlier proposed scheme is presented with a parameterization that ensures positivity of transition probability estimates.
Abstract: An on-line state and parameter identification scheme for hidden Markov models (HMMs) with states in a finite-discrete set is developed using recursive prediction error (RPE) techniques. The parameters of interest are the transition probabilities and discrete state values of a Markov chain. The noise density associated with the observations can also be estimated. Implementation aspects of the proposed algorithms are discussed, and simulation studies are presented to show that the algorithms converge for a wide variety of initializations. In addition, an improved version of an earlier proposed scheme (the Recursive Kullback-Leibler (RKL) algorithm) is presented with a parameterization that ensures positivity of transition probability estimates. >

75 citations


Journal ArticleDOI
TL;DR: Time-domain techniques for deinterleaving pulse trains from a finite number of periodic sources based on the time of arrival (TOA) and pulse energy, if available, of the pulses received on the one communication channel are proposed.
Abstract: Pulse trains from a number of different sources are often received on the one communication channel. It is then of interest to identify which pulses are from which source, based on different source characteristics. This sorting task is termed deinterleaving. the authors propose time-domain techniques for deinterleaving pulse trains from a finite number of periodic sources based on the time of arrival (TOA) and pulse energy, if available, of the pulses received on the one communication channel. They formulate the pulse train deinterleaving problem as a stochastic discrete-time dynamic linear model (DLM), the "discrete-time" variable k being associated with the kth received pulse. The time-varying parameters of the DLM depend on the sequence of active sources. The deinterleaving detection/estimation task can then be done optimally via linear signal processing using the Kalman filter (or recursive least squares when the source periods are constant) and tree searching. The optimal solution, however, is computationally infeasible for other than small data lengths since the number of possible sequences grow exponentially with data length. The authors propose and study two of a number of possible suboptimal solutions: 1) forward dynamic programming with fixed look-ahead rather than total look-ahead as required for the optimal scheme; 2) a probabilistic teacher Kalman filtering for the detection/estimation task. >

58 citations


Journal ArticleDOI
TL;DR: The authors propose two algorithms, based on a double Lie-bracket equation recently studied by Brockett, that appear to be suitable for implementation in parallel processing environments and achieve the eigenvalue decomposition of a symmetric matrix and the singular value decompose of an arbitrary matrix.
Abstract: Recent work has shown that the algebraic question of determining the eigenvalues, or singular values, of a matrix can be answered by solving certain continuous-time gradient flows on matrix manifolds. To obtain computational methods based on this theory, it is reasonable to develop algorithms that iteratively approximate the continuous-time flows. In this paper the authors propose two algorithms, based on a double Lie-bracket equation recently studied by Brockett, that appear to be suitable for implementation in parallel processing environments. The algorithms presented achieve, respectively, the eigenvalue decomposition of a symmetric matrix and the singular value decomposition of an arbitrary matrix. The algorithms have the same equilibria as the continuous-time flows on which they are based and inherit the exponential convergence of the continuous-time solutions.

48 citations


Journal ArticleDOI
TL;DR: It is shown that an optimal solution can be successfully computed by finding the limiting solution of an ordinary differential equation which is given in terms of the gradient flow associated with the cost function.
Abstract: This short communication considers the linear quadratic problem with static output feedback. It is shown that an optimal solution can be successfully computed by finding the limiting solution of an ordinary differential equation which is given in terms of the gradient flow associated with the cost function. Several properties are obtained concerning the gradient flow. For example, it is shown that the flow contains a subsequence convergent to a locally optimal output feedback gain. In the special case of state feedback the flow is guaranteed to converge to the optimal gain. The effectiveness of the method is demonstrated by an example.

34 citations


Journal ArticleDOI
TL;DR: The techniques of extended Kalman filtering (EKF) and hidden Markov mode!
Abstract: SUMMARY In this paper the techniques of extended Kalman filtering (EKF) and hidden Markov mode! (HMM) signal processing are combined to adaptively demodulate quadrature amplitude-modulated (QAM) signals in noisy fading channels. This HMM approach is particularly suited to signals for which the message symbols are not equally probable, as is the case with many types of coded signals. Our approach is to formulate the QAM signal by a finite-discrete state process and represent the channel model by a continuous state process. The mixed state model is then reformulated in terms of conditional information states using HMM theory. This leads to models which are amenable to standard EKF or related techniques. A sophisticated EKF scheme with an HMM subfilter is discussed, as well as more practical schemes coupling discrete state HMM filters and continuous state Kalman filters. The case of white noise is considered, as well as generalizations to cope with coloured noise. Simulation studies demonstrate the improvement gained over standard schemes.

25 citations


Journal ArticleDOI
TL;DR: This paper is concerned with solving a class of nonlinear algebraic matrix equations and two recursive algorithms are proposed in terms of matrix difference equations and are studied, and a locally exponential convergence property is proved for one of them.
Abstract: This paper is concerned with solving a class of nonlinear algebraic matrix equations. Two recursive algorithms are proposed in terms of matrix difference equations and are studied. A set of initial values is characterized, from which the convergence of the algorithms can be guaranteed. Based on the general results, several effective algorithms are presented to compute $L^2$-sensitivity optimal realizations, as well as Euclidean norm balancing realizations, of a given linear system. A locally exponential convergence property is proved for one of them. As is shown by simulation in this paper, these algorithms prove to be far more practical for digital computer implementation than the gradient flows previously proposed.

17 citations


Proceedings ArticleDOI
14 Dec 1994
TL;DR: This paper uses an information-state approach to obtain the solution to the linear risk-sensitive quadratic Gaussian control problem and considers the case of tracking a desired trajectory, giving some insight to more general information- state methods for nonlinear systems.
Abstract: In this paper we use an information-state approach to obtain the solution to the linear risk-sensitive quadratic Gaussian control problem. With these methods the solution is obtained without appealing to a certainty equivalence principle. Specifically we consider the case of tracking a desired trajectory. The result gives some insight to more general information-state methods for nonlinear systems. Limit results are presented which demonstrate the link to standard linear quadratic Gaussian control. Also, a risk-sensitive filtering result is presented which shows the relationship between tracking and filtering problems. Finally, simulation studies are presented to indicate some advantages gained via a risk-sensitive control approach. >

Proceedings ArticleDOI
19 Apr 1994
TL;DR: The demodulation scheme presented can be applied to both digital M-ary differential phase shift keyed (MDPSK) and analog frequency modulated (FM) signals and can easily be generalised for other transmission schemes, such as continuous phase modulate (CPM) signals.
Abstract: Kalman filtering (KF) and hidden Markov model (HMM) signal processing techniques are coupled to demodulate signals transmitted through noisy fading channels. The demodulation scheme presented can be applied to both digital M-ary differential phase shift keyed (MDPSK) and analog frequency modulated (FM) signals. Adaptive state and parameter estimation algorithms are devised based on the assumption that the transmission channel introduces time-varying gain and phase changes, modelled by a stochastic linear system, and has additive Gaussian noise. Our technique is to use an HMM filter, for signal estimation, coupled with a KF, for channel parameter tracking. The approach taken can easily be generalised for other transmission schemes, such as continuous phase modulated (CPM) signals. >

Journal ArticleDOI
TL;DR: In this article, a characterization of the spectrum of a symmetric matrix to remain real after a nonsymmetric sign-restricted border perturbation, including the case where the perturbations is skew-symmetric, is given in terms of the stationary points of a quadratic function on the unit sphere.
Abstract: A characterization is given for the spectrum of a symmetric matrix to remain real after a nonsymmetric sign-restricted border perturbation, including the case where the perturbation is skew-symmetric. The characterization is in terms of the stationary points of a quadratic function on the unit sphere. This yields interlacing relationships between the eigenvalues of the original matrix and those of the perturbed matrix. As a result of the linkage between the perturbation and stationarity problems, new theoretical insights are gained for each. Applications of the main results include a characterization of those matrices that are exponentially nonnegative with respect to the $n$-dimensional ice-cream cone, which in turn leads to a decomposition theorem for such matrices. In addition, results are obtained for nonsymmetric matrices regarding interlacing and majorization.

Journal ArticleDOI
TL;DR: A sub-optimal scheme which uses Forward Dynamic Programming with fixed look-ahead rather than totalLook-ahead as required for the optimal scheme is proposed and studied.

01 Jan 1994
TL;DR: Time-domain techniques for deinterleaving pulse trains from a finite number of periodic sources based on the time of arrival (TOA) and pulse energy, if available, of the pulses received on the one communication channel are proposed.
Abstract: Pulse trains from a number of different sources are often received on the one communication channel. It is then of interest to identify which pulses are from which source, based on different source characteristics. This sorting task is termed dein- terleaving. In this paper we next propose time-domain techniques for deinterleaving pulse trains from a finite number of periodic sources based on the time of arrival (TOA) and pulse energy, if available, of the pulses received on the one communication channel. We formulate the pulse train deinterleaving problem as a stochastic discrete-time dynamic linear model (DLM), the "discrete-time" variable k being associated with the kth received pulse. The time-varying parameters of the DLM depend on the se- quence of active sources. The deinterleaving detectionlestimation task can then be done optimally via linear signal processing using the Kalman filter (or recursive least squares when the source periods are constant) and tree searching. The optimal solution, however, is computationally infeasible for other than small data lengths since the number of possible sequences grow exponentially with data length. Here we propose and study two of a number of possible suboptimal solutions: 1) Forward dynamic programming with fixed look-ahead rather than total look-ahead as required for the optimal scheme; 2) a probabilistic teacher Kalman filtering for the detection/estimation task. In simulation studies we show that when the number of sources is small, the proposed suboptimal schemes yield near-optimal estimates even in the presence of relatively large jitter noise. Also, issues of robustness and generalizations of the approach to the case of missing pulses, unknown source number, and non-Gaussian jitter noise are addressed.

Patent
05 Apr 1994
TL;DR: In this article, a decision feedback approach is proposed for the processing of signals which have characteristics that are not exclusive to either the continuous-state or the discrete-state system, but fit only a mixed-state model.
Abstract: Techniques for optimal processing of signals which fit continuous-state and discrete-state system models are known. This invention concerns the processing of signals which have characteristics that are not exclusive to either the continuous-state or the discrete-state system, but fit only a mixed-state model, using a decision feedback approach. After establishing the relevant mixed-state model, the received signal is processed simultaneously, and in parallel, in a Kalman (or extended Kalman) filter and in a Hidden Markov Model filter. The output of the Kalman filter is coupled to a stage of the Hidden Markov filter and the information state estimate of the Hidden Markov filter is coupled to the Kalman filter. With this arrangement, the desired signal estimate is derived from the information state estimate of the output of the Hidden Markov filter.

01 Jan 1994
TL;DR: In this article, a high order plant is controlled at each time instant by one of a set of low order controllers, each designed to control one part of a partial fractions expansion of the plant.
Abstract: A method of control is proposed whereby a high order plant is controlled at each time instant by one of a set of low order controllers, each designed to control one part of a partial fractions expansion of the plant. The method is motivated toward the control of flexible structures, such as large space structures, exhibiting large model order, model uncertainty, and decentralisation. Certain switching algorithms are presented, and simulation results demonstrate the efficacy of such methods. These results perhaps point one way forward for tackling difficult control problems.