  In areas such as finance, engineering, and science, we often face situations
that change quickly and unpredictably. These situations are tough to handle and
require special tools and methods capable of understanding and predicting what
might happen next. Stochastic Differential Equations (SDEs) are renowned for
modeling and analyzing real-world dynamical systems. However, obtaining the
parameters, boundary conditions, and closed-form solutions of SDEs can often be
challenging. In this paper, we will discuss the application of Kalman filtering
theory to SDEs, including Extended Kalman filtering and Particle Extended
Kalman filtering. We will explore how to fit existing SDE systems through
filtering and track the original SDEs by fitting the obtained closed-form
solutions. This approach aims to gather more information about these SDEs,
which could be used in various ways, such as incorporating them into parameters
of data-based SDE models.
