Gaussian process-based state derivative estimator with temporal input in incremental flight control design

In this paper, a state derivative estimation technique is proposed using a derivative of Gaussian process regression method and applied to an incremental dynamics-based controller. The state derivative estimates of interest are with respect to time, and to obtain them, the temporal index array is used for Gaussian process state input. Using a Gaussian process, assumptions such as numerical differentiation of the state, parametric basis functions common in adaptive approaches, and the use of upper-bound information of the state derivative commonly used in robust methods are avoided. The proposed approach is compared with the backward difference formula (BDF) differentiator, first-order low-pass filter, second-order low-pass filter, and high-order sliding mode differentiator. Monte Carlo simulation with 1000 runs is performed under four different noise level measurement scenarios. The proposed Gaussian process-based differentiator with temporal index input resulted in better robustness and adaptability in state derivative estimation with similar or better performance.