Real-Time Numerical Differentiation of Sampled Data Using Adaptive Input and State Estimation
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.
Cite
@article{arxiv.2308.08074,
title = {Real-Time Numerical Differentiation of Sampled Data Using Adaptive Input and State Estimation},
author = {Shashank Verma and Sneha Sanjeevini and E. Dogan Sumer and Dennis S. Bernstein},
journal= {arXiv preprint arXiv:2308.08074},
year = {2024}
}
Comments
This paper is under review at the International Journal of Control