A Survey of Observers for Nonlinear Dynamical Systems

Kang, Wei; Krener, Arthur J.; Xiao, Mingqing; Xu, Liang

doi:10.1007/978-3-642-35088-7_1

Cited by 25 publications

(8 citation statements)

References 56 publications

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“…Adaptive localization is not only easily implemented in the ETKF, it also automatically ensures that the cross-process correlation is localized differently than the intra-process correlation, making it particularly suitable for data assimilation in coupled surfacesubsurface models. Others have encountered the problem with cross-process correlation, notably Zupanski (2013), Li et al (2013) and Wanders et al (2014), although no definitive solution to the problem has been presented. Adaptive localization, such as the method applied in this study, may be one possible solution.…”

Section: Discussionmentioning

confidence: 99%

Data assimilation in integrated hydrological modeling using ensemble Kalman filtering: evaluating the effect of ensemble size and localization on filter performance

Rasmussen¹,

Madsen²,

Jensen³

et al. 2015

Preprint

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Abstract. Groundwater head and stream discharge is assimilated using the Ensemble Transform Kalman Filter in an integrated hydrological model with the aim of studying the relationship between the filter performance and the ensemble size. In an attempt to reduce the required number of ensemble members, an adaptive localization method is used. The performance of the adaptive localization method is compared to the more common local analysis localization. The relationship between filter performance in terms of hydraulic head and discharge error and the number of ensemble members is investigated for varying numbers and spatial distributions of groundwater head observations and with or without discharge assimilation and parameter estimation. The study shows that (1) more ensemble members are needed when fewer groundwater head observations are assimilated, and (2) assimilating discharge observations and estimating parameters requires a much larger ensemble size than just assimilating groundwater head observations. However, the required ensemble size can be greatly reduced with the use of adaptive localization, which by far outperforms local analysis localization.

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Section: Discussionmentioning

confidence: 99%

Data assimilation in integrated hydrological modeling using ensemble Kalman filtering: evaluating the effect of ensemble size and localization on filter performance

Rasmussen¹,

Madsen²,

Jensen³

et al. 2015

Preprint

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“…In many applications, knowing the current state of a dynamical system is crucial either to build a controller or to obtain real time information on the system for decision-making or monitoring, see, e.g., [193,128,186] and references therein. A common way of addressing this problem is to place some sensors on the physical system in order to have access to such information.…”

Section: Introductionmentioning

confidence: 99%

Observer design for continuous-time dynamical systems

Bernard

Andrieu

Astolfi

2022

Annual Reviews in Control

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We review the main design techniques of state observer design for continuous-time dynamical systems, namely algorithms which reconstruct online the full information of a dynamical process on the basis of partially measured data. Starting from necessary conditions for the existence of such asymptotic observers, we classify the available methods depending on the detectability/observability assumptions they require. We show how each class of observer relies on transforming the system dynamics in a particular normal form which allows the design of an observer, and how each observability condition guarantees the invertibility of its associated transformation and the convergence of the observer. Finally, some implementation aspects and open problems are briefly discussed.

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“…The robust state estimation literature is indeed rich with two main classes of methods. The first class is based on robust observers and Lyapunov theory which often does not assume any statistical distribution for unknown inputs or noise [14], [15]. The second class is based on Kalman filter and its derivatives, that often assume statistical distribution of noise [16]- [18].…”

Section: Introductionmentioning

confidence: 99%

Tuning-Free, Low Memory Robust Estimator to Mitigate GPS Spoofing Attacks

Lee

Taha

Gatsis

et al. 2020

IEEE Control Syst. Lett.

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The operation of critical infrastructures such as the electrical power grid, cellphone towers, and financial institutions relies on precise timing provided by stationary GPS receivers. These GPS devices are vulnerable to a type of spoofing called Time Synchronization Attack (TSA), whose objective is to maliciously alter the timing provided by the GPS receiver. The objective of this paper is to design a tuning-free, low memory robust estimator to mitigate such spoofing attacks. The contribution is that the proposed method dispenses with several limitations found in the existing state-of-the-art methods in the literature that require parameter tuning, availability of the statistical distributions of noise, real-time optimization, or heavy computations. Specifically, we (i) utilize an observer design for linear systems under unknown inputs, (ii) adjust it to include a state-correction algorithm, (iii) design a realistic experimental setup with real GPS data and sensible spoofing attacks, and (iv) showcase how the proposed tuning-free, low memory robust estimator can combat TSAs. Numerical tests with real GPS data demonstrate that accurate time can be provided to the user under various attack conditions.

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A Survey of Observers for Nonlinear Dynamical Systems

Cited by 25 publications

References 56 publications

Data assimilation in integrated hydrological modeling using ensemble Kalman filtering: evaluating the effect of ensemble size and localization on filter performance

Data assimilation in integrated hydrological modeling using ensemble Kalman filtering: evaluating the effect of ensemble size and localization on filter performance

Observer design for continuous-time dynamical systems

Tuning-Free, Low Memory Robust Estimator to Mitigate GPS Spoofing Attacks

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