Quadrotor System Identification Using the Multivariate Multiplex B-Spline

A novel method for aircraft system identification is presented that is based on a new multivariate spline type; the multivariate multiplex B-spline. The multivariate multiplex B-spline is a generalization of the recently introduced tensor-simplex B-spline. Multivariate multiplex splines obtain similar or better approximation accuracy using less parameters (B-coefficients) than standard multivariate simplex B-splines which are currently used for aircraft system identification. The multiplex spline allows the user to incorporate a-priori knowledge of the modelled system in the definition of the model structure. In particular, while the standard simplex B-splines use a multi-dimensional triangulation in which all dimensions are coupled, the multiplex spline enables the user to decouple specific model dimensions based on expert knowledge of the system. The new method is used to approximate a 4-dimensional nonlinear quadrotor inflow dataset. The results show that the multiplex B-spline obtains a relative root mean square error of 0.672% using 1440 B-coefficients. This compares favorably to results obtained with the standard 4-dimensional simplex B-spline on the same dataset, which resulted in an relative root mean square error of 1.608% using 1540 B-coefficients.