Direction Of Arrival Measurements Research Articles

A geometric solution to microphone array position calibration and its confidence interval analysis

Wireless acoustic sensor networks (WASNs) comprised of spatially distributed acoustic nodes have been increasingly popular in many areas such as speech enhancement, blind source separation, and audio surveillance, where node position information is generally required to implement relevant processing algorithms. In this article, we focus on the node position calibration only using direction-of-arrival (DOA) information with each node consisting of a microphone array. State-of-the-art techniques translate the position calibration into optimization of DOA-based cost functions, and have shown notable success. However, a compromise between position calibration accuracy and computational load still exists. Furthermore, none of the existing studies can offer a quantitative evaluation of calibration performance before the optimization procedure is finished. To address these problems, a geometric solution to array node position calibration is proposed using DOA measurements. For a given array node, DOAs of three sources are first utilized to construct cylinder, plane, and cone equations. Next, the two-dimensional projection of intersections among these equations is calculated using Sylvesterresultantmatrix. Finally, a closed-form solution of node position in three-dimensional space is established. Moreover, explicit mathematical derivation of the confidence interval analysis on the calibration results under given node angle estimation error condition is presented, indicating that the proposed method can provide predictable performance with corresponding probabilities. The Cramér-Rao bound (CRB) is further investigated. Simulation results reveal that as compared with existing methods our approach achieves comparable calibration accuracy with much less computational burden. Real-world experiments also verify its effectiveness.

Novel cooperative localization method of over-the-horizon shortwave emitters based on direction-of-arrival and time-difference-of-arrival measurements

The location of long-distance shortwave radiation sources is practically significant in national defense security. Shortwave multistation-positioning systems mainly include direction-of-arrival (DOA) and time-difference-of-arrival (TDOA) intersection locations. These two systems have their advantages and disadvantages in terms of performance. To combine the advantages of these two positioning technologies, this study focuses on the cooperative positioning problem based on DOA and TDOA measurements. First, the two-dimensional DOA and TDOA observation models are established for the over-the-horizon propagation scenario. Subsequently, the Cramér-Rao lower bound (CRLB) of positioning accuracy is derived in the presence of measurement errors in virtual ionosphere height. Aiming at the strong nonlinear characteristics of the observation equations, a new DOA/TDOA cooperative localization method is proposed. Finally, the asymptotic efficiency of the new estimator is proved using the first-order error analysis theory. The new method comprises two stages. In the first stage, the shortwave DOA observation equation is transformed into a pseudo-linear observation equation by introducing an auxiliary variable, as well as solving a quadratic equation with one unknown. Next, an optimization model with two quadratic equality constraints is constructed, and an iterative optimization algorithm based on matrix $~\bf{QR}$ decomposition is proposed to obtain an intermediate estimate of the emitter position. The second stage transforms the shortwave TDOA observation equation into a pseudo-linear observation equation by combining the intermediate estimates given in the first phase. Also, an iterative-constrained weighted-least-squares estimator based on the matrix decomposition is proposed again to localize the emitter. Simulation results show that the new cooperative localization method has good global convergence, the localization performance can reach the CRLB, and the obtained cooperative gain is quite high.

On Performance Loss of DOA Measurement Using Massive MIMO Receiver With Mixed-ADCs

High hardware cost and high power consumption of massive multiple-input and multiple output (MIMO) are two challenges for the future wireless communications including sixth generation (6G). Adopting the low-resolution analog-to-digital converter (ADC) is viewed as a promising solution. Additionally, the direction of arrival (DOA) estimation is an indispensable technology for beam alignment and tracking in massive MIMO systems. Thus, in this letter, the performance of DOA estimation with mixed-ADC structure is firstly investigated. The Cramér-Rao lower bound (CRLB) for this architecture is derived based on the additive quantization noise model. Eventually, a performance loss factor and the associated energy efficiency factor is defined for analysis in detail. Simulation results show that the mixed-ADC architecture can strike a good balance among performance loss, circuit cost and energy efficiency. More importantly, just a few bits (up to 4 bits) of low-resolution ADCs can achieve a satisfactory performance for DOA measurement.

A Cooperative Positioning Method of Connected and Automated Vehicles with Direction-of-Arrival and Relative Distance Fusion

The rapid development of science and technology has created favorable conditions for Connected and Automated Vehicles (CAVs). Accurate localization is one of the fundamental functions of CAV to realize some advanced operations such as vehicle platooning. However, complicated urban traffic environments, such as the flyover, significantly influence vehicular positioning accuracy. The inability of CAV to accurately perceive self-localization information has become an urgent issue to be addressed. This paper proposed a novel cooperative localization method by introducing the relative Direction-of-Arrival (DOA) and Relative Distance (RD) into CAV to improve the localization accuracy of CAV in the multivehicle environment. First, the three-dimensional positioning error model of the host vehicle concerning adjacent vehicles in azimuth angle and pitch angle and intervehicle distances under the vehicle-to-vehicle communication was established. Second, two least-squares estimation algorithms, linear and nonlinear, are established to decrease the position errors by combining relative DOA and RD measurement information. To verify the proposed algorithm's effect, the PreScan-Simulink joint simulation is carried out. The results show that the host vehicle's localization accuracy by the proposed method can be improved by 25% compared with direct linearization. Besides, by combining relative DOA and relative RD measurement, the locating capability of the least-square-based nonlinear optimization method can be enhanced by 22%.

Hybrid TOA–DOA techniques for maneuvering underwater target tracking using the sensor nodes on the sea surface

This article handles tracking an underwater target utilizing multiple sensor nodes on the sea surface. This article focuses on hybrid usage of Time of Arrival (TOA), and Direction of Arrival (DOA) to track a maneuvering underwater target. In the considered DOA problem, a sensor node measures the bearing of the target, but not the elevation of the target. We show that at least two sensor nodes are required for hybrid TOA–DOA localization. Our tracking algorithm is based on the Interacting Multiple Model Kalman Filter (IMM KF) and generates a satisfactory target estimate in a time efficient manner. As far as we know, our article is novel in presenting an underwater target tracking algorithm based on hybrid usage of TOA–DOA measurements. The effectiveness of our tracking algorithm is verified utilizing MATLAB simulations.

Gaussian Tracking With Kent-Distributed Direction-of-Arrival Measurements

This paper presents a Gaussian tracking algorithm with direction-of-arrival (DOA) measurements modelled via the Kent distribution. The key aspect of the algorithm is that the Kent distribution directly models the specific characteristics of DOA measurements in the 3-D space, and can account for different uncertainties in azimuth and elevation, which the von Mises-Fisher distribution cannot. At each update step, the algorithm performs iterated statistical linear regressions. We provide two implementations of the algorithms, one based on sigma-points and the other on analytical linearisation. The effectiveness of the approach is evaluated via numerical simulations.

A New Rigid Body Localization Scheme Exploiting Participatory Search Algorithm

Since both the position and the orientation of a rigid target can be estimated with a few sensors, which are mounted on the target, it is well known that the rigid body localization (RBL) has various potential applications. In this paper, we propose a new RBL scheme exploiting a participatory search algorithm to simultaneously estimate the unknown parameters for both the three-dimensional displacement and the rotation angles of the target with a single base station using direction of arrival measurements. The performance of the proposed scheme is compared with that of the RBL scheme using a particle swarm optimization algorithm over various conditions such as different noise levels, iterations, various sizes of target, and various search space. According to the results of simulation, the proposed scheme provides higher hit success rate for the optimal solution, lower root mean squared errors in estimation, even with less computational complexity.

Electronic phase shift measurement for the determination of acoustic wave DOA using single MEMS biomimetic sensor

MEMS acoustic sensors have been developed to mimic the highly-accurate sound-locating system of the Ormia ochracea fly, which detects sound wavelengths much larger than its hearing organ. A typical ormia-based MEMS directional sound sensor possesses two coupled wings that vibrate in response to sound according to a superposition of its two main resonant modes, rocking and bending. Vibrations are transduced into electronic signals by interdigitated comb finger capacitors at each wing’s end along with a capacitance measuring circuitry. A sensor designed to exhibit resonant modes closely placed in frequency, enhancing their coupling, was operated with a closed cavity behind the wings. Simultaneous and independent measurements of electronic signals generated at each of the single sensor wings were used to determine incident sound direction of arrival (DOA). DOA was found proportional to the phase shift between them and to the difference over the sum of their amplitudes as well. Single sensor phase shift DOA measurement presented a resolution better than 3° for sound pressure levels of 25 mPa or greater. These results indicate that a single sensor operating in closed-cavity configuration can provide hemispherical unambiguous direction of arrival of sound waves which wavelength is much larger than the sensor size.

Machine-learning-based high-resolution DOA measurement and robust directional modulation for hybrid analog-digital massive MIMO transceiver

At hybrid analog-digital (HAD) transceiver, an improved HAD estimation of signal parameters via rotational invariance techniques (ESPRIT), called I-HAD-ESPRIT, is proposed to measure the direction of arrival (DOA) of a desired user, where the phase ambiguity due to HAD structure is dealt with successfully. Subsequently, a machine-learning (ML) framework is proposed to improve the precision of measuring DOA. Meanwhile, we find that the probability density function (PDF) of DOA measurement error (DOAME) can be approximated as a Gaussian distribution by the histogram method in ML. Then, a slightly large training data set (TDS) and a relatively small real-time set (RTS) of DOA are formed to predict the mean and variance of DOA/DOAME in the training stage and real-time stage, respectively. To improve the precisions of DOA/DOAME, three weight combiners are proposed to combine the-maximum-likelihood-learning outputs of TDS and RTS. Using the mean and variance of DOA/DOAME, their PDFs can be given directly, and we propose a robust beamformer for directional modulation (DM) transmitter with HAD by fully exploiting the PDF of DOA/DOAME, especially a robust analog beamformer on RF chain. Simulation results show that: (1) the proposed I-HAD-ESPRIT can achieve the HAD Cramer-Rao lower bound (CRLB); (2) the proposed ML framework performs much better than the corresponding real-time one without training stage; (3) the proposed robust DM transmitter can perform better than the corresponding non-robust ones in terms of secrecy rate.

Accuracy improvement in amplitude comparison‐based passive direction finding systems by adaptive squint selection

The direction of arrival (DOA) is one of the most important parameters measured by electronic warfare systems. Monopulse direction finding techniques based on amplitude comparison have many advantages because of their simplicity but they generally have limited accuracy. There are many sources of error in such a system. This work focuses on improving the noise error. An algorithm is proposed for error reduction in amplitude comparison-based direction finding systems. The algorithm, based on signal level and DOA, adaptively utilises either adjacent or alternate antennas for the DOA measurement. No additional hardware is required for the implementation of this algorithm. A prototype system is developed using spiral antennas and the performance of the proposed technique is compared against traditional ratio-based and correlation-based amplitude comparison schemes. Simulations and laboratory experiments show that the DOA accuracy can be improved by an average of 36 and 21% as compared to the ratio-based and correlation-based methods, respectively.

Maximum Likelihood Estimators for Three-Dimensional Rigid Body Localization in Internet of Things Environments

Different from the conventional point source localization, rigid body localization (RBL) not only aims to estimate the position of the target but also to acquire the attitude information, which is also essential information in many Internet of Things (IoT) applications, such as the virtual reality systems, smart parking systems. This paper develops three maximum likelihood estimators (MLEs) for the RBL purpose in 3 dimensional space via a single base station. The MLEs are designed for the RBL framework, which adopts the direction of arrival (DoA) of the signal from a small scale wireless sensor network (SSWSN) mounted on the surface of the rigid target as measurement and can be realized by a single base station. The three MLEs respectively exploit the SSWSN topology information, the DoA measurement information only, as well as the equality constraint of the rotation matrix and the DoA measurement information. In addition, we implement the modified Guass-newton algorithm for the MLEs of the rotation matrix and the translation vector. Simulations show that the proposed MLE fusing the equality constraint of the rotation matrix and the DoA measurement information most approaches the Cramer-Rao Lower Bound and also outperforms the other two MLEs in terms of convergence success rate and the computational cost.

Underwater object localization using compressive sensing

In this paper, we propose a technique to localize a moving submerged object with a sparse measurement using a hydrophone array. We used a natural muddy pond bottom with 9 m length, 5.5 m width, and 2 m depth. First, we measured the pond impulse response to identify the sound propagation characteristics. In the second phase namely static direction of arrival (DOA), the underwater speaker was placed at half-circle positions with respect to the array to simulate the underwater object trajectory, 0 deg, 30 deg, 60 deg, 90 deg, 120 deg, 150 deg, and 180 deg, respectively. The sound generated by a four-blade propeller submarine toy was measured to track its trajectory as a dynamic DOA measurement. The measured data were transformed into discrete cosine transform coefficients and reconstructed sparsely by using the basis pursuit algorithm. Based on the estimated incident angle and time delay, the reconstructed measurements were then compared to full dictionary measurement. The results showed that the error angle of the origin deviated about 2.5 deg with half of the measured data were lost. This may suggest that the sound propagation was degraded due to bottom reverberation and scatterers. Currently, we do a similar measurement in an open shallow water environment to eliminate the reverberation.

Accurate Rigid Body Localization Using DoA Measurements from a Single Base Station

Rigid body localization (RBL) is to simultaneously estimate the position and attitude of a rigid target. In this paper, we focus on the RBL problem using a single base station (BS) and direction of arrival (DoA) measurements. Several wireless sensors are mounted on the rigid body of interest, and their topology information is known a priori. The single BS measures the DoAs of wireless sensor signals and fuses them with the sensor topology information to estimate the position and orientation of the rigid body and achieve RBL. We propose two RBL methods, namely, the observation matching (OM) algorithm and topology matching (TM) algorithm with refinement. The emerging participatory searching algorithm (PSA) is adopted in both methods to solve the nonlinear matching problems. Simulations show that, compared with the existing approach, the OM method can achieve better RBL accuracy under high DoA noise levels, while the performance of the TM algorithm with refinement is closer to the constrained Cramér–Rao bound (CCRB) under low DoA noise levels.

Non-stationary source localization using direction of arrival measurements from multiple in-air vector sensors

Vector sensors utilize a combination of pressure sensors, particle velocity sensors, or both, to determine the acoustic intensity magnitude and direction pointing toward an acoustic source. This acoustic intensity vector is often referred to as the Direction of Arrival (DOA). By combining DOA information from multiple vector sensor measurement locations, a sound source may be instantaneously localized. The majority of vector sensor research has been conducted for underwater applications. A few studies of in-air vector sensors, which utilize multiple microphones, have been conducted; however, the majority of them study stationary sound sources in a laboratory environment or non-real-world settings. The focus of this paper is to study in-air vector sensor capabilities when sensing non-stationary mechanical noise sources—specifically ground vehicles—in a non-laboratory environment where ambient noise may be present. The DOA measurements at multiple vector sensor locations are used to test the acoustic source localization potential for this method. Vector sensors utilize a combination of pressure sensors, particle velocity sensors, or both, to determine the acoustic intensity magnitude and direction pointing toward an acoustic source. This acoustic intensity vector is often referred to as the Direction of Arrival (DOA). By combining DOA information from multiple vector sensor measurement locations, a sound source may be instantaneously localized. The majority of vector sensor research has been conducted for underwater applications. A few studies of in-air vector sensors, which utilize multiple microphones, have been conducted; however, the majority of them study stationary sound sources in a laboratory environment or non-real-world settings. The focus of this paper is to study in-air vector sensor capabilities when sensing non-stationary mechanical noise sources—specifically ground vehicles—in a non-laboratory environment where ambient noise may be present. The DOA measurements at multiple vector sensor locations are used to test the acoustic sourc...

A DOA-Based Factor Graph Technique for 3D Multi-Target Geolocation

The primary goal of this paper is to propose a new factor graph (FG) technique for the direction-of-arrival (DOA)-based three-dimensional (3D) multi-target geolocation. The proposed FG detector uses only the mean and the variance of the DOA measurement including both the azimuth and the elevation, assuming that they are suffering from errors following a Gaussian probability density function (PDF). Therefore, both the up-link (UL) transmission load and the detection complexity can be significantly reduced. The Cramer-Rao lower bound (CRLB) of the proposed DOA-based 3D geolocation system is mathematically derived. According to the root mean square error (RMSE) results obtained by simulations, the proposed FG algorithm is found to outperform the conventional linear least square (LS) approach, which achieves a very close performance to the derived CRLB. Moreover, we propose a sensor separation algorithm to solve the target-DOAs matching problem such that the DOAs, measured by each sensor, can be matched to their corresponding targets. With this technique, additional target identification is not needed, and the multi-target geolocation can be decomposed into multiple independent single-target detections.

3D WLS hybrid and non hybrid localization using TOA, TDOA, azimuth and elevation

In this paper, we propose a Three Dimensional (3D) Weighted Least Square (WLS) estimation of mobile position using Time Of Arrival (TOA), Time Difference Of Arrival (TDOA), Direction of Arrival (DOA) given by azimuth and elevation measurement. We present both hybrid and non hybrid localization techniques. Hybrid localization techniques use a combination of TOA, TDOA and DOA whereas non hybrid localization use only TOA or TDOA or DOA measurement. This is the first paper to tackle the problem of 3D hybrid localization using TOA, TDOA, azimuth and elevation. We also present a theoretical performance analysis of the hybrid localization technique where the covariance matrix of the WLS estimator is derived in closed form expression. The theoretical derivation is valid for any distribution of the observation noise. We show that the WLS estimator is unbiased and equivalent to the Maximum Likelihood estimator when the observation noise is Gaussian. We also optimize the localization accuracy by optimizing the base station location in order to minimize the Mean Square Error. Base station location optimization to enhance localization accuracy has not been yet proposed.

Scanning Emitter Localization Using DOA and TDOI Measurements

The determination of the scanning emitter position with known scan rate using Direction Of Arrival (DOA) and Time Difference Of Interception (TDOI) is investigated. The Cramr-Rao Lower Bound (CRLB) of the DOA and TDOI based localization regime is firstly derived. It demonstrates that the equivalent DOA measurements noise power ratio of the individual regime is closely related to the improvement of the combination regime. To exclusively determine the position of the scanning emitter, the TOI measurements are transformed to the corresponding DOA measurements and then a Weighted Pseudo-linear Least Square (WPLS) estimator is proposed. However, the WPLS is biased due to the noise correlation between the regressor and regressand of the pseudo-linear equation. The Instrumental Variable (IV) method is resorted to eliminate the bias caused by the WPLS, and a Weighted IV (WIV) estimator, at the cost of two times computational complexity of the WPLS, is proposed. Simulations show that the WIV performs approximately to the Maximum Likelihood (ML) estimator. It can reach the CRLB in one scan cycle, and is asymptotic unbiased within multiple cycles.

Cooperative Localisation of a GPS-Denied UAV in 3-Dimensional Space Using Direction of Arrival Measurements

This paper presents a novel approach for localising a GPS (Global Positioning System)-denied Unmanned Aerial Vehicle (UAV) with the aid of a GPS-equipped UAV in three-dimensional space. The GPS-equipped UAV makes discrete-time broadcasts of its global coordinates. The GPS-denied UAV receives the broadcast and in doing so takes a direction of arrival (DOA) measurement towards the origin of the broadcast in its local coordinate frame (obtained via an inertial navigation system (INS)). The aim is to determine the difference between the local and global frames, described by a rotation and a translation. In the noiseless case, global coordinates are recovered exactly by solving a system of linear equations. When DOA measurements are contaminated with noise, rank relaxed semidefinite programming (SDP) and the Orthogonal Procrustes algorithm are employed. Simulations are provided and factors affecting accuracy, such as noise levels and number of measurements, are explored.

Flight parameter estimation using instantaneous frequency and direction of arrival measurements from a single acoustic sensor node

When an airborne sound source travels past a stationary ground-based acoustic sensor node in a straight line at constant altitude and constant speed that is not much less than the speed of sound in air, the movement of the source during the propagation of the signal from the source to the sensor node (commonly referred to as the "retardation effect") enables the full set of flight parameters of the source to be estimated by measuring the direction of arrival (DOA) of the signal at the sensor node over a sufficiently long period of time. This paper studies the possibility of using instantaneous frequency (IF) measurements from the sensor node to improve the precision of the flight parameter estimates when the source spectrum contains a harmonic line of constant frequency. A simplified Cramer-Rao lower bound analysis shows that the standard deviations in the estimates of the flight parameters can be reduced when IF measurements are used together with DOA measurements. Two flight parameter estimation algorithms that utilize both IF and DOA measurements are described and their performances are evaluated using both simulated data and real data.

Fundamental Limits of TOA/DOA and Inertial Measurement Unit-Based Wireless Capsule Endoscopy Hybrid Localization

In this paper, performance analysis of hybrid localization based on radio-frequency (RF) and inertial measurement unit (IMU) measurements for a single wireless capsule endoscopy (WCE) traveling the gastrointestinal tract is studied. Specifically, the multiple body-mounted sensors are considered which are located on the front and back of a patient’s medical jacket and form the uniform rectangular arrays (URAs). With the aim of locating the WCE, two types of RF measurements, namely time-of-arrival (TOA) and direction-of-arrival (DOA), are estimated from the received signals at the URAs transmitted by the WCE, which are integrated with the IMU acceleration measurements via the standard extended Kalman filter. Here, a posterior Cramer–Rao Bound (PCRB) of the proposed TOA/DOA and IMU-based hybrid localization is derived as fundamental limits on squared position error, where the accuracies of TOA and DOA measurements are entailed by means of CRB to account for their dependency on the environmental parameters, while the accuracies of the IMU measurements are addressed with the acceleration measurement error standard deviation. Numerical results are provided, sustained by simulations which verify the millimeter accuracy of the TOA/DOA and IMU-based hybrid localization within the regulation of medical implant communication services and the exactness of the PCRB.