Mathematical Models and Algorithms of the Onboard Multi-Agent Integrated Motion Determination System

Abstract

The article describes the methodological and technological aspects of the numerical synthesis of an integrated multifunctional system for assimilation of navigation information delivered by spatially spaced on-board sensors for satellite positioning of a moving object (technological platform — TP) and three-component apparent acceleration vector meters combined with them — 3D-newtonometers. This is main formed image of the considered real physical system. Modern methods and practices of systems for monitoring and controlling moving objects are essentially focused on deep mathematically formalized representations of this subject area. In the light of such ideas, one should consider the content of the article on the problem of complementarity of two types of information that are different in physical nature and on the prospects for such a study. The main model mathematically formalized constructions follow the fundamental Kalman paradigm "state — measurement" and focused on the numerical solution of ill-posed inverse problems of determining the motion of a TP as a rigid body with the ability to work in real time. An ellipsoidal system was chosen as the base coordinate system, in addition other coordinate systems were introduced as well, which inevitably determine the solution of problems due to the formed set of corresponding transformations. Algorithms are presented for calculating the kinematic parameters of the trajectory and spatial orientation of the TP, the characteristics of the causality of motion — forces and moments, and also numerical solutions for problems of mobile vector gravimetry and gravitational gradiometry are proposed. An algorithm for simulating onboard multipositioning has been developed, which determines the conduct of verifying computational experiments. Some of their results are given in the article. The software package that implements the simulation algorithms and solutions is developed using Julia language and allows to obtain a complete set of data on the state of all systems at any discrete time point of the simulator.