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

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 an 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.

Keywords:

Stochastic differential equation , white noise , Kalman-Bucy filter , Ito formula , analytic solution