Zero effort miss formulation for longer range targeting

For long range targeting applications with significant ballistic coasting after burnout, determination of the zero effort miss must account for the different gravitational accelerations experienced by each vehicle. A new expression of relative motion is derived using the Newton's Binomial Theorem and Modern Control Theory, then the final time at miss is calculated by Newton iteration, and a new predicted method of zero effort miss is obtained. In order to validate the fidelity of proposed zero effort miss, several methods of determination of the zero effort miss are compared with proposed method by simulation. Simulation results show that zero effort miss formulation better than other methods and has obvious advantages of the application.