Open-loop asymptotically efficient model reduction with the Steiglitz–McBride method

Everitt, Niklas; Galrinho, Miguel; Hjalmarsson, Håkan

doi:10.1016/j.automatica.2017.12.016

Cited by 16 publications

(15 citation statements)

References 32 publications

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“…Although WNSF and the approach in [38] are different algorithms, they share the similarities of using high-order models and iterative least squares. However, [38] is only applicable in open loop. Here, to differentiate WNSF as a more general approach that is applicable in open or closed loop without changing the algorithm, we focus on the typically more challenging closed-loop setting, for which many standard methods are not consistent.…”

Section: Simulation Studiesmentioning

confidence: 99%

Parametric Identification Using Weighted Null-Space Fitting

Galrinho

Rojas

Hjalmarsson

2019

IEEE Trans. Automat. Contr.

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In identification of dynamical systems, the prediction error method using a quadratic cost function provides asymptotically efficient estimates under Gaussian noise and additional mild assumptions, but in general it requires solving a non-convex optimization problem. An alternative class of methods uses a non-parametric model as intermediate step to obtain the model of interest. Weighted null-space fitting (WNSF) belongs to this class. It is a weighted least-squares method consisting of three steps. In the first step, a high-order ARX model is estimated. In a second least-squares step, this high-order estimate is reduced to a parametric estimate. In the third step, weighted least squares is used to reduce the variance of the estimates. The method is flexible in parametrization and suitable for both open-and closedloop data. In this paper, we show that WNSF provides estimates with the same asymptotic properties as PEM with a quadratic cost function when the model orders are chosen according to the true system. Also, simulation studies indicate that WNSF may be competitive with state-of-the-art methods.

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Section: Simulation Studiesmentioning

confidence: 99%

Parametric Identification Using Weighted Null-Space Fitting

Galrinho

Rojas

Hjalmarsson

2019

IEEE Trans. Automat. Contr.

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“…First,Ŝ(q) is estimated by least-squares. Second, G is estimated using MORSM (Everitt, Galrinho and Hjalmarsson; from the simulated signalŵ obtained from (6) andw j . MORSM is an iterative method that is asymptotically efficient for open loop data.…”

Section: Nebmentioning

confidence: 99%

An empirical Bayes approach to identification of modules in dynamic networks

2018

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We present a new method of identifying a specific module in a dynamic network, possibly with feedback loops. Assuming known topology, we express the dynamics by an acyclic network composed of two blocks where the first block accounts for the relation between the known reference signals and the input to the target module, while the second block contains the target module. Using an empirical Bayes approach, we model the first block as a Gaussian vector with covariance matrix (kernel) given by the recently introduced stable spline kernel. The parameters of the target module are estimated by solving a marginal likelihood problem with a novel iterative scheme based on the Expectation-Maximization algorithm. Additionally, we extend the method to include additional measurements downstream of the target module. Using Markov Chain Monte Carlo techniques, it is shown that the same iterative scheme can solve also this formulation. Numerical experiments illustrate the effectiveness of the proposed methods.

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“…For example, [6], [7] considered a certain class of linear state-space models and proposed algorithms based on difference of convex programming problems, which may be approximately solved using sequentially convex relaxation. On the other hand, methods based on non-parametric approximations and iterative weighted least-square algorithms have been recently proposed [8], [9]. These methods can be applied to rational linear models, and local optima have been avoided in extensive simulation studies.…”

Section: Introductionmentioning

confidence: 99%

Toward Tractable Global Solutions to Maximum-Likelihood Estimation Problems via Sparse Sum-of-Squares Relaxations

Rodrigues

Abdalmoaty

Hjalmarssond

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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In system identification, the maximum-likelihood method is typically used for parameter estimation owing to a number of optimal statistical properties. However, in many cases, the likelihood function is nonconvex. The solutions are usually obtained by local numerical optimization algorithms that require good initialization and cannot guarantee global optimality. This paper proposes a computationally tractable method that computes the maximum-likelihood parameter estimates with posterior certification of global optimality via the concept of sum-of-squares polynomials and sparse semidefinite relaxations. It is shown that the method can be applied to certain classes of discrete-time linear models. This is achieved by taking advantage of the rational structure of these models and the sparsity in the maximum-likelihood parameter estimation problem. The method is illustrated on a simulation model of a resonant mechanical system where standard methods struggle.

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Open-loop asymptotically efficient model reduction with the Steiglitz–McBride method

Cited by 16 publications

References 32 publications

Parametric Identification Using Weighted Null-Space Fitting

Parametric Identification Using Weighted Null-Space Fitting

An empirical Bayes approach to identification of modules in dynamic networks

Toward Tractable Global Solutions to Maximum-Likelihood Estimation Problems via Sparse Sum-of-Squares Relaxations

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