Harmonic-Coupled Riccati Equation and Its Applications in Distributed Filtering

The coupled Riccati equations (CREs) are a set of multiple Riccati-like equations whose solutions are coupled with each other through matrix means. They are a fundamental mathematical tool to depict the inherent dynamics of many complex systems, including Markovian systems or multiagent systems. Thi...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2024-09, Vol.69 (9), p.5852-5866
Main Authors: Qian, Jiachen, Duan, Zhisheng, Duan, Peihu, Shi, Ling
Format: Article
Language:English
Subjects:
Algorithms
Complex systems
Complexity
Coupled Riccati equations (CRE)
Covariance matrices
distributed filtering
Filtration
Harmonic analysis
Iterative methods
matrix harmonic mean
Multiagent systems
Observability
Observability (systems)
Performance evaluation
Riccati equation
Riccati equations
Stability analysis
State estimation
Steady-state
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Summary:The coupled Riccati equations (CREs) are a set of multiple Riccati-like equations whose solutions are coupled with each other through matrix means. They are a fundamental mathematical tool to depict the inherent dynamics of many complex systems, including Markovian systems or multiagent systems. This article investigates a new kind of CREs called harmonic-CREs (HCREs), whose solutions are coupled using harmonic means. We first introduce the specific form of HCREs and then analyze the existence and uniqueness of its solutions under the conditions of collective observability and primitiveness of coupling matrices. In addition, we manage to find an iterative law with low computation-complexity to obtain the solutions to HCREs. Based on this newly established theory, we greatly simplify the steady-state estimation error covariance of consensus-on-information-based distributed filtering (CIDF) into the solutions to a discrete-time Lyapunov equation (DLE). This leads to a significant conservativeness reduction of traditional performance evaluation techniques for CIDF. The obtained results are remarkable since they not only enrich the theory of CREs but also provide a novel insight into the synthesis and analysis of CIDF algorithms. We finally validate our theoretical findings through several numerical experiments.
ISSN:0018-9286
1558-2523
1558-2523
DOI:10.1109/TAC.2024.3362867