Optimal discrete nonlinear filters of the object's order and their Gaussian approximations

We consider the problem of devising effici ent algorithms of estimating the current state of nonlinear stochastic dynamical systems by observing their outputs. We analyze the shortcomings of existing discrete Markov filtering approaches. For a previously suggested nonlinear filter of optimal structure and a new two-step filter, whose orders equal the number of components of the estimated state vector, we give procedures for both exact and approximately-analytic computation of their structural functions. We consider a way to enhance the precision of the designed filters with suboptimal structure by optimizing their auxiliary parameters once again. We compare the suggested and known estimation algorithms.