Feasibility Analysis of Numerical Integration Techniques in Onboard Flight Control Computer for Impact Point Prediction

The free-flight of a ballistic trajectory has been discussed in literature and closed-form solutions for the impact point i.e., down range, cross range and the time of flight presented and termed as Explicit Guidance Equations. However, these approximate analytical expressions have been developed by making certain assumptions and are accurate as long as those assumptions hold. Certain parameters such as atmospheric drag on the re-entry vehicle cannot be predicted or modelled accurately. Moreover, the aerodynamic forces acting on the body depend on the vehicle configuration. To cater for such uncertainties in the explicit guidance equations, implicit correction terms are added which are computed offline about the nominal trajectory profile. These correction terms are valid for a limited perturbation about the re-entry point. Furthermore, if there is an instantaneous change of target during flight, then the accurate solution may only be obtained through numerical integration of the governing equations of motion describing the dynamics of the system rather than the explicit guidance equations. This paper discusses a few variable adaptive step-size numerical methods for the solution of ordinary differential equations posed as initial value problem and presents a feasibility analysis in terms of accuracy as well as execution time. The simulations have been performed on MATLAB and the results from various methods have been compared. Although, numerical integration techniques are considered to be computationally expensive and require high processing power, however, considering the high-speed processors of today and by looking at the simulation results, the onboard computation requirements seem to be quite feasible.