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arXiv · 2308.08074

Real-Time Numerical Differentiation of Sampled Data Using Adaptive Input and State Estimation

Shashank Verma·Sneha Sanjeevini·E. Dogan Sumer·Dennis S. Bernstein
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Abstract

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.

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Shashank Verma, Sneha Sanjeevini, E. Dogan Sumer, Dennis S. Bernstein. 2023-08-16. Real-Time Numerical Differentiation of Sampled Data Using Adaptive Input and State Estimation. https://doi.org/10.1080/00207179.2024.2313046

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