On backward shift algorithm for estimating poles of systems

Mi, Wen; Qian, Tao

doi:10.1016/j.automatica.2014.04.030

Cited by 30 publications

(23 citation statements)

References 21 publications

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Order By: Relevance

“…Remark Information about system order is important to this estimation, if order is known, then the best estimation of { ξ 1 , ξ 2 ,…, ξ q } should be poles of the true system. In this case, we could estimate the poles first no matter what the multiplicities are by using method given by Mi and Qian, then estimate coefficients with ALM‐APG algorithm by model . Otherwise without knowing information of order, { ξ k }s may not poles of true system from the best approximation point of view.…”

Section: Identification By Using Almmentioning

confidence: 99%

“…With above properties, can be used in system identification instead of , in fact, e ξ s are used for system identification by applying least‐square algorithm but the poles ξ k are fixed in Partington and Mäkilä . They are also used to estimate poles of systems efficiently in Mi and Qian; however, this method has a limitation on estimating orders of systems.…”

Section: Introductionmentioning

confidence: 99%

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Mixed model identification for linear time‐invariant systems with mixed noises in frequency domain

Feng

2019

Math Methods in App Sciences

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In this paper, we present a new method for frequency domain identification of discrete linear time-invariant systems. We take consideration of the case where the output noises are mixed or unknown. In order to deal with this problem, a new mixed model structure is used correspondingly. The augmented Lagrangian method (ALM) is combined in selection of poles for the shifted Cauchy kernels to get solutions to the optimal problem. Simulations show the proposed method can get efficient approximation to the original systems. KEYWORDSfrequency domain, mixed noises, orthogonal basis, rational function, shifted Cauchy kernel MSC CLASSIFICATION A1420; 26C15Math Meth Appl Sci. 2019;42:7285-7295.wileyonlinelibrary.com/journal/mma

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Section: Identification By Using Almmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mixed model identification for linear time‐invariant systems with mixed noises in frequency domain

Feng

2019

Math Methods in App Sciences

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“…In particular, unwinding and higher‐order‐Szegö‐kernel AFDs are designed for decompose signals of high frequencies. Cyclic AFD offers a conditional solution for the open problem of finding a rational Hardy space function, whose degree does not exceed a pre‐described integer n that best approximates a given Hardy space function .Remark One‐dimensional adaptive Fourier decomposition and its variations have found significant applications to system identification and signal analysis .Remark Any complete TM system with a 1 =0 gives rise to signal decompositions of positive frequencies. To sufficiently characterize a signal, it is desirable to find the most suitable TM systems for the given signal.…”

Section: Preparationmentioning

confidence: 99%

“…In such case, f belongs to the backward shift invariant space. Backward shift invariant subspaces have significant applications to phase and amplitude retrieval problems and solutions of the Bedrosian equations, as well as to system identification . We note that for the index range 1 < p < ∞ , no matter whether is met or not, the generalized system { B k } is a Schauder basis of the L p ( ∂ D )‐topological closure of the span{ B k } .…”

Section: Preparationmentioning

confidence: 99%

Two‐dimensional adaptive Fourier decomposition

Qian

2016

Math Methods in App Sciences

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One-dimensional adaptive Fourier decomposition, abbreviated as 1-D AFD, or AFD, is an adaptive representation of a physically realizable signal into a linear combination of parameterized Szegö and higher order Szegö kernels of the context. In the present paper we study multi-dimensional AFDs based on multivariate complex Hardy spaces theory. We proceed with two approaches of which one uses Product-TM Systems; and the other uses Product-Szegö Dictionaries. With the Product-TM Systems approach we prove that at each selection of a pair of parameters the maximal energy may be attained, and, accordingly, we prove the convergence. With the Product-Szegö dictionary approach we show that Pure Greedy Algorithm is applicable. We next introduce a new type of greedy algorithm, called Pre-Orthogonal Greedy Algorithm (P-OGA). We prove its convergence and convergence rate estimation, allowing a weak type version of P-OGA as well. The convergence rate estimation of the proposed P-OGA evidences its advantage over Orthogonal Greedy Algorithm (OGA). In the last part we analyze P-OGA in depth and introduce the concept P-OGA-Induced Complete Dictionary, abbreviated as Complete Dictionary . We show that with the Complete Dictionary P-OGA is applicable to the Hardy H 2 space on 2-torus.

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“…The aim of this work is to propose an adaptive approximation method in the weighted Bergman A 2 α spaces analogous with the one established in the Hardy H 2 spaces of the unit disc and the upper-half complex plane (classical contexts) called adaptive Fourier decomposition (AFD) [17]. The theory established in the Hardy spaces has direct applications in system identification and in signal analysis [13,14,19]. It is well known that a function f ∈ L 2 (∂D) with Fourier expansion f (e it ) = ∞ −∞ c n e int has its Hardy space decomposition f = f + +f − , where f + (e it ) = ∞ 0 c n e int ∈ H 2 + (∂D), and f − (e it ) = −1 −∞ c n e int ∈ H 2 − (∂D).…”

Section: Introductionmentioning

confidence: 99%

Rational Approximation in a Class of Weighted Hardy Spaces

Dang

2018

Complex Anal. Oper. Theory

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It is known that adaptive Fourier decomposition (AFD) offers efficient rational approximations to functions in the classical Hardy H 2 spaces with significant applications. This study aims at rational approximation in Bergman, and more widely, in weighted Bergman spaces, the functions of which have more singularity than those in the Hardy spaces. Due to lack of an effective inner function theory, direct adaptation of the Hardy-space AFD is not performable. We, however, show that a pre-orthogonal method, being equivalent to AFD in the classical cases, is available for all weighted Bergman spaces. The theory in the Bergman spaces has equal force as AFD in the Hardy spaces. The methodology of approximation is via constructing the rational orthogonal systems of the Bergman type spaces, called Bergman space rational orthogonal (BRO) system, that have the same role as the Takennaka-Malmquist (TM) system in the Hardy spaces. Subsequently, we prove a certain type direct sum decomposition of the Bergman spaces that reveals the orthogonal complement relation between the span of the BRO system and the zero-based invariant spaces. We provide a sequence of examples with different and explicit singularities at the boundary along with a study on the inclusion relations of the weighted Bergman spaces. We finally present illustrative examples for effectiveness of the approximation.

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On backward shift algorithm for estimating poles of systems

Cited by 30 publications

References 21 publications

Mixed model identification for linear time‐invariant systems with mixed noises in frequency domain

Mixed model identification for linear time‐invariant systems with mixed noises in frequency domain

Two‐dimensional adaptive Fourier decomposition

Rational Approximation in a Class of Weighted Hardy Spaces

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