Estimation of air velocity for a high velocity spinning projectile using transerse accelerometers

In this article, we propose a method to estimate the velocity of a projectile from strapdown transverse accelerometers. The ballistic projectile under consideration has a high velocity and a high spin rate. The transverse accelerometers measure the aerodynamics forces in a frame that is oscillating due to the pitching and yawing motion. We exploit the linearized pendulum-like equations of motion of the rotation dynamics to determine the frequencies contained in the spectrum of the measurements. Analytically, we show that three frequencies are present, the expressions of which explicitely contain the air velocity. Further, it is shown that, for the most part of the flight, only one frequency is truly visible. Extracting the value of this frequency from accelerometer signals can be performed over short time windows with a super resolution algorithm. Eventually the velocity can be estimated from an inversion of the analytic formula of the theoretical value of the frequency obtained from the aerodynamic model of the projectile. Realistic simulation results are presented, stressing the relevance of the approach, along with perspectives on the treatment of real in-flight data.