Root-mean-square filtering of the state of polynomial stochastic systems with multiplicative noise

Some results obtained by the present author in the field of designing the finitedimensional root-mean-square filters for stochastic systems with polynomial equations of state and multiplicative noise from the linear observations were overviewed. A procedure to derive the finite-dimensional system of approximate filtering equations for a polynomial arbitrary-order equation of state was presented. The closed system of filtering equations for the root-mean-square estimate and covariance matrix error was deduced explicitly for special cases of linear and quadratic coefficients of drift and diffusion in the equation of state. For linear stochastic systems with unknown parameters, the problem of joint root-mean-square state filtering and identification of the parameters from linear observations was considered in the Appendix.