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<p>While the literature provides optimal solutions for the state estimation in linear systems, only suboptimal solutions are available for nonlinear systems. By considering a convex modeling of nonlinearities, using polytopes, differential mean value theorem, or factorization techniques, it is possible to derive conditions based on convex optimization, through linear matrix inequalities (LMIs), to ensure the state estimation in nonlinear systems. In this context, this work provides a new state estimation approach for discrete-time nonlinear systems that employs LMI conditions to synthesize state estimators. This approach adopts a new guaranteed covariance Kalman filter that is based on the steps of the classic Kalman filter. The effectiveness of the proposed approach is demonstrated through several simulated examples.</p>

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A Convex Approach to the Design of a Guaranteed Covariance Kalman Filter for Discrete-Time Nonlinear Systems

  • 期刊论文

  • 发表日期：

    2025年8月12日

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  • Pablo Henrique Gonçalves,
  • Bruno Otávio Soares Teixeira,
  • Víctor Costa da Silva Campos

摘要

While the literature provides optimal solutions for the state estimation in linear systems, only suboptimal solutions are available for nonlinear systems. By considering a convex modeling of nonlinearities, using polytopes, differential mean value theorem, or factorization techniques, it is possible to derive conditions based on convex optimization, through linear matrix inequalities (LMIs), to ensure the state estimation in nonlinear systems. In this context, this work provides a new state estimation approach for discrete-time nonlinear systems that employs LMI conditions to synthesize state estimators. This approach adopts a new guaranteed covariance Kalman filter that is based on the steps of the classic Kalman filter. The effectiveness of the proposed approach is demonstrated through several simulated examples.