A second order recursive least squares algorithm is derived. It is shown that the algorithm encompasses both the RLS and the LMS algorithms as special cases. The computational complexity is the same as for the RLS alg...
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A second order recursive least squares algorithm is derived. It is shown that the algorithm encompasses both the RLS and the LMS algorithms as special cases. The computational complexity is the same as for the RLS algorithm, but requires some extra memory storage. The associated Ordinary Differential Equation (ODE) for the algorithm is proven to be globally exponentially stable. Further, it is demonstrated that the proposed algorithm has a higher ability to track time-varying signals than has the RLS-algorithm. The proposed algorithm especially handles those situations well where there is a simultaneous system change and decrease of signal power.
This paper explains the inadequacies due to ill-conditioning of classical recursive least squares signal estimation algorithms based on Taylor series expansions, then shows how the algorithms may be restructured using...
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ISBN:
(纸本)0080417175
This paper explains the inadequacies due to ill-conditioning of classical recursive least squares signal estimation algorithms based on Taylor series expansions, then shows how the algorithms may be restructured using orthogonal expansions, at little cost in extra complexity, to provide well-conditioned versions suitable for implementation in a variety of digital signal processing applications. Several open questions are posed, mainly connected with the incorporation of signal windowing to provide smoothing filters.
The task of simultaneous tracking of time-varying parameters and estimation of the state is treated for a linear system described by a time-varying input-output ARMAX or Delta model with known c (noise) parameters. Fi...
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The task of simultaneous tracking of time-varying parameters and estimation of the state is treated for a linear system described by a time-varying input-output ARMAX or Delta model with known c (noise) parameters. First, a Bayesian approach-based conceptual solution is presented. Then it is shown that utilizing the properties of the observer canonical state model, algebraic recursion operating on the joint parameter and state mean and covariance matrix can be obtained with no approximation involved. Several illustrative examples are included.
This paper gives a state-of-the-art review of adaptive channel equalization in digital line-of-sight radio systems employing bandwidth-efficient modulation techniques. A particular emphasis is placed on decision-feedb...
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ISBN:
(纸本)0080417175
This paper gives a state-of-the-art review of adaptive channel equalization in digital line-of-sight radio systems employing bandwidth-efficient modulation techniques. A particular emphasis is placed on decision-feedback equalizer (DFE) implementation and performance in the presence of nonminimum-phase fading. Stability problems of fractionally-spaced equalizers (FSE's) are discussed, and a newly developed adaptation technique is outlined. We also discuss the blind adaptation algorithms that are used to reduce outage by preventing the equalizer coefficients to diverge during severe fade events and carrier synchronism loss. Finally, we discuss further issues related to asymmetric equalizers and to the interaction of the equalizer adaptation algorithm with the carrier recovery loop.
The issues of consistency and minimal parametrization of the prewindowed prediction problem are presented in detail. The paper establishes an equivalence class between the set of p×p symmetric, positive definite ...
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ISBN:
(纸本)0080417175
The issues of consistency and minimal parametrization of the prewindowed prediction problem are presented in detail. The paper establishes an equivalence class between the set of p×p symmetric, positive definite matrices P and the set of 2×1 stable causal all-pass functions ηp(z) or McMillan degree p. The minimal parametrization of such matrices P is obtained by parametrizing ηp(z), resulting in an inherently consistent parametrization. The application to numerically stable fast least-squares filtering is highlighted.
The paper describes a recent progress in searching for credible, well-grounded approximation of recursive Bayesian parameter estimation which would make the Bayesian paradigm feasible for a class of nonstandard (non-l...
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ISBN:
(纸本)0080417175
The paper describes a recent progress in searching for credible, well-grounded approximation of recursive Bayesian parameter estimation which would make the Bayesian paradigm feasible for a class of nonstandard (non-linear and/or non-Gaussian) models. The presented method is based on maximum-entropy approximation of the empirical distribution of data while just a reduced (non-sufficient) data statistic is available. The statistic is chosen so to induce an equivalence relation on the set of posterior probability distributions which is compatible with the Bayes-rule action. The approximating posterior density of unknown parameters is given by the standard Bayes-rule transformation of the approximating distribution of data. Numerical implementation of the general algorithm is considered using its discrete version or prior approximation of critical steps.
The pH control problem in a continuous stirred tank reactor is studied from both atheoretical and application point of view. A reaction invariant model for an acid-base system, which is one of the most complete descri...
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The pH control problem in a continuous stirred tank reactor is studied from both atheoretical and application point of view. A reaction invariant model for an acid-base system, which is one of the most complete descriptions for the pH control problem, is utilized. The new controller obtained for the pH control problem is based on a linearization technique and requires that some steady-state experilnents be carried out on the process, before a controller implementation can be achieved. The proposed controller has been applied toa 6th order nonlinear simulation model of a pH process for the case of:(i) time-varying input feed pH concentrations and buffer concentrations,(ii) set-point reference input changes for the desired pH output. Based on the results of these simulations, the controller appears to be quite effective;in particular it gives significant improvements in the response compared to existing controllers proposed in the literature
The identification of the ARMAX model and the state space model of the multivariable system is investigated in the presence of coloured noise. Firstly. the optimal input vector design is introduced to identify the Mar...
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The identification of the ARMAX model and the state space model of the multivariable system is investigated in the presence of coloured noise. Firstly. the optimal input vector design is introduced to identify the Markov parameter matrices. Secondly. in the description of the multi-dimensional ARMAX model. an order recursive algorithm is presented for estimating the order and the parameter matrices of the ARMAX model using the estimated Markov matrices. The aymptotic biases are compensated to achieve higher identification precision. Furthermore. the autocorrelation function matrices of the observation noise are estimated. Finally. the recursive algorithm of the identification of the Kronecker structure invariants and the parameters of the state space model of the multivariable system is suggested.
New numerically robust algorithms are presented for converting linear continuous-time constant-parameter state models into equivalent discrete-time state models ( discretization ) as well as the reverse problem of det...
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New numerically robust algorithms are presented for converting linear continuous-time constant-parameter state models into equivalent discrete-time state models ( discretization ) as well as the reverse problem of determining continuous-time models to represent given discrete-time models ( continualization ). Two methods of discretizing linear uniformly sampled systems have been considered for their utility in computer-aided design. These methods are the standard zero-order hold method which assumes that inputs are held constant at their previous sample value for the duration of the sample interval, and a method which assumes that the inputs are linearly interpolated between samples.
A mobile-based robot, a robot with an actuator failure, a manipulator with structural flexibility, and robots grasping an articulated object are systems with unactuated or "passive" joints. The dynamics and ...
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A mobile-based robot, a robot with an actuator failure, a manipulator with structural flexibility, and robots grasping an articulated object are systems with unactuated or "passive" joints. The dynamics and control of these robot systems is more complex than fully-actuated systems because unactuated joints may lead to uncontrollability. Based on a recursive formulation of the inverse dynamics for manipulators with some unactuated joints, control laws are developed for joint space control and task space control. Important in the task space control law for underactuated systems is the inversion of the generalized Jacobian. Spatial operator algebra techniques are used to develop computationally efficient algorithms for the inverse generalized Jacobian and the control laws.
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