Noise-Induced Miss Distance Analysis of First-Order Explicit Guidance Law

This study presents the miss distance analysis of the first-order explicit guidance law due to seeker noise using the adjoint method. for this purpose, linearized equations are utilized and the adjoint model is developed. then the first-order equations are obtained and converted into nondimensional ones. the analysis is carried out for different values of the power of the alpha function, defined as the time decrease rate of the zero-effort miss distance to unit control input. the unity power gives the first-order optimal guidance strategy, minimizing the integral of the square of the commanded acceleration during the total flight time. the seeker and control system is assumed as a fifth-order binomial transfer function. due to computational error and stability consideration, the effective navigation ratio is kept constant for very small time-to-go until intercept, and its effect on the miss distance is also investigated. finally, approximate formulas are obtained using curve fitting method for rms miss distance due to seeker noise.