Online aerodynamic model identification using a recursive sequential method for multivariate splines

Avoiding high computational loads is essential to online aerodynamic model identification algorithms, which are at the heart of any model-based adaptive flight-control system. Multivariate simplex B-spline methods are excellent function approximation tools for modeling the nonlinear aerodynamics of high-performance aircraft. However, the computational efficiency of the multivariate simplex B-spline method must be improved in order to enable real-time onboard applications, for example, in adaptive nonlinear flight-control systems. In this paper, a new recursive sequential identification strategy is proposed for the multivariate simplex B-spline method aimed at increasing its computational efficiency, thereby allowing its use in onboard system identification applications. The main contribution of this new method is a significant reduction of the computational load for large-scale online identification problems as compared to the existing multivariate simplex B-spline methods. The proposed method consists of two sequential steps for each time interval and makes use of a decomposition of the global problem domain into a number of subdomains, called modules. In the first step, the B-coefficients for each module are estimated using a least-squares estimator. In the second step, the local B-coefficients for each module are then smoothened into a single global B-coefficient vector using a linear minimum mean-square errors estimation. The new method is compared to existing batch and recursive multivariate simplex B-spline methods in a numerical experiment in which an aerodynamic model is recursively identified based on data from a NASA F-16 wind-tunnel model.