Neumann-Pearson Criterion Research Articles

Devising a method for detecting an aerial object by radar with an additional channel of passive reception

The object of this paper is the process of detecting an aerial object by a radar with active and passive reception channels. The main hypothesis of the study assumed that the introduction of an additional channel of passive reception would increase the conditional probability of correct detection at a fixed value of the conditional probability of false alarms. When detecting an aerial object, it was considered that the signals from aerial object represent a reflected signal after being emitted by the active radar channel elemitted own radio signals. A radar with active and passive reception channels assumes the presence of two channels. The active location channel provides reception of signals reflected from an aerial object, their processing and detection according to the Neumann-Pearson criterion. The passive location channel functions according to the principle of panoramic spectral analysis based on windowed Fourier transforms. The information combining device is intended for the compatible combining of information from active and passive channels of radar reception. At the output of the passive location channel, an output signal is formed, and the coordinates of the aerial object are measured. To ensure the functioning of the radar with active and passive reception channels, it is necessary to ensure the time synchronization of the reception channels. The quality of detection of aerial objects by radar with active and passive signal reception channels was evaluated. The quality indicator defines the conditional probability of correct detection. The dependences of the conditional probability of correct detection are given for a radar with only an active reception channel and a radar with active and passive reception channels. It was established that the introduction of an additional channel of passive reception to the radar increases the conditional probability of correct detection by an average of (20–40) %, depending on the signal-to-noise ratio.

Improving a method for non-coherent processing of signals by a network of two small-sized radars for detecting a stealth unmanned aerial vehicle

The object of this study is the process of detecting stealth unmanned aerial vehicles by a network of two small-sized radars with incoherent signal processing. The main hypothesis of the study assumed that combining two small-sized radars into a network could improve the quality of detection of stealth unmanned aerial vehicles with incoherent signal processing. The improved method for detecting a stealth unmanned aerial vehicle by a network of two small-sized radars with incoherent signal processing, unlike the known ones, provides for the following: – synchronous inspection of the airspace by small-sized radars; – sounding signal emission by each small-sized radar; – reception of echo signals from a stealth unmanned aerial vehicle by two small-sized radars; – coordinated filtering of incoming echo signals (separation of echo signals); – quadratic detection of signals at the outputs of matched filters; – summation of the detected signals at the outputs of the matched filters; – summation of the outputs of adders of two small-sized radars. The scheme of a stealth unmanned aerial vehicle detector is presented, optimal according to the Neumann-Pearson criterion, with incoherent signal processing. The quality of detection of a stealth unmanned aerial vehicle by a network of two small-sized radars with incoherent signal processing was evaluated. It was found that with incoherent processing, the gain in the value of the conditional probability of correct detection is on average from 19 % to 26 %, depending on the value of the signal-to-noise ratio. The gain in the value of the conditional probability of correct detection is greater at low values of the signal-to-noise ratio. At the same time, the gain in signal-to-noise value is more significant with coherent signal processing than with non-coherent signal processing by a network of two small-sized radars

THE PROBLEM OF RELIABILITY OF GEODESIC NETWORKS

Nowadays, the theory of reliability is widely used in the construction industry, and it is also used in the field of geodesy. By abstracting its position, it can be successfully transferred to systems that, it would seem, are not in a dynamic state. Let's take, for example, the points of the polygonal (leveling) network in the city. It would seem that such a network is in a static state, but over time it undergoes changes, that is, it is in imperceptible dynamics and its reliability gradually decreases.
 Reliability in the broadest sense of the word means the ability of a technical device (system, network) to operate without interruption (failure) for a given period of time under certain conditions. Such a period of time is usually determined by the time of execution of some task, which is carried out by the device or system and is part of the general operational task.
 Currently, the problem of reliability is becoming one of the central problems of engineering and management organization. Ensuring the reliable operation of all system elements is of primary importance.
 The modern interpretation of the term "reliability" in geodesy is associated with Baard's reliability theory, according to which reliability is defined as "the ability of the network to self-monitor against gross errors [1]. One of the indicators of reliability is the minimum amount of gross error that can be detected after statistical analysis of the corrections obtained after equalization. On this path, many difficulties arise, most of which remain unsolved, namely the impossibility of localizing a gross error, quantitative assessment of reliability, methods of designing reliable geodetic networks. The unsatisfactory state of reliability theory limits its practical application, but at the same time, the problem of product reliability is the main one in modern production and its importance is growing all the time. In this regard, there is an acute problem in highlighting new views on solutions to this problem in the field of designing and creating geodetic networks.
 A new scheme for constructing the theory of reliability of geodetic measurements is proposed. Its basis is a probabilistic determination of reliability, a system of tolerances, and methods of localizing gross errors. Reliability is defined as a probabilistic measure of the homogeneity of measurements that have passed control. Quantitative reliability is estimated by three indicators: differential, integral and the minimum gross error. The Neumann-Pearson criterion is recommended for establishing tolerance. This theory makes it possible to design geodetic networks with a given reliability.

Статистическая модель высоконаправленной цифровой антенной решетки пространственно-корреляционным методом обработки сигналов

The article presents a statistical model of a digital antenna array with a spatial correlation method of signal processing. The model is obtained on the basis of the Neumann-Pearson criterion for the conditions of a stationary Gaussian distribution of the output process in spatial correlation signal processing. This model makes it possible to numerically evaluate the probabilistic characteristics of radar signal detection for various orders of nonlinear processing under the influence of natural radio interference and can be recommended for the study and optimization of the construction of the antenna array aperture with spatial correlation signal processing, providing a given spatial noise immunity of radio engineering systems.

Статистические характеристики сигнала на выходе оптимальной радиолокационной системы распознавания подвижных воздушных объектов

This work can be considered as a continuation of the article, or as separate materials devoted to the recognition of moving air objects based on the theory of testing statistical hypotheses. In the future, when presenting the materials of this article, the terminology proposed in [1] will be used. The relevance of this article is due to the events taking place on the European continent, indicating the need for further development of radar systems for various purposes and the transition from radar to radio vision, which will significantly improve the effectiveness of air defense and airspace control in general. The construction of a radar portrait and further automatic recognition of moving air objects, as an element of artificial intelligence, will eliminate human error, as well as significantly reduce the time it takes to make a decision on the necessary measures to influence the detected aircraft. Studying the freely available scientific works of various scientists devoted to such a direction of research and development of artificial intelligence as the statistical theory of pattern recognition, one can note the absence of such an important element as the function of the dependence of the probability of correct recognition on the quality and noise of the image. Within the framework of this article, a variant of solving this problem in the form of a mathematical model will be proposed. Since in [1] a recognition method is considered that uses the correlation coefficient between the current image and the reference one, and the probability of correct recognition is estimated using the Neumann-Pearson criterion, it is proposed to plot the dependence of the probability of correct recognition on the ratio of the image energy EI to the spectral noise density (R = 2EI/N0R), for a given false recognition probability . In the future, in the presented work, this dependence will be called recognition characteristics. Graphs will also be considered, in this paper referred to as the distribution density of the recognition probability.

Обнаружение шумового сигнала в океаническом волноводе горизонтальной антенной

Interferometric processing of hydroacoustic information by using a horizontal linear antenna is described. The detection of a noise source signal is considered by using the Neumann-Pearson criterion. The expressions for the probability of correct detection and false alarm are obtained as dependence on the signal/noise (s/n) ratio and the number of antenna elements. Numerical calculations are performed. The curves of the probability of noise signal detection are given. The efficiency of signal detection by using an antenna in relation to a single receiver is estimated.

Significance Level and the Strength of Test Shift Through the Finite Rate of the Transient Response

A significance level and the strength of test shifts are studied then the error function as a transient response model of logical gate is used for testing of statistical hypothesis with Neumann-Pearson criterion. Shifts are rated for Rayleigh accumulated distributions. The generalized signalto-noise ratio is used as one of the variable parameters. The paper reveals that the finite slope of the transient response curve of logical gate results in a type I error increase. The significance level lock leads to bottom of critical region increase and the strength of test decrease in return. The twofold increase of the slope of the transient response curve leads to both the type I error and the bottom of critical region and the strength of test shifts decrease about 12 dB. The twofold increase of generalized signal-to-noise ratio causes the rise of the maximum displacement of a test power functions more than 3 dB up. As this takes place the extremum abscissa is diminished.

Synthesis of an algorithm for grouping air objects in radar systems

Any radar complex exercising control over the airspace has a limited capacity. When processing information about a large number of air objects, overloads occur in information systems and part of the information is inevitably lost. To solve this problem, you need to group the goals. If you refuse to group, then this can lead to oversaturation of the displayed situation on the monitor and the human operator, according to his physical capabilities, will not be able to cope with its assessment. That is, the more goals, the worse the quality of the tasks being solved. One of the ways to solve this problem is to reduce the number of tracked objects by grouping them. Therefore, grouping is a necessary measure taken to simplify the presentation and assessment of the situation. The currently used algorithms for grouping air objects are based on spatial gating, which have low efficiency in a difficult environment. Therefore, the development of new strobe-free methods of grouping air objects is an urgent task. Objective – to develop and research a new strobe-free algorithm for grouping air objects in radar complexes for detecting and tracking air targets. In work a new algorithm for grouping air objects is synthesized, which is based on one of the methods of cluster analysis and an optimal decision rule according to the Neumann-Pearson criterion about the belonging of the considered set of air objects to one group. Some results of simulation modeling of the synthesized algorithm in a complex air environment in comparison with the algorithm based on production rules are presented. Practical significance – the developed algorithm for grouping air objects is more efficient than both the grouping algorithm in the spatial strobe and the algorithm based on production rules. This is especially noticeable in cases of flight of several groups to air objects on intersecting trajectories. The developed algorithm does not impose great requirements on the computing system of the radar complex and can be implemented in practice without restrictions.

Optimization of data processing in aircraft transponder of the "friend or foe" identification system

The paper synthesizes the optimal structure of data processing of the aircraft transponder of the “friend or foe” identification system based on the Neumann-Pearson criterion. It is also shown, that when synthesizing and analyzing the optimal structure of signal data processing in aircraft transponders of "friend or foe" identification systems, it is necessary to take into account the multichannel reception of request signals and limitations of relative throughput of the aircraft transponder, which is caused by the existing principle of constructing the system as single-channel queuing system with failures. The proposed models make it possible to implement the structures of data processing of request signals for situations of inter-channel merging of previous channel decisions on the detection of request signals or pulse components of the request signals. In the proposed structure, the optimization of data processing is carried out not only in time but also in the spatial parameters of the request signals, and also takes into account the relative bandwidth of the aircraft responder. It is shown that the inter channel merging of the results of detecting the component pulses of the query signals is more preferable compared to the existing algorithm of merging the results of detecting the query signals, as it improves the quality of query signal detection and reduces the dependence of query signal detection of relative response.

Adaptive multichannel detection-resolution of stochastic signals in conditions of parametric prior uncertainty

The purpose of the study is to improve the quality indicators of adaptive multichannel detection-resolution-measurement parameters of stochastic signals under parametric a prior uncertainty.Materials and methods. The methodology for the synthesis of signal detectors of various structures, taking into account various factors, is used to achieve the goal. This makes it possible to exclude from the expression for estimating the signal power the terms due to “colored” internal noises and an uncorrelated background. The tools of correlation analysis, adaptive Bayes approach, criterion of generalized likelihood ratio, methods of calculating its logarithm are also used. Results. In this paper, the problems of synthesis of adaptive multichannel detection-resolution algorithms for stochastic signals of various structures under the influence of intense noise interference are considered. An integral element of the detection task is a joint assessment of the intensity of the useful signal and the correlation matrix of interference. This problem is effectively solved for highintensity signals, and the nonstationarity of the internal noise of the receiving uncorrelated background of the interfering signals is not taken into account. A multi-channel receiving system consisting of a number of independent spatially separated elements that form a linear antenna array is considered. The width of the spectrum of the received signals should be considered sufficiently narrow, so that the delay of the signals at the antenna aperture can be neglected. This provision can significantly improve the performance of detection and resolution of stochastic signals in the background of noise interference. Based on the analysis of a finite discrete sample of complex amplitudes of received oscillations, a detection problem was solved, which is formulated as a problem of checking statistical hypotheses regarding distribution parameters. The detection algorithm is reduced to a comparison with the likelihood ratio threshold, and the threshold level value is determined by the selected optimality criterion and for the Neumann-Pearson criterion remains dependent on the power of interfering oscillations.Conclusion. The presented detector possesses higher characteristics of detection and resolution of stochastic signals in comparison with the known ones. It can be shown that an important property of the obtained statistics is the stabilization of the probability of false detection. This is achieved by normalizing the noise power at the output of the adaptation device. In addition, the resulting algorithm is invariant to the form used for its calculation of the correlation matrix of interference. If we take into account that an uncorrelated background will be added to the internal noise power, with a large number of noise jammers, a significant improvement in the detection performance has been achieved.

Analysis of camouflage cover spectral characteristics by imaging spectrometer

Subject of Research.The paper deals with the problems of detection and identification of objects in hyperspectral imagery. The possibility of object type determination by statistical methods is demonstrated. The possibility of spectral image application for its data type identification is considered. Method. Researching was done by means of videospectral equipment for objects detection at "Fregat" substrate. The postprocessing of hyperspectral information was done with the use of math model of pattern recognition system. The vegetation indexes TCHVI (Three-Channel Vegetation Index) and NDVI (Normalized Difference Vegetation Index) were applied for quality control of object recognition. Neumann-Pearson criterion was offered as a tool for determination of objects differences. Main Results. We have carried out analysis of the spectral characteristics of summer-typecamouflage cover (Germany). We have calculated the density distribution of vegetation indexes. We have obtained statistical characteristics needed for creation of mathematical model for pattern recognition system. We have shown the applicability of vegetation indices for detection of summer camouflage cover on averdure background. We have presented mathematical model of object recognition based on Neumann-Pearson criterion. Practical Relevance. The results may be useful for specialists in the field of hyperspectral data processing for surface state monitoring.

Ellipticity angle of electromagnetic signals and its use for non-energetic detection optimal by the Neumann-Pearson criterion

621.396.969.11 An interval method of radar signal detection and selection based on non-energetic polarization parameter – the ellipticity angle – is suggested. The examined method is optimal by the Neumann–Pearson criterion. The probability of correct detection for a preset probability of false alarm is calculated for different signal/noise ratios. Recommendations for optimization of the given method are provided.

Neumann-Pearson-optimized algorithms for estimating white Gaussian pulse noise on images

Statistically optimal algorithms using the Neumann-Pearson criterion for estimating the spatial position of pulse noise with a white Gaussian brightness distribution on images have been synthesized, consisting of minimizing the pass-noise probability at a given false-alarm probability and the false-alarm probability at a fixed pass level. Results are presented for numerical studies of the synthesized algorithms, indicating their advantages over known nonoptimal algorithms.

Detection of determinate signals with a fixed false alarm probability in the case of unknown Toeplitz matrix of interference covariances

The paper is devoted to investigation of detection of determinate signals with a fixed false alarm probability in the case of unknown matrix of interference covariances, when the detection is based on the Neumann-Pearson criterion. The conditions are deduced for the detector ensuring a constant false alarm probability when the unknown matrix of interference covariances has the Toeplitz structure. The efficiency of this detector is assessed by the simulation method. It is shown that there may exist an acceptable loss with respect to the Neumann-Pearson optimal detector.

Nondestructive testing of highly inhomogeneous materials

Nondestructive testing (NDT) of highly inhomogeneous materials, such as carbon-filled plastics, composites, especially fiber-reinforced and using coarse-grain fillers, etc., is a quite difficult problem. Thus, when these materials are scanned by sensitive elements of conventional systems for NDT, the instability of initial signals caused by the structure of the material may exceed the signal emitted by the defect which, therefore, remains undetected. We investigate a principal possibility of detecting defects by representing them in the form of finite regions whose spatial signals are characterized by distribution functions whose shapes differ from the shape of the same function for the intact material. We analyze the most difficult case of complete overlapping of these functions. By applying both theoretical methods and numerical simulation, we demonstrate the possibility of detection of defect zones in highly inhomogeneous materials which are not visible in the process of human inspection even under the most favorable conditions for observation. We present a method for the calculation of the optimal statistical filter and a system of scanning of the investigated material in local zones. The experimental data of automatic detection are compared with the data of human control according to the Neumann-Pearson risk criterion. The regions of the optimal application of automatic and manual inspection are indicated.

Asymptotic distinguishing of autoregressive processes

We study the behavior of the probability of errors of the Neumann-Pearson criterion under various null and alternative hypotheses by the results of observations of autoregressive processes.

Large deviation theorems in the problem of testing two simple hypotheses

Limit theorems on large deviations of the logarithm of the likelihood ratio are proved for the problem of distinguishing two simple hypotheses in the general scheme of statistical experiments under the null hypothesis and under an alternative hypothesis. The theorems obtained are applied to the investigation of a decrease in the probability of errors of the first and second kind for the Neumann-Pearson criterion.