Method of spatial cross-coupling elimination of control system channels for object guidance using two TDoA measurements

Abstract

The problem of object guidance to the target point using two time difference of arrival (TDoA) measurements obtained from three navigation positions is considered. A general equation that describes a kinematic trajectory of the object along the line of intersection of two object position hyperboloids corresponding to the two TDoA measurements is obtained. It has been found out that the kinematic trajectory of the object lies in a plane perpendicular to the plane of three navigation positions. This kinematic trajectory can be described by the conic equation in the general case, and in the range of position parameters used in practice this equation yields a hyperbola. A method of elimination of object spatial cross-coupled link between control system channels, consisting in a special projection of accelerations of the object during their transformation from the measuring coordinate system to the wind coordinate system is described. This made it possible to implement object control in TDoA navigation system with three navigation positions only using two identical expressions of the kinematic link obtained for a planar case without full spatial equation for kinematic link of the object’s motion and TDoA information. A computer simulation of the object guidance to a target point in space using two TDoA measurements was performed to check the accordance of the acceleration design expressions, which produced a positive results of viewed method. The approach described in the article makes it possible to implement object guidance using TDoA navigation system if available only three of four required navigation positions.