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Distributed LMMSE Estimation for Large-Scale Systems Based on Local Information.

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    This study addresses distributed estimation in large-scale systems using only local information. A new framework and algorithms are presented to design estimators and ensure estimation error covariance boundedness.

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    Area of Science:

    • Control Systems Engineering
    • Signal Processing
    • Networked Systems

    Background:

    • Large-scale systems comprise numerous subsystems with limited communication, accessing only local information.
    • Designing distributed estimators under local information constraints presents challenges in gain design and error covariance analysis.

    Purpose of the Study:

    • To establish a framework for distributed Linear Minimum Mean Square Error (LMMSE) estimation in large-scale systems with local information (LSLI).
    • To develop methods for constructing LMMSE estimator gains and ensuring the boundedness of the estimation error covariance (EEC).

    Main Methods:

    • Constructing LMMSE estimator gains by solving linear matrix equations.
    • Employing a gradient descent algorithm for numerical gain design.
    • Deriving sufficient conditions for EEC boundedness.
    • Developing a gradient-based search algorithm to verify these conditions.

    Main Results:

    • A framework for distributed LMMSE estimation in LSLI is established.
    • Effective methods for constructing estimator gains and ensuring EEC boundedness are presented.
    • An illustrative example demonstrates the efficacy of the proposed approach.

    Conclusions:

    • The proposed framework and algorithms effectively address the challenges of distributed LMMSE estimation in LSLI.
    • The developed methods provide sufficient conditions and verification tools for ensuring estimation performance.
    • The study contributes to robust estimation techniques for complex, interconnected systems.