Maximum Likelihood optimal estimator of non-autonomous nonlinear dynamic systems

The Joint Maximum Likelihood criterion is used to derive the optimal estimator for non-autonomous nonlinear dynamic systems. 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.