S.V. Lazarenko1

1Don State Technical University (Rostov-on-Don, Russia)

1lazarenkosv@icloud.com

The Wiener-Kolmogorov theory of optimal filtration served as an incentive to overcome the problems created by the Wiener-Hopf equation. For stationary processes generated by linear differential equations, estimation equations were obtained without using the Wiener-Hopf equation, which differ primarily in the difference equation of the filtration error covariance. Despite the fact that these methods have developed independently, they are all closely related to the search for the extremum of quadratic forms. At the same time, such a synthesis of aircraft tracking filters is complicated by the lack of a priori information about the parameters of aerial target maneuvers. This led to the development of methods for solving extreme problems in conjunction with the development of procedures for restoring missing information, which was generically called adaptive filtering.

Within the framework of this approach, not a single object is considered, but a certain set of objects, each of which is assigned an abstract parameter. In addition, it is assumed that the dynamics of each object is set by a variety of changing configurable parameters (settings). Their combination is called a parameter setting strategy, which should ensure the functional purpose of the object's functioning. In the theory of statistical synthesis, settings are most often associated with the parameters of the forming filter. To identify them, the state space is often expanded and the evaluation problem is solved. However, in practice, for example, in the task of digitally processing the results of radar measurements of the motion parameters of maneuvering aircraft, it is not possible to accumulate the necessary statistics. The way out of such a situation may be based on fuzzy logic.

Various variants of alpha-beta filters are widely used among intelligent tracking filters. The mathematical models underlying such solutions are, as a rule, traditional and are not subject to adaptation. This leads to relatively simple computational procedures and does not allow us to approach the potential accuracy of the estimation. One of the constructive ways out of the described situation may be to use dynamic motion models in the synthesis of intelligent tracking filters.

The study develops an approach to the construction of dynamic motion models based on the use of the maximum condition of the generalized power function. This, as shown in the paper, allows us to obtain a nonlinear state transition matrix. Due to the choice of the adaptation parameter, it degenerates with a sufficient degree of accuracy in practice into a state transition matrix obtained using a mathematical model of object motion with constant velocity. This allows us to propose a procedure for adjusting the evaluation algorithm to the maneuvers of the aircraft, based on the expert choice of the adaptation parameter. The input data of the synthesized fuzzy filter is the acceleration of the aircraft and the value of the threshold for deciding on the beginning of the target maneuver, which allows us to attribute the observed movement to one of five options: rectilinear uniform motion, rectilinear equidistant motion, rotation with approximately constant speed, rotation with acceleration and maneuver. The decision-making process on the value of the output signal takes place in accordance with the Mamdani conjunctive type rule base. The centroid method was chosen for defasification.

The aim of the study is to synthesize an intelligent tracking filter from the condition of the maximum of the generalized power function and evaluate its effectiveness by mathematical modeling of digital processing of radar measurement results based on expert knowledge about the modes of movement of aircraft.

Lazarenko S.V. Fuzzy strategy for configuring the parameters of the tracking filter for automation of air traffic control. Information-measuring and Control Systems. 2024. V. 22. № 1. P. 33−43. DOI: https://doi.org/10.18127/j20700814-202401-05 (in Russian)

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