Real-time projectile motion trajectory estimation considering air resistance of obliquely thrown object using recursive least squares estimation

Abstract

This paper uses a recursive least squares method to estimate the projectile motion trajectory of an object in real time. The equations of motion of the object are obtained considering the air resistance which occurs in the actual experiment environment. Because these equations consider air resistance, parameter estimation of nonlinear terms is required. However, nonlinear recursive least squares estimation is not suitable for estimating trajectory of projectile in that it requires a lot of computation time. Therefore, parameter estimation for real-time trajectory prediction is performed by recursive least square estimation after using Taylor series expansion to approximate nonlinear terms to polynomials. The proposed method is verified through experiments by using VICON Bonita motion capture system which can get three dimensional coordinates of projectile. The results indicate that proposed method is more accurate than linear Kalman filter method based on the equations of motion of projectile that does not consider air resistance.