normalized miss distance

In this paper, the effect of system time delay on the miss distance of proportional navigation guidance law is studied for high-order binomial guidance and control systems. For this purpose, a linearized model is utilized in one dimension. The normalized miss distance due to heading error (HE), step, ramp, and parabolic target maneuvers, and seeker noise is computed using normalized adjoint equations. The glint, range-independent, and (semi-) active range-dependent noises are considered for the seeker, and the results are verified by straight-forward method. Moreover, the effects of system time lag, system time constant, effective navigation ratio, system order up to 30 in proportional navigation miss distance are also investigated. An extremum effective navigation ratio is also obtained to minimize the worst case miss distance with respect to the final time. Furthermore, approximate miss distance formulas are presented based on worst case analysis on final time using curve fitting for mentioned miss distance sources. Finally, the approximate formulas of steady state nondimensional coefficients due to seeker noise in terms of effective navigation coefficient, for example for system orders of 5 and 10, are obtained.

In this paper, the effect of non-minimum phase control system on the miss distance of a class of one-dimensional guidance law due to initial heading error and also constant and time-varying target maneuvers (including ramp and sinusoidal) is presented. The guidance and control system dynamics is modeled by a fifth-order transfer function with acceleration limit and radome effect. More precisely, each of the seeker and noise filter is taken as a first-order transfer function. The control system and airframe are modeled by a third-order non-minimum phase one. Miss distance analysis is made by using normalized governing equations and plotting normalized curves, resulting in useful curves for parametric study specially the effect of zero location of airframe dynamics for analysis, modification, and design of a class of linear and nonlinear guidance laws.