The protection of various objects against the impact of unmanned aerial vehicles (UAVs), which carry a potential threat in the military, economic and everyday areas of human activity, is one of the urgent tasks of our time. Currently, there are a large number of publications devoted to the description of methods and systems based on different physical principles designed to detect and observe UAVs against the background of existing interference. They consider the reception channels, methods of processing the received information signals and their subsequent intelligent analysis. It is shown, that the known methods of energy detection of UAV signals are insufficiently effective, since the operation is performed, as a rule, against a background of noise that has certain structural similarities with the UAV signal. Considerable attention is paid to the methods for interpreting the obtained data using trained neural networks. Since the number of publications in this area is constantly increasing, the task of analyzing, generalizing and systematizing the data available in the literature is relevant in accordance with this. The article is an overview and it is devoted to the generalization and systematization of known methods of receiving and processing radar, acoustic, optical and infrared signals for detection-recognition, measurement of coordinates and parameters of UAV movement.

Currently, classical means of detecting objects do not provide the necessary efficiency for detecting small UAVs, and acoustic location among the known methods for their observation is the most cost-effective solution. The article analyzes the well-known methods of direction finding of acoustic signals in order to select algorithms for processing UAV signals. Obtaining qualitative indicators of the analyzed algorithms was carried out by the method of statistical computer modeling in the Matlab environment. Based on the simulation results, it is shown that classical methods are the most stable under conditions of low signal-to-noise ratios. The GCC-PHAT direction finding algorithm, based on determining the difference in the time of arrival of a signal at spaced points, is computationally economical and simple enough to determine the direction to the UAV, but it is not capable of distinguishing more than one radiation source within the diagram orientation. Beamforming methods are also relatively easy to implement and computationally efficient, and are more robust at low signal-to-noise ratios. The SRP-NAM algorithm has a greater accuracy in determining angles than SRP-PHAT, so it can be an adequate replacement for the SRP-PHAT algorithm. High-resolution methods provide better directional resolution than classical methods, which, in the case of a limited microphone array aperture, is a positive factor in the design of an UAV direction finding station. High resolution methods were considered: non-coherent MUSIC, non-coherent normalized MUSIC and TOPS method. It is shown that incoherent MUSIC gives poor results in distinguishing close UAV signals, since unequal estimates of the entire frequency range are concentrated during bearing formation. The incoherent normalized MUSIC algorithm is able to efficiently use the entire frequency range of the UAV acoustic signal. The TOPS algorithm is inferior to the incoherent normalized MUSIC algorithm, and on the other hand, it does not require a priori estimates of the number of radiation sources.

The work examines methods and mathematical models that provide the possibility of researching the statistical characteristics of complex and non-stationary random processes describing a wide class of physical phenomena. The proposed models can be used to study the processes observed in various fields of human activity, namely, to analyze the trajectories of unmanned aerial vehicles, their acoustic signals, meteorological processes reflecting the state of the atmosphere. Real and simulated non-stationary random processes considered in the work are represented by the complex vector random process (CVRP) model. In this case, the length of the subvector is equal to the period of the seasonal component. In fact, in such a representation, the time series readings are replaced by their aggregate, i.e. subvectors. Statistical relationships are analyzed for subvectors, and not, as usual, for process counts. If the length of the subvector is equal to one, all operations in the SVVP representation are equivalent to the usual operations for time series. The mathematical apparatus developed in the article was used to analyze changes in time series of atmospheric temperature observed over a long period of time; average annual temperatures were estimated with subsequent smoothing with a low-pass filter. The results obtained can be used to analyze medium-term and long-term changes in atmospheric conditions, refine the results obtained by traditional methods of mathematical statistics, analyze and predict data flows in mobile communication networks, as well as in other areas of human activity.

The task of estimating the energy distribution over the observation interval of radar signals scattered on atmospheric inhomogeneities, arising as a result of UAV operation, is considered. The solution to this problem is necessary to improve detection algorithms, to classify the detected UAVs according to additional informational features, to improve the resolution when detecting several devices located at the same range during the group application of UAVs, to clarify the time parameters of the evolution of the movement of UAVs in time and space. A similar problem arises due to the need to process useful radar signals with a low signal-to-noise ratio in order to achieve the maximum possible range of reliable UAV detection. Because of this, it becomes impossible to estimate directly the energy of useful signals by the method of comparison with reference physical quantities due to a large measurement error. Therefore, an evaluation algorithm is proposed, based on the methods of the theory of ordinal statistics, which provide, instead of comparing numerical realizations with a certain standard, to form a variational series from them under the condition of a priori knowledge of the distribution function of these realizations. At the same time, the fact is used that for certain distributions of a random variable, among which there are normal and all limited ones, the variance of the estimate in the form of a mathematical expectation of certain ordinal statistics is significantly less than the variance of a direct measurement at a low signal-to-noise ratio. In order to save time and computing resources during real-time processing of received signals, it is proposed to use pre-calculated arrays of numerical values of mathematical expectation and dispersion of ordinal statistics for various parameters of the density distribution of a random variable.

No abstract