Оптимальная нелинейная фильтрация оценок информационного воздействия в стохастической модели информационного противоборства

Abstract

A computationally efficient algorithmic solution to the problem of optimal nonlinear filtering of information impact estimates in a generalized stochastic model of information warfare is developed in the article. The formed solution is applicable in the presence of heterogeneous rules for measuring the parameters of the information warfare model, on the basis of which a pair of systems of stochastic differential equations is formed. According to the criterion of maximum likelihood according to the determined evolution of the a posteriori conditional probability density function at a given observation interval, the evaluation of the information impact in the optimal nonlinear filtering model is performed. Taking into account the probability addition theorem, as the probability of the sum of two joint events, the density functions of which are established from the numerical solution of the corresponding robust Duncan-Mortensen-Zakai equations, finding a posteriori conditional probability density function at a given time is performed. For the first event, it is assumed that the first system of stochastic differential equations is the equation of state, and the second – is the equation of observation. For the second event, their definition is set in reverse order. The solution of the robust Duncan-Mortensen-Zakai equation is carried out in the formulation of the Galerkin spectral method when sampling the observation interval into subintervals and reducing the initial solution to a numerical recurrent study of the sequence of subtasks using the so-called Yau-Yau's algorithm, which assumes an estimate of the probability measure from the solution of the direct Kolmogorov equation with its subsequent correction by observation. To highlight the features of the algorithmic implementation of the compiled solution, an algorithm for optimal nonlinear filtering of information impact estimates in a generalized stochastic model of information confrontation when specifying the listing of the function implementing it, which is represented by a pseudocode, has been formed. To identify the preference of the compiled algorithmic solution for optimal nonlinear filtering of information impact assessments, a series of computational experiments on large-volume test samples was carried out. The result of the information impact assessment obtained by the proposed algorithm is compared with the determined solution: 1) by the average sample values from the observation models; 2) by an ensemble extended Kalman filter; 3) by a filtering algorithm involving a numerical study of the Duncan-Mortensen-Zakai equation. According to the conducted a posteriori study, quantitative indicators that establish the gain of the compiled algorithm and the limits of its applicability are highlighted.