Prediction and Control of Projectile Impact Point using Approximate Statistical Moments

TL;DR

This paper develops a stochastic model for projectile trajectory prediction under environmental noise, using approximate statistical moments to efficiently estimate impact point distribution and design control laws for accurate targeting.

Contribution

It introduces a method to approximate projectile impact point moments using a subset of statistical moments, improving prediction and control in noisy environments.

Findings

Selected moments reliably estimate impact point mean and standard deviation.

The control law effectively reduces impact point error.

The approach manages nonlinearities with mean-field approximation.

Abstract

In this paper, trajectory prediction and control design for a desired hit point of a projectile is studied. Projectiles are subject to environment noise such as wind effect and measurement noise. In addition, mathematical models of projectiles contain a large number of important states that should be taken into account for having a realistic prediction. Furthermore, dynamics of projectiles contain nonlinear functions such as monomials and sine functions. To address all these issues we formulate a stochastic model for the projectile. We showed that with a set of transformations projectile dynamics only contains nonlinearities of the form of monomials. In the next step we derived approximate moment dynamics of this system using mean-field approximation. Our method still suffers from size of the system. To address this problem we selected a subset of first- and second-order statistical moments and we showed that they give reliable approximations of the mean and standard deviation of the impact point for a real projectile. Finally we used these selected moments to derive a control law that reduces error to hit a desired point.