A Reduced Complexity Acoustic-Based 3D DoA Estimation with Zero Cyclic Sum.

Accurate direction of arrival (DoA) estimation is paramount in various fields, from surveillance and security to spatial audio processing. This work introduces an innovative approach that refines the DoA estimation process and demonstrates its applicability in diverse and critical domains. We propose a two-stage method that capitalizes on the often-overlooked secondary peaks of the cross-correlation function by introducing a reduced complexity DoA estimation method. In the first stage, a low complexity cost function based on the zero cyclic sum (ZCS) condition is used to allow for an exhaustive search of all combinations of time delays between pairs of microphones, including primary peak and secondary peaks of each cross-correlation. For the second stage, only a subset of the time delay combinations with the lowest ZCS cost function need to be tested using a least-squares (LS) solution, which requires more computational effort. To showcase the versatility and effectiveness of our method, we apply it to the challenging acoustic-based drone DoA estimation scenario using an array of four microphones. Through rigorous experimentation with simulated and actual data, our research underscores the potential of our proposed DoA estimation method as an alternative for handling complex acoustic scenarios. The ZCS method demonstrates an accuracy of 89.4%±2.7%, whereas the ZCS with the LS method exhibits a notably higher accuracy of 94.0%±3.1%, showcasing the superior performance of the latter.

Enhanced Coprime Array Structure and DOA Estimation Algorithm for Coherent Sources.

This paper presents a new enhanced coprime array for direction of arrival (DOA) estimation. Coprime arrays are capable of estimating the DOA using coprime properties and outperforming uniform linear arrays. However, the associated algorithms are not directly applicable for estimating the DOA of coherent sources. To overcome this limitation, we propose an enhanced coprime array in this paper. By increasing the number of array sensors in the coprime array, it is feasible to enlarge the aperture of the array and these additional array sensors can be utilized to achieve spatial smoothing, thus enabling estimation of the DOA for coherent sources. Additionally, applying the spatial smoothing technique to the signal subspace, instead of the conventional spatial smoothing method, can further improve the ability to reduce noise interference and enhance the overall estimation result. Finally, DOA estimation is accomplished using the MUSIC algorithm. The simulation results demonstrate improved performance compared to traditional algorithms, confirming its feasibility.

Low-Complexity 2D-DOD and 2D-DOA Estimation in Bistatic MIMO Radar Systems: A Reduced-Dimension MUSIC Algorithm Approach.

This paper presents a new technique for estimating the two-dimensional direction of departure (2D-DOD) and direction of arrival (2D-DOA) in bistatic uniform planar array Multiple-Input Multiple-Output (MIMO) radar systems. The method is based on the reduced-dimension (RD) MUSIC algorithm, aiming to achieve improved precision and computational efficiency. Primarily, this pioneering approach efficiently transforms the four-dimensional (4D) estimation problem into two-dimensional (2D) searches, thus reducing the computational complexity typically associated with conventional MUSIC algorithms. Then, exploits the spatial diversity of array response vectors to construct a 4D spatial spectrum function, which is crucial in resolving the complex angular parameters of multiple simultaneous targets. Finally, the objective is to simplify the spatial spectrum to a 2D search within a 4D measurement space to achieve an optimal balance between efficiency and accuracy. Simulation results validate the effectiveness of our proposed algorithm compared to several existing approaches, demonstrating its robustness in accurately estimating 2D-DOD and 2D-DOA across various scenarios. The proposed technique shows significant computational savings and high-resolution estimations and maintains high precision, setting a new benchmark for future explorations in the field.

Research and Implementation of Indoor Positioning Algorithm Based on Bluetooth 5.1 AOA and AOD.

With the addition of Bluetooth AOA/AOD direction-finding capabilities in the Bluetooth 5.1 protocol and the introduction of antenna array technology into the Bluetooth platform to further enhance positioning accuracy, Bluetooth has gradually become a research hotspot in the field of indoor positioning due to its standard protocol specifications, rich application ecosystem, and outstanding advantages such as low power consumption and low cost compared to other indoor positioning technologies. However, current indoor positioning based on Bluetooth AOA/AOD suffers from overly simplistic core algorithm implementations. When facing different application scenarios, the standalone AOA or AOD algorithms exhibit weak applicability, and they also encounter challenges such as poor positioning accuracy, insufficient real-time performance, and significant effects of multipath propagation. These existing problems and deficiencies render Bluetooth lacking an efficient implementation solution for indoor positioning. Therefore, this paper proposes a study on Bluetooth AOA and AOD indoor positioning algorithms. Through an analysis of the principles of Bluetooth's newly added direction-finding functionality and combined with research on array signal DOA estimation algorithms, the paper ultimately integrates the least squares algorithm to optimize positioning errors in terms of accuracy and incorporates an anti-multipath interference algorithm to address the impacts of multipath effects in different scenarios. Experimental testing demonstrates that the indoor positioning algorithms applicable to Bluetooth AOA and AOD can effectively mitigate accuracy errors and overcome multipath effects, exhibiting strong applicability and significant improvements in real-time performance.

Underwater Source Counting with Local-Confidence-Level-Enhanced Density Clustering.

Source counting is the key procedure of autonomous detection for underwater unmanned platforms. A source counting method with local-confidence-level-enhanced density clustering using a single acoustic vector sensor (AVS) is proposed in this paper. The short-time Fourier transforms (STFT) of the sound pressure and vibration velocity measured by the AVS are first calculated, and a data set is established with the direction of arrivals (DOAs) estimated from all of the time-frequency points. Then, the density clustering algorithm is used to classify the DOAs in the data set, with which the number of the clusters and the cluster centers are obtained as the source number and the DOA estimations, respectively. In particular, the local confidence level is adopted to weigh the density of each DOA data point to highlight samples with the dominant sources and downplay those without, so that the differences in densities for the cluster centers and sidelobes are increased. Therefore, the performance of the density clustering algorithm is improved, leading to an improved source counting accuracy. Experimental results reveal that the enhanced source counting method achieves a better source counting performance than that of basic density clustering.

High-Precision DOA Estimation Based on Synthetic Aperture and Sparse Reconstruction.

The direction-of-arrival (DOA) estimation is predominantly influenced by the antenna's aperture size. However, space constraints on flight platforms often necessitate the use of antennas with smaller apertures and fewer array elements. This inevitably imposes limitations on the DOA estimation's resolution and degrees of freedom. To address these precision constraints, we introduce an accurate DOA estimation method based on spatial synthetic aperture model. This method adopts a two-stage strategy to ensure both efficiency and precision in DOA estimation. Initially, the orthogonal matching pursuit (OMP) reconstruction algorithm processes the original aperture data, providing a rough estimate of target angles that guides the aircraft's flight direction. Subsequently, the early estimations merge with the aircraft's motion space samples, forming equivalent spatially synthesized array samples. The refined angle estimation then employs the OMP-RELAX algorithm. Moreover, with the off-grid issue in mind, we devise an estimation method integrating Bayesian parameter estimation with dictionary sequence refinement. The proposed technique harnesses the spatial synthetic aperture for pinpoint estimation, effectively addressing the challenges of atomic orthogonality and angular off-grid on estimation accuracy. Importantly, the efficiency of deploying sparse reconstruction for angle estimation is bolstered by our phased strategy, eliminating the necessity for fine grid analysis across the entire observation scene. Moreover, the poor estimation accuracy caused by coherent source targets and angular-flickering targets is improved by sparse reconstruction. Through simulation and experiment, we affirm the proposed method's efficacy in angle estimation. The results indicate that target angle estimation errors are limited to within 1°. Furthermore, we assess the impact of variables such as target state, heading angle, spatial sampling points, and target distance on the estimation accuracy of our method, showcasing its resilience and adaptability.

Non-Circular Signal DOA Estimation with Nested Array via Off-Grid Sparse Bayesian Learning.

For the traditional uniform linear array (ULA) direction of arrival (DOA) estimation method with a limited array aperture, a non-circular signal off-grid sparse Bayesian DOA estimation method based on nested arrays is proposed. Firstly, the extended matrix of the received data is constructed by taking advantage of the fact that the statistical properties of non-circular signals are not rotationally invariant. Secondly, we use the difference and sum co-arrays for the nested array technique, thus increasing the array aperture and improving the estimation accuracy. Finally, we take the noise as part of the interest signal and iteratively update the grid points using the sparse Bayesian learning (SBL) method to eliminate the modeling errors caused by off-grid gaps. The simulation results show that the proposed algorithm can improve the accuracy of DOA estimation compared with the existing algorithms.

An Enhanced Spatial Smoothing Technique of Coherent DOA Estimation with Moving Coprime Array.

This paper investigates the direction of arrival (DOA) estimation of coherent signals with a moving coprime array (MCA). Spatial smoothing techniques are often used to deal with the covariance matrix of coherent signals, but they cannot be used in sparse arrays. Therefore, super-resolution algorithms such as multiple signal classification (MUSIC) cannot be applied in the DOA estimation of coherent signals in sparse arrays. In this study, we propose an enhanced spatial smoothing method specifically designed for MCA. Firstly, we combine the signals received by the MCA at different times, which can be regarded as a sparse array with a larger number of array sensors. Secondly, we describe how to compute the covariance matrix, derive the signal subspace by eigenvalue decomposition, and prove that the signal subspace is also equivalent to a received signal. Thirdly, we apply enhanced spatial smoothing to the signal subspace and construct a rank recovered covariance matrix. Finally, the DOA of coherent signals are well estimated by the MUSIC algorithm. The simulation results validate the improved performance of the proposed algorithm compared with traditional methods, particularly in scenarios with low signal-to-noise ratios.

Coherent DOA Estimation Algorithm with Co-Prime Arrays for Low SNR Signals.

The Direction of Arrival (DOA) estimation of coherent signals in co-prime arrays has become a popular research topic. However, traditional spatial smoothing and subspace algorithms fail to perform well under low signal-to-noise ratio (SNR) and small snapshots. To address this issue, we have introduced an Enhanced Spatial Smoothing (ESS) algorithm that utilizes a space-time correlation matrix for de-noising and decoherence. Finally, an Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT) algorithm is used for DOA estimation. In comparison to other decoherence methods, when the SNR is -8 dB and the number of snapshots is 150, the mean square error (MSE) of the proposed algorithm approaches the Cramér-Rao bound (CRB), the probability of resolution (PoR) can reach over 88%, and, when the angular resolution is greater than 4°, the estimation accuracy can reach over 90%.

1-D and 2-D Direction of Arrival Estimation in a Conical Conformal Array: Design and Implementation.

Direction of arrival (DOA) estimation for conformal arrays is challenging due to non-omnidirectional element patterns and shadow effects. Conical conformal array (CCA) can avoid the shadow effect at small elevation angles. So CCA is suitable for DOA estimation on both azimuth and elevation angles at small elevation angles. However, the element pattern in CCA cannot be obtained by conventional directional element coordinate transformation. Its local element pattern also has connection with the cone angle. The paper establishes the CCA radiation pattern in local coordinate system using 2-D coordinate transformation. In addition, in the case of large elevation angle, only half elements of the CCA can receive signal due to the shadow effect. The array degrees of freedom (DOF) are reduced by halves. We introduce the difference coarray method, which increases the DOF. Moreover, we propose a more accurate propagator method for 2-D cases. This method constructs a new propagation matrix and reduces the estimation error. In addition, this method reduces computational complexity by using linear computations instead of eigenvalue decomposition (EVD) and avoids spectral search. Simulation and experiment verify the estimation performance of the CCA. Both demonstrate the CCA model established in this paper is corresponding to the designed CCA antenna, and the proposed algorithms meet the needs of CCA angle detection. When the number of array elements is 12, the estimation accuracy is about 5 degrees.

EM and SAGE Algorithms for DOA Estimation in the Presence of Unknown Uniform Noise.

The existing expectation maximization (EM) and space-alternating generalized EM (SAGE) algorithms are only applied to direction of arrival (DOA) estimation in known noise. In this paper, the two algorithms are designed for DOA estimation in unknown uniform noise. Both the deterministic and random signal models are considered. In addition, a new modified EM (MEM) algorithm applicable to the noise assumption is also proposed. Next, these EM-type algorithms are improved to ensure the stability when the powers of sources are not equal. After being improved, simulation results illustrate that the EM algorithm has similar convergence with the MEM algorithm, the SAGE algorithm outperforms the EM and MEM algorithms for the deterministic signal model, and the SAGE algorithm cannot always outperform the EM and MEM algorithms for the random signal model. Furthermore, simulation results show that processing the same snapshots from the random signal model, the SAGE algorithm for the deterministic signal model can require the fewest computations.

Reweighted Off-Grid Sparse Spectrum Fitting for DOA Estimation in Sensor Array with Unknown Mutual Coupling.

In the environment of unknown mutual coupling, many works on direction-of-arrival (DOA) estimation with sensor array are prone to performance degradation or even failure. Moreover, there are few literatures on off-grid direction finding using regularized sparse recovery technology. Therefore, the scenario of off-grid DOA estimation in sensor array with unknown mutual coupling is investigated, and then a reweighted off-grid Sparse Spectrum Fitting (Re-OGSpSF) approach is developed in this article. Inspired by the selection matrix, an undisturbed array output is formed to remove the unknown mutual coupling effect. Subsequently, a refined off-grid SpSF (OGSpSF) recovery model is structured by integrating the off-grid error term obtained from the first-order Taylor approximation of the higher-order term into the underlying on-grid sparse representation model. After that, a novel Re-OGSpSF framework is formulated to recover the sparse vectors, where a weighted matrix is developed by the MUSIC-like spectrum function to enhance the solution's sparsity. Ultimately, off-grid DOA estimation can be realized with the help of the recovered sparse vectors. Thanks to the off-grid representation and reweighted strategy, the proposed method can effectively and efficiently achieve high-precision continuous DOA estimation, making it favorable for real-time direction finding. The simulation results validate the superiority of the proposed method.

Fast DOA Estimation Algorithms via Positive Incremental Modified Cholesky Decomposition for Augmented Coprime Array Sensors.

This paper proposes a fast direction of arrival (DOA) estimation method based on positive incremental modified Cholesky decomposition atomic norm minimization (PI-CANM) for augmented coprime array sensors. The approach incorporates coprime sampling on the augmented array to generate a non-uniform, discontinuous virtual array. It then utilizes interpolation to convert this into a uniform, continuous virtual array. Based on this, the problem of DOA estimation is equivalently formulated as a gridless optimization problem, which is solved via atomic norm minimization to reconstruct a Hermitian Toeplitz covariance matrix. Furthermore, by positive incremental modified Cholesky decomposition, the covariance matrix is transformed from positive semi-definite to positive definite, which simplifies the constraint of optimization problem and reduces the complexity of the solution. Finally, the Multiple Signal Classification method is utilized to carry out statistical signal processing on the reconstructed covariance matrix, yielding initial DOA angle estimates. Experimental outcomes highlight that the PI-CANM algorithm surpasses other algorithms in estimation accuracy, demonstrating stability in difficult circumstances such as low signal-to-noise ratios and limited snapshots. Additionally, it boasts an impressive computational speed. This method enhances both the accuracy and computational efficiency of DOA estimation, showing potential for broad applicability.

A Nested-Nested Sparse Array Specially for Monostatic Colocated MIMO Radar with Increased Degree of Freedom.

This paper mainly investigates the problem of direction of arrival (DOA) estimation for a monostatic MIMO radar. Specifically, the proposed array, which is called a nested-nested sparse array (NNSA), is structurally composed of two nested subarrays, a NA with N1+N2 elements and a sparse NA, respectively, with N3+N4 elements. The design process of NNSA is optimized into two steps and presented in detail. Setting NNSA as transmitter/receiver arrays, we derive the closed-form expression of consecutive DOFs and calculate the mutual coupling coefficient. Eventually, extensive simulations are carried out and the results verify the superiority of the proposed array over the previous arrays in terms of consecutive DOFs, array aperture and mutual coupling effect.

Direction-of-Arrival Estimation Method Based on Neural Network with Temporal Structure for Underwater Acoustic Vector Sensor Array.

Acoustic vector sensor (AVS) is a kind of sensor widely used in underwater detection. Traditional methods use the covariance matrix of the received signal to estimate the direction-of-arrival (DOA), which not only loses the timing structure of the signal but also has the problem of weak anti-noise ability. Therefore, this paper proposes two DOA estimation methods for underwater AVS arrays, one based on a long short-term memory network and attention mechanism (LSTM-ATT), and the other based on Transformer. These two methods can capture the contextual information of sequence signals and extract features with important semantic information. The simulation results show that the two proposed methods perform much better than the multiple signal classification (MUSIC) method, especially in the case of low signal-to-noise ratio (SNR), the DOA estimation accuracy has been greatly improved. The accuracy of the DOA estimation method based on Transformer is comparable to that of the DOA estimation method based on LSTM-ATT, but the computational efficiency is obviously better than that of the DOA estimation method based on LSTM-ATT. Therefore, the DOA estimation method based on Transformer proposed in this paper can provide a reference for fast and effective DOA estimation under low SNR.

Research on Underdetermined DOA Estimation Method with Unknown Number of Sources Based on Improved CNN.

This paper proposes a joint estimation method for source number and DOA based on an improved convolutional neural network for unknown source number and undetermined DOA estimation. By analyzing the signal model, the paper designs a convolutional neural network model based on the existence of a mapping relationship between the covariance matrix and both the source number and DOA estimation. The model, which discards the pooling layer to avoid data loss and introduces the dropout method to improve generalization, takes the signal covariance matrix as input and the two branches of source number estimation and DOA estimation as outputs, and achieves the unfixed number of DOA estimation by filling in invalid values. Simulation experiments and analysis of the results show that the algorithm can effectively achieve the joint estimation of source number and DOA. Under the conditions of high SNR and a large snapshot number, both the proposed algorithm and the traditional algorithm have high estimation accuracy, while under the conditions of low SNR and a small snapshot, the algorithm is better than the traditional algorithm, and under the underdetermined conditions, where the traditional algorithm often fails, the algorithm can still achieve the joint estimation.

Centroid Optimization of DNN Classification in DOA Estimation for UAV.

Classifications based on deep learning have been widely applied in the estimation of the direction of arrival (DOA) of signal. Due to the limited number of classes, the classification of DOA cannot satisfy the required prediction accuracy of signals from random azimuth in real applications. This paper presents a Centroid Optimization of deep neural network classification (CO-DNNC) to improve the estimation accuracy of DOA. CO-DNNC includes signal preprocessing, classification network, and Centroid Optimization. The DNN classification network adopts a convolutional neural network, including convolutional layers and fully connected layers. The Centroid Optimization takes the classified labels as the coordinates and calculates the azimuth of received signal according to the probabilities of the Softmax output. The experimental results show that CO-DNNC is capable of acquiring precise and accurate estimation of DOA, especially in the cases of low SNRs. In addition, CO-DNNC requires lower numbers of classes under the same condition of prediction accuracy and SNR, which reduces the complexity of the DNN network and saves training and processing time.

Direction-of-Arrival Estimation for a Random Sparse Linear Array Based on a Graph Neural Network.

This article proposes a direction-of-arrival (DOA) estimation algorithm for a random sparse linear array based on a novel graph neural network (GNN). Unlike convolutional layers and fully connected layers, which do not interact well with information between different antennas, the GNN model can adapt to the goniometry problem of non-uniform random sparse linear arrays without any prior information by applying neighbor nodes' aggregation and update operations. This helps the model in learning signal features under complex environmental conditions. We train the model in an end-to-end way to reduce the complexity of the network. Experiments are conducted on the uniform and sparse linear arrays for various signal-to-noise ratio (SNR) and numbers of snapshots for comparison. We prove that the GNN model has superior angle estimation performance on arrays with large sparsity that cannot be used by traditional algorithms and surpasses existing deep learning models based on convolutional or fully connected structures. The proposed algorithm shows excellent DOA estimation performance under the complex conditions of limited snapshots, low signal-to-noise ratio, and large array sparsity as well. In addition, the algorithm has a low time calculation cost and is suitable for scenarios that require low latency.

Direction-of-Arrival (DoA) Estimation Performance for Satellite Applications in a Multipath Environment with Rician Fading and Spatial Correlation.

Direction-of-arrival (DoA) estimation methods are highly versatile and find extensive applications in satellite communication. DoA methods are employed across a range of orbits, from low Earth orbits (LEO) to geostationary Earth orbits (GEO). They serve multiple applications, including altitude determination, geolocation and estimation accuracy, target localization, and relative and collaborative positioning. This paper provides a framework for modeling the DoA angle in satellite communications with respect to the elevation angle. The proposed approach employs a closed-form expression that incorporates various factors, such as the antenna boresight angle, satellite and Earth station positions, and the altitude parameters of the satellite stations. By leveraging this formulation, the work accurately calculates the Earth station's elevation angle and effectively models the DoA angle. To the authors' knowledge, this contribution is unique and has not been previously addressed in the available literature. Furthermore, this paper studies the impact of spatial correlation in the channel on well-known DoA estimation techniques. As a significant part of this contribution, the authors introduce a signal model incorporating correlation in satellite communication. Although selected studies have presented spatial signal correlation models in satellite communications to analyze the performance metrics, such as the bit error or symbol error probability, outage probability, and ergodic capacity, this work stands out by presenting and adapting a correlation model in the signal specifically for studying DoA estimations. Accordingly, this paper evaluates DoA estimation performance using root mean square error (RMSE) measurements for different satellite communication link conditions (uplink and downlink) through extensive Monte Carlo simulations. The simulation's performance is evaluated by comparing it with the Cramer-Rao lower bound (CRLB) performance metric under additive white Gaussian noise (AWGN) conditions, i.e., thermal noise. The simulation results demonstrate that incorporating a spatial signal correlation model for DoA estimations significantly improves RMSE performance in satellite systems.

A New Gain-Phase Error Pre-Calibration Method for Uniform Linear Arrays.

In this paper, we consider the gain-phase error calibration problem for uniform linear arrays (ULAs). Based on the adaptive antenna nulling technique, a new gain-phase error pre-calibration method is proposed, requiring only one calibration source with known direction of arrival (DOA). In the proposed method, a ULA with M array elements is divided into M-1 sub-arrays, and the gain-phase error of each sub-array can be uniquely extracted one by one. Furthermore, in order to obtain the accurate gain-phase error in each sub-array, we formulate an errors-in-variables (EIV) model and present a weighted total least-squares (WTLS) algorithm by exploiting the structure of the received data on sub-arrays. In addition, the solution to the proposed WTLS algorithm is exactly analyzed in the statistical sense, and the spatial location of the calibration source is also discussed. Simulation results demonstrate the efficiency and feasibility of our proposed method in both large-scale and small-scale ULAs and the superiority to some state-of-the-art gain-phase error calibration approaches.