Dual Set Membership Filter With Minimizing Nonlinear Transformation of Ellipsoid

Wang, Zhiguo; Shen, Xiaojing; Liu, Haiqi; Meng, Fengyan; Zhu, Yunmin

doi:10.1109/tac.2021.3081078

Cited by 15 publications

(22 citation statements)

References 41 publications

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“…Remark 2. Equation ( 9) uses the information about the inverse function of the measurement function to estimate the state instead of linearizing the nonlinear system, thus leading to more accurate state estimates [16].…”

Section: Measurement Update Stepmentioning

confidence: 99%

“…In general, the assumption that there exists a continuous inverse function for h k+1 can be very restrictive. Here, it can be satisfied in some practical applications [16]. For example, the nonlinear measurement functions in two or three dimensional radar systems [38], which are the foundation for the measurement systems of many sensors [39].…”

Section: Measurement Update Stepmentioning

confidence: 99%

“…SMF is first considered by Schweppe [12] in the late 1960s. Since then, the idea of SMF has been widely studied [13,14,15,16,17,18]. It is worth noting that most studies on the SMF have focused on the state estimation problems for unconstrained linear dynamic systems.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, extending SMF to nonlinear dynamic systems is difficult, especially when online usage needs to be guaranteed. Some studies on nonlinear dynamic systems are presented in [15,16,19,20]. For example, in the extended set membership filter (ESMF) [21] and nonlinear set membership filter (NSMF) [22], the nonlinear functions in the dynamic system are linearized around the current state estimate, after which the higher-order remainder terms are bounded in different ways.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the nonlinear dynamic system is transformed into a linear dynamic system by treating the bounds of the higherorder remainder terms as noises. The dual set membership filter (DSMF) proposed in [16] is also a nonlinear set membership filter. Unlike ESMF and NSMF, DSMF directly finds the bounding ellipsoid of the nonlinearly transformed state bounding ellipsoid via dual theory and SIP, rather than linearizing the nonlinear dynamic system.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Set Membership Filter with State Estimation Constraints via Consensus-ADMM

Li¹,

Zhang²,

Wang³

et al. 2022

Preprint

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This paper considers the state estimation problem for nonlinear dynamic systems with unknown but bounded noises. Set membership filter (SMF) is a popular algorithm to solve this problem. In the set membership setting, we investigate the filter problem where the state estimation requires to be constrained by a linear or nonlinear equality. We propose a consensus alternating direction method of multipliers (ADMM) based SMF algorithm for nonlinear dynamic systems. To deal with the difficulty of nonlinearity, instead of linearizing the nonlinear system, a semi-infinite programming (SIP) approach is used to transform the nonlinear system into a linear one, which allows us to obtain a more accurate estimation ellipsoid. For the solution of the SIP, an ADMM algorithm is proposed to handle the state estimation constraints, and each iteration of the algorithm can be solved efficiently. Finally, the proposed filter is applied to typical numerical examples to demonstrate its effectiveness.

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Section: Measurement Update Stepmentioning

confidence: 99%

Section: Measurement Update Stepmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Nonlinear Set Membership Filter with State Estimation Constraints via Consensus-ADMM

Li¹,

Zhang²,

Wang³

et al. 2022

Preprint

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Outlier‐robust zonotope set‐membership filter for discrete‐time nonlinear system

Yang

Chen

Cheng

et al. 2023

Intl J Robust & Nonlinear

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Transient sensor malfunction, improper replacement measures, and large non‐Gaussian noise can cause data outliers in real‐world scenarios. In this article, an outlier‐robust zonotope set‐membership filter is proposed for uncertain nonlinear systems susceptible to outliers. In order to linearize nonlinear systems, a linearization method based on Stirling's interpolation formula is proposed. Then, an outlier detector utilizing the linearization error bounds, the prediction domain, and the output feasible domain is constructed. Based on the linearized system, a tight strip construction method is given to reduce the conservatism of the estimated enclosure. Moreover, a prediction‐correction‐backward reconstruction filter structure is designed to improve estimation accuracy and reduce conservatism. The proposed structure fuses historical data to attenuate the impact of uncertainty on the system. The robustness, guarantee, and convergence of the proposed filter are investigated. Finally, the effectiveness of the proposed approach is evaluated by two simulation examples.

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Set-Membership Estimation for Nonlinear Parameter-Varying Systems

Zhang¹,

Liu²

2022

Communications in Computer and Information Science

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Dual Set Membership Filter With Minimizing Nonlinear Transformation of Ellipsoid

Cited by 15 publications

References 41 publications

Nonlinear Set Membership Filter with State Estimation Constraints via Consensus-ADMM

Nonlinear Set Membership Filter with State Estimation Constraints via Consensus-ADMM

Outlier‐robust zonotope set‐membership filter for discrete‐time nonlinear system

Set-Membership Estimation for Nonlinear Parameter-Varying Systems

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