Direction Finding Method Research Articles

STREAMLINING DIGITAL CORRELATION-INTERFEROMETRIC DIRECTION FINDING WITH SPATIAL ANALYTICAL SIGNAL

This study investigated a search-free digital method for radio direction-finding that utilizes spatial analytical signal reconstruction. The research focused on optimizing the method's accuracy for estimating the direction of a radio source. The analysis identified the separation distance and number of chosen antenna elements for signal reconstruction as the key parameters influencing accuracy. Analytical optimization and simulations were employed to determine the optimal values for these parameters. The research successfully modeled the impact of antenna element selection on direction-finding errors under specific signal-to-noise conditions. This model can be used to guide further development and optimization of this radio direction-finding method.

Euler wavelets method for optimal control problems of fractional integro-differential equations

This research introduces an efficient direct method for finding the numerical solution to optimal control problems involving linear and nonlinear fractional integro-differential equations using orthonormal Euler wavelets. Using orthonormal Euler wavelets, fractional integral, and product operational matrices have been obtained. By using these fractional operational matrices and collocation points, optimal control problems of fractional Volterra integro-differential equations have been reduced to a system of linear or non-linear equations. We establish the convergence analysis and error bound of the proposed method. Orthonormal Euler wavelets have been utilized to solve numerical examples and determine the approximate value of the cost function by approximating state and control functions. This has been done in order to verify the effectiveness of the proposed numerical technique.

Direction-finding for unmanned aerial vehicles using radio frequency methods

Nowadays, drones, also known as unmanned aerial vehicles (UAVs), are used for a wide range of purposes in the civil, industrial, and military domains. The greater the number of UAVs, the more serious the potential security risks correlated to them. To address these risks, it became necessary to develop systems that can detect, locate, and possibly neutralize such an object. The detection can be performed using different sensors such as imaging, radar, acoustic, and radio frequency (RF) sensors. The localization of the target drone, which can be done using direction finding (DF) methods, is an essential part of such a system. Thus, an RF-based DF testbed is designed and experimentally assessed in this paper. The testbed is implemented using software defined radio (SDR) platforms from the Universal Software Radio Peripheral (USRP) family as hardware equipment, and the MUSIC algorithm for processing the signals received on four different phase-coherent RF channels. A DJI Mavic Air UAV is used as target. For assessing the DF estimation performance, the direction obtained from the drone flight record is compared with the one estimated using the proposed DF testbed. Two different scenarios, a static one and a dynamic one, are considered to highlight the effectiveness of the proposed DF testbed across various conditions. The obtained results indicate an average estimation error of 1.15 degrees from the drone's actual position, in the case of the static scenario, and of 1.86 degrees in the case of the dynamic scenario, results which are on parity with or surpassed those of other drone DF systems described in the literature. The paper also outlines the benefits and challenges of the current approach.

Research on Direction Finding Method under Impulsive Noise Based on Nonuniform Linear Array

Direction of arrival (DOA) estimation under impulsive noise has always been an important research area in array signal processing. The traditional methods under impulsive noise mostly rely on prior parameters and have high computational complexity. Based on the filtering theory, we present an effective pretreatment filtering technology to cut out the impulse mixed in the array received data and employ the nonuniform linear array to improve the estimation performance further. First, according to the amplitude characteristics of impulse noise, the pretreatment filtering technology is proposed to cut out the impulse based on the median filter and sliding average filter, which is valid for both strong and weak impulsive noise. Second, the minimum redundant array is adopted to carry out array virtual expansion so that the array aperture can be increased and the estimation performance can be improved. Finally, based on the idea of matrix reconstruction, we propose the improved estimation of signal parameters via rotational invariance techniques algorithm and an improved root multiple signal classification algorithm for DOA estimation. Theoretical analysis and simulation results show that the proposed method has a simple processing process, small calculation load, good array expansion ability, and excellent noise adaptability. Moreover, the proposed methods greatly improve the direction-finding performance under the condition of low signal-to-noise ratio and strong impulsive noise.

A Deep Reinforcement Learning-based Shortwave Multistation Autonomous Cooperative Direction Finding and Localization Method

A Deep Reinforcement Learning-based Shortwave Multistation Autonomous Cooperative Direction Finding and Localization Method

CRB-based comparative study of array signal processing direction finding methods supported with SDR platform implementation

Radio Direction-Finding (DF) is an extremely important process in numerous commercial and military applications. Array signal processing-based DF methods have been developed to improve estimation performance in recent applications that require higher resolution and accuracy. Practically, angle of arrival (AOA) estimation is challenging due to various intrinsic and extrinsic parameters that affect the results. Therefore, clarifying these parameters and researching their impact on various DF methods are considered important research topics. The Cramer-Rao Bound (CRB) for estimating AOA is calculated based on a model of a linear antenna array system. This bound identify the factors that significantly impact the estimation performance. The current study conducts a comparative analysis of the most widely used array-signal-processing-based direction-finding (DF) methods under different conditions of the CRB parameters. According to the simulation results, Multiple Signal Classification (MUSIC) AOA estimator provides more accurate and stable results. Accordingly, it is chosen for implementation using a prototype testbed based on Software Defined Radio (SDR) technology using National Instruments Universal Software Radio Peripheral (NI-USRP) platform version 2930. Experimental outcomes were tested at various AOA values. The appendix includes the complete derivation for the CRB relation applied on the system model.

Improving the accuracy of a digital spectral correlation-interferometric method of direction finding with analytical signal reconstruction for processing an incomplete spectrum of the signal

A method of correlation-interferometric direction finding has been improved, which effectively solves the problem of radio direction finding of radio emission sources under conditions of exposure to one or two masking interference. The problem was solved using the selection of an unmasked fragment of the spatial spectrum of the signal and the reconstruction of the missing samples of its signal group. As a result of the synthesis of the proposed method, estimates of signal samples were obtained as exact solutions to the proposed energy balance equations. The resulting solutions provide a significant increase in the signal-to-interference ratio and, accordingly, direction-finding accuracy without increasing the number of reception channels of the antenna array. As a result of the simulation, the dependences of the standard deviation of the bearing estimate on the signal-to-noise ratio in the presence of interference were built. Under the influence of one or two masking interferences and a signal-to-interference ratio of 0 dB, the use of the known direction-finding method without interference selection produces an anomalously large direction-finding error of more than 0.42 degrees, which is practically independent of the signal-to-noise ratio. The direction-finding method with selection of spectral signal samples masked by interference reduces the direction-finding error to 0.22 degrees when exposed to one interference and to 0.3 degrees when exposed to two interferences. This is due to the presence of power losses of the usable signal during the selection of its samples masked by interference. The proposed method of direction finding with reconstruction of signal samples provides a significant gain in accuracy by 3–30 times compared to the method of selection of masked samples in the range of changes in the signal-to-noise ratio (–20.5) dB. The direction-finding error of the proposed method decreases with increasing signal/noise according to a hyperbolic dependence. It is advisable to use the proposed direction-finding method when masking no more than two samples of the signal group

Methodology for processing information of a multi-base phase direction finder and assessing the quality of results, taking into account failures and deterioration in the operation quality of individual MPDF bases

When conducting radio-electronic monitoring (SEM) by systems of various types of basing, phase direction finding methods are widely used. To obtain both high accuracy and unambiguity of direction finding, a reusable phase direction finder (MBFP) is used. In the literature, quite a lot of works are devoted to methods for optimizing MBFP structures. In this paper, the issues of automation of accounting for failures or deterioration of the quality of work of individual MBPF databases in the process of processing direction finding information obtained during the management of SEM are considered. The determination of the bearing (guiding sine) on the radiation source with the phase direction finding method is carried out by a set of phase differences obtained at the output of a multi-phase phase direction finder (MBFP).

1-Bit Programmable Metasurface-Based 2-D Direction Finding

A novel two-dimensional (2-D) direction finding method is proposed, relying on a 1-bit programmable metasurface and the time modulation method. Both the azimuth and elevation angles of far-field signals are estimated simultaneously by analyzing the harmonic characteristic of received signals in the frequency domain. Low hardware cost and computational complexity can be achieved owing to the intrinsic nature of the single radio frequency (RF) chain in the proposed method. Extensive numerical results confirm that the direction finding attains a near-zero mean square error (MSE), when the signal-to-noise ratio (SNR) attains 10 dB. A Ka-band reflective programmable metasurface with 400 elements is fabricated and tested to verify its effectiveness partly.

Three-spatial-channel method for amplitude monopulse direction-finding of radar object

Three-spatial-channel method for amplitude monopulse direction-finding of radar object

Direction finding of electromagnetic radiation sources using the volumetric phased arrays consisting of the small number of elements

Problem statement. This article proposes a method to measure the bearing of electromagnetic radiation sources in the conditions of passive interference with multipath propagation and in the conditions of using "rough" (small number of elements) statistics taking into account particular design features of the direction finder located on a mobile object. The technical design of an adaptive direction finder (ADF) with a small number of channels M = 7 and “short spatial samples” m = 2 (bases) is substantiated, which leads to reducing hardware and software costs. Target. Determine the method of direction finding of electromagnetic radiation sources by volumetric phased arrays consisting of the small number of elements, which allow for the presence of passive interference with multipath radiation of electromagnetic radiation sources, and include spatial digital filters (DF) of a low order r = 2. Results. The problem of measuring the bearing of electromagnetic radiation sources under the conditions of correlated multipath passive interference and limited hardware and computing resources was solved. Direction finder includes a 7-element monopulse direction finder, which was built according to a sequential scheme at the nodes of a volumetric hexagonal grid with an equivalent spatial quantization step of 0.5l, forming programmable small-sized bases with a size of no more than l using the method of multiplexing (HF switching). Practical significance. The relevance of the proposed approach is substantiated due to the need to notch "multipath components", parasitic reflections from local objects surrounding the adaptive direction finder, and reduce the instrumental error in bearing measurement. A new approach to the construction of a volumetric phased array of an adaptive direction finder is proposed. Novelty. The synthesis of the optimal estimate is based on the principle of “whitewashing” passive correlated interference and the maximum likelihood method, which guarantees the achievement of potential direction finding accuracy in the conditions of using rough statistics that reduce hardware and software costs.

BD-CVSA: A Broadband Direction Finding Method Based on Constructing Virtual Sparse Arrays

As the electromagnetic environment becomes more complex, radio direction finding systems need to cover a wide frequency range. However, the phase ambiguity of high frequency limits the development of broadband direction finding technology. The existing methods in solving the phase ambiguity problem heavily rely on designing the precise actual sparse array structure by theoretical derivation, which is expensive and time-consuming. To solve this problem, we propose a broadband direction finding method based on constructing virtual sparse arrays. First, we perform the convolutional operation on the direction feature matrix to achieve the weighted summation of the original baselines, which generates numerous virtual array elements and virtual baselines with different directions. The virtual array elements are combined to form virtual sparse arrays with different aperture sizes. Second, we optimize the parameters through the error backpropagation algorithm and obtain the optimal combination of virtual sparse arrays, which eliminates the phase ambiguity. Meanwhile, the virtual sparse arrays can maintain the advantages of sparse arrays, which can accomplish high-precision broadband direction finding. The experimental results demonstrate that the proposed method can solve the phase ambiguity problem effectively. It has high accuracy and strong robustness in simulation environment.

Direction finding method via acoustic vector sensor array with fluctuating misorientation

In this paper, we consider the direction-of-arrival (DOA) estimation problem under fluctuating misorientation via acoustic vector sensor array (AVSA). A covariance matrix focusing fitting (CMFF) method is proposed to tackle this issue. Firstly, a new AVSA data model is created by incorporating the fluctuation parameter into different time segments. Then, to overcome the deterioration of DOA estimation performance under fluctuating misorientation in the total observation time, a covariance matrix focusing technique is formulated. By using the covariance matrix focusing technique, different time segments with fluctuating misorientation are converted into the desired data sets. Finally, to obtain more accurate DOA estimation performance, an iterative weighted covariance matrix fitting method is presented. Simulation and experimental results are carried out to demonstrate the superiority and robustness of our proposed method in the case of fluctuating misorientation for an AVSA.

A GNSS Spoofing Detection and Direction-Finding Method Based on Low-Cost Commercial Board Components

The Global Navigation Satellite System (GNSS) is vulnerable to deliberate spoofing signal attacks. Once the user wrongly locks on the spoofing signal, the wrong position, velocity, and time (PVT) information will be calculated, which will harm the user. GNSS spoofing signals are difficult to carry out spoofing attacks in the direction of arrival (DOA) of the real signal, so the spoofing detection method based on DOA is very effective. On the basis of identifying spoofing signals, accurate DOA information of the signal can be further used to locate the spoofer. At present, the existing DOA monitoring methods for spoofing signals are mainly based on dedicated antenna arrays and receivers, which are costly and difficult to upgrade and are not conducive to large-scale deployment, upgrade, and maintenance. This paper proposes a spoofing detection and direction-finding method based on a low-cost commercial GNSS board component (including an antenna). Based on the traditional principle of using a multi-antenna carrier phase to solve DOA, this paper innovatively solves the following problems: the poor direction-finding accuracy caused by the unstable phase center of low-cost commercial antennas, the low success rate of spoofing detection in a multipath environment, and the inconsistent sampling time among multiple low-cost commercial GNSS boards. Moreover, the corresponding prototype equipment for spoofing detection and direction-finding is developed. The measured results show that it can effectively detect spoofing signals in open environments. Under a certain false alarm rate, the detection success rate can reach 100%, and the typical direction-finding accuracy can reach 5°.

Radio Direction Finding Method to Mitigate Tsunami Risk in Sierra Leone

In this study, the Radio Direction Finding method is proposed for the detection of electromagnetic signals, in the VLF band, to try to anticipate the occurrence of potentially destructive geophysical events. The experimentation concerns the interception of electromagnetic anomalies in Sierra Leone, in the five-day time window, associated with seismic events that could potentially generate tsunamis. The area of investigation is Sierra Leone, whose coastline is subjected to tidal wave hazards triggered by earthquakes generated in the Mid-Atlantic Ridge. Although Sierra Leone is not affected by recurrent earthquakes, there is nevertheless a low probability, estimated at 2 percent, of the occurrence of destructive earthquakes in the next 50 years. Also in estimates, the risk of rogue and potentially damaging waves is estimated to strike the Sierra Leone coast at least once in the next 10 years. The Radio Direction Finding experiment carried out continuously 24/7, has shown a close relationship between increased radio-anomalies, in the frequencies of 6,000 Hz, a time window between electromagnetic anomaly detection and the imminence of an earthquake, and higher frequency times for the risk of earthquake occurrence in the Mid-Atlantic Ridge.

Microwave Passive Direction-Finding Method Based on NV Color Center in Diamond

In this study, we established a passive direction-finding scheme based on microwave power measurement: Microwave intensity was detected using microwave-frequency proportion integration differentiation control and coherent population oscillation effect converting the change in microwave resonance peak intensity into a shift of the microwave frequency spectrum, for which the minimum microwave intensity resolution was −20 dBm. The direction angle of the microwave source was calculated using the weighted global least squares method of microwave field distribution. This lay in the 12~26 dBm microwave emission intensity range, and the measurement position was in the range of (−15°~15°). The average angle error of the angle measurement was 0.24°, and the maximum angle error was 0.48°. In this study, we established a microwave passive direction-finding scheme based on quantum precision sensing, which measures the microwave frequency, intensity, and angle in a small space and has a simple system structure, small equipment size, and low system power consumption. In this study, we provide a basis for the future application of quantum sensors in microwave direction measurements.

Graph-based sequential beamforming.

This paper presents a Bayesian estimation method for sequential direction finding. The proposed method estimates the number of directions of arrivals (DOAs) and their DOAs performing operations on the factor graph. The graph represents a statistical model for sequential beamforming. At each time step, belief propagation predicts the number of DOAs and their DOAs using posterior probability density functions (pdfs) from the previous time and a different Bernoulli-von Mises state transition model. Variational Bayesian inference then updates the number of DOAs and their DOAs. The method promotes sparse solutions through a Bernoulli-Gaussian amplitude model, is gridless, and provides marginal posterior pdfs from which DOA estimates and their uncertainties can be extracted. Compared to nonsequential approaches, the method can reduce DOA estimation errors in scenarios involving multiple time steps and time-varying DOAs. Simulation results demonstrate performance improvements compared to state-of-the-art methods. The proposed method is evaluated using ocean acoustic experimental data.

Group analysis tasks. Conservation laws

Differential equations of mechanics are derived from the laws of conservation of mass, momentum and energy. Other conservation laws can be obtained using the symmetries of these equations. Any conservation law can be derived from one using canonical operators, special cases of which are symmetry operators. The calculation of canonical conservation law operators is equivalent to a direct method of finding a divergent form of equations that are valid by virtue of the equations of mechanics. Using the example of one-dimensional equations of gas dynamics, all zero-order conservation laws are obtained by the direct method. For special equations of state, an infinite set of conservation laws have been obtained, many of which are new.

Robust Gridless Estimation of Angles and Delays for Full-Dimensional Wideband mmWave Channels

In this paper, we consider robust channel estimation for a millimeter wave (mmWave) massive MIMO system with uniform planar arrays (UPA). For many gridless angle estimation methods of mmWave channels, the channel gains needs to be time-invariant during training. We propose a gridless method that is applicable to time-invariant and time-varying channels, and the proposed method is robust to channel variations. This is done by employing time-varying precoders and combiners that are banded block Toeplitz (BBT) matrices. The advantage of time-varying BBT precoders is two-fold. First, with time-varying BBT precoding we can fabricate time-varying channels. Thus the channel can be estimated as if it is a time-varying channel whether the actual channel is time-varying or not. We will show that, thanks to fabricated time variation in the channel, a small training overhead can be used. Secondly, BBT precoding and combining preserve the shift invariance property of the received data matrix. Due to the preservation of shift invariance property, we can employ most existing direction finding methods for estimating the angles and delays, including low complexity gridless subspace based algorithms. Simulation results are given to show that the proposed time-varying BBT precoding provides robust and accurate channel estimates with a low complexity.

АНАЛІЗ ЗАСТОСОВНОСТІ МЕТОДУ ДВОЧАСТОТНОЇ ІНТЕРФЕРОМЕТРІЇ ДЛЯ ВИМІРЮВАННЯ КУТА МІСЦЯ ЦІЛЕЙ У ДВОКООРДИНАТНИХ РЛС

Subject and Purpose. The study deals with the dual-frequency radio interferometry technique, which is based on the employment of two fairly close frequencies with the aim to remove ambiguity of the radar target elevation estimation using 2D-radar and eliminate 2 pm-uncertainty of the signal phase difference measurement. Analysis of random noise action on the accuracy of the elevation angle estimation by the dual-frequency radio interferometry and assessment of practical applicability of the method make up the purpose of the paper. Methods and Methodology. The noise action on the elevation angle measurement accuracy is examined through a series of an- alytical calculations with the use of statistical analysis methods. The noise in each receiving channel is modeled in terms of additive, statistically independent stationary Gaussian processes with zero mean values and equal variances. The calculation results are checked via computer simulations with statistics estimations for 106 random noise realizations. Results. A correct condition has been developed for the sector width where the target elevation angle is unambiguously estimated depending on the space separation of the antennas (baselines) and the frequency ratio. Expressions for elevation angle estimation errors have been obtained, showing that the error is mainly contributed by the faults in the determination of the ambiguity interval number. A probability of the correct determination of the ambiguity interval number has been derived depending on the signal- to-noise ratio and the frequency difference, indicating that almost one hundred per cent probability of the correct determination of the ambiguity interval number is only achieved when the signal-to-noise ratio exceeds 30 dB. A comparative analysis has been performed between the methods of dual-frequency interferometry and conventional phase-difference direction finding in the case of close X-band frequencies and the same sectors of survey. Conclusions. The dual-frequency radio interferometry technique with close frequencies has been shown to outperform the stand- ard phase-difference direction-finding method only when the signal-to-noise ratio is sufficiently high (over 30 dB). In principle, the accuracy of the technique seems possible to improve by taking significantly different frequencies selected with regard to the scale negotiation condition. However, it should be mentioned that the implementation of the relevant algorithm in practice is much more complicated than the conventional scheme with a single frequency and several antenna baselines.