Maximum likelihood optimal estimator of continuous nonlinear dynamic systems1

The Joint Maximum Likelihood criterion is used to derive the optimal estimator for continuous nonlinear systems with nonlinear dynamics and measurement. The solution is explicit and gives recursive formulas of the optimal estimator. The computation of the estimator´s gains needs the solution of non-symmetric Differential Matrix Riccati Equation (DMRE). For linear systems this solution constitutes the structure of the Kalman Filter.