Estimation of the Velocity of a Projectile Using Radial Accelerometers—validation on 155 Mm Free Flight Test

Abstract

This paper addresses the problem of velocity estimation for a 155 mm projectile. Indeed, to correctly feed the guidance and control algorithms of such a guided munition, it is essential to estimate its speed autonomously (without any external system) onboard and in real-time. Knowledge of the velocity (and thus the Mach number) is required to infer the aerodynamic coefficients governing its dynamics. From the analysis of the frequencies present on one of the radial accelerometers, and from a reduced 6DOF model describing the epicyclic rotation of the shell, we are able to estimate the velocity of the ammunition. The roll speed can be determined from magnetometers. For frequency estimation, we employ a subspace method of the Pisarenko type, relying on the auto-correlation matrix of the accerelometer signal. This matrix is estimated from samples and its dominant eigenvalues are related to the precession and nutation frequencies. In turn, the velocity can be estimated from the analytical values of the epicyclic motion. In this paper, we offer an efficient method to estimate the velocity of an artillery shell in free-flight, using only embedded sensors. The next step will be to use these results to improve the estimation of the projectile’s attitude and position.