Method of description for the dynamics of the signal delay change in discrete time with changing aircraft position in space

Abstract

The article presents an innovative approach to the description of the aircraft range parameter in discrete time when simulating the process of its repositioning in space. A method of describing the dynamics of changes in signal delay in discrete time when the aircraft is changing its spatial position is proposed. Such a model adequately describes the change in signal delay in discrete time. The direction of estimation for the adequacy of radio signal delay change simulation in algorithms of optimum filtration is defined in accordance with the aerodynamic properties of the aircraft. Simulation of the signal delay dynamic change is carried out (it is completely described by the dynamics of change in the distance to the aircraft). The transformation stages of simulation data for the initial model in continuous time with realization of the standard Gaussian random numbers are justified. Information on the simulation data transformation taking into account the correlation matrix of discrete white noise is provided. A method of calculating the transition matrix through the Laplace transform is proposed. The scientific-applied direction of research is determined – it lies in the development of a method for the legitimate representation for the mathematical model of aircraft’s changing range in discrete time within one-dimensional space: the longitudinal and the transverse dimensions. This approach takes into account the continuous description for a system of stochastic differential equations. A comprehensive algorithm for modeling the values of discrete white noise on modern computer equipment and calculating the dynamics of the aircraft range parameter changes is proposed. This algorithm allows to correctly form the a priori information about the change of the vector parameters of the aircraft spatial position at discrete moments of time. As a result, it was shown that the use of the obtained information in the optimal filtering algorithms minimizes the error when determining distance to the aircraft and, accordingly, allows to increase the accuracy and adequacy of the signal delay simulation in discrete time. The results of this research can be used in modernization of the existing models and development of promising on-board radar stations, integrated rangefinders, systems of radio technical reconnaissance and electronic warfare systems, as well as in technical implementation of aircraft flight simulation systems.