Practical Assessment of Real-Time Impact Point Estimators for Smart Weapons

Abstract

There are numerous ways to estimate the trajectory and subsequent impact point of a projectile. Some complex methods are highly accurate and require a lot of input data while others are fairly trivial and less accurate but require minimal input data. Projectile impact point predictors (IPPs) have three primary error sources: model error, parameter error, and initial state error. While model error typically shrinks as model complexity increases, parameter and initial state errors grow with increasing model complexity. Since all input data feeding an IPP are uncertain to some level, the ideal IPP for an overall situation is not clear cut by any means. This paper examines several different projectile IPPs that span the range of complex nonlinear rigid projectile models to simple vacuum point mass models with the intent to better understand relative merits of each algorithm in relation to the other algorithms and as a function of parameter uncertainty and initial state error. Monte Carlo simulation is employed to compute impact point statistics as a function of the range to the target for an indirect fire 155-mm spin stabilized round. For this specific scenario, results indicated neglecting physical phenomena in the formulation of the equations of motion can degrade impact point prediction, especially early in the flight. Adding uncertainty to the parameters and states induces impact point errors that dominate model error contributions. Impact point prediction errors scaled linearly with parameter and state errors. All IPPs investigated converged to the actual impact point as the time at which the estimate took place approached the time of impact.