Design and Implementation of a Kalman Filter-Based Frequency-Adaptive Differentiator for a Wide Frequency Range

This paper presents the design and implementation of a Kalman filter-based Frequency-Adaptive Differentiator capable of operating over a wide frequency range. The modeling of a sinusoidal signal is carefully described in both continuous-time and discrete-time domains, leading to the derivation of the matrices used in the Kalman filter. Then, the frequency-adaptive Kalman filter is introduced, demonstrating that the state prediction matrix adapts to the angular frequency of the input signal. This adaptability is achieved through the proposed frequency estimation algorithm, enabling the differentiator to compute the derivative of a sinusoidal signal with a fundamental frequency varying from 30 Hz to 400 Hz. The proposed differentiator was implemented on the TMS320F28335 microcontroller, and results from a controller hardware-in-the-loop setup show that it accurately computes the derivative of a sinusoidal signal without changing its amplitude or amplifying noise. A brief comparison with other differentiators highlights the superior performance of the proposed approach.