Discrete-time state estimation for stochastic polynomial systems over polynomial observations

Abstract

This paper presents a solution to the mean-square state estimation problem for stochastic nonlinear polynomial systems over polynomial observations confused with additive white Gaussian noises. The solution is given in two steps: (a) computing the time-update equations and (b) computing the measurement-update equations for the state estimate and error covariance matrix. A closed form of this filter is obtained by expressing conditional expectations of polynomial terms as functions of the state estimate and error covariance. As a particular case, the mean-square filtering equations are derived for a third-degree polynomial system with second-degree polynomial measurements. Numerical simulations show effectiveness of the proposed filter compared to the extended Kalman filter.

Keywords:

• Filteringa
• polynomial systems
• nonlinear observations

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors thank for financial support the Mexican National Council of Science and Technology (CONACyT) [grant number 250611] and the Russian Foundation for Basic Research (RFBR) [grant number 18-08-01261].