Recursive least squares fixed-lag Wiener smoothing using autoregressive signal models for linear discrete-time systems

<p class="Author">This paper presents a recursive least-squares approach to estimate simultaneously the state and the unknown input of linear time varying discrete time systems with unknown input. The method is based on the assumption that no prior knowledge about the dynamical evolution of the input is available. The joint input and state estimation are obtained by recursive least-squares formulation by applying the inversion lemmas. The proposed filter is equivalent to recursive three step filter. To illustrate the performance of the proposed filter an example is given.</p>

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Optimal least squares model approximation for large-scale linear discrete-time systems

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331216649023 ◽

2016 ◽

Vol 40 (1) ◽

pp. 35-48 ◽

Cited By ~ 4

Author(s):

G Vasu ◽

M Siva Kumar ◽

M Ramalingaraju

Keyword(s):

Least Squares ◽

Discrete Time ◽

Large Scale ◽

Time Moment ◽

Original System ◽

Approximate Model ◽

Model Approximation ◽

Polynomial Coefficients ◽

Discrete Time Systems ◽

Time Systems

A new computationally simple and precise model approximation method is described for large-scale linear discrete-time systems. By least squares matching of a suitable number of time moment proportionals and Markov parameters about [Formula: see text] of the original higher order system within the approximate model, stable denominator polynomial coefficients of the approximate model are determined. To improvise the accuracy of the approximate model, numerator polynomial coefficients are determined by minimizing the integral squared error (ISE) between the unit impulse responses of the original system and its approximate model. A matrix formula is formulated for evaluating numerator coefficients of the approximate model that leads to minimum ISE, and also for evaluating ISE. The efficacy of the proposed method is shown by illustrating three typical numerical examples employed from the literature, and the results are compared with many familiar reduction methods in terms of the ISE and relative ISE values pertaining to impulse input. Furthermore, time and frequency responses of the original system and the respective approximate model are plotted.

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Discrete-time least-squares Padé order reduction: A stability preserving method

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1243/0959651981539280 ◽

1998 ◽

Vol 212 (1) ◽

pp. 49-56 ◽

Cited By ~ 2

Author(s):

T N Lucas ◽

I D Smith

Keyword(s):

Least Squares ◽

Discrete Time ◽

Reduction Method ◽

Order Reduction ◽

Model Parameter ◽

Discrete Time Systems ◽

The Stability ◽

Order Reduction Method ◽

Preservation Property ◽

Time Systems

A new stability preservation property is proved for the least-squares Padé order reduction method when applied to discrete-time systems. It is shown that the property depends on which free reduced model parameter is chosen to be unity. Clarification is also given on how the system is actually approximated using this method. An example illustrates the enhanced appeal of the method as a result of the stability preservation property.

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