Multi-Dimensional Motion Parameter Estimation of a Rotating Object Based on Orbital Angular Momentum

This paper considers the multi-dimensional motion patterns of a rotating object and presents methods to estimate its motion parameters, including the rotational direction, angular velocity, motion trajectory, and inclination angle, using orbital angular momentum. Firstly, the rotational direction and the angular velocity are analyzed and estimated from the aspects of time domain and frequency domain, respectively. In the time domain, the rotational direction is inferred by analyzing phase variations based on the angular momentum theorem. Then, an iterative phase retrieval algorithm is introduced to obtain the angular velocity. In the frequency domain, a dynamic sparse step-size matching algorithm is developed to determine the rotational direction and the angular velocity simultaneously. Secondly, an analytical equation for the electric field is derived to determine the translational motion, facilitating analysis of the motion trajectory. Moreover, an objective function that incorporates polarizations, reflection coefficients, and inclination angle is established. A weighted iterative gradient algorithm is then applied to solve this function, ultimately obtaining the inclination angle. The results demonstrate that the estimated values agree well with the theoretical values. Both the rotational direction and the angular velocity are accurately estimated. The translational motion exhibits an error of 6.33%, while the error in the inclination angle is 2.6%. These findings indicate that the proposed methods offer reliable approaches for evaluating the multi-dimensional motion parameters of a rotating object. The methods also show potential for engineering applications, such as drone-based surveillance and industrial instrument monitoring involving rotating components.