Optimal Joint Maximum Likelihood based Estimator for Discrete Nonlinear Dynamic Systems

The Joint Maximum Likelihood (JML) criterion is used to derive the optimal recursive-iterative estimator for discrete nonlinear dynamic systems. For linear systems this approach constitutes, in its recursive form, the structure of the Kalman Filter. The JML approach to estimation of nonlinear systems can be solved by batch formulas at the cost of extensive computational effort, i.e. with each new measurement the for derivation of the new estimate all available data has to be processed. This paper presents recursive-iterative implicit closed form solution that gives formulas of the optimal estimator, i.e. gives the value of the optimal estimated state. The computation of the estimator's gains needs the solution of non-symmetric Difference Matrix Riccati Equation (DMRE).