Discrete-time state estimation for stochastic polynomial systems over polynomial observations

Hernández‐González, Miguel; Степанов, О. А.

doi:10.1080/03081079.2018.1461098

Cited by 13 publications

(5 citation statements)

References 29 publications

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“…Finally, a simulation example has been given to validate the effectiveness of the proposed filter design scheme. A possible topic for future research is to extend the main results to more general nonlinear systems such as nonlinear polynomial systems, 44,45 Markovian jumping systems, 46 time‐delay systems 47‐49 …”

Section: Discussionmentioning

confidence: 99%

Protocol‐based extended Kalman filtering with quantization effects: The Round‐Robin case

Liu

Wang

et al. 2020

Intl J Robust & Nonlinear

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This article investigates the extended Kalman filtering problem for a class of stochastic nonlinear systems with quantization effects and Round-Robin (RR) communication protocols. The uniform quantization is considered and the resulting quantization error is characterized as an additive white noise sequence obeying the uniform distribution over certain intervals. For the sake of reducing communication traffic of the network as well as alleviating data collisions, the RR mechanism is introduced to schedule the data transmission from the sensors to the filter. By combining the periodic property of the RR protocol and the zero-order holder strategy, the input signal of the filter is modeled by a sequence of delayed quantized measurements. The main purpose of this article is to design an extended Kalman filter for the stochastic nonlinear systems, in the simultaneous presence of quantization errors, stochastic nonlinearities, and stochastic noises, such that an optimized upper bound for the filtering error covariance is derived. By solving two coupled Riccati-like difference equations, the filter gain matrix is explicitly formulated. An RR protocol-based recursive filtering algorithm is developed for the online implementation. Furthermore, a sufficient condition is established to ensure the uniform boundedness of the filtering error in the mean-square sense. Finally, a simulation example is given to demonstrate the practical validity of the designed filter algorithm.

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Section: Discussionmentioning

confidence: 99%

Protocol‐based extended Kalman filtering with quantization effects: The Round‐Robin case

Liu

Wang

et al. 2020

Intl J Robust & Nonlinear

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“…).A similar approach was considered in [29][30][31]. Index sub indicates the type of a suboptimal algorithm:sub = PF corresponds to the polynomial filter,sub = EKF corresponds to the EKF.…”

Section: Polynomial and Extended Kalman Filtersmentioning

confidence: 99%

“…Suboptimal algorithms proposed to solve the stated problem are based on the assumption that the prediction p.d.f. is close to the Gaussian one

p false({\overset{x}{true}}_{k} / {bold-italicY}_{k - 1} false) = N false({\overset{x}{true}}_{k}, {\overset{\tilde{bold-italicx}}{true}}_{k / k - 1}^{s u b}, {bold-italicP}_{k / k - 1}^{s u b} false(Y_{k - 1} false) false) .

A similar approach was considered in [29–31]. Index

s u b

indicates the type of a suboptimal algorithm:

s u b = P F

corresponds to the polynomial filter,

s u b = E K F

corresponds to the EKF.…”

Section: Polynomial and Extended Kalman Filtersmentioning

confidence: 99%

“…It should be noted that nonlinearities in state and measurement equations are often represented by polynomials. From this point of view, polynomial filtering methods have been quite successfully used to solve estimation problems [25][26][27][28][29][30][31][32][33][34][35][36][37][38]. In particular, in [24,31], the authors consider problems whose specific feature is nonlinearity of measurements, whereas the equations of the shaping filter that describe the estimated sequence are linear.…”

Section: Introductionmentioning

confidence: 99%

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Efficiency analysis of polynomial filtering algorithms in navigation data processing for a class of nonlinear discrete dynamical systems

Степанов

Vasiliev

Tupysev

et al. 2020

IET Control Theory & Appl

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A polynomial filtering algorithm is designed for estimating a Markov sequence based on linear measurements. The feature of the estimation problem is that the Markov sequence is described by a nonlinear shaping filter, which is a second-order polynomial with respect to the state vector components. The algorithm efficiency is illustrated by three examples of navigation data processing. It is shown that the polynomial filter provides accuracy close to the best potential one calculated using the particle filter. At the same time, the amount of computation required to implement this algorithm is much smaller than that for the particle filter. In addition, the polynomial filter provides a consistent calculated accuracy characteristic.

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“…Finite-dimensional filters are obtained by expressing the conditional expectations of polynomial terms as functions of the state estimate and the error covariance matrix. Filtering algorithms for discretetime polynomial systems have been reported in Hernandez-Gonzalez and Basin (2014) and Hernandez-Gonzalez et al (2018).…”

Section: Introductionmentioning

confidence: 99%

Discrete-time estimation of switched stochastic polynomial systems and its application to reconstruction of induction motor variables

Hernández‐González

Степанов

2021

Transactions of the Institute of Measurement and Control

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This paper presents a solution to the filtering problem for a class of stochastic discrete-time nonlinear polynomial systems with switching in the state equation over linear observations and its application to a mechatronic system. The switching in the state equation is performed between two different nonlinear functions according to a sequence of independent Bernoulli random variables that take the quantities of zero and one. The mean-square filtering solution is obtained for a general nonlinear discrete-time polynomial system and a finite-dimensional system of filtering equations is then obtained for a second degree polynomial system as a particular case. The mean-square estimates of polynomial state terms are expressed as functions of the estimate and covariance matrix. Finally, some numerical simulations are carried out to reconstruct the variable states given a vector output measurement for a linear system, a second degree polynomial system, and an induction motor model to show effectiveness of the proposed algorithm. The proposed method is compared with an extended Kalman filter-based algorithm for discrete-time switched nonlinear systems.

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Discrete-time state estimation for stochastic polynomial systems over polynomial observations

Cited by 13 publications

References 29 publications

Protocol‐based extended Kalman filtering with quantization effects: The Round‐Robin case

Protocol‐based extended Kalman filtering with quantization effects: The Round‐Robin case

Efficiency analysis of polynomial filtering algorithms in navigation data processing for a class of nonlinear discrete dynamical systems

Discrete-time estimation of switched stochastic polynomial systems and its application to reconstruction of induction motor variables

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