The Kantorovich inequality for error analysis of the Kalman filter with unknown noise distributions

Spall, James C.

doi:10.1016/0005-1098(95)00069-9

Cited by 56 publications

(3 citation statements)

References 18 publications

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“…However, in real-world systems, due to parameter changes, model reduction, linearisation, and a hard external environment, the noises are non-Gaussian [11]. These noises have widely been studied in filtering problems in the last decades [12][13][14]. Some modelling for non-Gaussian noises is directly inspired by physical phenomena.…”

Section: Introductionmentioning

confidence: 99%

Distributed robust error‐constrained filter for sensor networks with polytopic uncertainty and non‐Gaussian noises

Khamesi

Rahmani

2022

IET Signal Processing

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A distributed robust error‐constrained filter is proposed for time‐varying uncertain systems with non‐Gaussian noises over a sensor network. In this problem, some challenges are raised. The distributed filter should be designed for a sensor network with uncertain parameters that are supposed to belong to a polytope with known vertices, and the non‐Gaussian noises that are unknown but bounded by a set of specific ellipsoids. According to the network topology, available measurements at each sensor node came not only from the individual sensor but also from its neighbours. In this approach, to consider the effects of the neighbouring node's estimation and output in the filtering algorithm, first, a distributed filter structure is introduced at each node. Then, a collective model of the sensor network is presented with the aim of distributed filtering. Next, a linear matrix inequality‐based optimisation problem is presented to guarantee the optimal performance of filtering by minimising the upper bound of the estimation error in the presence of non‐Gaussian bounded noises and polytopic uncertainty. The proposed distributed approach can be easily applied as a decentralised robust error‐constrained filter. In the end, two illustrative examples are presented to show the applicability and performance of the proposed error‐constrained filtering approach.

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Section: Introductionmentioning

confidence: 99%

Distributed robust error‐constrained filter for sensor networks with polytopic uncertainty and non‐Gaussian noises

Khamesi

Rahmani

2022

IET Signal Processing

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“…Under such an assumption, the popular linear‐quadratic‐Gaussian (LQG) control and Kalman filtering theories can be applied. However, in many processes of chemical and manufacture processing, the involved inputs are of the non‐Gaussian type 13–17. Actually, non‐Gaussian noises are a kind of more general signals than the widely studied Gaussian noises 18–21.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, since bounded noises serve as an important type of non‐Gaussian noises, the control and filtering problem for systems with bounded noises have received considerable research attention for two decades, see e.g. 14–17, 22–24. Nevertheless, in order to reflect the engineering system in a more realistic and comprehensive way, the system model should account for the nonlinearities, time delays, bounded noises as well as time‐varying parameters.…”

Section: Introductionmentioning

confidence: 99%

Error‐constrained finite‐horizon tracking control with incomplete measurements and bounded noises

Wei

Wang

Shen

2011

Intl J Robust & Nonlinear

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SUMMARYThis paper is concerned with the finite-horizon tracking control problem for discrete nonlinear time-varying systems with state delays, bounded noises and incomplete measurement output. The exogenous bounded noises are unknown and confined to specified ellipsoidal sets. A deterministic measurement output model is proposed to account for the incomplete data transmission phenomenon caused by possible sensor aging or failures. The aim of the addressed tracking control problem is to develop an observer-based control over a finite-horizon such that, for the admissible time delays, nonlinearities and bounded noises, both the quadratic tracking error and the estimation error are not more than certain upper bounds that are minimized at every time step. A recursive linear matrix inequality approach is used to solve the problem addressed. The observer and controller parameters are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programme method. A simulation example is exploited to illustrate the effectiveness of the proposed design procedures.

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Inequalities for One Operator

Dragomir

2013

Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces

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The Kantorovich inequality for error analysis of the Kalman filter with unknown noise distributions

Cited by 56 publications

References 18 publications

Distributed robust error‐constrained filter for sensor networks with polytopic uncertainty and non‐Gaussian noises

Distributed robust error‐constrained filter for sensor networks with polytopic uncertainty and non‐Gaussian noises

Error‐constrained finite‐horizon tracking control with incomplete measurements and bounded noises

Inequalities for One Operator

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