A Novel Method for Estimating Pitch and Yaw of Rotating Projectiles Based on Dynamic Constraints

Abstract

This paper addresses the difficult problem of measuring the attitude of a high-spinning projectile and presents a novel method for estimating the pitch and yaw angles of the projectile in flight. The method is based on analysis of the external moment of the rotating projectile during flight and theoretical derivations obtained from the dynamics’ equations. First, the principle of zero-crossing method is introduced, which explains the process of geomagnetic azimuth and roll measurements by the non-orthogonal geomagnetic sensor combination. Then, the dynamics constraint equations between the Euler angles and flight-path angle, trajectory deflection angle of the projectile are derived using the dynamics equations of the projectile rotating around the centroid, and analysis of the flight characteristics of the projectile in stable flight. Next, the spatial orientation relationship between pitch, yaw angles and magnetic azimuth is established based on the physical principle of geomagnetic azimuth. Finally, the pitch and yaw angles are estimated using the unscented Kalman filter (UKF), with the dynamics constraint equations serving as the driving equations. In the UKF prediction stage, the Runge-Kutta method is used to discretize the state equation that improves the prediction accuracy. Simulation results show that the proposed method can be used to accurately calculate the pitch and yaw angles, and results of experimental data processing also verify the feasibility of the proposed method for real-world applications.