Miss Distance Analysis of Proportional Navigation for High-Order Binomial Control Systems in Presence of Noise and Target Maneuvers

In this paper, the miss distance analysis of proportional navigation for high-order binomial guidance and control system is presented in presence of seeker noise using normalized adjoint method. In this analysis, the effects of effective navigation ratio and system order up to 30 are studied due to heading error, target maneuvers, and seeker noise. Numerical solutions for the cases of initial heading error, target with constant, linear, and parabolic maneuvers show a quasi-asymptotic behavior with respect to system order. In addition, the quasi-asymptotic behavior occurs for higher system order due to seeker noise. The values for the infinity's order system are obtained numerically and analytically. Based on the analysis and its assumptions, an order of 8 to 10 is suggested for miss distance analysis of a binomial guidance and control system.