State Estimation with Protecting Exogenous Inputs via Cramér-Rao Lower Bound Approach
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912755206848512 |
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| author | Guo, Liping Wang, Jimin Zhao, Yanlong Zhang, Ji-Feng |
| author_facet | Guo, Liping Wang, Jimin Zhao, Yanlong Zhang, Ji-Feng |
| contents | This paper addresses the real-time state estimation problem for dynamic systems while protecting exogenous inputs against adversaries, who may be honest-but-curious third parties or external eavesdroppers. The Cramér-Rao lower bound (CRLB) is employed to constrain the mean square error (MSE) of the adversary's estimate for the exogenous inputs above a specified threshold. By minimizing the MSE of the state estimate while ensuring a certain privacy level measured by CRLB, the problem is formulated as a constrained optimization. To solve the optimization problem, an explicit expression for CRLB is first provided. As the computational complexity of the CRLB increases with the time step, a low-complexity approach is proposed to make the complexity independent of time. Then, a relaxation approach is proposed to efficiently solve the optimization problem. Finally, a privacy-preserving state estimation algorithm with low complexity is developed, which also ensures $(ε, δ)$-differential privacy. Two illustrative examples, including a practical scenario for protecting building occupancy, demonstrate the effectiveness of the proposed algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08756 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | State Estimation with Protecting Exogenous Inputs via Cramér-Rao Lower Bound Approach Guo, Liping Wang, Jimin Zhao, Yanlong Zhang, Ji-Feng Systems and Control This paper addresses the real-time state estimation problem for dynamic systems while protecting exogenous inputs against adversaries, who may be honest-but-curious third parties or external eavesdroppers. The Cramér-Rao lower bound (CRLB) is employed to constrain the mean square error (MSE) of the adversary's estimate for the exogenous inputs above a specified threshold. By minimizing the MSE of the state estimate while ensuring a certain privacy level measured by CRLB, the problem is formulated as a constrained optimization. To solve the optimization problem, an explicit expression for CRLB is first provided. As the computational complexity of the CRLB increases with the time step, a low-complexity approach is proposed to make the complexity independent of time. Then, a relaxation approach is proposed to efficiently solve the optimization problem. Finally, a privacy-preserving state estimation algorithm with low complexity is developed, which also ensures $(ε, δ)$-differential privacy. Two illustrative examples, including a practical scenario for protecting building occupancy, demonstrate the effectiveness of the proposed algorithm. |
| title | State Estimation with Protecting Exogenous Inputs via Cramér-Rao Lower Bound Approach |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2410.08756 |