An Adaptive Derivative-free Nonlinear Kalman Filtering Approach using Flat Inputs

Abstract

The concept of flat inputs has been proved to be a valuable tool for control design if the system is nondifferentially flat. Recently, flat inputs have also found to be useful to provide efficient solutions to solve state estimation problems for these systems. However, to the best of our knowledge no studies have yet investigated the impact of incorrectly describing the noise statistics in the accuracy of state estimation for Kalman filter approaches using flat inputs. Considering such background, this paper introduces an adaptive state estimation-based control strategy in order to handle the unknown process noise covariance for observable non-differentially flat nonlinear systems as long as the internal dynamics of the system are stable. A numerical simulation of an underactuated ship was performed to demonstrate the effectiveness of the proposed adaptive method.