Real-Time Numerical Differentiation of Sampled Data Using Adaptive Input and State Estimation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866917702162972672 |
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| author | Verma, Shashank Sanjeevini, Sneha Sumer, E. Dogan Bernstein, Dennis S. |
| author_facet | Verma, Shashank Sanjeevini, Sneha Sumer, E. Dogan Bernstein, Dennis S. |
| contents | Real-time numerical differentiation plays a crucial role in many digital control algorithms, such as PID control, which requires numerical differentiation to implement derivative action. This paper addresses the problem of numerical differentiation for real-time implementation with minimal prior information about the signal and noise using adaptive input and state estimation. Adaptive input estimation with adaptive state estimation (AIE/ASE) is based on retrospective cost input estimation, while adaptive state estimation is based on an adaptive Kalman filter in which the input-estimation error covariance and the measurement-noise covariance are updated online. The accuracy of AIE/ASE is compared numerically to several conventional numerical differentiation methods. Finally, AIE/ASE is applied to simulated vehicle position data generated from CarSim. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_08074 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Real-Time Numerical Differentiation of Sampled Data Using Adaptive Input and State Estimation Verma, Shashank Sanjeevini, Sneha Sumer, E. Dogan Bernstein, Dennis S. Systems and Control Signal Processing Real-time numerical differentiation plays a crucial role in many digital control algorithms, such as PID control, which requires numerical differentiation to implement derivative action. This paper addresses the problem of numerical differentiation for real-time implementation with minimal prior information about the signal and noise using adaptive input and state estimation. Adaptive input estimation with adaptive state estimation (AIE/ASE) is based on retrospective cost input estimation, while adaptive state estimation is based on an adaptive Kalman filter in which the input-estimation error covariance and the measurement-noise covariance are updated online. The accuracy of AIE/ASE is compared numerically to several conventional numerical differentiation methods. Finally, AIE/ASE is applied to simulated vehicle position data generated from CarSim. |
| title | Real-Time Numerical Differentiation of Sampled Data Using Adaptive Input and State Estimation |
| topic | Systems and Control Signal Processing |
| url | https://arxiv.org/abs/2308.08074 |