Analysis of the Effects of Numerical Differentiation Methods on the Estimation of Longitudinal Stability and Control Derivatives of the Aircraft Mathematical Model

The estimation of the longitudinal stability and control derivatives of aircraft mathematical model was performed using the least square method, which requires the use of numerical differentiation. For the purpose of approximating the derivatives of pitch rate, the numerical differentiation methods such as: forward difference method, backward difference method, central difference method, combination of three finite difference methods “gradient” and Poplavsky method are applied. Based on the results that demonstrate the advantages and disadvantages of each of these methods, two approaches are proposed to ensure the improvement of the accuracy of the parameters estimation. The approach proposed in this paper combines the results obtained by separately using three finite difference methods to enhance of the accuracy of parameter estimation. This approach strengthens efficiency and compensates for weaknesses due to the nature and properties of finite difference methods.