Mathematical Model of Satellite-Inertial Mobile Computational Gravimetry

Abstract

The article proposes a mathematical model of a hybrid system installed on board of a moving object and represented by an inertial sensor of the vector of specific forces — a three-component newtonometer with orthogonal sensitivity axes and a network of receivers of a navigation satellite system (HSS). The purpose of this hybrid system is the temporal estimations of the nearEarth gravitational field on the trajectory of the object. Within the Newtonian mechanics the possibility of choosing an inertial reference system with a beginning at the center of mass of the Earth is assumed; сomplementary to the PZ-90 (Russia) and WGS-84 (USA) standards, the following are introduced: 1) an ellipsoidal (geodesic) coordinate system, rigidly connected with the solid Earth; 2) two movable accompanying right-angled trihedrals with a common origin as a point whose movement forms the trajectory of the object; the instrument one, is rigidly connected with the object as a solid body, and is thus freely oriented, other one are geographic, and permanently oriented to the cardinal points (East, North, Zenith). In the presentation of kinematics, attention is drawn to the fact that the variability of the absolute linear velocity in inertial space explained by the motion of an object relative to solid Earth and its own rotation is characterized by rotational vectors of relative and portable velocities which identify the vectors of relative and portable angular rotational velocities of the undeformable geographic trihedron and are represented projections on its axis. The causality of the trajectory is determined by Newton’s second law; in projections on the axis of the moving geographic trihedron, component-wise recording of the equations of dynamics is performed, which are resolved with respect to the components of the strength of the gravitational field. It is noted that the previous article by the authors is devoted to the problem of a high-precision estimate of the kinematic parameters of motion equations. In such a context it is indicated that direct calculation of the gravitational field strength requires the convertting of Newtonometer measurements from the instrument trihedron to the geographic one. The required linear transformation for this is constructed considering the possibilities of multiposition of the NSS object. A computational experiment is described and some of its results are presented.