Optimal filtering of stochastic systems with state-dependent noises: The exact dynamics

This paper develops the exact dynamics for the optimal filtering of continuous-time (nonlinear) stochastic systems with state-dependent noises. They are derived based on the duality principle between maximum likelihood estimation and optimal control theory proposed in Surya (2024) as a generalization that of Mortensen (1968). The results show that the heteroskedasticity in the measurement noise changes both the dynamics of state estimator and the covariance matrix.