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<p>This paper proposes a novel algorithm for simultaneous state and input estimation (SSIE) in linear discrete-time stochastic systems with partial input observability. First, we introduce a constrained mixture least squares (CMLS) framework, which systematically incorporates partial input observations while ensuring unbiased estimation for both system parameters and input variables. This approach extends the existing mixture least squares methods by explicitly accounting for partially available input data. Second, within this framework, we derive an original SSIE solution that rigorously addresses the challenges of partial input observability through a compact mathematical formulation. Third, comprehensive numerical simulations demonstrate the superior performance of the proposed algorithm over existing methods in terms of estimation accuracy and computational efficiency. The proposed method thus offers a more general and efficient solution to SSIE under partial input observability.</p>

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A constrained mixture least squares approach for simultaneous state and input estimation with partial input observability

  • 期刊论文

  • 发表日期：

    2026年5月18日

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  • Bo Ding,
  • Jinge Ma,
  • Wenwen Shen,
  • Dongzhen Wang

摘要

This paper proposes a novel algorithm for simultaneous state and input estimation (SSIE) in linear discrete-time stochastic systems with partial input observability. First, we introduce a constrained mixture least squares (CMLS) framework, which systematically incorporates partial input observations while ensuring unbiased estimation for both system parameters and input variables. This approach extends the existing mixture least squares methods by explicitly accounting for partially available input data. Second, within this framework, we derive an original SSIE solution that rigorously addresses the challenges of partial input observability through a compact mathematical formulation. Third, comprehensive numerical simulations demonstrate the superior performance of the proposed algorithm over existing methods in terms of estimation accuracy and computational efficiency. The proposed method thus offers a more general and efficient solution to SSIE under partial input observability.