Development of the numerical differentiation method for approximating pitch acceleration using sensor fusion approach

In this paper, a novel algorithm is proposed to accurately estimate pitch acceleration that is crucial for moment coefficient estimation of the mathematical model of aircraft and control design in the presence of measurement noise. The angular velocity of the body as well as the Euler angles provided by the navigation system are used to interpolate the attitude trajectories using an algorithm based on the Hermite-spline polynomial. By differentiating the resultant trajectory function, the angular acceleration can be estimated accurately. This paper also analyzes a well-known method-Poplavski method based on polynomial regression, developed by the Russian scientist B.K. Poplavski to estimate derivatives. The simulation results obtained from the novel algorithm are compared with those obtained using the Poplavski method. The results verified that the novel algorithm that uses both pitch angle and angular velocity provides better accuracy in estimating pitch acceleration than the Poplavski method does, regardless of the sampling rate, which is very important in numerical differentiation and the noise level.