Recursive Models of Randomized Processes in Foreign Intelligence Tasks. Part 1. Simplified Lower Order Models

摘要

For the state, foreign intelligence has always been a sphere of special attention. The role of foreign intelligence has grown significantly in our time when new forms of interstate conflicts appeared (network and hybrid wars, large-scale terrorist acts, systemic interference in the internal affairs of another state, etc.) and the space for their conduct became more complicated (for traditional maritime, land and airspace added a new sphere, cyberspace). Due to this, the conditions for obtaining intelligence and requirements for their processing have become more complicated. Of most interest is the context of intelligence operations, i.e. study of the potential possibilities of data processing models for financial transactions, the movement of human, material, information and other resources from the standpoint of the theory of random processes. However, the classical theory of random processes was developed for tasks when observations of an object were made at regular time intervals (for example, yield, fertility, etc.). Equidistance was implied by default. However, for reconnaissance tasks, such representation of the observed object is unacceptable, since information about it, being random, arrives at random time. We call such processes randomized, emphasizing the very randomization of the moments of receipt of intelligence. There is another important circumstance, the high dynamics of data obsolescence and the limitedness of their volume. Naturally, in this case, recurrence models are necessary that take into account both the lack of information and its «obsolescence» in the context of randomized observations. All these points are taken into account in the proposed models based on modified splines. The models presented in this work are investigated for the cases, when the moments of the appearance of the data are known exactly, or we cannot know these moments for one reason or another. Corresponding algorithms for distinguishing trends of the observed data are constructed, as well as the analyzed statistical properties of their parameters. The results of simulation are presented. In the first part of this work, rather simple models of a relatively low order are studied, while in the second part of the publication the problem is solved by construction of a model of a higher order.