Evolutionary-programming-based Kalman Filter for Discrete-time Nonlinear Uncertain Systems

Some observations and improvements on the conventional Kalman filtering scheme to function properly are presented. The improvements can be achieved using the minimal principle evolutionary programming (EP) technique. A new linearization methodology is presented to obtain the exact linear models of a class of discrete-time nonlinear time-invariant systems at operating states of interest, so that the conventional Kalman filter can work for the nonlinear stochastic systems. Furthermore, a Kalman innovation filtering algorithm and such an algorithm based on the evolutionary programming optimal-search technique are proposed in this paper for discrete-time time-invariant nonlinear stochastic systems with unknown-but-bounded plant uncertainties and noise uncertainties to find a practically implementable “best” Kalman filter. The worst-case realization of the discrete-time nonlinear stochastic uncertain systems represented by the interval form with respect to the implemented “best” nominal filter is also found in this paper for demonstrating the effectiveness of the proposed filtering scheme.