Nonlinear filtering theory

Nonlinear filtering theory involves estimating the true state of a system that changes over time when measurements are noisy or imperfect. Unlike linear filtering, which assumes straightforward relationships, nonlinear filtering accounts for complex, real-world dynamics where changes and observations are not proportional or directly related. It uses mathematical models to update predictions based on new data, helping us accurately track and predict the system's behavior despite uncertainties. This approach is essential in fields like robotics, navigation, and financial modeling, enabling more reliable decision-making in complex, unpredictable environments.