Abstract
This paper presents a new approach for state estimation problems. It is based on the representation of random variables using stochastic functions. Its main idea is to expand the state variables in terms of the noise variables of the system, and then estimate the unnoisy value of the state variables by taking the mean value of the stochastic expansion. Moreover, it was shown that in some situations, the proposed approach may be adapted to the determination of the probability distribution of the state noise. For the determination of the coefficients of the expansions, we present three approaches: moment matching (MM), collocation (COL) and variational (VAR). In the numerical analysis section, three examples are analyzed including a discrete linear system, the Influenza in a boarding school and the state estimation problem in the Hodgkin-Huxley's model. In all these examples, the proposed approach was able to estimate the values of the state variables with precision, i.e., with very low RMS values.