Aiming trajectory analysis based on ARMAX model

In this paper, the linear time invariant auto-regressive moving average exogeneous (ARMAX) process is adopted to model the aiming trajectory. Both of the vertical and the horizontal deviations are studied instead of the radius or score only. The magnitude of associated poles of the auto-regressive part whether slightly greater than one is used to determine the fairness of the proposed model. The exogeneous input is designed to model the adjustment of the deviation between the aiming point and the center of target. In other words, the normal aiming style can be modeled by the combination of these two parts. Afterwards, the moving average part is related to the muscle strength and stability of archers. The mean and variance of the drive noise of the moving average part are also calculated and utilized to justify the correctness of the proposed model. Previous study based on AR2 model can not reveal the importance of the exogeneous input, but in the paper it becomes very significant for the correctness of the proposed model. As expected, there are some similar results. However, some results show that even though the attendants are all expertise in archery, some of their data are so distinct.