Application of the Kalman-Bucy filter in the stochastic differential equation for the modeling of RL circuit


1 Department of Mathematics, Faculty of Basic Sciences, Islamic Azad University, Sciences and Research Branch, Tehran, Iran.

2 Department of Mathematics, Islamic Azad University Ghaemshahr Branch, Ghaemshahr, Iran.


In this paper, we present an application of the stochastic calculus
to the problem of modeling electrical networks. The filtering problem have an
important role in the theory of stochastic differential equations(SDEs). In this
article, we present an application of the continuous Kalman-Bucy filter for a RL
circuit. The deterministic model of the circuit is replaced by a stochastic model by
adding a noise term in the source. The analytic solution of the resulting stochastic
integral equations are found using the Ito formula.