Optimal Filtering for Polynomial Systems over Switching Delayed Observations

The problem of designing an optimal filter for a class of nonlinear systems confused with white Gaussian noise over linear time delayed observations is presented in this paper. Output observations may or may not experience sensor delays due to a random variable which is modeled as a Bernoulli distributed one that takes the quantities of zero and one. A closed form of this filter is obtained by expressing the conditional expectation of polynomial terms as a function of its expectation and covariance matrix. As a particular case, finite-dimensional filtering equations are obtained for a third degree polynomial function. Numerical simulations are performed on an induction motor in order to show the effectiveness of proposed filter.