Unstable Aircraft Parameter Estimation Using Neural Partial Differentiation

Abstract

An approach based on neural partial differentiation is suggested, to overcome the numerical problems faced by classical methods, for the parameter estimation of an aerodynamically unstable aircraft. Theoretical analysis of the neural modeling, the parameter estimation process, and the nature of the estimates pertaining to unstable aircraft dynamics using the neural partial differential method, are discussed. Equation for the relative standard deviation, which is equivalent to the Cramer-Rao bound in the method like output error approach, is derived using the neural partial differential method and verified through numerical simulation. The aerodynamic derivatives are derived for the simulated and real longitudinal flight data of an unstable aircraft, and the estimates obtained using the neural partial differentiation are compared with the classical methods such as the equation error and the output error methods. The parameter estimates from the simulated noisy data are also presented to assess and support the theoretical developments presented in this paper. The theoretical analysis and the results presented in this paper make the neural partial differential approach more reliable and widely applicable.