Direction Finding Algorithm Research Articles

Two-Dimensional Direction Finding for L-Shaped Coprime Array via Minimization of the Ratio of the Nuclear Norm and the Frobenius Norm

More recently, the ability of the coprime array to yield large array apertures and high degrees of freedom in comparison with the uniform linear array (ULA) has drawn an enormous amount of attention. In light of this, we propose a low-rank matrix completion algorithm via minimization of the ratio of the nuclear norm and the Frobenius norm (N/F) to solve the two-dimensional (2D) direction finding problem for the L-shaped coprime array (LsCA). Specifically, we first interpolate the virtual co-array signal related to the cross-correlation matrix (CCM) and utilize the interpolated virtual signal for Toeplitz matrix reconstruction. Then, the N/F method is employed to perform low-rank matrix completion on the reconstructed matrix. Finally, exploiting the conjugate symmetry characteristics of the completed matrix, we further develop a direction-finding algorithm that enables 2D angle estimation. Remarkably, the 2D angles are able to be automatically paired by the proposed algorithm. Numerical simulation findings demonstrate that the proposed N/F algorithm generates excellent angular resolution and computational complexity. Furthermore, this algorithm yields better estimation accuracy compared to the competing algorithms.

Dynamic Phase Comparison Planar Direction-Finding Algorithm on Satellite Radio Receiver

Dynamic Phase Comparison Planar Direction-Finding Algorithm on Satellite Radio Receiver

Simultaneous Correlative Interferometer Technique for Direction Finding of Signal Sources.

In this paper, we propose a novel simultaneous Correlative Interferometer (CI) technique that elaborately estimates the Direction of Arrival (DOA) of multiple source signals incident on an antenna array. The basic idea of the proposed technique is that the antenna-array-based receiver compares the phase of the received signal with one of the candidates at each time sample and jointly exploits these multiple time samples to estimate the DOAs of multiple signal sources. The proposed simultaneous CI-based DOA estimation technique collectively utilizes multiple time-domain samples and can be regarded as a generalized version of the conventional CI algorithm for the case of multiple time-domain samples. We first thoroughly review the conventional CI algorithm to comprehensively explain the procedure of the direction-finding algorithm that adopts the phase information of received signals. We also discuss several technical issues of conventional CI-based DOA estimation techniques that are originally proposed for the case of a single time-domain sample. Then, we propose a simultaneous CI-based DOA estimation technique with multi-sample diversity as a novel solution for the case of multiple time-domain samples. We clearly compare the proposed simultaneous CI technique with the conventional CI technique and we compare the existing Multiple Signal Classification (MUSIC)-based DOA estimation technique with the conventional CI-based technique by using the DOA spectrum as well. To the best of our knowledge, the simultaneous CI-based DOA estimation technique that effectively utilizes the characteristics of multiple signal sources over multiple time-domain samples has not been reported in the literature. Through extensive computer simulations, we show that the proposed simultaneous CI technique significantly outperforms both the conventional CI technique in terms of DOA estimation even in harsh environments and with various antenna array structures. It is worth noting that the proposed simultaneous CI technique results in much better performance than the classical MUSIC algorithm, which is one of the most representative subspace-based DOA estimation techniques.

Guiding an Unmanned Aerial Vehicle with a Thermal Imaging Correlation-Contrast Algorithm of Automatic Tracking in Conditions of Information Counteraction

The problem of constructing an algorithm for automatic tracking of a ground object for a guidance system (GS) for an unmanned aerial vehicle (UAV) is considered. The guidance system includes a thermal imaging target coordinator with a combined correlation-contrast direction finding algorithm and a strapdown inertial navigation system. Guidance takes place under conditions of information counteraction, which causes random interruptions in information and random changes in the power of interference, which are recorded by the corresponding indicators. A combined noise-resistant automatic tracking algorithm is obtained, using the readings of information interruption indicators, interference power, and measuring bearing angles, based on the theory of systems with a random jump structure. An example is given that illustrates the operation of the algorithm and demonstrates the satisfactory accuracy of automatic tracking.

The effect of lamppost scatterers on direction finding by cylindrical arrays of dipoles intended for smart antenna application in wireless communications

Smart antennas are widely used to enhance the capacity of the wireless communication systems in urban areas. To enhance the capacity by increasing the signal to noise ratio, one should estimate the angle of arrival precisely. In urban areas, the scattering from the lampposts in a boulevard or a highway is not negligible and its effect should be considered in direction finding algorithms. In this paper the lampposts are modelled by thick and long cylindrical scatterers and the scattered electric field is computed in terms of the cylindrical harmonics analytically. Then the total electric field is evaluated to estimate the angle of arrival by MUSIC direction finding algorithm. The computed total electric field with the proposed method shows a good agreement with precise HFSS simulation results for different incident angles. Monte-Carlo simulations are conducted to evaluate the RMS error values using cylindrical array of dipole antennas for direction finding and the results show that the proposed method can model the effects of the finite number of the lampposts in a wireless propagation scenario adequately, with reduced burden of computations. This fact contributes to a better planning of the beamforming in smart antennas with corresponding resolution.

Using coherent processing algorithms for direction finding of UAV acoustic signals

Small UAVs are often used in a group, since their signals are highly correlated, their resolution is reduced when using non-coherent processing.
 The article analyzes the well-known methods of coherent processing of acoustic signals in order to increase the resolution in the direction finding of signals with a high degree of correlation. 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 coherent signal processing methods are the most stable in conditions of low signal-to-noise ratios, while non-coherent ones show the best results in the region of high signal-to-noise ratio, while coherent algorithms can potentially distinguish more targets. the WAVES coherent algorithm performs better in the high signal-to-noise ratio region, but loses to the CSSM algorithm in the low signal-to-noise region.
 To increase the efficiency of coherent processing of multipath signals, it applies spatial filtering of the inputsignal.

Coarray Interpolation for Direction Finding and Polarization Estimation Using Coprime EMVS Array via Atomic Norm Minimization

In this paper, we develop an efficient algorithm for direction finding and polarization estimation using coprime electromagnetic vector sensor (EMVS) array. First of all, we represent the coarray outputs of coprime EMVS array as the multiple-component form and perform interpolation on each coarray output component. Using the interpolated measurement matrix, we subsequently formulate an atomic norm minimization problem to reconstruct the noise-free covariance matrix and measurement matrix of the interpolated ULA measurements. Finally, we estimate the directions-of-arrival (DOAs) of sources by applying MUSIC on the reconstructed covariance matrix, and utilize the reconstructed measurement matrix and the estimated DOAs to derive the closed-form estimates of polarization parameters. Compared with various existing methods, the proposed algorithm can provide higher estimation accuracy. Furthermore, our algorithm is able to handle more sources and has lower computational complexity. Numerical results illustrate the superiority of the proposed algorithm over the state-of-the-art methods.

A Comparison of Beamforming and Direction Finding Algorithms (Beamscan and MUSIC) on a Linear Array HF Radar in a Medium to Low Wave Energy Environment

Abstract We assess the performance of three different algorithms for estimating surface ocean currents from two linear array HF radar systems. The delay-and-sum beamforming algorithm, commonly used with beamforming systems, is compared with two direction-finding algorithms: Multiple Signal Classification (MUSIC) and direction finding using beamforming (Beamscan). A 7-month dataset from two HF radar sites (CSW and GTN) on Long Bay, South Carolina (United States), is used to compare the different methods. The comparison is carried out on three locations (midpoint along the baseline and two locations with in situ Eulerian current data available) representing different steering angles. Beamforming produces surface current data that show high correlation near the radar boresight (R2 ≥ 0.79). At partially sheltered locations far from the radar boresight directions (59° and 48° for radar sites CSW and GTN, respectively) there is no correlation for CSW (R2 = 0) and the correlation is reduced significantly for GTN (R2 = 0.29). Beamscan performs similarly near the radar boresight (R2 = 0.8 and 0.85 for CSW and GTN, respectively) but better than beamforming far from the radar boresight (R2 = 0.52 and 0.32 for CSW and GTN, respectively). MUSIC’s performance, after significant tuning, is similar near the boresight (R2 = 0.78 and 0.84 for CSW and GTN) while worse than Beamscan but better than beamforming far from the boresight (R2 = 0.42 and 0.27 for CSW and GTN, respectively). Comparisons at the midpoint (baseline comparison) show the largest performance difference between methods. Beamforming (R2 = 0.01) is the worst performer, followed by MUSIC (R2 = 0.37) while Beamscan (R2 = 0.76) performs best.

基于信号子空间的快速多项式求根测向算法

基于信号子空间的快速多项式求根测向算法

Two-dimensional Direction Finding Based on Cylindrical Nested Conformal Array

Recently, nested conformal arrays have attracted considerable interest due to their ability of providing increased array aperture and enhanced degrees of freedom compared to uniform conformal arrays. In this paper, we address the problem of two-dimensional (2-D) direction finding using cylindrical nested conformal array (CNCA). First of all, we derive the coarray signal model of the CNCA, and utilize different coarray signal components to construct multiple Toeplitz matrices. Based on the constructed Toeplitz matrices, we further develop two direction finding algorithms to achieve the decoupled estimation of 2-D direction. Unlike the exiting approaches, the proposed two algorithms exploit more coarray output components, and hence they have better direction finding performance. Moreover, our algorithms can be applied to a larger number of nested subarrays in the CNCA. Numerical results demonstrate the superiority of the proposed algorithms in comparison to the exiting methods.

Source Direction Finding and Direct Localization Exploiting UAV Array With Unknown Gain-Phase Errors

An unmanned aerial vehicle (UAV) array is composed of multiple UAVs carrying array elements, which can sense signals synchronously through a global positioning system (GPS) trigger. However, gain-phase errors caused by synchronization errors and the inconsistent complex gains of receiving array channels result in array manifold perturbation, which makes the performance of traditional localization methods degrade or even fail. In this article, two efficient algorithms for source direction finding and direct localization using a UAV array are, respectively, presented. First, the array manifold changes with the movement of UAVs, which contributes to multiposition fusion, thus avoiding the infinite solutions of underdetermined equations. Then, the quadratic optimization problem can be constructed by using the orthogonal relation between noise subspaces and contaminated steering vectors obtained from multiple observations. Thereafter, we can construct the cost function and obtain the spectral function, from which the source directions and positions can be all estimated by grid search. Meanwhile, the gain-phase error values can be solved successively. Moreover, in order to avoid the influence of heteroscedasticity of different observation positions in direct localization, we carry out a blind weighting operation. Simulation results demonstrate the effectiveness and superiority of the proposed algorithms.

Implementation of stochastic signal processing algorithms in radar CAD

Objectives. In 2020, development work on the creation of a Russian computer-assisted design system for radars (radar CAD) was completed. Radar CAD provides extensive opportunities for creating simulation models for developing the hardware-software complex of radar algorithms, which take into account the specific conditions of aerospace environment observation. The purpose of the present work is to review and demonstrate the capabilities of radar CAD in terms of implementing and testing algorithms for processing stochastic signals.Methods. The work is based on the mathematical apparatus of linear algebra. Analysis of algorithms characteristics was carried out using the simulation method.Results. A simulation model of a sector surveillance radar with a digital antenna array was created in the radar CAD visual functional editor. The passive channel included the following algorithms: algorithm for detecting stochastic signals; algorithm for estimating the number of stochastic signals; direction finding algorithm for stochastic signal sources; adaptive spatial filtering algorithm. In the process of simulation, the algorithms for detecting and estimating the number of stochastic signals produced a correct detection sign and an estimate of the number of signals. The direction-finding algorithm estimated the angular position of the sources with an accuracy of fractions of degrees. The adaptive spatial filtering algorithm suppressed interfering signals to a level below the antenna's intrinsic noise power.Conclusions. The processing of various types of signals can be simulated in detail on the basis of the Russian radar CAD system for the development of functional radar models. According to the results of the simulation, coordinates of observing objects were obtained and an assessment of the effectiveness of the algorithms was given. The obtained results are fully consistent with the theoretical prediction. The capabilities of radar CAD systems demonstrated in this work can be used by specialists in the field of radar and signal processing.

Analysis of acoustic direction finding methods for unmanned aerial vehicles

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.

Direction-Finding Using Co-prime Array under Impulsive Noise

In order to achieve more accurate estimates of the existing direction-finding approaches under impulsive noise, a robust direction-finding algorithm using a coprime array is proposed in this work. In order to suppress the strong impulsive noise, we introduce an infinite norm normalization approach, and on this basis, a weighted signal subspace fitting equation using a coprime array is derived. Furthermore, we propose a quantum-inspired moth-flame algorithm to minimize the derived weighted signal subspace fitting function. Simulation results represent that our direction-finding method has the most excellent performance compared to other conventional methods. Besides, our method can address coherent sources without any additional approach.

Passive direction finding with a pair of acoustic vector sensors using fourth-order cumulants

In this paper, an elevation-azimuth direction finding algorithm with the use of a pair of identically oriented acoustic vector sensors, which can be arbitrarily deployed at unknown locations, is proposed. Two fourth-order cumulant (FOC) matrices, which impose the so-called translational invariance property in the coarray domain, are defined. Such invariant structure allows recovering the coarray steering vectors of the acoustic vector sensors in closed-form from the generalized eigenvectors of the matrix pencil, which is built from the two defined FOC matrices. The identifiability performance of the proposed algorithm is further investigated. It is shown that up to 9 sources can be uniquely identified. The extension of the proposed algorithm for accommodating arbitrary AVS arrays with unknown sensor locations is also addressed. Afterward, the asymptotic performance bound of the considered problem is derived. Finally, the efficacy of the proposed algorithm is verified by numerical examples.

Dir-MUSIC Algorithm for DOA Estimation of Partial Discharge Based on Signal Strength Represented by Antenna Gain Array Manifold.

Inspection robots are widely used in the field of smart grid monitoring in substations, and partial discharge (PD) is an important sign of the insulation state of equipment. PD direction of arrival (DOA) algorithms using conventional beam forming and time difference of arrival (TDOA) require large-scale antenna arrays and high computational complexity, making them difficult to implement on inspection robots. To address this problem, a novel directional multiple signal classification (Dir-MUSIC) algorithm for PD direction finding based on signal strength is proposed, and a miniaturized directional spiral antenna circular array is designed in this paper. First, the Dir-MUSIC algorithm is derived based on the array manifold characteristics. This method uses strength intensity information rather than the TDOA information, which could reduce the computational difficulty and the requirement of array size. Second, the effects of signal-to-noise ratio (SNR) and array manifold error on the performance of the algorithm are discussed through simulations in detail. Then, according to the positioning requirements, the antenna array and its arrangement are developed and optimized. Simulation results suggested that the algorithm has reliable direction-finding performance in the form of six elements. Finally, the effectiveness of the algorithm is tested by using the designed spiral circular array in real scenarios. The experimental results show that the PD direction-finding error is , which meets the need for partial discharge DOA estimation using inspection robots in substations.

Алгоритмы обработки радиолокационной информации в специализированной системе автоматизированного проектирования

A brief description of the radar CAD software modules responsible for this functionality is given. The module of engineering calculations and simulations allows you to set the scenario of the interference-target situation and conduct a complete, close to reality, simulation of the behavior of the radar in combat conditions. The visual functional editor provides the ability to create a radar simulation model in the form of a graph of streaming calculations from interconnected parameterizable blocks. The library of parameterizable modeling blocks contains modeling blocks designed for calculations and modeling of structural and functional parts of developed radar stations, complexes, systems. Simulation model of an active single-position pulse-Doppler sector-observation radar with electronic beam scanning was created. The following algorithms are implemented in the model: the sum-difference monopulse direction finding algorithm, the MUSIC superresolution direction finding algorithm, and the projection adaptive spatial filtering algorithm. A simulation experiment was carried out with a radar model in three scenarios of an interference-target environment, which differ in the presence of interfering signals. Analysis of the results of the simulation experiment shows that the operation of the algorithms corresponds to the theoretical prediction. The abilities of radar CAD presented in this article can be used by specialists in radar and signal processing.

Effect of Approximate Planar Wavefront on Far-Field Direction Finding

Existing sensor array direction-finding algorithms in the open literature simplify the far-field source wavefront as exactly planar in order to facilitate the algorithmic development. In fact, since the wavefront of a point emitter is necessarily spherical, this planar wavefront assumption should actually be approximate, especially for large-scale arrays. Mismatch between the actual and approximate propagation models would introduce a non-random bias on the performance of the direction-finding algorithms. This non-random bias is inevitable due to the mismatch between the algorithm’s presumptions and the data it actually processes. This work derives the mathematical expression of this non-random bias, along with several qualitative analyses. The analysis is carried out using the Taylor-series expansion. Also, the effect of the model mismatch on direction-finding algorithms is evaluated numerically.

A High-Precision Algorithm for DOA Estimation Using a Long-Baseline Array Based on the Hearing Mechanism of the Ormia Ochracea.

Inspired by the Ormia Ochracea hearing mechanism, a new direction of arrival estimation using multiple antenna arrays has been considered in spatially colored noise fields. This parasitoid insect can locate s cricket’s position accurately using the small distance between its ears, far beyond the standard array with the same aperture. This phenomenon can be understood as a mechanical coupled structure existing between the Ormia ears. The amplitude and phase differences between the received signals are amplified by the mechanical coupling, which is functionally equivalent to a longer baseline. In this paper, we regard this coupled structure as a multi-input multi-output filter, where coupling exists between each pair of array elements. Then, an iterative direction-finding algorithm based on fourth-order cumulants with fully coupled array is presented. In this manner, the orientation of the mainlobe can direct at the incident angle. Hence, the direction-finding accuracy can be improved in all possible incident angles. We derive the Cramér-Rao lower bound for our proposed algorithm and validate its performance based on simulations. Our proposed DOA estimation algorithm is superior to the existing biologically inspired direction-finding and fourth-order cumulants-based estimation algorithms.

Ambiguity Resolution in Direction of Arrival Estimation with Linear Antenna Arrays Using Differential Geometry

Linear antenna arrays (LAs) can be used to accurately predict the direction of arrival (DOAs) of various targets of interest in a given area. However, under certain conditions, LA suffers from the problem of ambiguities among the angles of targets, which may result in misinterpretation of such targets. In order to cope up with such ambiguities, various techniques have been proposed. Unfortunately, none of them fully resolved such a problem because of rank deficiency and high computational cost. We aimed to resolve such a problem by proposing an algorithm using differential geometry. The proposed algorithm uses a specially designed doublet antenna array, which is made up of two individual linear arrays. Two angle observation models, ambiguous observation model (AOM) and estimated observation model (EOM), are derived for each individual array. The ambiguous set of angles is contained in the AOM, which is obtained from the corresponding array elements using differential geometry. The EOM for each array, on the other hand, contains estimated angles of all sources impinging signals on each array, as calculated by a direction-finding algorithm such as the genetic algorithm. The algorithm then contrasts the EOM of each array with its AOM, selecting the output of that array whose EOM has the minimum correlation with its corresponding AOM. In comparison to existing techniques, the proposed algorithm improves estimation accuracy and has greater precision in antenna aperture selection, resulting in improved resolution capabilities and the potential to be used more widely in practical scenarios. The simulation results using MATLAB authenticates the effectiveness of the proposed algorithm.