Learning augmented recursive estimation for uncertain nonlinear dynamical systems

This paper describes a learning augmented recursive estimation approach for nonlinear dynamical systems having unmodeled nonlinearities. Utilizing a passive spatially-localized learning system, an approximation of the unknown nonlinearity is synthesized online, based on state and parameter estimates from a nonlinear recursive estimator (an adaptive form of the extended Kalman filter). The learned model of the nonlinearity is used, in turn, to improve the performance of the recursive estimator. We demonstrate the approach on a second-order, mass-spring-damper system, where the spring stiffness is a nonlinear function of position. Simulation results indicate that, relative to more traditional adaptive estimation schemes, markedly improved estimation performance can be achieved.