Normal and orthogonal suboptimal filters for nonlinear stochastic systems on manifolds

For nonlinear differential stochastic systems on manifolds (MStS) with Wiener and Poisson noises, the theory of synthesis of suboptimal filters based on the normal approximation method, the statistical linearization method, the orthogonal expansions method, and quasi-moment method is developed. Exact optimal (for mean square error criteria) equations for MStS with Gaussian noises in observation equations for one-dimensional a posteriori characteristic function are derived. Special attention is paid to modified filters based on unnormed distributions. Problems of approximate solving of exact equations are discussed. Accuracy and sensitivity equations are presented. A test example for nonlinear scalar differential equation with additive and multiplicative noises is given. Some generalizations are mentioned.