On the predicted errors of atmospheric guidance laws

Abstract

PurposeThe purpose of this paper is to develop a novel solution for the predicted error and introduces a systematic method to develop optimal and explicit guidance strategies for different missions.Design/methodology/approachThe predicted error is derived from its basic definition through analytical dynamics. The relations are developed for two classes of systems. First, for systems in which the acceleration commands are truncated at a specified time. Second, for systems in which the corrective maneuvers are cut off at a specified time. The predicted error differential equation is obtained in a way that allows for derivation of several optimal and explicit guidance schemes.FindingsThe effect of tangential acceleration in conjunction with autopilot dynamics can be realized in guidance gain and the predicted error. The differential equation of velocity‐to‐be‐gained is obtained assuming the gravitational acceleration to be given as a vectorial function of time. The relations for different velocity profiles are obtained and discussed including the effective navigation ratio.Research limitations/implicationsThe guidance/control system is modeled as a linear time‐varying dynamic and of arbitrary‐order. The gravitational acceleration is assumed as a given vectorial function of time.Practical implicationsThe presented schemes are applicable to both midcourse and terminal guidance laws with/without velocity constraints.Originality/valueProviding a new analytical solution of predicted errors with final position and velocity constraints and their differential equations considering the thrust/drag acceleration and autopilot dynamics in the presence of gravity.

Approximate solution of two-body problem using weighted combination of linear and inversely cubic gravity models

“…Several papers in guidance theory dealt with the calculation of predicted errors in spherical-earth model. The predicted errors in position and velocity are two important parameters in guidance theory, which are known as zero-effort miss (ZEM) distance and zero-effort velocity error (ZEV), respectively [13,14]. The predicted position vector without further corrective maneuver (ZEM) may be solved using approximate methods, in relative or absolute coordinates.…”