M.E. Gurbatov1, P.A. Dudkin2, A.S. Gontarev3

1 JSC «Radiofizika» (Moscow, Russia)
2,3 Moscow Institute of Physics and Technology (National Research University) (Moscow, Russia)
1 gurbatovv@yandex.ru

In modern conditions of intensive implementation of neural network technologies in the field of trajectory processing of radar information, there is a significant imbalance between the practical application and the theoretical justification of these methods. The existing methodology is based primarily on an empirical approach, which creates significant limitations for predicting the effectiveness of algorithms in conditions of atypical scenarios of functioning.

In this regard, an urgent scientific task arises to develop a theoretical justification for the applicability of artificial neural networks to solve the problems of trajectory processing of radar information. Solving this problem will create a fundamental theoretical basis for the further development and practical application of neural network technologies in the field of radar information processing, ensuring the necessary level of reliability and predictability of their functioning.

Within the framework of this work, a special but critically important aspect of the theoretical justification is considered – the proof of convergence of the results of the neural network algorithm to the results obtained by classical filtering methods.

It should be noted that a complete theoretical justification of the applicability of neural network methods requires solving a much wider range of tasks, including stability analysis, perturbation robustness, computational complexity assessment, and determining optimal architectures for various classes of trajectory processing tasks.

The development of a theoretical basis for convergence is a necessary first step towards creating a fundamental basis for the further development and practical application of neural network technologies in the field of radar information processing.

The aim of the work is to obtain a rigorous mathematical justification for the applicability of neural network methods in special cases of trajectory processing of radar information by proving the convergence of the results of operation of a multilayer perceptron to the behavior of a simple linear filter type α−β, which is a special case of the Kalman filter in stationary mode. The choice of this particular case is explained by two main reasons:

the simplicity of the structure and the clarity of the mathematical description make it possible to build a clear and visual proof of convergence;

the Kalman filter is widely used in practice due to its computational efficiency and sufficient accuracy in a number of applied tasks.

However, the result obtained is limited to considering only the stationary mode of operation of the filter and does not apply directly to the general Kalman theory, which includes the dynamics of transient processes and nonlinear models of objects.

As a result of solving the research problem, the statement about the convergence of the results of the multilayer perceptron to the behavior of the Kalman filter in the stationary mode is proved. The results obtained are valid exclusively for the stationary mode of operation of the Kalman filter and do not apply to general dynamic processes and nonlinear models of objects.

The possibility of approximating the behavior of the Kalman filter by a neural network with a given accuracy over a limited range of input influences has been experimentally confirmed. The testing was carried out on sinusoidal and polynomial-type model trajectories.

Gurbatov M.E., Dudkin P.A., Gontarev A.S. Theoretical substantiation of the possibility of approximation of the Kalman filter by neural network methods in the tasks of trajectory processing of radar information // Achievements of modern radioelectronics. 2026. V. 80. № 6. P. 87–102. DOI: https://doi.org/10.18127/j20700784-202606-08

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