State estimation for nonlinear dynamic systems using Gaussian processes and pre-computed local linear models

State estimation of nonlinear dynamic systems is an important problem in practice. This paper proposes a recursive state estimation method for nonlinear dynamic systems using Gaussian processes (GP) and pre-computed local linear models. Gaussian processes exhibit remarkable learning, or nonlinear regression capabilities from measurement data. The incorporation of pre-computed local linear models reduces the amount of data required and improves the regression performance of the GP. Based on such an improved GP model for nonlinear dynamic systems, a recursive Bayesian filtering method is implemented for the estimation of the unknown states of the system. Simulations on an aircraft benchmark model demonstrate that the proposed method is capable of estimating the unknown angle of attack of the aircraft, and the existence of the local linear models significantly improves the estimation performance of the filter. This method is especially useful in a control systems design context in which local linearisations of nonlinear dynamic systems are usually readily available.