GNSS Spoofing Detection via the Intersection Angle between Two Directions of Arrival in a Single Rotating Antenna

Spoofing against the Global Navigation Satellite System (GNSS) is an attack with strong concealment, posing a significant threat to the security of the GNSS. Many strategies have been developed to prevent such attacks, but current detection methods based on signal direction for multi-agent spoofing require multiple antennas/receivers, leading to increased cost and complexity in implementation. Additionally, methods utilizing a moving single antenna cannot effectively detect multi-agent spoofing. Therefore, we introduce a novel spoofing-detection technique based on the intersection angle between two directions of arrival (IA-DOA) using a single rotating antenna. The essence of this approach lies in estimating the IA-DOA between a pair of signals by utilizing the carrier-to-noise ratio (CNR) and carrier phase single difference (CPSD) of the received signal. The estimation of IA-DOA should be consistent with the prediction when there is no spoofing. With spoofing, it is difficult to accurately simulate the directionality of navigation signals, which can disrupt the consistency between the estimation and prediction of IA-DOA. Therefore, estimations and predictions of IA-DOA can be used to establish detection variables through generalized likelihood ratio testing (GLRT) to detect multi-agent spoofing. We conducted a simulation to analyze the impact of the antenna's parameters on the detection performance and evaluated it through on-site experiments. The results indicate that the method proposed in this article can efficiently achieve real-time detection of multi-agent spoofing.

Blind Source Separation of Intermittent Frequency Hopping Sources over LOS and NLOS Channels

This paper studies blind source separation (BSS) for frequency hopping (FH) sources. These radio frequency (RF) signals are observed by a uniform linear array (ULA) over (i) line-of-sight (LOS), (ii) single-cluster, and (iii) multiple-cluster Spatial Channel Model (SCM) settings. The sources are stationary, spatially sparse, and their activity is intermittent and assumed to follow a hidden Markov model (HMM). BSS is achieved by leveraging direction of arrival (DOA) information through an FH estimation stage, a DOA estimation stage, and a pairing stage with the latter associating FH patterns with physical sources via their estimated DOAs. Current methods in the literature do not perform the association of multiple frequency hops to the sources they are transmitted from. We bridge this gap by pairing the FH estimates with DOA estimates and labeling signals to their sources, irrespective of their hopped frequencies. A state filtering technique, referred to as hidden state filtering (HSF), is developed to refine DOA estimates for sources that follow a HMM. Numerical results demonstrate that the proposed approach is capable of separating multiple intermittent FH sources.

Simultaneous Estimation of Azimuth and Elevation Angles Using a Decision Tree-Based Method

This study addresses the problem of accurately predicting azimuth and elevation angles of signals impinging on an antenna array employing Machine Learning (ML). Using the information obtained at a receiving system when a transmitter's signal hits it, a Decision Tree (DT) model is trained to estimate azimuth and elevation angles simultaneously. Simulation results demonstrate the robustness of the proposed DT-based method, showcasing its ability to predict the Direction of Arrival (DOA) in diverse conditions beyond the ones present in the training dataset, i.e., the results display the model's generalization capability. Additionally, the comparative analysis reveals that DT-based DOA estimation outperforms the state-of-the-art MUltiple SIgnal Classification (MUSIC) algorithm. Our results demonstrate an average reduction of over 90% in the prediction error and 50% in the prediction time achieved by our proposal when compared to the MUSIC algorithm. These results establish DTs as competitive alternatives for DOA estimation in signal reception systems.

A Flexible Design Strategy for Three-Element Non-Uniform Linear Arrays

This paper illustrates a flexible design strategy for a three-element non-uniform linear array (NULA) aimed at estimating the direction of arrival (DoA) of a source of interest. Thanks to the spatial diversity resulting from non-uniform sensor spacings, satisfactory DoA estimation accuracies can be achieved by employing a very limited number of receiving elements. This makes NULA configurations particularly attractive for low-cost passive location applications. To estimate the DoA of the source of interest, we resort to the maximum likelihood estimator, and the proposed design strategy is obtained by constraining the maximum pairwise error probability to control the errors occurring due to outliers. In fact, it is well known that the accuracy of the maximum likelihood estimator is often degraded by outliers, especially when the signal-to-noise power ratio does not belong to the so-called asymptotic region. The imposed constraint allows for the defining of an admissible region in which the array should be selected. This region can be further modified to incorporate practical design constraints concerning the antenna element size and the positioning accuracy. The best admissible array is then compared to the one obtained with a conventional NULA design approach, where only antenna spacings multiple of λ/2 are considered, showing improved performance, which is also confirmed by the experimental results.

Alias-Free Arrays

Nonuniform array geometries provide freedom for increased aperture and reduced mutual coupling. A necessary and sufficient condition is given for an array of isotropic sensor elements to be unambiguous for any specified set of directions of arrival. The set of unambiguous spatial frequencies is shown to be a parallelepiped, admitting simple geometrical interpretation. Results are used in design of linear, planar, and 3D arrays.

Displacement Estimation Using 3D-Printed RFID Arrays for Structural Health Monitoring

Radio frequency identification (RFID) tags are small, low-cost, wearable, and wireless sensors that can detect movement in structures, humans, or robots. In this paper, we use passive RFID tags for structural health monitoring by detecting displacements. We employ a novel process of using 3D printable embedded passive RFID tags within uniform linear arrays together with the multiple signal classification algorithm to estimate the direction of arrival using only the phase of the backscattered signals. We validate our proposed approach via data collected from real-world experiments using a unipolar RFID reader antenna and both narrowband and wideband measurements.

Adaptive Beamforming Approaches to Improve Passive Radar Performance in Sea and Wind Farms' Clutter

This article presents the problem of passive radar vessel detection in a real coastal scenario in the presence of sea and wind farms' clutter, which are characterised by high spatial and time variability due to the influence of weather conditions. Deterministic and adaptive beamforming techniques are proposed and evaluated using real data. Key points such as interference localisation and characterisation are tackled in the passive bistatic scenario with omnidirectional illuminators that critically increase the area of potential clutter sources to areas far from the surveillance area. Adaptive beamforming approaches provide significant Signal-to-Interference improvements and important radar coverage improvements. In the presented case study, an aerial target is detected 28 km far from the passive radar receiver, fulfilling highly demanding performance requirements.

Optimal Array Design and Directive Sensors for Guided Waves DoA Estimation

The estimation of Direction of Arrival (DoA) of guided ultrasonic waves is an important task in many Structural Health Monitoring (SHM) applications. The aim is to locate sources of elastic waves which can be generated by impacts or defects in the inspected structures. In this paper, the array geometry and the shape of the piezo-sensors are designed to optimize the DoA estimation on a pre-defined angular sector, from acquisitions affected by noise and interference. In the proposed approach, the DoA of a wave generated by a single source is considered as a random variable that is uniformly distributed in a given range. The wave velocity is assumed to be unknown and the DoA estimation is performed by measuring the Differences in Time of Arrival (DToAs) of wavefronts impinging on the sensors. The optimization procedure of sensors positioning is based on the computation of the DoA and wave velocity parameters Cramér-Rao Matrix Bound (CRMB) with a Bayesian approach. An efficient DoA estimator is found based on the DToAs Gauss-Markov estimator for a three sensors array. Moreover, a novel directive sensor for guided waves is introduced to cancel out undesired Acoustic Sources impinging from DoAs out of the given angles range. Numerical results show the capability to filter directional interference of the novel sensor and a considerably improved DoA estimation performance provided by the optimized sensor cluster in the pre-defined angular sector, as compared to conventional approaches.

An Enhanced Smoothed L0-Norm Direction of Arrival Estimation Method Using Covariance Matrix

An enhanced smoothed l0-norm algorithm for the passive phased array system, which uses the covariance matrix of the received signal, is proposed in this paper. The SL0 (smoothed l0-norm) algorithm is a fast compressive-sensing-based DOA (direction-of-arrival) estimation algorithm that uses a single snapshot from the received signal. In the conventional SL0 algorithm, there are limitations in the resolution and the DOA estimation performance, since a single sample is used. If multiple snapshots are used, the conventional SL0 algorithm can improve performance in terms of the DOA estimation. In this paper, a covariance-fitting-based SL0 algorithm is proposed to further reduce the number of optimization variables when using multiple snapshots of the received signal. A cost function and a new null-space projection term of the sparse recovery for the proposed scheme are presented. In order to verify the performance of the proposed algorithm, we present the simulation results and the experimental results based on the measured data.

Parameter Estimation for Two-Dimensional Incoherently Distributed Source with Double Cross Arrays

A direction of arrival (DOA) estimator for two-dimensional (2D) incoherently distributed (ID) sources is presented under proposed double cross arrays, satisfying both the small interval of parallel linear arrays and the aperture equalization in the elevation and azimuth dimensions. First, by virtue of a first-order Taylor expansion for array manifold vectors of parallel linear arrays, the received signal of arrays can be reconstructed by the products of generalized manifold matrices and extended signal vectors. Then, the rotating invariant relations concerning the nominal elevation and azimuth are derived. According to the rotating invariant relationships, the rotating operators are obtained through the subspace of the covariance matrix of the received vectors. Last, the angle matching approach and angular spreads are explored based on the Capon principle. The proposed method for estimating the DOA of 2D ID sources does not require a spectral search and prior knowledge of the angular power density function. The proposed DOA estimation has a significant advantage in terms of computational cost. Investigating the influence of experimental conditions and angular spreads on estimation, numerical simulations are carried out to validate the effectiveness of the proposed method. The experimental results show that the algorithm proposed in this paper has advantages in terms of estimation accuracy, with a similar number of sensors and the same experimental conditions when compared with existing methods, and that it shows a robustness in cases of model mismatch.

An Array Switching Strategy for Direction of Arrival Estimation with Coprime Linear Array in the Presence of Mutual Coupling

While the coprime array still suffers from performance degradation due to the mutual coupling dominated by the interleaved subarrays, we propose an array switching strategy for coprime linear array (CLA) by utilizing the large inter-element spacings of the subarrays to mitigate the mutual coupling. Specifically, we first collect the signals by separately activating the two subarrays, where the severe mutual coupling effect is significantly reduced. As a result, well-performed initial direction of arrival (DOA) estimates can be achieved. Subsequently, we establish a quadratic optimization problem by reconstructing the contaminated steering vector of the total CLA elaborately to calculate the mutual coupling coefficients with the initial DOA estimates. Finally, we can obtain refined DOA estimates by an iteration procedure based on the estimated mutual coupling matrix. In addition, numerical simulations are provided to demonstrate the merits of the proposed scheme.

Automatic Acoustic Target Detecting and Tracking on the Azimuth Recording Diagram with Image Processing Methods

Passive acoustic target detection has been a hot research topic for a few decades. Azimuth recording diagram is one of the most promising techniques to estimate the arrival direction of the interested signal by visualizing the sound wave information. However, this method is challenged by the random ambient noise, resulting in low reliability and short effective distance. This paper presents a real-time postprocessing framework for passive acoustic target detection modalities by using a sonar array, in which image processing methods are used to automate the target detecting and tracking on the azimuth recording diagram. The simulation results demonstrate that the proposed approach can provide a higher reliability compared with the conventional ones, and is suitable for the constraints of real-time tracking.

Ultra-Wideband Angle of Arrival Estimation Based on Angle-Dependent Antenna Transfer Function

Ultra-wideband radio signals are used in communication, indoor localization and radar systems, due to the high data rates, the high resilience to fading and the fine temporal resolution that can be achieved with a large bandwidth. This paper introduces a new method to estimate the angle of arrival of ultra-wideband radio signals with which existing time-of-flight based localization and radar systems can be augmented at no additional hardware cost. The method does not require multiple transmitter or receiver antennas, or relative motion between transmitter and receiver. Instead, it is solely based on the angle-dependent impulse response function of ultra-wideband antennas. Datasets on which the method is evaluated are publicly available. The method is further applied to a localization problem and it is shown how a robot can self-localize solely based on these angle of arrival estimates, and how they can be combined with time-of-flight measurements. Even though existing angle of arrival techniques that use multiple antennas show better accuracy, the method presented herein looks promising enough to be developed further and could potentially lead to electronically and mechanically simpler angle of arrival estimation technology.

Bayesian Inference for Acoustic Direction of Arrival Analysis Using Spherical Harmonics

This work applies two levels of inference within a Bayesian framework to accomplish estimation of the directions of arrivals (DoAs) of sound sources. The sensing modality is a spherical microphone array based on spherical harmonics beamforming. When estimating the DoA, the acoustic signals may potentially contain one or multiple simultaneous sources. Using two levels of Bayesian inference, this work begins by estimating the correct number of sources via the higher level of inference, Bayesian model selection. It is followed by estimating the directional information of each source via the lower level of inference, Bayesian parameter estimation. This work formulates signal models using spherical harmonic beamforming that encodes the prior information on the sensor arrays in the form of analytical models with an unknown number of sound sources, and their locations. Available information on differences between the model and the sound signals as well as prior information on directions of arrivals are incorporated based on the principle of the maximum entropy. Two and three simultaneous sound sources have been experimentally tested without prior information on the number of sources. Bayesian inference provides unambiguous estimation on correct numbers of sources followed by the DoA estimations for each individual sound sources. This paper presents the Bayesian formulation, and analysis results to demonstrate the potential usefulness of the model-based Bayesian inference for complex acoustic environments with potentially multiple simultaneous sources.

Robust Directional Angle Estimation of Underwater Acoustic Sources Using a Marine Vehicle

Acoustic source localization is used in many underwater applications. Acquiring an accurate directional angle for an acoustic source is crucial for source localization. To achieve this purpose, this paper presents a method for directional angle estimation of underwater acoustic sources using a marine vehicle. It is assumed that the vehicle is equipped with two hydrophones and that the acoustic source transmits a specific signal repeatedly. The proposed method provides a probabilistic model for time delay estimation. The probability is recursively updated by prediction and update steps. The prediction step performs a probability transition using the angular displacement of the marine vehicle. The predicted probability is updated using a generalized cross correlation function with a verification process using entropy measurement. The proposed method can provide a reliable and accurate estimation of the directional angles of underwater acoustic sources. Experimental results demonstrate good performance of the proposed probabilistic directional angle estimation method in both an inland water environment and a harbor environment.

Sparse Reconstruction Based Robust Near-Field Source Localization Algorithm

Non-Gaussian impulsive noise widely exists in the real world, this paper takes the α-stable distribution as the mathematical model of non-Gaussian impulsive noise and works on the joint direction-of-arrival (DOA) and range estimation problem of near-field signals in impulsive noise environment. Since the conventional algorithms based on the classical second order correlation statistics degenerate severely in the impulsive noise environment, this paper adopts two robust correlations, the fractional lower order correlation (FLOC) and the nonlinear transform correlation (NTC), and presents two related near-field localization algorithms. In our proposed algorithms, by exploring the symmetrical characteristic of the array, we construct the robust far-field approximate correlation vector in relation with the DOA only, which allows for bearing estimation based on the sparse reconstruction. With the estimated bearing, the range can consequently be obtained by the sparse reconstruction of the output of a virtual array. The proposed algorithms have the merits of good noise suppression ability, and their effectiveness is demonstrated by the computer simulation results.

Double-Layer Compressive Sensing Based Efficient DOA Estimation in WSAN with Block Data Loss

Accurate information acquisition is of vital importance for wireless sensor array network (WSAN) direction of arrival (DOA) estimation. However, due to the lossy nature of low-power wireless links, data loss, especially block data loss induced by adopting a large packet size, has a catastrophic effect on DOA estimation performance in WSAN. In this paper, we propose a double-layer compressive sensing (CS) framework to eliminate the hazards of block data loss, to achieve high accuracy and efficient DOA estimation. In addition to modeling the random packet loss during transmission as a passive CS process, an active CS procedure is introduced at each array sensor to further enhance the robustness of transmission. Furthermore, to avoid the error propagation from signal recovery to DOA estimation in conventional methods, we propose a direct DOA estimation technique under the double-layer CS framework. Leveraging a joint frequency and spatial domain sparse representation of the sensor array data, the fusion center (FC) can directly obtain the DOA estimation results according to the received data packets, skipping the phase of signal recovery. Extensive simulations demonstrate that the double-layer CS framework can eliminate the adverse effects induced by block data loss and yield a superior DOA estimation performance in WSAN.

Wideband Direction of Arrival Estimation in the Presence of Unknown Mutual Coupling

This paper investigates a subarray based algorithm for direction of arrival (DOA) estimation of wideband uniform linear array (ULA), under the presence of frequency-dependent mutual coupling effects. Based on the Toeplitz structure of mutual coupling matrices, the whole array is divided into the middle subarray and the auxiliary subarray. Then two-sided correlation transformation is applied to the correlation matrix of the middle subarray instead of the whole array. In this way, the mutual coupling effects can be eliminated. Finally, the multiple signal classification (MUSIC) method is utilized to derive the DOAs. For the condition when the blind angles exist, we refine DOA estimation by using a simple approach based on the frequency-dependent mutual coupling matrixes (MCMs). The proposed method can achieve high estimation accuracy without any calibration sources. It has a low computational complexity because iterative processing is not required. Simulation results validate the effectiveness and feasibility of the proposed algorithm.

Acoustical Direction Finding with Time-Modulated Arrays

Time-Modulated Linear Arrays (TMLAs) offer useful efficiency savings over conventional phased arrays when applied in parameter estimation applications. The present paper considers the application of TMLAs to acoustic systems and proposes an algorithm for efficiently deriving the arrival angle of a signal. The proposed technique is applied in the frequency domain, where the signal and harmonic content is captured. Using a weighted average method on harmonic amplitudes and their respective main beam angles, it is possible to determine an estimate for the signal’s direction of arrival. The method is demonstrated and evaluated using results from both numerical and practical implementations and performance data is provided. The use of Micro-Electromechanical Systems (MEMS) sensors allows time-modulation techniques to be applied at ultrasonic frequencies. Theoretical predictions for an array of five isotropic elements with half-wavelength spacing and 1000 data samples suggest an accuracy of ±1∘ within an angular range of approximately ±50∘. In experiments of a 40 kHz five-element microphone array, a Direction of Arrival (DoA) estimation within ±2.5∘ of the target signal is readily achieved inside a ±45∘ range using a single switched input stage and a simple hardware setup.

A Simulation Study of a Radiofrequency Localization System for Tracking Patient Motion in Radiotherapy

One of the most widely used tools in cancer treatment is external beam radiotherapy. However, the major risk involved in radiotherapy is excess radiation dose to healthy tissue, exacerbated by patient motion. Here, we present a simulation study of a potential radiofrequency (RF) localization system designed to track intrafraction motion (target motion during the radiation treatment). This system includes skin-wearable RF beacons and an external tracking system. We develop an analytical model for direction of arrival measurement with radio frequencies (GHz range) for use in a localization estimate. We use a Monte Carlo simulation to investigate the relationship between a localization estimate and angular resolution of sensors (signal receivers) in a simulated room. The results indicate that the external sensor needs an angular resolution of about 0.03 degrees to achieve millimeter-level localization accuracy in a treatment room. This fundamental study of a novel RF localization system offers the groundwork to design a radiotherapy-compatible patient positioning system for active motion compensation.

Auditory Model-Based Sound Direction Estimation With Bilateral Cochlear Implants

Users of bilateral cochlear implants (CIs) show above-chance performance in localizing the source of a sound in the azimuthal (horizontal) plane; although localization errors are far worse than for normal-hearing listeners, they are considerably better than for CI listeners with only one implant. In most previous studies, subjects had access to interaural level differences and to interaural time differences conveyed in the temporal envelope. Here, we present a binaural model that predicts the azimuthal direction of sound arrival from a two-channel input signal as it is received at the left and right CI processor. The model includes a replication of a clinical speech-coding strategy, a model of the electrode-nerve interface and binaural brainstem neurons, and three different prediction stages that are trained to map the neural response rate to an azimuthal angle. The model is trained and tested with various noise and speech stimuli created by means of virtual acoustics. Localization error patterns of the model match experimental data and are explicable largely in terms of the nonmonotonic relationship between interaural level difference and azimuthal angle.