Title :
Sliding mode filtering for polynomial states over polynomial observations
Author :
Basin, Michael ; Rodriguez-Ramirez, Pablo
Author_Institution :
Dept. of Phys. & Math. Sci., Autonomous Univ. of Nuevo Leon, San Nicolas de los Garza, Mexico
Abstract :
In this paper, the mean-square and mean-module filtering problems for polynomial system states over polynomial observations are studied proceeding from the general expression for the stochastic Ito differentials of the estimate and the error variance. The paper deals with the general case of nonlinear polynomial states and observations. As a result, the Ito differentials for the estimates and error variances corresponding to the stated filtering problems are first derived. The procedure for obtaining an approximate closed-form finite-dimensional system of the sliding mode filtering equations for any polynomial state over observations with any polynomial drift is then established. In the examples, the obtained sliding mode filters are applied to solve the third order sensor filtering problems for a quadratic state, assuming a conditionally Gaussian initial condition for the extended second order state vector. The simulation results show that the designed sliding mode filters yield reliable and rapidly converging estimates.
Keywords :
Gaussian processes; filtering theory; mean square error methods; multidimensional systems; nonlinear systems; polynomials; variable structure systems; vectors; Gaussian initial condition; closed-form finite-dimensional system; error variance; estimate; mean-module filtering problems; mean-square; nonlinear polynomial system states; polynomial drift; polynomial observations; second order state vector; sliding mode filtering; stochastic Ito differentials; third order sensor filtering problems; Conferences; Differential equations; Indium tin oxide; Mathematical model; Polynomials; Vectors;
Conference_Titel :
Variable Structure Systems (VSS), 2012 12th International Workshop on
Conference_Location :
Mumbai, Maharashtra
Print_ISBN :
978-1-4577-2066-6
Electronic_ISBN :
2158-3978
DOI :
10.1109/VSS.2012.6163518