Showing papers by "Brian D. O. Anderson published in 1999"

The Realization Problem for Hidden Markov Models

Abstract: If {X t} is a finite-state Markov process, and {Y t} is a finite-valued output process with Y t+1 depending (possibly probabilistically) on X t, then the process pair is said to constitute a hidden Markov model. This paper considers the realization question: given the probabilities of all finite-length output strings, under what circumstances and how can one construct a finite-state Markov process and a state-to-output mapping which generates an output process whose finite-length strings have the given probabilities? After reviewing known results dealing with this problem involving Hankel matrices and polyhedral cones, we develop new theory on the existence and construction of the cones in question, which effectively provides a solution to the realization problem. This theory is an extension of recent theoretical developments on the positive realization problem of linear system theory.

Filtering through combination of positive filters

Abstract: The linear filters characterized by a state-variable realization given by matrices with nonnegative entries (called positive filters) are heavily restricted in their achievable performance. Nevertheless, such filters are the only choice when dealing with the charged coupled device MOS technology of charge routing networks (CRN's), since nonnegativity is a consequence of the underlying physical mechanism. In order to exploit the advantages offered by this technology, the authors try to overcome the above-mentioned limitation by realizing an arbitrary transfer function as a difference of two positive filters.

From Wiener to hidden Markov models

Abstract: The authors investigate common properties of 3 types of filters obtained by considering various stochastic models; Wiener filters, Kalman filters and hidden Markov model (HMM) filters. Unifying features which particularly stand out are the forgetting of old data and of initial conditions, and protection from round-off error effects' overpowering the calculations. They differentiate the concept of fixed-lag smoothing from filtering, and expose the comparative advantages and disadvantages. Once again, there are common properties which allow a unified viewpoint. We focus especially on characterizations of a maximally effective smoothing lag, and identification of the SNR circumstances under which smoothing is especially beneficial. The motivation is the processing of data from an array of acoustic sensors towed by a submarine.

Closed-loop output error identification algorithms for nonlinear plants

Abstract: A family of algorithms for the identification of continuous time nonlinear plants operating in closed-loop is presented. An adjustable output error type predictor is parametrized in terms of the existing controller and the estimated plant model. The algorithms are derived from stability considerations in the absence of noise and assuming that the plant model is in the model set. Subsequently the algorithms are analyzed in the presence of noise and when the plant model is not in the model set.

Positive system realizations

Abstract: Consider a rational discrete-time transfer function H(z) with the property that the associated causal impulse response h(k) is nonnegative for all k. A positive realization is a quadruple A, b, c, d such that $$ H\left( z \right) = d + c{\left( {zI - A} \right)^{ - 1}}b $$ and all entries of A, b, c, d are nonnegative.

Robustness to fractionally-spaced equalizer length using the constant modulus criterion

Abstract: This article studies robustness properties of the constant modulus (CM) criterion and the constant modulus algorithm (CMA) to the suboptimal but practical situation where the number of fractionally-spaced equalizer coefficients is less than what is needed to remove all intersymbol interference (ISI). Hence, there necessarily exists an error in the equalized signal. Relationships between CM and mean squared error cost functions are established.

Optimum subband coding of cyclostationary signals

Abstract: We consider the optimal orthonormal subband coding of zero mean cyclostationary signals, with N-periodic second order statistics. A 2-channel uniform filter bank, with N-periodic analysis and synthesis filters, is used as the subband coder. A dynamic scheme involving N-periodic bit allocation is employed. An average variance condition is used to measure the output distortion. The conditions for maximizing the coding gain parallel those for the case when the signals are wide sense stationary (WSS) and the analysis and synthesis filters and the bit allocation time invariant, in that the blocked subband signals must be decorrelated and the subband power spectral densities must obey an ordering. Some additional conditions on this ordering, over and above those required for the WSS case, are needed.

Variable constraint control of underactuated free flying robots-mechanical design and convergence

Abstract: A new control method for underactuated nonlinear systems called a variable constraint control (VCC) is proposed. In this control method the first integral obtained by adding control constraints is used as an invariant manifold. The results are applied to the posture control problems of free flying robots and relations between convergence of the control and structural parameters of robots are discussed.

Direct reduced order discretization of continuous-time controller

Abstract: The problem of closed-loop approximation of a continuous-time controller by a low order discrete-time controller is investigated. The operator representing the error in approximation can be approximated (arbitrarily closely) by a time-invariant discrete-time system resulting from applying fast sampling and lifting. We propose a method for obtaining a low-order discrete-time controller which makes small the approximation error based on recasting the approximation problem as a four-block H/sub /spl infin// problem.

Recursive iterative feedback tuning

Abstract: We propose a methodology for iterative recursive feedback tuning of a given controller structure. The algorithm and its convergence (stability) properties are analyzed. The algorithm can be viewed as the dual of the recursive closed-loop output-error identification algorithm as studied in Landau and Karimi (1997).

Riccati Equations, Network Theory and Brune Synthesis: Old Solutions for Contemporary Problems

Abstract: Riccati equations have a natural connection with network theory. Classical passive network synthesis procedures, employing often frequency domain spectral factorization, can be mirrored by state variable procedures which rely on knowledge of a steady state Riccati equation solution. In contrast to many occurrences of steady state Riccati equations, it is possible (especially in network applications) to encounter equations which have strong, but not stabilizing solutions. Such equations constitute a problem for much software. Classical network synthesis procedures actually dealt with a frequency domain version of this problem using tools such as the Brune synthesis. The Riccati equation equivalent involves a deflation technique which will be exposed.

Remarks on filtering error due to quantisation of a 2-state hidden Markov model

Abstract: This paper considers the problem of quantisation from the perspective of minimising filtering error when quantised instead of continuous measurements are used as inputs to the nonlinear filter, specialising to a discrete-time 2-state hidden Markov model (HMM) with continuous output.

From Wiener to hidden Markov models: Common threads of filtering and smoothing

Abstract: Filtering of random signals to eliminate the effects of noise is a very old topic. Optimal filter design probably commenced with Wiener, and received a significant impulse with the work of Kalman, and in recent times with techniques for filtering hidden Markov models. In many circumstances, smoothing can give improved performance relative to filtering. In this talk, we shall trace (with almost no mathematics) some of the main streams of development, up to current research thrusts.

Implementation issues for a nonlinear version of the Hansen scheme

Abstract: We propose a method for the identification of a nonlinear plant under possibly nonlinear feedback. This procedure is a nonlinear extension of a method known as the Hansen scheme in the literature. It is shown that using nonlinear left fractional descriptions one can convert a general nonlinear closed-loop identification problem to one of open-loop identification by parametrizing the model using a Youla-Kucera parameter. The open-loop problem can be implemented by parametrizing the nonlinear Youla parameter in terms of a model of the plant. We provide gradient expressions for implementation in a steepest descent algorithm.