Orthogonal supoptimal filters for nonlinear stochastic systems on manifolds

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