On the convergence of the unscented Kalman filter

Daid, Assia; Busvelle, Éric; Mohamed, Azah

doi:10.1016/j.ejcon.2020.05.003

Cited by 16 publications

(5 citation statements)

References 48 publications

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“…Theorem 3: Let us suppose that for a given T > 0, there exists two constants m 1 end m 2 such that for any value of θ, 0 < m 1 Id ≤ S(t) ≤ m 2 Id, then there exists θ and c such that the high-gain unscented Kalman observer (11) is a globally exponentially converging observer for of the system (9). In Theorem 3, S(t) is supposed to be bounded independently from θ for t > T .…”

Section: Resultsmentioning

confidence: 99%

“…They consist mainly in straightforward adaptations of the proof in the book [12] and some analytic computations (such as Taylor series expansion to obtain (13) which use also some identities from the unscented transformation, see [23]). Theorems 1 and 2 are proved in details in [9]. Theorem 3 is a very simple result and it is proved in the Ph.D. of Assia Daid, in preparation.…”

Section: Resultsmentioning

confidence: 99%

“…We build the high-gain version of the UKO (called high-gain unscented Kalman observer, HG-UKO) and we give some convergence results. In fact, HG-UKO is a local exponentially converging observer (see also [9]) and it becomes a global converging observer if we assume that the solution of the Riccati equation is bounded.…”

Section: Introductionmentioning

confidence: 99%

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Unscented Kalman Observer

Daid

Busvelle

Mohamed

2019

2019 8th International Conference on Systems and Control (ICSC)

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The extended Kalman filter is an exponentially converging observer as soon as it is written in a canonical form of observability and in its high-gain form. It is shown that unlike extended Kalman filter, unscented Kalman filter can not be an exponentially converging observer. We propose a slight modification of the unscented Kalman filter to build an exponentially converging observer called unscented Kalman observer. Performances of this new observer are illustrated on an example of geolocation problem.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Unscented Kalman Observer

Daid

Busvelle

Mohamed

2019

2019 8th International Conference on Systems and Control (ICSC)

Self Cite

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“…In [82−84], the filtering problem has been discussed for a class of multi-rate sampled-data systems where the lifting technique has been employed to accommodate the multi-rate sampling. In [63,85], the distributed filtering problem has been considered for the networked control systems with network-induced phenomena.…”

Section: Kalman Filtering and Its Variantsmentioning

confidence: 99%

An Overview of Filtering for Sampled-Data Systems under Communication Constraints

Wang,

Liu,

Tan

2023

IJNDI

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Survey/Review Study An Overview of Filtering for Sampled-Data Systems under Communication Constraints Ye Wang 1,2, Hong-Jian Liu 1,2, and Hai-Long Tan 1,2 1 School of Mathematics-Physics and Finance, Anhui Polytechnic University, Wuhu 241000, China 2 Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment, Ministry of Education, Anhui Polytechnic University, Wuhu 241000, China Received: 5 May 2023 Accepted: 21 July 2023 Published: 26 September 2023 Abstract: The sampled-data systems have been extensively applied to practical engineering because the digital signal shows great advantages in data transmission, storage and exchange. As a result, the analysis and synthesis problems of sampled-data systems have attracted ever-growing research interest due mainly to their significant application potential. On the other hand, the filtering or state estimation (which intends to reconstruct real system states from noisy measurements) is viewed as one of the most fundamental research topics in the control community. Until now, a lot of research efforts have been devoted to the filtering problem of sampled-data systems. The objective of the survey is to exhibit a systematic review with respect to filtering and control methods for sampled-data systems under communication constraints. First, some effective filtering algorithms are given. Then, the recent advances are shown in the filtering and control of sampled-data systems subject to network-induced phenomena based on the sampling methods. Finally, some future research topics are given on state estimation of sampled-data systems.

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“…The unscented Kalman Filter, a special case of sigma point filters based on unscented transformation, is introduced to improve filtering performance. Unscented transformation [24,25] is a powerful tool to estimate the statistics of a random variable that undergoes a nonlinear transformation [26] and is used in many applications ranging from sensor fusion for state estimation [27] to an unscented Kalman observer [28]. Moreover, in recent studies, Sieberg et al combined an artificial neural network with confidence level adjustment and presented a hybrid state estimation structure using unscented transformation [29].…”

Section: Introductionmentioning

confidence: 99%

Stochastic stability analysis of legged locomotion using unscented transformation

Er,

Ankarali

2023

Bioinspir. Biomim.

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In this manuscript, we present a novel method for estimating the stochastic stability characteristics of metastable legged systems using the unscented transformation. Prior methods for stability analysis in such systems often required high-dimensional state space discretization and a broad set of initial conditions, resulting in signiﬁcant computational complexity. Our approach aims to alleviate this issue by reducing the dimensionality of the system and utilizing the unscented transformation to estimate the output distribution. This technique allows us to account for multiple sources of uncertainty and high-dimensional system dynamics, while leveraging prior knowledge of noise statistics to inform the selection of initial conditions for experiments. As a result, our method enables the eﬃcient assessment of controller performance and analysis of parametric dependencies with fewer experiments. To demonstrate the eﬃcacy of our proposed method, we apply it to the analysis of a one-dimensional hopper and an underactuated bipedal walking simulation with a hybrid zero dynamics controller.

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On the convergence of the unscented Kalman filter

Cited by 16 publications

References 48 publications

Unscented Kalman Observer

Unscented Kalman Observer

An Overview of Filtering for Sampled-Data Systems under Communication Constraints

Stochastic stability analysis of legged locomotion using unscented transformation

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