Stochastic modeling and state estimation of RL circuits under noisy environments using random Runge-Kutta methods and Kalman filtering

Abstract

This research investigates the behavior of an RL circuit under a stochastic voltage source by deriving and analyzing the circuit equation using stochastic differential equations. The study establishes mean square convergence for the obtained solution, ensuring the stability and accuracy of the stochastic model. A numerical example is implemented to validate the theoretical findings, leading to the derivation of a current equation, which is then visualized through a graph. Additionally, a kalman filter is applied using Python to estimate the current in the RL circuit, and the corresponding graph is generated. The comparison between the two graphical representations highlights the effectiveness of the kalman filter in producing a smoother and more stable current flow. The results demonstrate that while the direct stochastic model captures the inherent fluctuations due to noise, the kalman filter effectively reduces these variations, providing a more refined estimation of the circuit's response. The comparison highlights the effectiveness of filtering techniques in refining circuit responses and mitigating fluctuations due to stochastic perturbations, contributing to improved modeling accuracy in electrical circuits.