Analytical synthesis of suboptimal filters by moments methods

On the basis of initial and central moments, the theory of analytical synthesis of suboptimal and modificated filters (SOF and MSOF) for differential (on manifolds) nonlinear stochastic systems (StS) is developed. The authors suppose that: ($i$) state equation includes Gaussian and Poisson noises; and ($ii$) observation equation contains Gaussian noises only. For SOF synthesis, the authors use normalized densities and for MOF, unnormalized densities. Questions of instrumental accuracy and sensitivity are discussed. The algorithms are the basis of the software tool StS-Filter 2018. Two test examples for angular information-measurement system are given. Some generalizations are mentioned.