A discrete Kalman filter for a class of non-linear stochastic systemsf

TLDR: In this article, a discrete (in time) Kalman filter is proposed for the estimation of {x(tk)}, which is more economical in the amount of computation and in memory storage requirements than the linearized or extended Kalman filters, or the truncated non-linear filters.

Abstract: A class of non-linear systems of the form dx=A(x)x dl + σdW, t>0, XER m , A(x)ERm×m, where W is an Rm-valued standard Wiener process ; together with an observation process given by y(tk) = Mx(tk) + v(tk), y(tk)ERp, t0<t1< … < tk< … is considered. A procedure for the discretization (in time) of the system's equation is introduced. Based on this procedure, a version of the discrete (in time) Kalman filter is suggested for the estimation of {x(tk)}. The filter proposed here proves to be more economical in the amount of computation and in memory storage requirements than the linearized or extended Kalman filters, or the truncated non-linear filters. Two examples are numerically solved.