State estimation for stochastic polynomial systems with switching in the state equation

Abstract

The problem of designing a mean-square filter has been studied for stochastic polynomial systems, where the state equation switches between two different nonlinear functions, over linear observations. A switching signal depends on a random variable modelled as a Bernoulli distributed sequence that takes the quantities of zero and one. The differential equations for the state estimate and the error covariance matrix are obtained in a closed form by expressing the conditional expectation of polynomial terms as functions of the estimate and covariance matrix. Finite-dimensional filtering equations are obtained for a particular case of a third-degree polynomial system. Numerical simulations are carried out in two cases of switching between different linear and second degree polynomial functions.