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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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    This study introduces a robust Bayesian inference method for state estimation in linear state-space models. It effectively handles nonstationary, heavy-tailed noise and measurement outliers for improved accuracy.

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    Area of Science:

    • Robust Bayesian inference
    • State-space modeling
    • Nonstationary and heavy-tailed noise analysis

    Background:

    • Linear state-space models are crucial for dynamic system analysis.
    • Traditional methods struggle with nonstationary and heavy-tailed noise, leading to inaccurate state estimation.
    • Measurement outliers and modeling uncertainties further degrade performance.

    Purpose of the Study:

    • To develop a robust Bayesian inference approach for linear state-space models.
    • To address challenges posed by nonstationary and heavy-tailed noise.
    • To enhance state estimation accuracy in the presence of uncertainties and outliers.

    Main Methods:

    • Modeling the predicted distribution using a hierarchical Student-t distribution.
    • Modifying the likelihood function to a Student-t mixture distribution.
    • Employing variational Bayesian (VB) techniques and fixed-point iterations to manage parameter coupling.

    Main Results:

    • The proposed method demonstrates superior performance in state estimation compared to existing approaches.
    • Effective adaptation to potential uncertainties through online parameter learning.
    • Successful handling of modeling uncertainties and measurement outliers in simulations.

    Conclusions:

    • The robust Bayesian inference approach provides accurate state estimation for linear state-space models.
    • The method is resilient to nonstationary, heavy-tailed noise and outliers.
    • Validated through Newtonian tracking and a 3-DOF hover system example.