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 calculusto the problem of modeling electrical networks. The filtering problem have animportant role in the theory of stochastic differential equations(SDEs). In thisarticle, we present an application of the continuous Kalman-Bucy filter for a RLcircuit. The deterministic model of the circuit is replaced by a stochastic model byadding a noise term in the source. The analytic solution of the resulting stochasticintegral equations are found using the Ito formula.