Узагальнена математична модель виконання вогневих задач екіпажем танка

Abstract

To determine the rational parameters of the sightseeing complex of armored vehicles, it is necessary to design a mathematical model capable to account for the process of target reconnaissance and possibility to determine the expected increase in combat effectiveness of weapons samples, as well as the impact of full range of natural and artificial obstacles.
In a number of scientific works in recent years, mathematical models have been developed to evaluate information processes for the samples of armored armament, though without taking into account the influence of external factors on the process of reconnaissance and destruction of the target. Also, these models do not allow one to estimate the expected increase in combat effectiveness because they do not take into account the characteristics of modern multichannel sightseeing systems with the integration of information received from different channels, environmental parameters. A Markov analytical model was proposed in the literature to describe the functioning of the tank armament complex. This model serves as a basic platform to develop more advanced models by detailing certain states and transitions between them.
In this paper we propose a mathematical model of fire tasks performed by a tank crew equipped with a multi-channel sightseeing complex, in which the state of observation considered in previous publications is separated into two states: march and actual observation, and the state of data acquisition into three states: detection, recognition and identification of enemy targets. The corresponding states involve completely different independent risks and, as a consequence, different probabilities of the corresponding transitions. Thereby, they should be considered as separate states. Namely, the developed mathematical model of fire tasks by the tank crew includes the following sequence of states: the initial state of the sample of armored weapons in the area of concentration, march from the place of concentration to the intended place of battle, the beginning of observation, detection, recognition and identification of the target, combat application of the armament, defeat/nondefeat of the enemy target, which form the Markov chain.
The stationary probability distribution obtained as the solution of the equation on eigenvectors and eigenvalues gives the probability of performance of the fire task by the tank crew as a function of probabilities of transitions between the corresponding states.