Real-time numerical differentiation of sampled data using adaptive input and state estimation

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 proposes an algorithm for estimating the numerical derivative of a signal from noisy sampled data meas...

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Bibliographic Details
Published in:International journal of control 2024-12, Vol.97 (12), p.2962-2974
Main Authors: Verma, Shashank, Sanjeevini, Sneha, Sumer, E. Dogan, Bernstein, Dennis S.
Format: Article
Language:English
Subjects:
Adaptive algorithms
Adaptive control
Adaptive sampling
Adaptive system
Input estimation
Kalman filter
Numerical differentiation
Proportional integral derivative
Real time
Sampled data
State estimation
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Summary: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 proposes an algorithm for estimating the numerical derivative of a signal from noisy sampled data measurements. The method uses adaptive input estimation with adaptive state estimation (AIE/ASE), and thus it requires only minimal prior information about the signal and noise statistics. Furthermore, since the estimates of the derivative at step k provided by AIE/ASE depend only on data available up to step k, AIE/ASE is thus implementable in real time. 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 in the CarSim simulator software.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2024.2313046