Stability of the distributed Kalman filter using general random coefficients

Gan, Die; Xie, Siyu; Liu, Zhixin

doi:10.1007/s11432-020-2962-9

Cited by 15 publications

(3 citation statements)

References 27 publications

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“…For the time-varying parameter vector, Xie and Guo (2018) provided a cooperative information condition to guarantee the stability of the consensus-based LMS adaptive filters. Moreover, Gan et al (2021) introduced the collective random observability condition and provided the stability analysis of the distributed Kalman filter algorithm. Nevertheless, these asymptotical results are established as the number of the observation data obtained by sensors tends to infinity, which may not be suitable for the sparse identification problem with limited observation data.…”

Section: Introductionmentioning

confidence: 99%

Distributed Sparse Identification for Stochastic Dynamic Systems under Cooperative Non-Persistent Excitation Condition

Gan¹,

Liu²

2022

Preprint

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This paper considers the distributed sparse identification problem over wireless sensor networks such that all sensors cooperatively estimate the unknown sparse parameter vector of stochastic dynamic systems by using the local information from neighbors. A distributed sparse least squares algorithm is proposed by minimizing a local information criterion formulated as a linear combination of accumulative local estimation error and L1-regularization term. The upper bounds of the estimation error and the regret of the adaptive predictor of the proposed algorithm are presented. Furthermore, by designing a suitable adaptive weighting coefficient based on the local observation data, the set convergence of zero elements with a finite number of observations is obtained under a cooperative non-persistent excitation condition. It is shown that the proposed distributed algorithm can work well in a cooperative way even though none of the individual sensors can fulfill the estimation task. Our theoretical results are obtained without relying on the independency assumptions of regression signals that have been commonly used in the existing literature. Thus, our results are expected to be applied to stochastic feedback systems. Finally, the numerical simulations are provided to demonstrate the effectiveness of our theoretical results.

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Section: Introductionmentioning

confidence: 99%

Distributed Sparse Identification for Stochastic Dynamic Systems under Cooperative Non-Persistent Excitation Condition

Gan¹,

Liu²

2022

Preprint

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“…In the investigation of distributed estimation algorithms, how to use the local information to design the algorithms is important for the property of the algorithms. Three types of strategies are often adopted in the current literature: incremental strategy (cf., [7]), consensus strategy (cf., [8]), and diffusion strategy (cf., [9] [10]). Based on these three strategies, many different distributed adaptive estimation algorithms are proposed, such as the diffusion least mean squares (LMS), the consensus-based Kalman filter, the diffusion least squares.…”

Section: Introductionmentioning

confidence: 99%

Convergence of the Distributed SG Algorithm Under Cooperative Excitation Condition

Gan¹,

Liu²

2022

Preprint

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In this paper, a distributed stochastic gradient (SG) algorithm is proposed where the estimators are aimed to collectively estimate an unknown time-invariant parameter from a set of noisy measurements obtained by distributed sensors. The proposed distributed SG algorithm combines the consensus strategy of the estimation of neighbors with the diffusion of regression vectors. A cooperative excitation condition is introduced, under which the convergence of the distributed SG algorithm can be obtained without relying on the independency and stationarity assumptions of regression vectors which are commonly used in existing literature. Furthermore, the convergence rate of the algorithm can be established. Finally, we show that all sensors can cooperate to fulfill the estimation task even though any individual sensor can not by a simulation example.

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“…The time-delay and stochastic terms are usually the important reasons for system instability or poor performance. Due to their complexity and comprehensive application fields, LSTDSs have become very active and have developed in various areas based on different focuses, such as stability analysis and stabilization [1][2][3], control system synthesis [4][5][6], uncertain system control [7][8][9], filter design [10][11][12], etc.…”

Section: Introductionmentioning

confidence: 99%

A Precise Stabilization Method for Linear Stochastic Time-Delay Systems

et al. 2022

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Based on ensuring the steady-state performance of the system, some dynamic performance indicators that have not yet been realized in linear stochastic systems with time-delay are discussed in this paper. First, in view of the relationship between system eigenvalues and system performances, the region stability is provided, which can reflect the dynamic performance of the systems. Second, the design scheme of the region stabilization controller is given based on the region stability, so that the closed-loop system has the corresponding dynamic performance. Third, this paper also designs an algorithm to deal with the situation in which the eigenvalues are located in the non-connected region in order to obtain more accurate control system dynamic performance. Finally, an example shows how the precise control method dominates the dynamic performance of the system.

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Stability of the distributed Kalman filter using general random coefficients

Cited by 15 publications

References 27 publications

Distributed Sparse Identification for Stochastic Dynamic Systems under Cooperative Non-Persistent Excitation Condition

Distributed Sparse Identification for Stochastic Dynamic Systems under Cooperative Non-Persistent Excitation Condition

Convergence of the Distributed SG Algorithm Under Cooperative Excitation Condition

A Precise Stabilization Method for Linear Stochastic Time-Delay Systems

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