Analytical Solution of Missile Terminal Guidance

Abstract

A new guidance law, which combines pursuit guidance and proportional navigation is proposed. This guidance law depends on two parameters that determine the relative importance of pursuit guidance and proportional navigation. Numerical simulations of the nonlinear equations of motion suggest that the parameters of this law can be chosen to reduce the peak value of the missile acceleration. When the engagement ends in a tail chase, and linearization is valid, the linearized equations of motion lead to a confluent hypergeometric equation. This equation is solved in closed form, in the general case where the target performs maneuvers such that its heading angle is a polynomial function of time. The analytic solution based on linearization and the numerical simulation of the nonlinear equations show good agreement.

Nonlinear Multiple Integrator and Application to Aircraft Navigation

“…The problem of the multiple integrals is that of estimating the number I n (a) = t 0 · · · s 0 n a (σ ) dσ · · · dτ n with [0, t] a finite time interval. Obtaining the positions and velocities from the acceleration measurements is crucial for several kinds of systems with correct and timely performances, such as the missile flying control systems [1] and the antilock braking systems [2]. Integrals play the important roles in the inertial navigation system (INS).…”