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.